Chemical Potential of a Lennard Jones Fluid
NASA Astrophysics Data System (ADS)
Celebonovic, V.
2010-12-01
The aim of this paper is to present results of analytical calculation of chemical potential of a Lennard Jones (LJ) fluid performed in two ways: by using the thermodynamical formalism and the formalism of statistical mechanics. The integration range is divided into two regions. In the small distance region, which is r≤σ in the usual notation, the integration range had to be cut off in order to avoid the occurence of divergences. In the large distance region, the calculation is technically simpler. The calculation reported here will be useful in all kinds of studies concerning phase equilibrium in a LJ fluid. Interesting kinds of such systems are the giant planets and the icy satellites in various planetary systems, but also the (so far) hypothetical quark stars.
Second virial coefficient of a generalized Lennard-Jones potential.
González-Calderón, Alfredo; Rocha-Ichante, Adrián
2015-01-21
We present an exact analytical solution for the second virial coefficient of a generalized Lennard-Jones type of pair potential model. The potential can be reduced to the Lennard-Jones, hard-sphere, and sticky hard-sphere models by tuning the potential parameters corresponding to the width and depth of the well. Thus, the second virial solution can also regain the aforementioned cases. Moreover, the obtained expression strongly resembles the one corresponding to the Kihara potential. In fact, the Fk functions are the same. Furthermore, for these functions, the complete expansions at low and high temperature are given. Additionally, we propose an alternative stickiness parameter based on the obtained second virial coefficient.
Second virial coefficient of a generalized Lennard-Jones potential
NASA Astrophysics Data System (ADS)
González-Calderón, Alfredo; Rocha-Ichante, Adrián
2015-01-01
We present an exact analytical solution for the second virial coefficient of a generalized Lennard-Jones type of pair potential model. The potential can be reduced to the Lennard-Jones, hard-sphere, and sticky hard-sphere models by tuning the potential parameters corresponding to the width and depth of the well. Thus, the second virial solution can also regain the aforementioned cases. Moreover, the obtained expression strongly resembles the one corresponding to the Kihara potential. In fact, the Fk functions are the same. Furthermore, for these functions, the complete expansions at low and high temperature are given. Additionally, we propose an alternative stickiness parameter based on the obtained second virial coefficient.
Corresponding states law for a generalized Lennard-Jones potential
NASA Astrophysics Data System (ADS)
Orea, P.; Romero-Martínez, A.; Basurto, E.; Vargas, C. A.; Odriozola, G.
2015-07-01
It was recently shown that vapor-liquid coexistence densities derived from Mie and Yukawa models collapse to define a single master curve when represented against the difference between the reduced second virial coefficient at the corresponding temperature and that at the critical point. In this work, we further test this proposal for another generalization of the Lennard-Jones pair potential. This is carried out for vapor-liquid coexistence densities, surface tension, and vapor pressure, along a temperature window set below the critical point. For this purpose, we perform molecular dynamics simulations by varying the potential softness parameter to produce from very short to intermediate attractive ranges. We observed all properties to collapse and yield master curves. Moreover, the vapor-liquid curve is found to share the exact shape of the Mie and attractive Yukawa. Furthermore, the surface tension and the logarithm of the vapor pressure are linear functions of this difference of reduced second virial coefficients.
Corresponding states law for a generalized Lennard-Jones potential.
Orea, P; Romero-Martínez, A; Basurto, E; Vargas, C A; Odriozola, G
2015-07-14
It was recently shown that vapor-liquid coexistence densities derived from Mie and Yukawa models collapse to define a single master curve when represented against the difference between the reduced second virial coefficient at the corresponding temperature and that at the critical point. In this work, we further test this proposal for another generalization of the Lennard-Jones pair potential. This is carried out for vapor-liquid coexistence densities, surface tension, and vapor pressure, along a temperature window set below the critical point. For this purpose, we perform molecular dynamics simulations by varying the potential softness parameter to produce from very short to intermediate attractive ranges. We observed all properties to collapse and yield master curves. Moreover, the vapor-liquid curve is found to share the exact shape of the Mie and attractive Yukawa. Furthermore, the surface tension and the logarithm of the vapor pressure are linear functions of this difference of reduced second virial coefficients.
A Sensible Estimate for the Stability Constant of the Lennard-Jones Potential
NASA Astrophysics Data System (ADS)
Yuhjtman, Sergio A.
2015-09-01
We show that the stability constant of the Lennard-Jones potential in , , is smaller than 14.316. This is remarkably smaller than the best previously known bound. Our method is very elementary, and probably applicable to other similar potentials such as the Morse potentials. We also improve slightly, in the Lennard-Jones case, the lower bound for the minimum interparticle distance of an optimal n-particle configuration to 0.684.
Melting line of the Lennard-Jones system, infinite size, and full potential.
Mastny, Ethan A; de Pablo, Juan J
2007-09-14
Literature estimates of the melting curve of the Lennard-Jones system vary by as much as 10%. The origin of such discrepancies remains unclear. We present precise values for the Lennard-Jones melting temperature, and we examine possible sources of systematic errors in the prediction of melting points, including finite-size and interaction-cutoff effects. A hypothetical thermodynamic integration path is used to find the relative free energies of the solid and liquid phases, for various system sizes, at constant cutoff radius. The solid-liquid relative free energy and melting temperature scale linearly as the inverse of the number of particles, and it is shown that finite-size effects can account for deviations in the melting temperature (from the infinite-size limit) of up to 5%. An extended-ensemble density-of-states method is used to determine free energy changes for each phase as a continuous function of the cutoff radius. The resulting melting temperature predictions exhibit an oscillatory behavior as the cutoff radius is increased. Deviations in the melting temperature (from the full potential limit) arising from a finite cutoff radius are shown to be of comparable magnitude as those resulting from finite-size effects. This method is used to identify melting temperatures at five different pressures, for the infinite-size and full potential Lennard-Jones system. We use our simulation results as references to connect the Lennard-Jones solid equation of state of van der Hoef with the Lennard-Jones fluid equation of state of Johnson. Once the references are applied the two equations of state are used to identify a melting curve. An empirical equation that fits this melting curve is provided. We also report a reduced triple point temperature T(tr)=0.694.
Modified Jeans instability in Lorentzian dusty self-gravitating plasmas with Lennard-Jones potential
NASA Astrophysics Data System (ADS)
Qian, Y. Z.; Chen, H.; Liu, S. Q.
2014-11-01
The Jeans instability in self-gravitating plasma with Kappa distributed dust grains is investigated basing on assumption that the mutual interaction among dust grains is governed by Lennard-Jones potential. It is shown that the presence of additional suprathermal particles has significant effects on the range of unstable modes and growth rate of Jeans instability. Compared with Maxwellian scenario, suprathermality stabilized the Jeans instability.
Modified Jeans instability in Lorentzian dusty self-gravitating plasmas with Lennard-Jones potential
Qian, Y. Z. Chen, H. Liu, S. Q.
2014-11-15
The Jeans instability in self-gravitating plasma with Kappa distributed dust grains is investigated basing on assumption that the mutual interaction among dust grains is governed by Lennard-Jones potential. It is shown that the presence of additional suprathermal particles has significant effects on the range of unstable modes and growth rate of Jeans instability. Compared with Maxwellian scenario, suprathermality stabilized the Jeans instability.
Evaluation of Quantum Corrections to Second Virial Coefficient with Lennard-Jones (12-6) Potential
NASA Astrophysics Data System (ADS)
Mamedov, B. A.; Somuncu, E.
2016-10-01
The efficient method is developed for analytical evalualtion of quantum corrections to second virial coefficient with Lennard-Jones (12-6) potential. The quantum corrections to second virial coefficient played a significant role in the investigation of real gases in the low temperatures range. In this paper, we obtained a series of formula in terms of gamma and exponential integral functions which is one of the useful approaches for analytical evaluation of quantum corrections to second virial coefficient. The calculation results excellently agreement with of the literature data.
Morse, Lennard-Jones, and Kratzer Potentials: A Canonical Perspective with Applications.
Walton, Jay R; Rivera-Rivera, Luis A; Lucchese, Robert R; Bevan, John W
2016-10-12
Canonical approaches are applied to classic Morse, Lennard-Jones, and Kratzer potentials. Using the canonical transformation generated for the Morse potential as a reference, inverse transformations allow the accurate generation of the Born-Oppenheimer potential for the H2(+) ion, neutral covalently bound H2, van der Waals bound Ar2, and the hydrogen bonded one-dimensional dissociative coordinate in a water dimer. Similar transformations are also generated using the Lennard-Jones and Kratzer potentials as references. Following application of inverse transformations, vibrational eigenvalues generated from the Born-Oppenheimer potentials give significantly improved quantitative comparison with values determined from the original accurately known potentials. In addition, an algorithmic strategy based upon a canonical transformation to the dimensionless form applied to the force distribution associated with a potential is presented. The resulting canonical force distribution is employed to construct an algorithm for deriving accurate estimates for the dissociation energy, the maximum attractive force, and the internuclear separations corresponding to the maximum attractive force and the potential well.
The potential energy landscape for crystallisation of a Lennard-Jones fluid
NASA Astrophysics Data System (ADS)
de Souza, Vanessa K.; Wales, David J.
2016-07-01
Crystallisation pathways are explored by direct analysis of the potential energy landscape for a system of Lennard-Jones particles with periodic boundary conditions. A database of minima and transition states linking liquid and crystalline states is constructed using discrete path sampling and the entire potential energy landscape from liquid to crystal is visualised. We demonstrate that there is a strong negative correlation between the number of atoms in the largest crystalline cluster and the potential energy. In common with previous results we find a strong bias towards the growth of FCC rather than HCP clusters, despite a very small potential energy difference. We characterise three types of perfect crystals with very similar energies: pure FCC, pure HCP, and combinations of FCC and HCP layers. There are also many slightly defective crystalline structures. The effect of the simulation box is analysed for a supercell containing 864 atoms. There are low barriers between some of the different crystalline structures via pathways involving sliding layers, and many different defective structures with FCC layers stacked at an angle to the periodic box. Finally, we compare a binary Lennard-Jones system and visualise the potential energy landscape from supercooled liquid to crystal.
Transfer coefficients for evaporation of a system with a Lennard-Jones long-range spline potential.
Ge, Jialin; Kjelstrup, S; Bedeaux, D; Simon, J M; Rousseau, B
2007-06-01
Surface transfer coefficients are determined by nonequilibrium molecular dynamics simulations for a Lennard-Jones fluid with a long-range spline potential. In earlier work [A. Røsjorde, J. Colloid Interface Sci. 240, 355 (2001); J. Xu, ibid. 299, 452 (2006)], using a short-range Lennard-Jones spline potential, it was found that the resistivity coefficients to heat and mass transfer agreed rather well with the values predicted by kinetic theory. For the long-range Lennard-Jones spline potential considered in this paper we find significant discrepancies from the values predicted by kinetic theory. In particular the coupling coefficient, and as a consequence the heat of transfer on the vapor side of the surface are much larger. Thermodynamic data for the liquid-vapor equilibrium confirmed the law of corresponding states for the surface, when it is described as an autonomous system. The importance of these findings for modelling phase transitions is discussed.
Variable soft sphere molecular model for inverse-power-law or Lennard-Jones potential
NASA Astrophysics Data System (ADS)
Koura, Katsuhisa; Matsumoto, Hiroaki
1991-10-01
The variable soft sphere (VSS) molecular model is introduced for both the viscosity and diffusion cross sections (coefficients) to be consistent with those of the inverse-power-law (IPL) or Lennard-Jones (LJ) potential. The VSS model has almost the same analytical and computational simplicity (computation time) as the variable hard sphere (VHS) model in the Monte Carlo simulation of rarefied gas flows. The null-collision Monte Carlo method is used to make comparative calculations for the molecular diffusion in a heat-bath gas and the normal shock wave structure in a simple gas. For the most severe test of the VSS model for the IPL potential, the softest practical model corresponding to the Maxwell molecule is chosen. The agreement in the molecular diffusion and shock wave structure between the VSS model and the IPL or LJ potential is remarkably good.
Phase Transitions For Dilute Particle Systems with Lennard-Jones Potential
NASA Astrophysics Data System (ADS)
Collevecchio, Andrea; König, Wolfgang; Mörters, Peter; Sidorova, Nadia
2010-11-01
We consider a classical dilute particle system in a large box with pair-interaction given by a Lennard-Jones-type potential. The inverse temperature is picked proportionally to the logarithm of the particle density. We identify the free energy per particle in terms of a variational formula and show that this formula exhibits a cascade of phase transitions as the temperature parameter ranges from zero to infinity. Loosely speaking, the particle system separates into spatially distant components in such a way that within each phase all components are of the same size, which is the larger the lower the temperature. The main tool in our proof is a new large deviation principle for sparse point configurations.
Pai, Sung Jin; Bae, Young Chan
2010-10-21
A simple and analytical pair potential function was developed to represent the osmotic pressures in aqueous protein/salt systems under various conditions. Based on a hard core Lennard-Jones (HCLJ) potential model, the new potential function considers various interactions by extending the attractive Lennard-Jones potential. A temperature-dependent coefficient term was introduced to take into account the specific properties of given materials. Comparison of the new potential function with the HCLJ model in hydrocarbon and water systems showed that consideration of the temperature dependence in the potential function was effective, especially for strong polar systems such as water. To predict the osmotic pressures of aqueous lysozyme/(NH(4))(2)SO(4) solutions of various ionic strength and pH, the energy parameters of lysozyme were correlated with the experimental cloud point temperature. The proposed model agreed fairly well with the experimental osmotic pressure data with only previously obtained parameters.
NASA Astrophysics Data System (ADS)
Pai, Sung Jin; Bae, Young Chan
2010-10-01
A simple and analytical pair potential function was developed to represent the osmotic pressures in aqueous protein/salt systems under various conditions. Based on a hard core Lennard-Jones (HCLJ) potential model, the new potential function considers various interactions by extending the attractive Lennard-Jones potential. A temperature-dependent coefficient term was introduced to take into account the specific properties of given materials. Comparison of the new potential function with the HCLJ model in hydrocarbon and water systems showed that consideration of the temperature dependence in the potential function was effective, especially for strong polar systems such as water. To predict the osmotic pressures of aqueous lysozyme/(NH4)2SO4 solutions of various ionic strength and pH, the energy parameters of lysozyme were correlated with the experimental cloud point temperature. The proposed model agreed fairly well with the experimental osmotic pressure data with only previously obtained parameters.
Taylor, Mark P; Ye, Yuting; Adhikari, Shishir R
2015-11-28
The conformation of a polymer chain in solution is coupled to the local structure of the surrounding solvent and can undergo large changes in response to variations in solvent density and temperature. The many-body effects of solvent on the structure of an n-mer polymer chain can be formally mapped to an exact n-body solvation potential. Here, we use a pair decomposition of this n-body potential to construct a set of two-body potentials for a Lennard-Jones (LJ) polymer chain in explicit LJ solvent. The solvation potentials are built from numerically exact results for 5-mer chains in solvent combined with an approximate asymptotic expression for the solvation potential between sites that are distant along the chain backbone. These potentials map the many-body chain-in-solvent problem to a few-body single-chain problem and can be used to study a chain of arbitrary length, thereby dramatically reducing the computational complexity of the polymer chain-in-solvent problem. We have constructed solvation potentials at a large number of state points across the LJ solvent phase diagram including the vapor, liquid, and super-critical regions. We use these solvation potentials in single-chain Monte Carlo (MC) simulations with n ≤ 800 to determine the size, intramolecular structure, and scaling behavior of chains in solvent. To assess our results, we have carried out full chain-in-solvent MC simulations (with n ≤ 100) and find that our solvation potential approach is quantitatively accurate for a wide range of solvent conditions for these chain lengths.
The impact of surface area, volume, curvature, and Lennard-Jones potential to solvation modeling.
Nguyen, Duc D; Wei, Guo-Wei
2017-01-05
This article explores the impact of surface area, volume, curvature, and Lennard-Jones (LJ) potential on solvation free energy predictions. Rigidity surfaces are utilized to generate robust analytical expressions for maximum, minimum, mean, and Gaussian curvatures of solvent-solute interfaces, and define a generalized Poisson-Boltzmann (GPB) equation with a smooth dielectric profile. Extensive correlation analysis is performed to examine the linear dependence of surface area, surface enclosed volume, maximum curvature, minimum curvature, mean curvature, and Gaussian curvature for solvation modeling. It is found that surface area and surfaces enclosed volumes are highly correlated to each other's, and poorly correlated to various curvatures for six test sets of molecules. Different curvatures are weakly correlated to each other for six test sets of molecules, but are strongly correlated to each other within each test set of molecules. Based on correlation analysis, we construct twenty six nontrivial nonpolar solvation models. Our numerical results reveal that the LJ potential plays a vital role in nonpolar solvation modeling, especially for molecules involving strong van der Waals interactions. It is found that curvatures are at least as important as surface area or surface enclosed volume in nonpolar solvation modeling. In conjugation with the GPB model, various curvature-based nonpolar solvation models are shown to offer some of the best solvation free energy predictions for a wide range of test sets. For example, root mean square errors from a model constituting surface area, volume, mean curvature, and LJ potential are less than 0.42 kcal/mol for all test sets. © 2016 Wiley Periodicals, Inc.
NASA Astrophysics Data System (ADS)
Hajigeorgiou, Photos G.
2016-12-01
An analytical model for the diatomic potential energy function that was recently tested as a universal function (Hajigeorgiou, 2010) has been further modified and tested as a suitable model for direct-potential-fit analysis. Applications are presented for the ground electronic states of three diatomic molecules: oxygen, carbon monoxide, and hydrogen fluoride. The adjustable parameters of the extended Lennard-Jones potential model are determined through nonlinear regression by fits to calculated rovibrational energy term values or experimental spectroscopic line positions. The model is shown to lead to reliable, compact and simple representations for the potential energy functions of these systems and could therefore be classified as a suitable and attractive model for direct-potential-fit analysis.
NASA Astrophysics Data System (ADS)
Chang, Jaeeon; Sandler, Stanley I.
2004-10-01
We propose Lennard-Jones potential parameters for interatomic interactions of linear and branched alkanes based on matching the results of Gibbs ensemble simulations of vapor-liquid equilibria to experimental data. The alkane model is similar as in the OPLS-AA [W. L. Jorgensen, D. S. Maxwell, and J. Tirado-Rives, J. Am. Chem. Soc. 118, 11225 (1996)], but multiple atom types for carbon based on the number of covalently bonded hydrogen atoms are necessary to accurately reproduce liquid densities and enthalpies of vaporization with the errors of 2.1% and 3.3%, respectively, for hydrocarbons of various chain lengths and structures. We find that the attraction energies of the carbon atoms are almost proportional to the number of covalent hydrogen atoms with each increasing the carbon energy parameter by ≈0.033 kcal/mol. Though the present force field outperforms the OPLS-AA force field for alkanes we studied, systematic deviations for vapor pressures are still observed with errors of 15%-30%, and critical temperatures are slightly underestimated. We think that these shortcomings are probably due to the inadequacy of the two-parameter Lennard-Jones potential, and especially its behavior at short distances.
NASA Astrophysics Data System (ADS)
Temelkov, K. A.; Slaveeva, S. I.; Fedchenko, Yu I.
2016-03-01
Thermal conductivities of helium, neon, bromine, and hydrogen are calculated on the basis of the (12-6) Lennard-Jones interaction approximation. Where necessary for a more precise approximation, a generalized (n-m) Lennard-Jones interaction potential is used. Thermal conductivities of binary gas systems are calculated and compared through two different empirical methods for the case of gas discharges in He, Ne, and Ne-He mixtures with small admixtures of bromine and hydrogen. A new simple method is proposed for the thermal conductivity determination for the 3- and 4-component gas mixtures of our interest.
Wilson, D Scott; Lee, Lloyd L
2005-07-22
We explore the vapor-liquid phase behavior of binary mixtures of Lennard-Jones-type molecules where one component is supercritical, given the system temperature. We apply the self-consistency approach to the Ornstein-Zernike integral equations to obtain the correlation functions. The consistency checks include not only thermodynamic consistencies (pressure consistency and Gibbs-Duhem consistency), but also pointwise consistencies, such as the zero-separation theorems on the cavity functions. The consistencies are enforced via the bridge functions in the closure which contain adjustable parameters. The full solution requires the values of not only the monomer chemical potentials, but also the dimer chemical potentials present in the zero-separation theorems. These are evaluated by the direct chemical-potential formula [L. L. Lee, J. Chem. Phys. 97, 8606 (1992)] that does not require temperature nor density integration. In order to assess the integral equation accuracy, molecular-dynamics simulations are carried out alongside the states studied. The integral equation results compare well with simulation data. In phase calculations, it is important to have pressure consistency and valid chemical potentials, since the matching of phase boundaries requires the equality of the pressures and chemical potentials of both the liquid and vapor phases. The mixtures studied are methane-type and pentane-type molecules, both characterized by effective Lennard-Jones potentials. Calculations on one isotherm show that the integral equation approach yields valid answers as compared with the experimental data of Sage and Lacey. To study vapor-liquid phase behavior, it is necessary to use consistent theories; any inconsistencies, especially in pressure, will vitiate the phase boundary calculations.
Figure-eight choreographies of the equal mass three-body problem with Lennard-Jones-type potentials
NASA Astrophysics Data System (ADS)
Fukuda, Hiroshi; Fujiwara, Toshiaki; Ozaki, Hiroshi
2017-03-01
We report on figure-eight choreographic solutions to a system of three identical particles interacting through a potential of Lennard-Jones-type 1/{{r}12}-1/{{r}6} , where r is distance between the particles. By numerical search, we found there are a multitude of such solutions. A series of them are close to a figure-eight solutions to a homogeneous system with no 1/r 12 term in the potential. The rest are very different, and have several points with large curvatures in their figure-eight orbits at which particles are repelled. Here figure-eight choreographies are periodic motions whose shape is symmetric in both horizontal and vertical axes, starting with an isosceles triangle configuration and going back to an isosceles triangle configuration with opposite direction through Euler configuration. Thus the lobe of such a figure-eight may be complex in shape, and need not be convex.
NASA Astrophysics Data System (ADS)
Lima, N. W.; Gutierres, L. I.; Gonzalez, R. I.; Müller, S.; Thomaz, R. S.; Bringa, E. M.; Papaléo, R. M.
2016-11-01
In this paper, the surface effects of individual heavy ions impacting thin polymerlike films were investigated, using molecular dynamics simulations with the finite extensible nonlinear elastic (FENE) potential to describe the molecular chains. The perturbation introduced by the ions in the lattice was modeled assuming that the initial excitation energy in the ion track is converted into an effective temperature, as in a thermal spike. The track was heated only within the film thickness h , leaving a nonexcited substrate below. The effect of decreasing thickness on cratering and sputtering was evaluated. The results were compared to experimental data of thin polymer films bombarded by MeV-GeV ions and to simulations performed with the Lennard-Jones potential. While several qualitative results observed in the experiments were also seen in the simulations, irrespective of the potential used, there are important differences observed on FENE films. Crater dimensions, rim volume, and sputtering yields are substantially reduced, and a threshold thickness for molecular ejection appears in FENE simulations. This is attributed to the additional restrictions on mass transport out of the excited track region imposed by interchain interactions (entanglements) and by the low mobility of the molten phase induced by the spike.
of state . Calcu lations are made of various pressures of equilibrium products from detonation of RDX. (Author)...priori estimate of the system parameters. It is an extension of the work on the three-shell modification of the Lennard Jones - Devonshire equation
Zhou, Shiqi
2010-09-09
Local self-consistent Ornstein-Zernike (OZ) integral equation theory (IET) provides a rapid and easy route for obtaining independently thermodynamic and structural information for a single state point. Because of neglect of information of neighboring state points in determining a self-consistent adjustable parameter performance of the local self-consistent OZ IET is somewhat vulnerable and worthy of intensive investigation. For this reason, we have performed Monte Carlo simulations to obtain thermodynamic and structural properties of fluid with a generalized Lennard-Jones potential, and the present simulation results are employed to verify the quality of a local version of a recently developed global self-consistent OZ IET and a local expression for computation of excess chemical potential directly from the structural functions of the state point of interest. Comprehensive comparison and analysis demonstrate the following (i) the present local self-consistent OZ IET performs quite well for calculation of pressure and excess internal energy; (ii) using the same structural functions from the present local self-consistent OZ IET, the previously derived local expression by the present author has by and large the same accuracy in calculating the excess chemical potential as an exact virial formula for the pressure; (iii) although the excellent performance exhibited for the above thermodynamic quantities persists to very low temperature and very short-ranged potential and remains even in the liquid-solid coexistence region, the excess Helmholtz free energy calculated from the pressure and excess chemical potential shows evident inaccuracy for a density-temperature combination deep in the liquid-solid coexistence region, and this makes it necessary to derive a local formulation for the excess free energy.
NASA Astrophysics Data System (ADS)
Matsumoto, Hiroaki
2002-12-01
The variable sphere (VS) molecular model for the Monte Carlo simulation of rarefied gas flow is introduced to provide consistency for diffusion and viscosity cross-sections with those of any realistic intermolecular potential. It is then applied to the inverse power law (IPL) and Lennard-Jones (LJ) potentials. The VS model has a much simpler scattering law than either the variable hard sphere (VHS) or variable soft sphere (VSS) models; also, it has almost the same computational efficiency as the VHS and VSS models. A simulation of velocity relaxation in a homogeneous space and two comparative simulations of molecular diffusion in a homogeneous heat-bath gas and normal shock wave structure in a monatomic gas are made to examine VS model validity. The relaxation to a Maxwellian distribution function and equipartition between all degrees of freedom are well established; good agreement is shown in the molecular diffusion and shock wave structure between the VS model and the IPL and LJ potentials. The VS model is combined with the statistical inelastic cross-section (SICS) model and applied to simulation of translational and rotational energy relaxation in a homogeneous space. The VS model shows the relaxation of Maxwellian and Boltzmann distribution functions and equipartition between all degrees of freedom. Comparative calculation between the VS model with the SICS (VS-SICS) model and the VSS model with the SICS (VSS-SICS) model is made for rotational relaxation in a nitrogen normal shock wave. Good agreement is shown in the shock wave structure and rotational energy distribution function between the VS-SICS model and the VSS-SICS model. This study demonstrates that diffusion and viscosity cross-sections, rather than the scattering law of each molecular collision, affect macroscopic transport phenomena.
Hydrophobicity in Lennard-Jones solutions.
Ishizaki, Mario; Tanaka, Hideki; Koga, Kenichiro
2011-02-14
The analogue of the hydrophobic hydration is explored for Lennard-Jones solutions. The free energy of solvation and its temperature derivatives, both in the constant-pressure process and in the constant-volume process, are obtained numerically for a variety of the size and energy parameters for the solute-solvent Lennard-Jones potential. We identify in the parameter space a region in which the solvation is of hydrophobic character, with an understanding that hydrophobicity is characterized by both the solvation free energy being positive and the solvation process being exothermic. Such a region is found in each case of the isobaric and isochoric conditions and the region is seen to be much wider in the isochoric process than in the isobaric one. Its origin and implication are discussed.
Xantheas, Sotiris S; Werhahn, Jasper C
2014-08-14
Based on the formulation of the analytical expression of the potential V(r) describing intermolecular interactions in terms of the dimensionless variables r* = r/r(m) and ɛ* = V/ɛ, where r(m) is the separation at the minimum and ɛ the well depth, we propose more generalized scalable forms for the commonly used Mie, Lennard-Jones, Morse, and Buckingham exponential-6 potential energy functions. These new generalized forms have an additional parameter from the original forms and revert to the original ones for some choice of that parameter. In this respect, the original forms of those potentials can be considered as special cases of the more general forms that are introduced. We also propose a scalable, non-revertible to the original one, 4-parameter extended Morse potential.
Xantheas, Sotiris S.; Werhahn, Jasper C.
2014-08-14
Based on the formulation of the analytical expression of the potential V(r) describing intermolecular interactions in terms of the dimensionless variables r*=r/rm and !*=V/!, where rm is the separation at the minimum and ! the well depth, we propose more generalized scalable forms for the commonly used Lennard-Jones, Mie, Morse and Buckingham exponential-6 potential energy functions (PEFs). These new generalized forms have an additional parameter from and revert to the original ones for some choice of that parameter. In this respect, the original forms can be considered as special cases of the more general forms that are introduced. We also propose a scalable, but nonrevertible to the original one, 4-parameter extended Morse potential.
NASA Astrophysics Data System (ADS)
Matsumoto, Hiroaki; Koura, Katsuhisa
1991-12-01
The velocity distribution functions (VDF's) in an argon normal shock wave at an upstream high Mach number 7.183 and low temperature 16 K are calculated using the null-collision direct-simulation Monte Carlo method for the Lennard-Jones (LJ) potential to compare with the experimental results of Holtz and Muntz (1983). The convolved VDF's for the LJ potential are in reasonable agreement with the measured data in early and late regions of the shock wave but significantly different in the middle region. This discrepancy cannot be explained by a possible uncertainty in the potential well depth. Moreover, the difference in the convolved VDF's between the LJ potential and the softest and hardest unrealistic molecular models with no attractive force, i.e., the Maxwell molecule and hard sphere, is much smaller than the discrepancy between the experiments and Monte Carlo calculations.
NASA Astrophysics Data System (ADS)
Matsumoto, Hiroaki; Koura, Katsuhisa
1991-12-01
The velocity distribution functions (VDF's) in an argon normal shock wave at an upstream high Mach number 7.183 and low temperature 16 K are calculated using the null-collision direct-simulation Monte Carlo method for the Lennard-Jones (LJ) potential to compare with the experimental results of Holtz and Muntz [Phys. Fluids 26, 2425 (1983)]. The convolved VDF's for the LJ potential are in reasonable agreement with the measured data in early and late regions of the shock wave but significantly different in the middle region. This discrepancy cannot be explained by a possible uncertainty in the potential well depth. Moreover, the difference in the convolved VDF's between the LJ potential and the softest and hardest unrealistic molecular models with no attractive force, i.e., the Maxwell molecule and hard sphere, is much smaller than the discrepancy between the experiments and Monte Carlo calculations.
Freezing of Lennard-Jones-type fluids
Khrapak, Sergey A.; Chaudhuri, Manis; Morfill, Gregor E.
2011-02-07
We put forward an approximate method to locate the fluid-solid (freezing) phase transition in systems of classical particles interacting via a wide range of Lennard-Jones-type potentials. This method is based on the constancy of the properly normalized second derivative of the interaction potential (freezing indicator) along the freezing curve. As demonstrated recently it yields remarkably good agreement with previous numerical simulation studies of the conventional 12-6 Lennard-Jones (LJ) fluid [S.A.Khrapak, M.Chaudhuri, G.E.Morfill, Phys. Rev. B 134, 052101 (2010)]. In this paper, we test this approach using a wide range of the LJ-type potentials, including LJ n-6 and exp-6 models, and find that it remains sufficiently accurate and reliable in reproducing the corresponding freezing curves, down to the triple-point temperatures. One of the possible application of the method--estimation of the freezing conditions in complex (dusty) plasmas with ''tunable'' interactions--is briefly discussed.
Tillack, Andreas F; Johnson, Lewis E; Eichinger, Bruce E; Robinson, Bruce H
2016-09-13
We have developed an approach to coarse-grained (CG) modeling of the van der Waals (vdW) type of interactions among molecules by representing groups of atoms within those molecules in terms of ellipsoids (rather than spheres). Our approach systematically translates an arbitrary underlying all-atom (AA) representation of a molecular system to a multisite ellipsoidal potential within the family of Gay-Berne type potentials. As the method enables arbitrary levels of coarse-graining, or even multiple levels of coarse-graining within a single simulation, we describe the method as a Level of Detail (LoD) model. The LoD model, as integrated into our group's Metropolis Monte Carlo computational package, is also capable of reducing the complexity of the molecular electrostatics by means of a multipole expansion of charges obtained from an AA force field (or directly from electronic structure calculations) of the charges within each ellipsoid. Electronic polarizability may additionally be included. The present CG representation does not include transformation of bonded interactions; ellipsoids are connected at the fully atomistic bond sites by freely rotating links that are constrained to maintain a constant distance. The accuracy of the method is demonstrated for three distinct types of self-assembling or self-organizing molecular systems: (1) the interaction between benzene and perfluorobenzene (dispersion interactions), (2) linear hydrocarbon chains (a system with large conformational flexibility), and (3) the self-organization of ethylene carbonate (a highly polar liquid). Lastly, the method is applied to the interaction of large (∼100 atom) molecules, which are typical of organic nonlinear optical chromophores, to demonstrate the effect of different CG models on molecular assembly.
Partitioned density functional approach for a Lennard-Jones fluid.
Zhou, Shiqi
2003-12-01
The existing classical density functional approach for nonuniform Lennard-Jones fluid, which is based on dividing the Lennard-Jones interaction potential into a short-range, repulsive part, and a smoothly varying, long-range, attractive tail, was improved by dividing the bulk second-order direct correlation function into strongly density-depending short-range part and weakly density-depending long-range part. The latter is treated by functional perturbation expansion truncated at the lowest order whose accuracy depends on how weakly the long-range part depends on the bulk density. The former is treated by the truncated functional perturbation expansion which is rewritten in the form of the simple weighted density approximation and incorporates the omitted higher-order terms by applying Lagrangian theorem of differential calculus to the reformulated form. The two approximations are put into the density profile equation of the density functional theory formalism to predict the density distribution for Lennard-Jones fluid in contact with a hard wall or between two hard walls within the whole density range for reduced temperature T(*)=1.35 and a density point for reduced temperature T(*)=1. The present partitioned density functional theory performs much better than several previous density functional perturbation theory approaches and a recently proposed bridge density functional approximation.
Accurate Critical Parameters for the Modified Lennard-Jones Model
NASA Astrophysics Data System (ADS)
Okamoto, Kazuma; Fuchizaki, Kazuhiro
2017-03-01
The critical parameters of the modified Lennard-Jones system were examined. The isothermal-isochoric ensemble was generated by conducting a molecular dynamics simulation for the system consisting of 6912, 8788, 10976, and 13500 particles. The equilibrium between the liquid and vapor phases was judged from the chemical potential of both phases upon establishing the coexistence envelope, from which the critical temperature and density were obtained invoking the renormalization group theory. The finite-size scaling enabled us to finally determine the critical temperature, pressure, and density as Tc = 1.0762(2), pc = 0.09394(17), and ρc = 0.331(3), respectively.
Phase diagram of power law and Lennard-Jones systems: Crystal phases
Travesset, Alex
2014-10-28
An extensive characterization of the low temperature phase diagram of particles interacting with power law or Lennard-Jones potentials is provided from Lattice Dynamical Theory. For power law systems, only two lattice structures are stable for certain values of the exponent (or softness) (A15, body centered cube (bcc)) and two more (face centered cubic (fcc), hexagonal close packed (hcp)) are always stable. Among them, only the fcc and bcc are equilibrium states. For Lennard-Jones systems, the equilibrium states are either hcp or fcc, with a coexistence curve in pressure and temperature that shows reentrant behavior. The hcp solid never coexists with the liquid. In all cases analyzed, for both power law and Lennard-Jones potentials, the fcc crystal has higher entropy than the hcp. The role of anharmonic terms is thoroughly analyzed and a general thermodynamic integration to account for them is proposed.
Phase diagram of power law and Lennard-Jones systems: crystal phases.
Travesset, Alex
2014-10-28
An extensive characterization of the low temperature phase diagram of particles interacting with power law or Lennard-Jones potentials is provided from Lattice Dynamical Theory. For power law systems, only two lattice structures are stable for certain values of the exponent (or softness) (A15, body centered cube (bcc)) and two more (face centered cubic (fcc), hexagonal close packed (hcp)) are always stable. Among them, only the fcc and bcc are equilibrium states. For Lennard-Jones systems, the equilibrium states are either hcp or fcc, with a coexistence curve in pressure and temperature that shows reentrant behavior. The hcp solid never coexists with the liquid. In all cases analyzed, for both power law and Lennard-Jones potentials, the fcc crystal has higher entropy than the hcp. The role of anharmonic terms is thoroughly analyzed and a general thermodynamic integration to account for them is proposed.
Phase diagram of power law and Lennard-Jones systems: Crystal phases
NASA Astrophysics Data System (ADS)
Travesset, Alex
2014-10-01
An extensive characterization of the low temperature phase diagram of particles interacting with power law or Lennard-Jones potentials is provided from Lattice Dynamical Theory. For power law systems, only two lattice structures are stable for certain values of the exponent (or softness) (A15, body centered cube (bcc)) and two more (face centered cubic (fcc), hexagonal close packed (hcp)) are always stable. Among them, only the fcc and bcc are equilibrium states. For Lennard-Jones systems, the equilibrium states are either hcp or fcc, with a coexistence curve in pressure and temperature that shows reentrant behavior. The hcp solid never coexists with the liquid. In all cases analyzed, for both power law and Lennard-Jones potentials, the fcc crystal has higher entropy than the hcp. The role of anharmonic terms is thoroughly analyzed and a general thermodynamic integration to account for them is proposed.
Phase diagram of the modified Lennard-Jones system.
Asano, Yuta; Fuchizaki, Kazuhiro
2012-11-07
An investigation of the precise determination of melting temperature in the modified Lennard-Jones system under pressure-free conditions [Y. Asano and K. Fuchizaki, J. Phys. Soc. Jpn. 78, 055002 (2009)] was extended under finite-pressure conditions to obtain the phase diagram. The temperature and pressure of the triple point were estimated to be 0.61 ε∕k(B) and 0.0018(5) ε∕σ(3), and those of the critical point were 1.0709(19) ε∕k(B) and 0.1228(20) ε∕σ(3), where ε and σ are the Lennard-Jones parameters for energy and length scales, respectively, and k(B) is the Boltzmann constant. The potential used here has a finite attractive tail and does not suffer from cutoff problems. The potential can thus be a useful standard in examining statistical-mechanical problems in which different treatments for the tail would lead to different conclusions. The present phase diagram will then be a useful guide not only for equilibrium calculations but also for nonequilibrium problems such as discussions of the limits of phase (in)stability.
Closed-form equation of state for Lennard-Jones molecules based on perturbation theory
Bokis, C.P.; Donohue, M.D.
1995-08-17
A comparison of virial theory and perturbation theory for spherical molecules is presented. A new equation of state is derived. This new model has the exact second virial coefficient behavior, converges to the correct mean-field behavior at high densities, and successfully interpolates between these two limits. This new equation of state is applied to molecules that interact via the Lennard-Jones potential. Comparison is made with computer simulation results for the configurational energy, the compressibility factor, and the second virial coefficient of Lennard-Jones molecules. 25 refs., 7 figs.
Solid-liquid equilibria and triple points of n-6 Lennard-Jones fluids
NASA Astrophysics Data System (ADS)
Ahmed, Alauddin; Sadus, Richard J.
2009-11-01
Molecular dynamics simulations are reported for the solid-liquid coexistence properties of n-6 Lennard-Jones fluids, where n =12, 11, 10, 9, 8, and 7. The complete phase behavior for these systems has been obtained by combining these data with vapor-liquid simulations. The influence of n on the solid-liquid coexistence region is compared using relative density difference and miscibility gap calculations. Analytical expressions for the coexistence pressure, liquid, and solid densities as a function of temperature have been determined, which accurately reproduce the molecular simulation data. The triple point temperature, pressure, and liquid and solid densities are estimated. The triple point temperature and pressure scale with respect to 1/n, resulting in simple linear relationships that can be used to determine the pressure and temperature for the limiting ∞-6 Lennard-Jones potential. The simulation data are used to obtain parameters for the Raveché, Mountain, and Streett and Lindemann melting rules, which indicate that they are obeyed by the n-6 Lennard Jones potentials. In contrast, it is demonstrated that the Hansen-Verlet freezing rule is not valid for n-6 Lennard-Jones potentials.
The Lennard-Jones melting line and isomorphism.
Heyes, D M; Brańka, A C
2015-12-21
The location of the melting line (ML) of the Lennard-Jones (LJ) system and its associated physical properties are investigated using molecular dynamics computer simulation. The radial distribution function and the behavior of the repulsive and attractive parts of the potential energy indicate that the ML is not a single isomorph, but the isomorphic state evolves gradually with temperature, i.e., it is only "locally isomorphic." The state point dependence of the unitless isomorphic number, X̃, for a range of static and dynamical properties of the LJ system in the solid and fluid states, and for fluid argon, are also reported. The quantity X̃ typically varies most with state point in the vicinity of the triple point and approaches a plateau in the high density (temperature) limit along the ML.
NASA Astrophysics Data System (ADS)
Mamedov, Bahtiyar A.; Somuncu, Elif; Askerov, Iskender M.
2016-08-01
In this work, a new theoretical approach is proposed for calculating fourth virial coefficient with Leonard-Jones potential. The established algorithm can be used to evaluate the thermodynamics properties and the intermolecular interaction potentials of liquids and gases with an improved accuracy. Note that the evaluation of the high-order virial coefficients is very valuable for accurate calculation of thermodynamic parameters. By using the suggested method, the fourth virial coefficient of CH4, Ar,C2H6 and SF6 molecules are evaluated. The calculation results are useful for accurate interpretation of the experimental data and of the determination of related physical properties.
Conformation of a Lennard-Jones polymer in explicit solvent
NASA Astrophysics Data System (ADS)
Ye, Yuting; Taylor, Mark
2012-04-01
The conformation of a polymer chain is solution is coupled to the local structure of the surrounding solvent and can undergo large changes in response to variations in solvent density and temperature. The many-body effects of solvent on the structure of an n-mer chain can be formally mapped to an exact n-body solvation potential. These potentials map the chain-solvent system to a single chain, thereby dramatically reducing the computational complexity of the polymer chain-in-solvent problem. We have recently shown that a pair-decomposition of this n-body potential is valid for short Lennard-Jones (LJ) chains in explicit LJ solvent [1]. Here we use these short chain results to construct solvation potentials for long chains. We present results for the size and intramolecular structure of LJ chains up to length n=400 in LJ solvent at state points spanning the solvent phase diagram (including vapor, liquid, and super-critical regions). In comparison with simulation results for the corresponding full chain-in-solvent system, our solvation potential approach is found to be quantitatively accurate for a wide range of solvent conditions and chain lengths.[4pt] [1] M.P. Taylor and S.R. Adhikari, J. Chem. Phys. 135, 044903 (2011).
Conformation of a Lennard-Jones polymer in explicit solvent
NASA Astrophysics Data System (ADS)
Ye, Yuting; Taylor, Mark
2011-10-01
The conformation of a polymer chain is solution is coupled to the local structure of the surrounding solvent and can undergo large changes in response to variations in solvent density and temperature. The many-body effects of solvent on the structure of an n-mer chain can be formally mapped to an exact n-body solvation potential. These potentials map the chain-solvent system to a single chain, thereby dramatically reducing the computational complexity of the polymer chain-in-solvent problem. We have recently shown that a pair-decomposition of this n-body potential is valid for short Lennard-Jones (LJ) chains in explicit LJ solvent [1]. Here we use these short chain results to construct solvation potentials for long chains. We present results for the size and intramolecular structure of LJ chains up to length n=400 in LJ solvent at state points spanning the solvent phase diagram (including vapor, liquid, and super-critical regions). In comparison with simulation results for the corresponding full chain-in-solvent system, our solvation potential approach is found to be quantitatively accurate for a wide range of solvent conditions and chain lengths.[4pt] [1] M.P. Taylor and S.R. Adhikari, J. Chem. Phys. 135, 044903 (2011).
Phase equilibra in binary Lennard-Jones mixtures: phase diagram simulation
NASA Astrophysics Data System (ADS)
Canongia Lopes, J. N.
A three-box version of the Gibbs ensemble Monte Carlo method was used to determine the phase diagram type of several binary mixtures of one-centre Lennard-Jones particles. The method can be used to establish a direct link between the intermolecular potential modelling the interactions in a given system and its fluid phase diagram, without the knowledge of the corresponding equation of state governing its pV T behaviour. As an example of the application of the method, closed-loop behaviour in an isotropic system could be found using a set of Lennard-Jones parameters exhibiting a cross-interaction diameter with a negative deviation from the Lorentz-Berthelot combination rule.
Anisotropy effect on global minimum structures of clusters: two-center Lennard-Jones model.
Feng, Yan; Wu, Jing; Cheng, Longjiu; Liu, Haiyan
2011-12-28
Using a two-center Lennard-Jones (2CLJ) model, the simplest anisotropic case, we investigated how anisotropy affects global minimum structures of clusters and obtained some interesting results. The anisotropy parameter, R, is defined as the ratio of the bond length of 2CLJ dimer to the LJ equilibrium pair separation, where a larger R value means higher anisotropy. For low R values, the structures resemble those of the Lennard-Jones atomic clusters. However, as the pairwise interaction becomes more anisotropic, the "magic numbers" change, and several novel cluster patterns emerge as particularly stable structures, and the global minima change from icosahedral, to polyicosahedral and to novel irregular structures. Moreover, increasing the anisotropy effectively softens the 2CLJ potential. Given the general importance of the LJ cluster as a simple model cluster, 2CLJ model can provide a straightforward and useful analysis of the effect of molecular shape on the structures of clusters.
Pressure-energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems.
Schrøder, Thomas B; Gnan, Nicoletta; Pedersen, Ulf R; Bailey, Nicholas P; Dyre, Jeppe C
2011-04-28
This series of papers is devoted to identifying and explaining the properties of strongly correlating liquids, i.e., liquids with more than 90% correlation between their virial W and potential energy U fluctuations in the NVT ensemble. Paper IV [N. Gnan et al., J. Chem. Phys. 131, 234504 (2009)] showed that strongly correlating liquids have "isomorphs," which are curves in the phase diagram along which structure, dynamics, and some thermodynamic properties are invariant in reduced units. In the present paper, using the fact that reduced-unit radial distribution functions are isomorph invariant, we derive an expression for the shapes of isomorphs in the WU phase diagram of generalized Lennard-Jones systems of one or more types of particles. The isomorph shape depends only on the Lennard-Jones exponents; thus all isomorphs of standard Lennard-Jones systems (with exponents 12 and 6) can be scaled onto a single curve. Two applications are given. One tests the prediction that the solid-liquid coexistence curve follows an isomorph by comparing to recent simulations by Ahmed and Sadus [J. Chem. Phys. 131, 174504 (2009)]. Excellent agreement is found on the liquid side of the coexistence curve, whereas the agreement is less convincing on the solid side. A second application is the derivation of an approximate equation of state for generalized Lennard-Jones systems by combining the isomorph theory with the Rosenfeld-Tarazona expression for the temperature dependence of the potential energy on isochores. It is shown that the new equation of state agrees well with simulations.
Contact angle of sessile drops in Lennard-Jones systems.
Becker, Stefan; Urbassek, Herbert M; Horsch, Martin; Hasse, Hans
2014-11-18
Molecular dynamics simulations are used for studying the contact angle of nanoscale sessile drops on a planar solid wall in a system interacting via the truncated and shifted Lennard-Jones potential. The entire range between total wetting and dewetting is investigated by varying the solid-fluid dispersive interaction energy. The temperature is varied between the triple point and the critical temperature. A correlation is obtained for the contact angle in dependence of the temperature and the dispersive interaction energy. Size effects are studied by varying the number of fluid particles at otherwise constant conditions, using up to 150,000 particles. For particle numbers below 10,000, a decrease of the contact angle is found. This is attributed to a dependence of the solid-liquid surface tension on the droplet size. A convergence to a constant contact angle is observed for larger system sizes. The influence of the wall model is studied by varying the density of the wall. The effective solid-fluid dispersive interaction energy at a contact angle of θ = 90° is found to be independent of temperature and to decrease linearly with the solid density. A correlation is developed that describes the contact angle as a function of the dispersive interaction, the temperature, and the solid density. The density profile of the sessile drop and the surrounding vapor phase is described by a correlation combining a sigmoidal function and an oscillation term.
Scaling of the dynamics of flexible Lennard-Jones chains: Effects of harmonic bonds.
Veldhorst, Arno A; Dyre, Jeppe C; Schrøder, Thomas B
2015-11-21
The previous paper [A. A. Veldhorst et al., J. Chem. Phys. 141, 054904 (2014)] demonstrated that the isomorph theory explains the scaling properties of a liquid of flexible chains consisting of ten Lennard-Jones particles connected by rigid bonds. We here investigate the same model with harmonic bonds. The introduction of harmonic bonds almost completely destroys the correlations in the equilibrium fluctuations of the potential energy and the virial. According to the isomorph theory, if these correlations are strong a system has isomorphs, curves in the phase diagram along which structure, dynamics, and the excess entropy are invariant. The Lennard-Jones chain liquid with harmonic bonds does have curves in the phase diagram along which the structure and dynamics are invariant. The excess entropy is not invariant on these curves, which we refer to as "pseudoisomorphs." In particular, this means that Rosenfeld's excess-entropy scaling (the dynamics being a function of excess entropy only) does not apply for the Lennard-Jones chain with harmonic bonds.
Static and Restricted Rigid Rotor Configurations of Three Classical 12-6-Lennard-Jones Particles
NASA Astrophysics Data System (ADS)
Rupp, Florian
2015-03-01
Motivated by the continuous search for stable geometric configurations of atom and molecule clusters, we analyse the planar evolution of two freely movable point particles around a third immovable one subject to the 12-6-Lennard-Jones potential. This tailors our discussion to systems with one very heavy particle that can be assumed to be permanently at rest in the moving reference frame for the whole ensemble. Relating to Lennard-Jones interactions, we allow all three point particles to take different parameters. This breaks the symmetry conditions that are usually imposed on such systems. Through a classical non-regularized Hamiltonian description of our restricted three particle system, we study the existence of genuine equilibria and rigid rotor solutions around a single axis of rotation. We prove, depending on the choice of the Lennard-Jones parameters, that for these genuine equilibria, collinear alignments and triangular configurations of any shape can occur. Moreover, for the discussed type of relative equilibria a complete classification is provided by proving the existence of rigid rotor configurations in the plane of rotation (collinear cis and trans as well as triangle shaped configurations) and out of the plane of rotation (triangle shaped and flag-like configurations). Furthermore, we show that there are no further rigid rotor solutions of the underlying equations of motion.
Thermal conductivity of the Lennard-Jones chain fluid model
NASA Astrophysics Data System (ADS)
Galliero, Guillaume; Boned, Christian
2009-12-01
Nonequilibrium molecular dynamics simulations have been performed to estimate, analyze, and correlate the thermal conductivity of a fluid composed of short Lennard-Jones chains (up to 16 segments) over a large range of thermodynamic conditions. It is shown that the dilute gas contribution to the thermal conductivity decreases when the chain length increases for a given temperature. In dense states, simulation results indicate that the residual thermal conductivity of the monomer increases strongly with density, but is weakly dependent on the temperature. Compared to the monomer value, it has been noted that the residual thermal conductivity of the chain was slightly decreasing with its length. Using these results, an empirical relation, including a contribution due to the critical enhancement, is proposed to provide an accurate estimation of the thermal conductivity of the Lennard-Jones chain fluid model (up to 16 segments) over the domain 0.8≤T∗≤6 and 0≤ρ∗≤1 . Additionally, it has been noted that all reduced thermal conductivity values of the Lennard-Jones chain fluid model merge on the same “universal” curve when plotted as a function of the excess entropy. Furthermore, it is shown that the reduced configurational thermal conductivity of the Lennard-Jones chain fluid model is approximately proportional to the reduced excess entropy for all fluid states and all chain lengths.
Mairhofer, Jonas; Sadus, Richard J
2013-10-21
Molecular dynamics simulations are reported for the thermodynamic properties of n-m Lennard-Jones fluids, where n = 10 and 12, and m = 5 and 6. Results are reported for the thermal expansion coefficient, isothermal and adiabatic compressibilities, isobaric and isochoric heat capacities, Joule-Thomson coefficient, and speed of sound at supercritical conditions covering a wide range of fluid densities. The thermodynamic criteria for maxima∕minima in the isochoric and isobaric heat capacities are identified and the simulation results are also compared with calculations from Lennard-Jones equations of state. The Johnson et al. [Mol. Phys. 78, 591 (1993)] equation of state can be used to reproduce all heat capacity phenomena reported [T. M. Yigzawe and R. J. Sadus, J. Chem. Phys. 138, 194502 (2013)] from molecular dynamics simulations for the 12-6 Lennard-Jones potential. Significantly, these calculations and molecular dynamics results for other n-m Lennard-Jones potentials support the existence of Cp minima at supercritical conditions. The values of n and m also have a significant influence on many other thermodynamic properties.
NASA Astrophysics Data System (ADS)
Mairhofer, Jonas; Sadus, Richard J.
2013-10-01
Molecular dynamics simulations are reported for the thermodynamic properties of n-m Lennard-Jones fluids, where n = 10 and 12, and m = 5 and 6. Results are reported for the thermal expansion coefficient, isothermal and adiabatic compressibilities, isobaric and isochoric heat capacities, Joule-Thomson coefficient, and speed of sound at supercritical conditions covering a wide range of fluid densities. The thermodynamic criteria for maxima/minima in the isochoric and isobaric heat capacities are identified and the simulation results are also compared with calculations from Lennard-Jones equations of state. The Johnson et al. [Mol. Phys. 78, 591 (1993)] equation of state can be used to reproduce all heat capacity phenomena reported [T. M. Yigzawe and R. J. Sadus, J. Chem. Phys. 138, 194502 (2013)] from molecular dynamics simulations for the 12-6 Lennard-Jones potential. Significantly, these calculations and molecular dynamics results for other n-m Lennard-Jones potentials support the existence of Cp minima at supercritical conditions. The values of n and m also have a significant influence on many other thermodynamic properties.
Solid-liquid transition in polydisperse Lennard-Jones systems
NASA Astrophysics Data System (ADS)
Sarkar, Sarmistha; Biswas, Rajib; Santra, Mantu; Bagchi, Biman
2013-08-01
We study melting of a face-centered crystalline solid consisting of polydisperse Lennard-Jones spheres with Gaussian polydispersity in size. The phase diagram reproduces the existence of a nearly temperature invariant terminal polydispersity (δt ≃ 0.11), with no signature of reentrant melting. The absence of reentrant melting can be attributed to the influence of the attractive part of the potential upon melting. We find that at terminal polydispersity the fractional density change approaches zero, which seems to arise from vanishingly small compressibility of the disordered phase. At constant temperature and volume fraction the system undergoes a sharp transition from crystalline solid to the disordered amorphous or fluid state with increasing polydispersity. This has been quantified by second- and third-order rotational invariant bond orientational order, as well as by the average inherent structure energy. The translational order parameter also indicates a similar sharp structural change at δ ≃ 0.09 in case of T* = 1.0, ϕ = 0.58. The free energy calculation further supports the sharp nature of the transition. The third-order rotationally invariant bond order shows that with increasing polydispersity, the local cluster favors a more icosahedral arrangement and the system loses its local crystalline symmetry. Interestingly, the value of structure factor S(k) of the amorphous phase at δ ≃ 0.10 (just beyond the solid-liquid transition density at T* = 1) becomes 2.75, which is below the value of 2.85 required for freezing given by the empirical Hansen-Verlet rule of crystallization, well known in the theory of freezing.
Solid-liquid transition in polydisperse Lennard-Jones systems.
Sarkar, Sarmistha; Biswas, Rajib; Santra, Mantu; Bagchi, Biman
2013-08-01
We study melting of a face-centered crystalline solid consisting of polydisperse Lennard-Jones spheres with Gaussian polydispersity in size. The phase diagram reproduces the existence of a nearly temperature invariant terminal polydispersity (δ(t) =/~ 0.11), with no signature of reentrant melting. The absence of reentrant melting can be attributed to the influence of the attractive part of the potential upon melting. We find that at terminal polydispersity the fractional density change approaches zero, which seems to arise from vanishingly small compressibility of the disordered phase. At constant temperature and volume fraction the system undergoes a sharp transition from crystalline solid to the disordered amorphous or fluid state with increasing polydispersity. This has been quantified by second- and third-order rotational invariant bond orientational order, as well as by the average inherent structure energy. The translational order parameter also indicates a similar sharp structural change at δ =/~ 0.09 in case of T(*) = 1.0, φ = 0.58. The free energy calculation further supports the sharp nature of the transition. The third-order rotationally invariant bond order shows that with increasing polydispersity, the local cluster favors a more icosahedral arrangement and the system loses its local crystalline symmetry. Interestingly, the value of structure factor S(k) of the amorphous phase at δ =/~ 0.10 (just beyond the solid-liquid transition density at T(*) = 1) becomes 2.75, which is below the value of 2.85 required for freezing given by the empirical Hansen-Verlet rule of crystallization, well known in the theory of freezing.
Ushcats, M V
2014-09-14
The regularity of the existing data on the virial coefficients for the Lennard-Jones and modified Lennard-Jones models has allowed a rough extrapolation to the coefficients of higher orders. The corresponding approximation of the infinite virial series has been proposed for the limited temperature interval: 0.4-0.8 of the critical temperature. The loci of zero points of isothermal bulk modulus obtained on the basis of this approximation are close to the vapor-liquid branch of the experimental binodal rather than spinodal. In addition, those points ((dP/dV)T = 0) almost coincide with the divergence points of the approximated virial series that may eliminate some disputable questions about the boundaries of adequacy for the virial equation of state and makes the theoretical isotherms qualitatively similar to the real in the condensation region.
Modified Lennard-Jones model: virial coefficients to the 7th order.
Ushcats, M V
2014-06-21
The modified Lennard-Jones potential, which simplifies the numerical simulations and maintains the realistic behavior of its parent, is proposed to a role of the standard interaction model for both the experimental and theoretical studies. The virial coefficients of this model up to the seventh order have been calculated for the range of temperatures kT/ɛ = 0.3-70. In the computations, a technique has been used, that combines the quadrature integration and Mayer Sampling Monte Carlo method (MSMC). Unlike the original MSMC, this technique does not require the reference coefficients of another potential and can be used in a wide range of temperatures for various interaction models.
NASA Astrophysics Data System (ADS)
Kim, Sun Ung; Monroe, Charles W.
2014-09-01
The inverse problem of parameterizing intermolecular potentials given macroscopic transport and thermodynamic data is addressed. Procedures are developed to create arbitrary-precision algorithms for transport collision integrals, using the Lennard-Jones (12-6) potential as an example. Interpolation formulas are produced that compute these collision integrals to four-digit accuracy over the reduced-temperature range 0.3≤T*≤400, allowing very fast computation. Lennard-Jones parameters for neon, argon, and krypton are determined by simultaneously fitting the observed temperature dependences of their viscosities and second virial coefficients-one of the first times that a thermodynamic and a dynamic property have been used simultaneously for Lennard-Jones parameterization. In addition to matching viscosities and second virial coefficients within the bounds of experimental error, the determined Lennard-Jones parameters are also found to predict the thermal conductivity and self-diffusion coefficient accurately, supporting the value of the Lennard-Jones (12-6) potential for noble-gas transport-property correlation.
Kim, Sun Ung; Monroe, Charles W.
2014-09-15
The inverse problem of parameterizing intermolecular potentials given macroscopic transport and thermodynamic data is addressed. Procedures are developed to create arbitrary-precision algorithms for transport collision integrals, using the Lennard-Jones (12–6) potential as an example. Interpolation formulas are produced that compute these collision integrals to four-digit accuracy over the reduced-temperature range 0.3≤T{sup ⁎}≤400, allowing very fast computation. Lennard-Jones parameters for neon, argon, and krypton are determined by simultaneously fitting the observed temperature dependences of their viscosities and second virial coefficients—one of the first times that a thermodynamic and a dynamic property have been used simultaneously for Lennard-Jones parameterization. In addition to matching viscosities and second virial coefficients within the bounds of experimental error, the determined Lennard-Jones parameters are also found to predict the thermal conductivity and self-diffusion coefficient accurately, supporting the value of the Lennard-Jones (12–6) potential for noble-gas transport-property correlation.
Molecular dynamics simulation of graphene on Cu (111) with different Lennard-Jones parameters
NASA Astrophysics Data System (ADS)
Sidorenkov, Alexander V.; Kolesnikov, Sergey V.; Saletsky, Alexander M.
2016-10-01
The interaction between graphene and copper (111) surface have been investigated using the molecular dynamics simulations. The range of Lennard-Jones parameters which correspond to the binding energies and the binding distances calculated via ab initio methods was found. The dependencies of the binding energy, the binding distance and the graphene thickness on the parameters of the potential and the rotational angle are presented. We have found minima of the binding energy which can be related to experimentally observed Moiré superstructures.
Structure diagram of binary Lennard-Jones clusters.
Mravlak, Marko; Kister, Thomas; Kraus, Tobias; Schilling, Tanja
2016-07-14
We analyze the structure diagram for binary clusters of Lennard-Jones particles by means of a global optimization approach for a large range of cluster sizes, compositions, and interaction energies and present a publicly accessible database of 180 000 minimal energy structures (http://softmattertheory.lu/clusters.html). We identify a variety of structures such as core-shell clusters, Janus clusters, and clusters in which the minority species is located at the vertices of icosahedra. Such clusters can be synthesized from nanoparticles in agglomeration experiments and used as building blocks in colloidal molecules or crystals. We discuss the factors that determine the formation of clusters with specific structures.
Bubble nucleation in a Lennard-Jones binary liquid mixture
NASA Astrophysics Data System (ADS)
Baidakov, Vladimir G.; Protsenko, Sergey P.; Bryukhanov, Vasiliy M.
2016-10-01
We report a molecular dynamics (MD) study of homogeneous bubble nucleation in a stretched Lennard-Jones binary mixture at a temperature close to the solvent triple point. The pressure of the limiting stretching pn corresponding to a fixed value of the nucleation rate has been determined. The values of pn achieved in MD simulation are lower than those calculated from classical nucleation theory (CNT). The discrepancy between the data of MD simulation and CNT may be connected with the neglect in the latter of the size dependence of the surface tension of critical bubbles.
Enhanced Crystal Growth in Binary Lennard-Jones Mixtures.
Radu, M; Kremer, K
2017-02-03
We study the crystal growth in binary Lennard-Jones mixtures by molecular dynamics simulations. Growth dynamics, the structure of the liquid-solid interfaces as well as droplet incorporation into the crystal vary with solution properties. For demixed systems we observe a strongly enhanced crystal growth at the cost of enclosed impurities. Furthermore, we find different interface morphologies depending on solubility. We relate our observations to growth mechanisms based on the Gibbs-Thomson effect as well as to predictions of the Kardar-Parisi-Zhang theory in 2+1 dimensions.
Structure diagram of binary Lennard-Jones clusters
NASA Astrophysics Data System (ADS)
Mravlak, Marko; Kister, Thomas; Kraus, Tobias; Schilling, Tanja
2016-07-01
We analyze the structure diagram for binary clusters of Lennard-Jones particles by means of a global optimization approach for a large range of cluster sizes, compositions, and interaction energies and present a publicly accessible database of 180 000 minimal energy structures (http://softmattertheory.lu/clusters.html). We identify a variety of structures such as core-shell clusters, Janus clusters, and clusters in which the minority species is located at the vertices of icosahedra. Such clusters can be synthesized from nanoparticles in agglomeration experiments and used as building blocks in colloidal molecules or crystals. We discuss the factors that determine the formation of clusters with specific structures.
Lennard-Jones and lattice models of driven fluids.
Díez-Minguito, M; Garrido, P L; Marro, J
2005-08-01
We introduce a nonequilibrium off-lattice model for anisotropic phenomena in fluids. This is a Lennard-Jones generalization of the driven lattice-gas model in which the particles' spatial coordinates vary continuously. A comparison between the two models allows us to discuss some exceptional, hardly realistic features of the original discrete system--which has been considered a prototype for nonequilibrium anisotropic phase transitions. We thus help to clarify open issues, and discuss on the implications of our observations for future investigation of anisotropic phase transitions.
Origin of line tension for a Lennard-Jones nanodroplet
NASA Astrophysics Data System (ADS)
Weijs, Joost H.; Marchand, Antonin; Andreotti, Bruno; Lohse, Detlef; Snoeijer, Jacco H.
2011-02-01
The existence and origin of line tension has remained controversial in literature. To address this issue, we compute the shape of Lennard-Jones nanodrops using molecular dynamics and compare them to density functional theory in the approximation of the sharp kink interface. We show that the deviation from Young's law is very small and would correspond to a typical line tension length scale (defined as line tension divided by surface tension) similar to the molecular size and decreasing with Young's angle. We propose an alternative interpretation based on the geometry of the interface at the molecular scale.
Enhanced Crystal Growth in Binary Lennard-Jones Mixtures
NASA Astrophysics Data System (ADS)
Radu, M.; Kremer, K.
2017-02-01
We study the crystal growth in binary Lennard-Jones mixtures by molecular dynamics simulations. Growth dynamics, the structure of the liquid-solid interfaces as well as droplet incorporation into the crystal vary with solution properties. For demixed systems we observe a strongly enhanced crystal growth at the cost of enclosed impurities. Furthermore, we find different interface morphologies depending on solubility. We relate our observations to growth mechanisms based on the Gibbs-Thomson effect as well as to predictions of the Kardar-Parisi-Zhang theory in 2 +1 dimensions.
Transitioning Model Potentials to Real Systems
2001-02-01
were those of a modified Lennard - Jones potential and a Lennard - Jones potential ( Lennard - Jones , J. E. Physica, Vol. 4. p. 941, 1937). The optimized...within 0.83% of experimental values. These results show that when properly parameterized, Lennard - Jones -like potentials could describe a system well over
A New Large-Scale Global Optimization Method and Its Application to Lennard-Jones Problems
1992-11-01
stochastic methods. Computational results on Lennard - Jones problems show that the new method is considerably more successful than any other method that...our method does not find as good a solution as has been found by the best special purpose methods for Lennard - Jones problems. This illustrates the inherent difficulty of large scale global optimization.
Wennberg, Christian L; Murtola, Teemu; Hess, Berk; Lindahl, Erik
2013-08-13
The accuracy of electrostatic interactions in molecular dynamics advanced tremendously with the introduction of particle-mesh Ewald (PME) summation almost 20 years ago. Lattice summation electrostatics is now the de facto standard for most types of biomolecular simulations, and in particular, for lipid bilayers, it has been a critical improvement due to the large charges typically present in zwitterionic lipid headgroups. In contrast, Lennard-Jones interactions have continued to be handled with increasingly longer cutoffs, partly because few alternatives have been available despite significant difficulties in tuning cutoffs and parameters to reproduce lipid properties. Here, we present a new Lennard-Jones PME implementation applied to lipid bilayers. We confirm that long-range contributions are well approximated by dispersion corrections in simple systems such as pentadecane (which makes parameters transferable), but for inhomogeneous and anisotropic systems such as lipid bilayers there are large effects on surface tension, resulting in up to 5.5% deviations in area per lipid and order parameters-far larger than many differences for which reparameterization has been attempted. We further propose an approximation for combination rules in reciprocal space that significantly reduces the computational cost of Lennard-Jones PME and makes accurate treatment of all nonbonded interactions competitive with simulations employing long cutoffs. These results could potentially have broad impact on important applications such as membrane proteins and free energy calculations.
Metastable Lennard-Jones fluids. III. Bulk viscosity.
Baidakov, Vladimir G; Protsenko, Sergey P
2014-09-21
The method of equilibrium molecular-dynamics simulation in combination with the Green-Kubo formula has been used to calculate the bulk viscosity of a Lennard-Jones fluid. Calculations have been made at temperatures 0.4 ≤ k(B)T/ɛ ≤ 2.0 and densities 0.0075 ≤ ρσ(3) ≤ 1.2 at 116 stable and 106 metastable states of liquid and gas. The depth of penetration into the region of metastable states was limited by spontaneous nucleation. In the region of stable states the data obtained are compared with the results of previous investigations. It has been established that the system transition across the lines of liquid-gas and liquid-crystal phase equilibrium and penetration into the metastable regions of liquid and gas are connected with increasing bulk viscosity. The behavior of bulk viscosity close to the spinodal of a superheated liquid and supersaturated vapor is discussed.
Phase behavior of the 38-atom Lennard-Jones cluster.
Sehgal, Ray M; Maroudas, Dimitrios; Ford, David M
2014-03-14
We have developed a coarse-grained description of the phase behavior of the isolated 38-atom Lennard-Jones cluster (LJ38). The model captures both the solid-solid polymorphic transitions at low temperatures and the complex cluster breakup and melting transitions at higher temperatures. For this coarse model development, we employ the manifold learning technique of diffusion mapping. The outcome of the diffusion mapping analysis over a broad temperature range indicates that two order parameters are sufficient to describe the cluster's phase behavior; we have chosen two such appropriate order parameters that are metrics of condensation and overall crystallinity. In this well-justified coarse-variable space, we calculate the cluster's free energy landscape (FEL) as a function of temperature, employing Monte Carlo umbrella sampling. These FELs are used to quantify the phase behavior and onsets of phase transitions of the LJ38 cluster.
Phase behavior of the 38-atom Lennard-Jones cluster
Sehgal, Ray M.; Maroudas, Dimitrios E-mail: ford@ecs.umass.edu; Ford, David M. E-mail: ford@ecs.umass.edu
2014-03-14
We have developed a coarse-grained description of the phase behavior of the isolated 38-atom Lennard-Jones cluster (LJ{sub 38}). The model captures both the solid-solid polymorphic transitions at low temperatures and the complex cluster breakup and melting transitions at higher temperatures. For this coarse model development, we employ the manifold learning technique of diffusion mapping. The outcome of the diffusion mapping analysis over a broad temperature range indicates that two order parameters are sufficient to describe the cluster's phase behavior; we have chosen two such appropriate order parameters that are metrics of condensation and overall crystallinity. In this well-justified coarse-variable space, we calculate the cluster's free energy landscape (FEL) as a function of temperature, employing Monte Carlo umbrella sampling. These FELs are used to quantify the phase behavior and onsets of phase transitions of the LJ{sub 38} cluster.
Freezing point depression in model Lennard-Jones solutions
NASA Astrophysics Data System (ADS)
Koschke, Konstantin; Jörg Limbach, Hans; Kremer, Kurt; Donadio, Davide
2015-09-01
Crystallisation of liquid solutions is of uttermost importance in a wide variety of processes in materials, atmospheric and food science. Depending on the type and concentration of solutes the freezing point shifts, thus allowing control on the thermodynamics of complex fluids. Here we investigate the basic principles of solute-induced freezing point depression by computing the melting temperature of a Lennard-Jones fluid with low concentrations of solutes, by means of equilibrium molecular dynamics simulations. The effect of solvophilic and weakly solvophobic solutes at low concentrations is analysed, scanning systematically the size and the concentration. We identify the range of parameters that produce deviations from the linear dependence of the freezing point on the molal concentration of solutes, expected for ideal solutions. Our simulations allow us also to link the shifts in coexistence temperature to the microscopic structure of the solutions.
Nicolini, Paolo; Guàrdia, Elvira; Masia, Marco
2013-11-14
In this work, ab initio parametrization of water force field is used to get insights into the functional form of empirical potentials to properly model the physics underlying dispersion interactions. We exploited the force matching algorithm to fit the interaction forces obtained with dispersion corrected density functional theory based molecular dynamics simulations. We found that the standard Lennard-Jones interaction potentials poorly reproduce the attractive character of dispersion forces. This drawback can be resolved by accounting for the distinctive short range behavior of dispersion interactions, multiplying the r(-6) term by a damping function. We propose two novel parametrizations of the force field using different damping functions. Structural and dynamical properties of the new models are computed and compared with the ones obtained from the non-damped force field, showing an improved agreement with reference first principle calculations.
Temperature-dependent mechanisms of homogeneous crystal nucleation in quenced Lennard-Jones liquids
Peng, L.; Morris, James R; Lo, Y. C.
2008-01-01
We have observed homogeneous crystal nucleation in Lennard-Jones liquid by molecular dynamics simulations. A clear nucleation time delay has been observed at T=0.677T{sub m} and T=0.629T{sub m} indicating the presence of a barrier, in contrast to recent reports [Trudu et al., Phys. Rev. Lett. 97, 105701 (2006)]. The structure of nuclei observed in the previous results and in the present work is evidence of transient-time dominated nucleation, not of a spinodal. Very rapid nucleation is observed at T=0.484T{sub m}, indicating either a low (but finite) barrier or possibly a spinodal transformation. No spinodal effect has been observed in similar simulations of crystal nucleation in aluminum at any temperature [Aga et al., Phys. Rev. Lett. 96, 245701 (2006)], suggesting that different qualitative behaviors may be possible in what would seem to be similar potentials.
Accurate freezing and melting equations for the Lennard-Jones system.
Khrapak, Sergey A; Morfill, Gregor E
2011-03-07
Analyzing three approximate methods to locate liquid-solid coexistence in simple systems, an observation is made that all of them predict the same functional dependence of the temperature on density at freezing and melting of the conventional Lennard-Jones (LJ) system. The emerging equations can be written as T=Aρ(4)+Bρ(2) in normalized units. We suggest to determine the values of the coefficients A at freezing and melting from the high-temperature limit, governed by the inverse 12th power repulsive potential. The coefficients B can be determined from the triple point parameters of the LJ fluid. This produces freezing and melting equations which are exact in the high-temperature limit and at the triple point and show remarkably good agreement with numerical simulation data in the intermediate region.
Nucleation rates of Lennard-Jones clusters from growth and decay simulations
NASA Astrophysics Data System (ADS)
Vehkamäki, Hanna; Ford, Ian J.
2000-08-01
We have studied singles clusters of Lennard-Jones atoms using a novel Monte Carlo simulation technique. We computed canonical ensemble averages of the grand canonical growth and decay probabilities of the cluster as a function of the cluster size. The critical size is identified as the one for which growth and decay are equally probable. The size and average internal energy the critical cluster was found for different temperatures and vapor chemical potentials. We used this information together with nucleation theorems to predict the behavior of the nucleation rate as function of the two external parameters. Our results are in line with the results found in the literature, and roughly correspond to the predictions of classical theory.
Melting transition of Lennard-Jones fluid in cylindrical pores.
Das, Chandan K; Singh, Jayant K
2014-05-28
Three-stage pseudo-supercritical transformation path and multiple-histogram reweighting technique are employed for the determination of solid-liquid coexistence of the Lennard-Jones (12-6) fluid, in a structureless cylindrical pore of radius, R, ranging from 4 to 20 molecular diameters. The Gibbs free energy difference is evaluated using thermodynamic integration method by connecting solid and liquid phases under confinement via one or more intermediate states without any first order phase transition among them. The thermodynamic melting temperature, Tm, is found to oscillate for pore size, R < 8, which is in agreement with the behavior observed for the melting temperature in slit pores. However, Tm for almost all pore sizes is less than the bulk case, which is contrary to the behavior seen for the slit pore. The oscillation in Tm decays at around pore radius R = 8, and beyond that shift in the melting temperature with respect to the bulk case is in line with the prediction of the Gibbs-Thomson equation.
Metastable Lennard-Jones fluids. II. Thermal conductivity.
Baidakov, Vladimir G; Protsenko, Sergey P
2014-06-07
The method of equilibrium molecular dynamics with the use of the Green-Kubo formalism has been used to calculate the thermal conductivity λ in stable and metastable regions of a Lennard-Jones fluid. Calculations have been made in the range of reduced temperatures 0.4 ≤ T* = k(b)T/ε ≤ 2.0 and densities 0.01 ≤ ρ* = ρσ³ ≤ 1.2 on 15 isotherms for 234 states, 130 of which refer to metastable regions: superheated and supercooled liquids, supersaturated vapor. Equations have been built up which describe the dependence of the regular part of the thermal conductivity on temperature and density, and also on temperature and pressure. It has been found that in (p, T) variables in the region of a liquid-gas phase transition a family of lines of constant value of excess thermal conductivity Δλ = λ - λ0, where λ0 is the thermal conductivity of a dilute gas, has an envelope which coincides with the spinodal. Thus, at the approach to the spinodal of a superheated liquid and supersaturated vapor (∂Δλ/∂p)T → ∞, (∂Δλ/∂T)p → ∞.
Melting transition of Lennard-Jones fluid in cylindrical pores
Das, Chandan K.; Singh, Jayant K.
2014-05-28
Three-stage pseudo-supercritical transformation path and multiple-histogram reweighting technique are employed for the determination of solid-liquid coexistence of the Lennard-Jones (12-6) fluid, in a structureless cylindrical pore of radius, R, ranging from 4 to 20 molecular diameters. The Gibbs free energy difference is evaluated using thermodynamic integration method by connecting solid and liquid phases under confinement via one or more intermediate states without any first order phase transition among them. The thermodynamic melting temperature, T{sub m}, is found to oscillate for pore size, R < 8, which is in agreement with the behavior observed for the melting temperature in slit pores. However, T{sub m} for almost all pore sizes is less than the bulk case, which is contrary to the behavior seen for the slit pore. The oscillation in T{sub m} decays at around pore radius R = 8, and beyond that shift in the melting temperature with respect to the bulk case is in line with the prediction of the Gibbs-Thomson equation.
Freezing of Lennard-Jones fluid on a patterned substrate.
Zhang, Huijun; Peng, Shuming; Mao, Li; Zhou, Xiaosong; Liang, Jianhua; Wan, Chubin; Zheng, Jian; Ju, Xin
2014-06-01
Using molecular dynamics simulations, we study freezing of Lennard-Jones particles at commensurate substrate with triangular pattern. Throughout the box particles freeze onto the substrate and form close-packed layers. For the moderately attractive substrates, an intermediate hexatic phase between liquid and crystal is detected in the first two layers where the hexatic-solid freezing process is continuous while, counterintuitively, the liquid-hexatic process is of first order. Moreover, we observe that liquid-hexatic and hexatic-solid transitions shift towards higher temperatures with the attraction strength increasing. By contrast, the liquid-hexatic transition shifts faster than the hexatic-solid process, significantly widening the temperature range of the hexatic phase. When this phenomenon appears, freezing in the bulk always proceeds through a first-order transition at the same temperature. In addition, changes in the average structural order (three-dimensional) of the layers indicate that freezing processes in layers near substrates seem to cost the structural order of the bulk particles in their vicinity, and an intermediate prestructural cloud of medium-ordered particles is always observed before the layering freezing.
Vacancy behavior in a compressed fcc Lennard-Jones crystal
Beeler, J.R. Jr.
1981-12-01
This computer experiment study concerns the determination of the stable vacancy configuration in a compressed fcc Lennard-Jones crystal and the migration of this defect in a compressed crystal. Isotropic and uniaxial compression stress conditions were studied. The isotropic and uniaxial compression magnitudes employed were 0.94 less than or equal to eta less than or equal to 1.5, and 1.0 less than or equal to eta less than or equal to 1.5, respectively. The site-centered vacancy (SCV) was the stable vacancy configuration whenever cubic symmetry was present. This includes all of the isotropic compression cases and the particular uniaxial compression case (eta = ..sqrt..2) that give a bcc structure. In addition, the SCV was the stable configuration for uniaxial compression eta < 1.29. The out-of-plane split vacancy (SV-OP) was the stable vacancy configuration for uniaxial compression 1.29 < eta less than or equal to 1.5 and was the saddle-point configuration for SCV migration when the SCV was the stable form. For eta > 1.20, the SV-OP is an extended defect and, therefore, a saddle point for SV-OP migration could not be determined. The mechanism for the transformation from the SCV to the SV-OP as the stable form at eta = 1.29 appears to be an alternating sign (101) and/or (011) shear process.
Second-order Percus Yevick theory for mixtures of Lennard-Jones fluids
NASA Astrophysics Data System (ADS)
Sokolowski, Douglas Henderson Stefan
The second-order integral equation formalism of Attard, applied recently, with good results, to one-component hard spheres and Lennard-Jones fluids, is applied to some binary mixtures of Lennard-Jones fluids. Comparison with molecular dynamic simulations of the pair correlation functions shows that this method is also quite accurate for mixtures. This is true not only when the Lorentz Berthelot mixing rules are obeyed but also when there are substantial deviations from these rules.
NASA Astrophysics Data System (ADS)
Polak, Wiesław Z.
2016-08-01
Simulated growth of four global-minimum Lennard-Jones clusters of sizes N = 561, 823, 850 and 923, representing multishell icosahedra and decahedron, always leads to formation of regular polyicosahedral clusters. Observation of cluster structure evolution revealed that new atoms form anti-Mackay islands spreading over the cluster surface by making strong island-island junctions at cluster edges. Analysis of potential energies of atoms composing different local structures shows that energy-driven preference for decahedral arrangement of several atoms initiating the junction of pentagonal symmetry on the cluster surface is responsible for kinetic effect in the cluster growth.
NASA Astrophysics Data System (ADS)
Tarzimanov, A. A.; Klinov, A. V.; Malygin, A. V.; Nurgalieva, A. A.
2008-08-01
Integral equation theory was used to study the binary distribution functions of the excess properties of three-component Lennard-Jones mixtures. The results obtained for the behavior of the excess functions of caloric properties (internal energy, enthalpy, and isochoric heat capacity) are reported. The influence of the third component with various potential parameters on excess functions was studied. Calculations were performed for systems under super-and subcritical conditions with different sizes of molecules, σ1/σ2 = 1 4, and attraction energies between them, ɛ1/ɛ2 = 1 4. The results were compared with numerical experiment data to find that the approach used was fairly accurate
Scaling of the dynamics of flexible Lennard-Jones chains.
Veldhorst, Arno A; Dyre, Jeppe C; Schrøder, Thomas B
2014-08-07
The isomorph theory provides an explanation for the so-called power law density scaling which has been observed in many molecular and polymeric glass formers, both experimentally and in simulations. Power law density scaling (relaxation times and transport coefficients being functions of ρ(γ(S)), where ρ is density, T is temperature, and γ(S) is a material specific scaling exponent) is an approximation to a more general scaling predicted by the isomorph theory. Furthermore, the isomorph theory provides an explanation for Rosenfeld scaling (relaxation times and transport coefficients being functions of excess entropy) which has been observed in simulations of both molecular and polymeric systems. Doing molecular dynamics simulations of flexible Lennard-Jones chains (LJC) with rigid bonds, we here provide the first detailed test of the isomorph theory applied to flexible chain molecules. We confirm the existence of isomorphs, which are curves in the phase diagram along which the dynamics is invariant in the appropriate reduced units. This holds not only for the relaxation times but also for the full time dependence of the dynamics, including chain specific dynamics such as the end-to-end vector autocorrelation function and the relaxation of the Rouse modes. As predicted by the isomorph theory, jumps between different state points on the same isomorph happen instantaneously without any slow relaxation. Since the LJC is a simple coarse-grained model for alkanes and polymers, our results provide a possible explanation for why power-law density scaling is observed experimentally in alkanes and many polymeric systems. The theory provides an independent method of determining the scaling exponent, which is usually treated as an empirical scaling parameter.
Sousa, J M G; Ferreira, A L; Barroso, M A
2012-05-07
The solid-fluid coexistence properties of the n - 6 Lennard-Jones system, n from 7 to 12, are reported. The procedure relies on determining Helmholtz free energy curves as a function of volume for each phase independently, from several NVT simulations, and then connecting it to points of known absolute free energy. For n = 12 this requires connecting the simulated points to states of very low densities on the liquid phase, and to a harmonic crystal for the solid phase, which involves many extra simulations for each temperature. For the reference points of the remaining systems, however, the free energy at a given density and temperature can be calculated relative to the n = 12 system. The method presented here involves a generalization of the multiple histogram method to combine simulations performed with different potentials, provided they visit overlapping regions of the phase space, and allows for a precise calculation of relative free energies. The densities, free energies, average potential energies, pressure, and chemical potential at coexistence are presented for up to T∗ = 5.0 and new estimations of the triple points are given for the n - 6 Lennard-Jones system.
Bárcenas, M; Reyes, Y; Romero-Martínez, A; Odriozola, G; Orea, P
2015-02-21
Coexistence and interfacial properties of a triangle-well (TW) fluid are obtained with the aim of mimicking the Lennard-Jones (LJ) potential and approach the properties of noble gases. For this purpose, the scope of the TW is varied to match vapor-liquid densities and surface tension. Surface tension and coexistence curves of TW systems with different ranges were calculated with replica exchange Monte Carlo and compared to those data previously reported in the literature for truncated and shifted (STS), truncated (ST), and full Lennard-Jones (full-LJ) potentials. We observed that the scope of the TW potential must be increased to approach the STS, ST, and full-LJ properties. In spite of the simplicity of TW expression, a remarkable agreement is found. Furthermore, the variable scope of the TW allows for a good match of the experimental data of argon and xenon.
Hoang, Hai; Galliero, Guillaume
2013-12-04
This work aims at providing a tractable approach to model the local shear viscosity of strongly inhomogeneous dense fluids composed of spherical molecules, in which the density variations occur on molecular distance. The proposed scheme, which relies on the local density average model, has been applied to the quasi-hard-sphere, the Week-Chandler-Andersen and the Lennard-Jones fluids. A weight function has been developed to deal with the hard-sphere fluid given the specificities of momentum exchange. To extend the approach to the smoothly repulsive potential, we have taken into account that the non-local contributions to the viscosity due to the interactions of particles separated by a given distance are temperature dependent. Then, using a simple perturbation scheme, the approach is extended to the Lennard-Jones fluids. It is shown that the viscosity profiles of inhomogeneous dense fluids deduced from this approach are consistent with those directly computed by non-equilibrium molecular dynamics simulations.
Flory-Huggins parameter χ, from binary mixtures of Lennard-Jones particles to block copolymer melts.
Chremos, Alexandros; Nikoubashman, Arash; Panagiotopoulos, Athanassios Z
2014-02-07
In this contribution, we develop a coarse-graining methodology for mapping specific block copolymer systems to bead-spring particle-based models. We map the constituent Kuhn segments to Lennard-Jones particles, and establish a semi-empirical correlation between the experimentally determined Flory-Huggins parameter χ and the interaction of the model potential. For these purposes, we have performed an extensive set of isobaric-isothermal Monte Carlo simulations of binary mixtures of Lennard-Jones particles with the same size but with asymmetric energetic parameters. The phase behavior of these monomeric mixtures is then extended to chains with finite sizes through theoretical considerations. Such a top-down coarse-graining approach is important from a computational point of view, since many characteristic features of block copolymer systems are on time and length scales which are still inaccessible through fully atomistic simulations. We demonstrate the applicability of our method for generating parameters by reproducing the morphology diagram of a specific diblock copolymer, namely, poly(styrene-b-methyl methacrylate), which has been extensively studied in experiments.
Flory-Huggins parameter χ, from binary mixtures of Lennard-Jones particles to block copolymer melts
Chremos, Alexandros; Nikoubashman, Arash Panagiotopoulos, Athanassios Z.
2014-02-07
In this contribution, we develop a coarse-graining methodology for mapping specific block copolymer systems to bead-spring particle-based models. We map the constituent Kuhn segments to Lennard-Jones particles, and establish a semi-empirical correlation between the experimentally determined Flory-Huggins parameter χ and the interaction of the model potential. For these purposes, we have performed an extensive set of isobaric–isothermal Monte Carlo simulations of binary mixtures of Lennard-Jones particles with the same size but with asymmetric energetic parameters. The phase behavior of these monomeric mixtures is then extended to chains with finite sizes through theoretical considerations. Such a top-down coarse-graining approach is important from a computational point of view, since many characteristic features of block copolymer systems are on time and length scales which are still inaccessible through fully atomistic simulations. We demonstrate the applicability of our method for generating parameters by reproducing the morphology diagram of a specific diblock copolymer, namely, poly(styrene-b-methyl methacrylate), which has been extensively studied in experiments.
NASA Astrophysics Data System (ADS)
Heffelfinger David, Grant S.; Ford, M.
A new algorithm to enable the implementation of dual control volume grand canonical molecular dynamics (DCV-GCMD) on massively parallel (MP) architectures is presented. DCVGCMD can be thought of as hybridization of molecular dynamics (MD) and grand canonical Monte Carlo (GCMC) and was developed recently to make possible the simulation of gradient-driven diffusion. The method has broad application to such problems as membrane separations, drug delivery systems, diffusion in polymers and zeolites, etc. The massively parallel algorithm for the DCV-GCMD method has been implemented in a code named LADERA which employs the short range Lennard-Jones potential for pure fluids and multicomponent mixtures including bulk and confined (single pore as well as amorphous solid materials) systems. Like DCV-GCMD, LADERA's MP algorithm can be thought of as a hybridization of two different algorithms, spatial MD and spatial GCMC. The DCV-GCMD method is described fully followed by the DCV-GCMD parallel algorithm employed in LADERA. The scaling characteristics of the new MP algorithm are presented together with the results of the application of LADERA to ternary and quaternary Lennard-Jones mixtures.
Flory-Huggins parameter χ, from binary mixtures of Lennard-Jones particles to block copolymer melts
NASA Astrophysics Data System (ADS)
Chremos, Alexandros; Nikoubashman, Arash; Panagiotopoulos, Athanassios Z.
2014-02-01
In this contribution, we develop a coarse-graining methodology for mapping specific block copolymer systems to bead-spring particle-based models. We map the constituent Kuhn segments to Lennard-Jones particles, and establish a semi-empirical correlation between the experimentally determined Flory-Huggins parameter χ and the interaction of the model potential. For these purposes, we have performed an extensive set of isobaric-isothermal Monte Carlo simulations of binary mixtures of Lennard-Jones particles with the same size but with asymmetric energetic parameters. The phase behavior of these monomeric mixtures is then extended to chains with finite sizes through theoretical considerations. Such a top-down coarse-graining approach is important from a computational point of view, since many characteristic features of block copolymer systems are on time and length scales which are still inaccessible through fully atomistic simulations. We demonstrate the applicability of our method for generating parameters by reproducing the morphology diagram of a specific diblock copolymer, namely, poly(styrene-b-methyl methacrylate), which has been extensively studied in experiments.
Peng, Lu Jian; Morris, James R; Aga, Rachel S
2010-08-28
Large scale simulations of crystal nucleation from the liquid are performed using the Lennard-Jones potential to determine the time required for nucleation. By considering both transient and finite-size effects, we for the first time successfully predict the nucleation time without any parameter fitting in the Lennard-Jones system. All necessary parameters are derived from separate, equilibrium simulations. At small undercoolings, large system size effects are observed. The required system size is not only determined by the size of the critical nuclei, but also the characteristic spacing between them. Two distinct nucleation regions are predicted by theory and observed by the simulations, which are dominated by the transient time and the steady-state nucleation time, respectively.
Properties of the two-dimensional heterogeneous Lennard-Jones dimers: An integral equation study
NASA Astrophysics Data System (ADS)
Urbic, Tomaz
2016-11-01
Structural and thermodynamic properties of a planar heterogeneous soft dumbbell fluid are examined using Monte Carlo simulations and integral equation theory. Lennard-Jones particles of different sizes are the building blocks of the dimers. The site-site integral equation theory in two dimensions is used to calculate the site-site radial distribution functions and the thermodynamic properties. Obtained results are compared to Monte Carlo simulation data. The critical parameters for selected types of dimers were also estimated and the influence of the Lennard-Jones parameters was studied. We have also tested the correctness of the site-site integral equation theory using different closures.
A Lennard-Jones-like perspective on first order transitions in biological helices
NASA Astrophysics Data System (ADS)
Oskolkov, Nikolay; Bohr, Jakob
2013-03-01
Helical structures with Lennard-Jones self-interactions are studied for optimal conformations. For this purpose, their self-energy is analyzed for extrema with respect to the geometric parameters of the helices. It is found that Lennard-Jones helices exhibit a first order phase transition from a state with large curvature of the helical backbone to one with a small curvature. I.e. from a dense helix to an extended helix. A transition from one helical structure to another is a phenomenon known to take place in self-assembling helices formed in multicomponent solutions with cholesterol.
Properties of the two-dimensional heterogeneous Lennard-Jones dimers: An integral equation study.
Urbic, Tomaz
2016-11-21
Structural and thermodynamic properties of a planar heterogeneous soft dumbbell fluid are examined using Monte Carlo simulations and integral equation theory. Lennard-Jones particles of different sizes are the building blocks of the dimers. The site-site integral equation theory in two dimensions is used to calculate the site-site radial distribution functions and the thermodynamic properties. Obtained results are compared to Monte Carlo simulation data. The critical parameters for selected types of dimers were also estimated and the influence of the Lennard-Jones parameters was studied. We have also tested the correctness of the site-site integral equation theory using different closures.
Effect of Size Polydispersity on the Nature of Lennard-Jones Liquids.
Ingebrigtsen, Trond S; Tanaka, Hajime
2015-08-27
Polydisperse fluids are encountered everywhere in biological and industrial processes. These fluids naturally show a rich phenomenology exhibiting fractionation and shifts in critical point and freezing temperatures. We study here the effect of size polydispersity on the basic nature of Lennard-Jones (LJ) liquids, which represent most molecular liquids without hydrogen bonds, via two- and three-dimensional molecular dynamics computer simulations. A single-component liquid constituting spherical particles and interacting via the LJ potential is known to exhibit strong correlations between virial and potential energy equilibrium fluctuations at constant volume. This correlation significantly simplifies the physical description of the liquid, and these liquids are now known as Roskilde-simple (RS) liquids. We show that this simple nature of the single-component LJ liquid is preserved even for very high polydispersities (above 40% polydispersity for the studied uniform distribution). We also investigate isomorphs of moderately polydisperse LJ liquids. Isomorphs are curves in the phase diagram of RS liquids along which structure, dynamics, and some thermodynamic quantities are invariant in dimensionless units. We find that isomorphs are a good approximation even for polydisperse LJ liquids. The theory of isomorphs thus extends readily to size polydisperse fluids and can be used to improve even further the understanding of these intriguing systems.
Effect of Energy Polydispersity on the Nature of Lennard-Jones Liquids.
Ingebrigtsen, Trond S; Tanaka, Hajime
2016-08-11
In the companion paper [ Ingebrigtsen , T. S. ; Tanaka , H. J. Phys. Chem. B 2015 , 119 , 11052 ] the effect of size polydispersity on the nature of Lennard-Jones (LJ) liquids, which represent most molecular liquids without hydrogen bonds, was studied. More specifically, it was shown that even highly size polydisperse LJ liquids are Roskilde-simple (RS) liquids. RS liquids are liquids with strong correlation between constant volume equilibrium fluctuations of virial and potential energy and are simpler than other types of liquids. Moreover, it was shown that size polydisperse LJ liquids have isomorphs to a good approximation. Isomorphs are curves in the phase diagram of RS liquids along which structure, dynamics, and some thermodynamic quantities are invariant in dimensionless (reduced) units. In this paper, we study the effect of energy polydispersity on the nature of LJ liquids. We show that energy polydisperse LJ liquids are RS liquids. However, a tendency of particle segregation, which increases with the degree of polydispersity, leads to a loss of strong virial-potential energy correlation but is mitigated by increasing temperature and/or density. Isomorphs are a good approximation also for energy polydisperse LJ liquids, although particle-resolved quantities display a somewhat poorer scaling compared to the mean quantities along the isomorph.
High Precision Calculations of the Lennard-Jones Lattice Constants for Five Lattices
NASA Astrophysics Data System (ADS)
Stein, Matthew
2017-01-01
The total potential energy of a crystal as described by the Lennard-Jones (L-J) potential depends in part upon the calculation of lattice constants. Knowing these constants to high precision is useful for prediction of the lattice type and simulation of crystals such as rare-gas solids or germanium detectors, but reaching higher precision is computationally costly and challenging. Presented here is the extension of the precision of the lattice constants, Lp, up to 32 decimal digits, and in some cases corrections from previous publication. The Lp terms are given for 4 <= p <= 30 in the simple cubic, face-centered cubic, body-centered cubic, hexagonal-close-pack, and diamond lattices. This precision was obtained through the use of careful parallelization technique, exploitation of the symmetries of each lattice, and the ``onionization'' of the simulated crystal. The results of this computation, along with the tools and algorithm strategies to make this computation possible, are explained in detail graphically.
Molecular Simulation of the Vapor-Liquid Phase Behavior of Lennard-Jones Mixtures in Porous Solids
2006-09-01
is used to simulate Lennard - Jones fluid mixtures at several porosities: 0.9, 0.95, and 0.975. Effects based on the size and the energetics of the...to the bulk fluid behavior, dramatic shifts in the phase envelope were found for even highly porous structures. Both the Lennard - Jones size and energy
Molecular dynamics study of nanobubbles in the equilibrium Lennard-Jones fluid.
Zhukhovitskii, D I
2013-10-28
We employ a model, in which the density fluctuations in a bulk liquid are represented as presence of the clusters of molecules with the lowered number of nearest neighbors (number of bonds). The nanobubble size distribution is calculated on the basis of a close analogy between the surface part of the work of formation for a cluster and for a nanobubble. The pre-exponential factor for this distribution is related to the fluid compressibility. Estimates made for different liquids show that it can be noticeably different from that adopted in the classical nucleation theory (CNT). Molecular dynamics (MD) simulation is performed for a liquid inside a macroscopic droplet of molecules interacting via the Lennard-Jones potential plus a long-range tail. The nanobubbles are identified by clusters of bond-deficient particles with the optimum number of bonds that provide the maximum nanobubble number density and maximum resolvable nanobubble equimolar size. The results of MD simulation are in qualitatively better agreement with proposed theory than with CNT.
Benjamin, Ronald; Horbach, Jürgen
2013-08-28
Different computational techniques in combination with molecular dynamics computer simulation are used to determine the wall-liquid and the wall-crystal interfacial free energies of a modified Lennard-Jones (LJ) system in contact with a solid wall. Two different kinds of solid walls are considered: a flat structureless wall and a structured wall consisting of an ideal crystal with the particles rigidly attached to fcc lattice sites. Interfacial free energies are determined by a thermodynamic integration scheme, the anisotropy of the pressure tensor, the non-equilibrium work method based on Bennett acceptance criteria, and a method using Cahn's adsorption equations based on the interfacial thermodynamics of Gibbs. For the flat wall, interfacial free energies as a function of different densities of the LJ liquid and as a function of temperature along the coexistence curve are calculated. In the case of a structured wall, the interaction strength between the wall and the LJ system and the lattice constant of the structured wall are varied. Using the values of the wall-liquid and wall-crystal interfacial energies along with the value for the crystal-liquid interfacial free energy determined previously for the same system by the "cleaving potential method," we obtain the contact angle as a function of various parameters; in particular, the conditions are found under which partial wetting occurs.
Pressure Profile for an Associating Lennard-Jones Fluid Confined in a Spherical Cavity.
Wang, Li-Yuan; Gu, Fang; Wang, Hai-Jun; Sun, Zong-Li
2017-03-09
We present the pressure tensor of an associating Lennard-Jones (LJ) fluid confined in a spherical cavity of hard wall, where a high-order density correlation has been taken into account. To give the two-body association potential for calculating the pressure tensor, an angle-average of site-site attraction over all orientations of two particles is performed. Furthermore, the classical density functional theory is employed to obtain the density profile of the confined fluid, by which the normal and tangential pressure profiles are illustrated under various conditions to show the dependence of the pressure tensor on the association strength, number of associating sites, radius of cavity, and bulk density. As an application, the corresponding surface tension is calculated. It is shown that under a strong association interaction (both association strength and the number of associating sites are large), the pressure profiles are depleted from the wall of the cavity instead of the oscillatory behavior under a weak association interaction. Such a tendency is mainly determined by the competition between association interaction and excluded volume interaction. Therefore, the aggregation state and related properties of an associating LJ fluid within a confinement of nanoscale can be efficiently regulated by the association interaction.
Weighted density-functional theory for simple fluids: Prewetting of a Lennard-Jones fluid
NASA Astrophysics Data System (ADS)
Sweatman, M. B.
2002-01-01
The prewetting of a Lennard-Jones fluid is studied using weighted density-functional theory. The intrinsic Helmholtz free-energy functional is separated into repulsive and attractive contributions. An accurate functional for hard spheres is used for the repulsive functional and a weighted density-functional method is used for the attractive part. The results for this theory are compared against mean-field density-functional theory, the theory of Velasco and Tarazona [E. Velasco and P. Tarazona, J. Chem. Phys. 91, 7916 (1989)] and grand canonical ensemble simulation results. The results demonstrate that the weighted density functional for attractive forces may offer a significant increase in accuracy over the other theories. The density-functional and simulation results also indicate that a previous estimate of the wetting temperature for a model of the interaction of argon with solid carbon dioxide, obtained from simulations [J. E. Finn and P. A. Monson, Phys. Rev. A, 39, 6402 (1989)], is incorrect. The weighted density-functional method indicates that triple-point prewetting is observed for this model potential.
Widom line for the liquid-gas transition in Lennard-Jones system.
Brazhkin, V V; Fomin, Yu D; Lyapin, A G; Ryzhov, V N; Tsiok, E N
2011-12-08
The locus of extrema (ridges) for heat capacity, thermal expansion coefficient, compressibility, and density fluctuations for model particle systems with Lennard-Jones (LJ) potential in the supercritical region have been obtained. It was found that the ridges for different thermodynamic values virtually merge into a single Widom line at T < 1.1T(c) and P < 1.5P(c) and become practically completely smeared at T < 2.5T(c) and P < 10P(c), where T(c) and P(c) are the critical temperature and pressure. The ridge for heat capacity approaches close to critical isochore, whereas the lines of extrema for other values correspond to density decrease. The lines corresponding to the supercritical maxima for argon and neon are in good agreement with the computer simulation data for LJ fluid. The behavior of the ridges for LJ fluid, in turn, is close to that for the supercritical van der Waals fluid, which is indicative of a fairly universal behavior of the Widom line for a liquid-gas transition.
Understanding the interfacial behavior in isopycnic Lennard-Jones mixtures by computer simulations.
Garrido, José Matías; Piñeiro, Manuel M; Mejía, Andrés; Blas, Felipe J
2016-01-14
The physical characterization of the singular interfacial behavior of heterogeneous fluid systems is a very important step in preliminary stages of the design process, and also in the subsequent procedures for the determination of the optimal operating conditions. Molar isopycnicity or molar density inversion is a special case of phase equilibrium behavior that directly affects the relative position of phases in heterogeneous mixtures, without being affected by gravitational fields. This work is dedicated to characterize the impact of molar density inversion on the interfacial properties of Lennard-Jones binary mixtures. The results and specific trends of the molar density inversion phenomena on the peculiar calculated composition profiles across the interface and interfacial tensions are explored by using canonical molecular dynamics simulations of the Lennard-Jones binary mixtures. Our results show that the density inversion causes drastic changes in the density profiles of the mixtures. In particular, symmetrical and equal-sized Lennard-Jones mixtures always exhibit desorption along the interfacial zone, i.e. the interfacial concentration profiles show a relative minimum at the interface of the total density profiles that increases when the dispersive energy parameter (ε(ij)) between unlike species decreases. However, as the asymmetry of the Lennard-Jones mixtures increases (σ(i) ≠ σ(j)), the concentration profiles display a relative maximum at the interface, which implies the adsorption of the total density profiles along the interfacial zone.
Benjamin, Ronald; Horbach, Jürgen
2015-07-07
Kinetics of crystal-growth is investigated along the solid-liquid coexistence line for the (100), (110), and (111) orientations of the Lennard-Jones (LJ) and Weeks-Chandler-Andersen (WCA) fcc crystal-liquid interface, using non-equilibrium molecular dynamics simulations. A slowing down of the growth kinetics along the coexistence line is observed, which is due to the decrease of the melting enthalpy with increasing coexistence temperature and pressure. Other quantities such as the melting pressure and liquid self-diffusion coefficient have a comparatively lesser impact on the kinetic growth coefficient. Growth kinetics of the LJ and WCA potentials become similar at large values of the melting temperature and pressure, when both resemble a purely repulsive soft-sphere potential. Classical models of crystallization from the melt are in reasonable qualitative agreement with our simulation data. Finally, several one-phase empirical melting/freezing rules are studied with respect to their validity along the coexistence line.
NASA Astrophysics Data System (ADS)
Hardy, Robert J.; Day, Michael A.; Shukla, Ramesh C.; Cowley, E. Roger
1994-04-01
The equations for determining the free energy of a solid with two-body interactions in the uncorrelated-factors approximation (UFA) are derived from the correlated-factors theorem. A self-consistent choice of the parameters in the harmonic Hamiltonian causes the approximation to be accurate through second order. The specific heat, thermal expansion, and bulk modulus of an fcc Lennard-Jones solid with nearest-neighbor interactions only are calculated in the UFA and the results are compared with the predictions of lowest-order and improved self-consistent phonon theory (SC1 and ISC), perturbation theory through fourth order, and other approximations. The predictions of the UFA are in very good agreement with new classical Monte Carlo estimates and with recent effective potential Monte Carlo results. The calculational effort required in the UFA is similar to that in SC1, while the accuracy of the predictions is similar to that of ISC.
Crystallization of Lennard-Jones nanodroplets: From near melting to deeply supercooled.
Malek, Shahrazad M A; Morrow, Gregory P; Saika-Voivod, Ivan
2015-03-28
We carry out molecular dynamics (MD) and Monte Carlo (MC) simulations to characterize nucleation in liquid clusters of 600 Lennard-Jones particles over a broad range of temperatures. We use the formalism of mean first-passage times to determine the rate and find that Classical Nucleation Theory (CNT) predicts the rate quite well, even when employing simple modelling of crystallite shape, chemical potential, surface tension, and particle attachment rate, down to the temperature where the droplet loses metastability and crystallization proceeds through growth-limited nucleation in an unequilibrated liquid. Below this crossover temperature, the nucleation rate is still predicted when MC simulations are used to directly calculate quantities required by CNT. Discrepancy in critical embryo sizes obtained from MD and MC arises when twinned structures with five-fold symmetry provide a competing free energy pathway out of the critical region. We find that crystallization begins with hcp-fcc stacked precritical nuclei and differentiation to various end structures occurs when these embryos become critical. We confirm that using the largest embryo in the system as a reaction coordinate is useful in determining the onset of growth-limited nucleation and show that it gives the same free energy barriers as the full cluster size distribution once the proper reference state is identified. We find that the bulk melting temperature controls the rate, even though the solid-liquid coexistence temperature for the droplet is significantly lower. The value of surface tension that renders close agreement between CNT and direct rate determination is significantly lower than what is expected for the bulk system.
Density functional theory for crystal-liquid interfaces of Lennard-Jones fluid.
Wang, Xin; Mi, Jianguo; Zhong, Chongli
2013-04-28
A density functional approach is presented to describe the crystal-liquid interfaces and crystal nucleations of Lennard-Jones fluid. Within the theoretical framework, the modified fundamental measure theory is applied to describe the free energy functional of hard sphere repulsion, and the weighted density method based on first order mean spherical approximation is used to describe the free energy contribution arising from the attractive interaction. The liquid-solid equilibria, density profiles within crystal cells and at liquid-solid interfaces, interfacial tensions, nucleation free energy barriers, and critical cluster sizes are calculated for face-centered-cubic and body-centered-cubic nucleus. Some results are in good agreement with available simulation data, indicating that the present model is quantitatively reliable in describing nucleation thermodynamics of Lennard-Jones fluid.
Low density shear viscosity of Lennard-Jones chains of variable rigidities.
Santacreu, S Delage; Galliero, G; Odunlami, M; Boned, C
2012-11-28
The zero-density shear viscosity of different types of short Lennard-Jones chains, up to the hexa-decamer, has been evaluated using a non-equilibrium molecular dynamics scheme. Simulations have been performed on chains of variable rigidities going from the fully flexible to the fully rigid chains. Very interestingly, it is found that there exists a universal relation (a power law) between the zero-density viscosity of the Lennard-Jones chains and their radius of gyration whatever the rigidity of the chain and for all tested temperatures (ranging from 2.5 to 6 in reduced units). Furthermore, for the studied range of temperature, it is shown that the zero-density viscosity of both fully flexible chains and fully rigid chains models can be obtained with an accuracy of a few percents knowing only the dimer viscosity and the length of the chain.
Finite-size scaling of Lennard-Jones droplet formation at fixed density
NASA Astrophysics Data System (ADS)
Zierenberg, Johannes; Janke, Wolfhard
2016-09-01
We reaccess the droplet condensation-evaporation transition of a three-dimensional Lennard-Jones system upon a temperature change. With the help of parallel multicanonical simulations we obtain precise estimates of the transition temperature and the width of the transition for systems with up to 2048 particles. This allows us to supplement previous observations of finite-size scaling regimes with a clearer picture also for the case of a continuous particle model.
Metastability, spectrum, and eigencurrents of the Lennard-Jones-38 network
Cameron, Maria K.
2014-11-14
We develop computational tools for spectral analysis of stochastic networks representing energy landscapes of atomic and molecular clusters. Physical meaning and some properties of eigenvalues, left and right eigenvectors, and eigencurrents are discussed. We propose an approach to compute a collection of eigenpairs and corresponding eigencurrents describing the most important relaxation processes taking place in the system on its way to the equilibrium. It is suitable for large and complex stochastic networks where pairwise transition rates, given by the Arrhenius law, vary by orders of magnitude. The proposed methodology is applied to the network representing the Lennard-Jones-38 cluster created by Wales's group. Its energy landscape has a double funnel structure with a deep and narrow face-centered cubic funnel and a shallower and wider icosahedral funnel. However, the complete spectrum of the generator matrix of the Lennard-Jones-38 network has no appreciable spectral gap separating the eigenvalue corresponding to the escape from the icosahedral funnel. We provide a detailed description of the escape process from the icosahedral funnel using the eigencurrent and demonstrate a superexponential growth of the corresponding eigenvalue. The proposed spectral approach is compared to the methodology of the Transition Path Theory. Finally, we discuss whether the Lennard-Jones-38 cluster is metastable from the points of view of a mathematician and a chemical physicist, and make a connection with experimental works.
Metastability, spectrum, and eigencurrents of the Lennard-Jones-38 network.
Cameron, Maria K
2014-11-14
We develop computational tools for spectral analysis of stochastic networks representing energy landscapes of atomic and molecular clusters. Physical meaning and some properties of eigenvalues, left and right eigenvectors, and eigencurrents are discussed. We propose an approach to compute a collection of eigenpairs and corresponding eigencurrents describing the most important relaxation processes taking place in the system on its way to the equilibrium. It is suitable for large and complex stochastic networks where pairwise transition rates, given by the Arrhenius law, vary by orders of magnitude. The proposed methodology is applied to the network representing the Lennard-Jones-38 cluster created by Wales's group. Its energy landscape has a double funnel structure with a deep and narrow face-centered cubic funnel and a shallower and wider icosahedral funnel. However, the complete spectrum of the generator matrix of the Lennard-Jones-38 network has no appreciable spectral gap separating the eigenvalue corresponding to the escape from the icosahedral funnel. We provide a detailed description of the escape process from the icosahedral funnel using the eigencurrent and demonstrate a superexponential growth of the corresponding eigenvalue. The proposed spectral approach is compared to the methodology of the Transition Path Theory. Finally, we discuss whether the Lennard-Jones-38 cluster is metastable from the points of view of a mathematician and a chemical physicist, and make a connection with experimental works.
Espinosa, J R; Young, J M; Jiang, H; Gupta, D; Vega, C; Sanz, E; Debenedetti, P G; Panagiotopoulos, A Z
2016-10-21
Direct coexistence molecular dynamics simulations of NaCl solutions and Lennard-Jones binary mixtures were performed to explore the origin of reported discrepancies between solubilities obtained by direct interfacial simulations and values obtained from the chemical potentials of the crystal and solution phases. We find that the key cause of these discrepancies is the use of crystal slabs of insufficient width to eliminate finite-size effects. We observe that for NaCl crystal slabs thicker than 4 nm (in the direction perpendicular to the interface), the same solubility values are obtained from the direct coexistence and chemical potential routes, namely, 3.7 ± 0.2 molal at T = 298.15 K and p = 1 bar for the JC-SPC/E model. Such finite-size effects are absent in the Lennard-Jones system and are likely caused by surface dipoles present in the salt crystals. We confirmed that μs-long molecular dynamics runs are required to obtain reliable solubility values from direct coexistence calculations, provided that the initial solution conditions are near the equilibrium solubility values; even longer runs are needed for equilibration of significantly different concentrations. We do not observe any effects of the exposed crystal face on the solubility values or equilibration times. For both the NaCl and Lennard-Jones systems, the use of a spherical crystallite embedded in the solution leads to significantly higher apparent solubility values relative to the flat-interface direct coexistence calculations and the chemical potential values. Our results have broad implications for the determination of solubilities of molecular models of ionic systems.
NASA Astrophysics Data System (ADS)
Espinosa, J. R.; Young, J. M.; Jiang, H.; Gupta, D.; Vega, C.; Sanz, E.; Debenedetti, P. G.; Panagiotopoulos, A. Z.
2016-10-01
Direct coexistence molecular dynamics simulations of NaCl solutions and Lennard-Jones binary mixtures were performed to explore the origin of reported discrepancies between solubilities obtained by direct interfacial simulations and values obtained from the chemical potentials of the crystal and solution phases. We find that the key cause of these discrepancies is the use of crystal slabs of insufficient width to eliminate finite-size effects. We observe that for NaCl crystal slabs thicker than 4 nm (in the direction perpendicular to the interface), the same solubility values are obtained from the direct coexistence and chemical potential routes, namely, 3.7 ± 0.2 molal at T = 298.15 K and p = 1 bar for the JC-SPC/E model. Such finite-size effects are absent in the Lennard-Jones system and are likely caused by surface dipoles present in the salt crystals. We confirmed that μs-long molecular dynamics runs are required to obtain reliable solubility values from direct coexistence calculations, provided that the initial solution conditions are near the equilibrium solubility values; even longer runs are needed for equilibration of significantly different concentrations. We do not observe any effects of the exposed crystal face on the solubility values or equilibration times. For both the NaCl and Lennard-Jones systems, the use of a spherical crystallite embedded in the solution leads to significantly higher apparent solubility values relative to the flat-interface direct coexistence calculations and the chemical potential values. Our results have broad implications for the determination of solubilities of molecular models of ionic systems.
Kaukonen, M; Gulans, A; Havu, P; Kauppinen, E
2012-03-05
Lennard-Jones (LJ) parameters are derived for classical nonpolarizable force fields for carbon nanotubes (CNTs) and for CNT-water interaction from van der Waals (vdW) enhanced density functional calculations. The new LJ parameters for carbon-carbon interactions are of the same order as those previously used in the literature but differ significantly for CNT-water interactions. This may partially originate from the fact that in addition to pure vdW interactions the polarization and other quantum mechanics effects are embedded into the LJ-potential.
Hess, Peter
2014-08-07
An improved microscopic cleavage model, based on a Morse-type and Lennard-Jones-type interaction instead of the previously employed half-sine function, is used to determine the maximum cleavage strength for the brittle materials diamond, tungsten, molybdenum, silicon, GaAs, silica, and graphite. The results of both interaction potentials are in much better agreement with the theoretical strength values obtained by ab initio calculations for diamond, tungsten, molybdenum, and silicon than the previous model. Reasonable estimates of the intrinsic strength are presented for GaAs, silica, and graphite, where first principles values are not available.
Properties of Organic Liquids when Simulated with Long-Range Lennard-Jones Interactions.
Fischer, Nina M; van Maaren, Paul J; Ditz, Jonas C; Yildirim, Ahmet; van der Spoel, David
2015-07-14
In order to increase the accuracy of classical computer simulations, existing methodologies may need to be adapted. Hitherto, most force fields employ a truncated potential function to model van der Waals interactions, sometimes augmented with an analytical correction. Although such corrections are accurate for homogeneous systems with a long cutoff, they should not be used in inherently inhomogeneous systems such as biomolecular and interface systems. For such cases, a variant of the particle mesh Ewald algorithm (Lennard-Jones PME) was already proposed 20 years ago (Essmann et al. J. Chem. Phys. 1995, 103, 8577-8593), but it was implemented only recently (Wennberg et al. J. Chem. Theory Comput. 2013, 9, 3527-3537) in a major simulation code (GROMACS). The availability of this method allows surface tensions of liquids as well as bulk properties to be established, such as density and enthalpy of vaporization, without approximations due to truncation. Here, we report on simulations of ≈150 liquids (taken from a force field benchmark: Caleman et al. J. Chem. Theory Comput. 2012, 8, 61-74) using three different force fields and compare simulations with and without explicit long-range van der Waals interactions. We find that the density and enthalpy of vaporization increase for most liquids using the generalized Amber force field (GAFF, Wang et al. J. Comput. Chem. 2004, 25, 1157-1174) and the Charmm generalized force field (CGenFF, Vanommeslaeghe et al. J. Comput. Chem. 2010, 31, 671-690) but less so for OPLS/AA (Jorgensen and Tirado-Rives, Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 6665-6670), which was parametrized with an analytical correction to the van der Waals potential. The surface tension increases by ≈10(-2) N/m for all force fields. These results suggest that van der Waals attractions in force fields are too strong, in particular for the GAFF and CGenFF. In addition to the simulation results, we introduce a new version of a web server, http
Effect of molecular flexibility of Lennard-Jones chains on vapor-liquid interfacial properties.
Blas, F J; Moreno-Ventas Bravo, A I; Algaba, J; Martínez-Ruiz, F J; MacDowell, L G
2014-03-21
We have determined the interfacial properties of short fully flexible chains formed from tangentially bonded Lennard-Jones monomeric units from direct simulation of the vapor-liquid interface. The results obtained are compared with those corresponding to rigid-linear chains formed from the same chain length, previously determined in the literature [F. J. Blas, A. I. M.-V. Bravo, J. M. Míguez, M. M. Piñeiro, and L. G. MacDowell, J. Chem. Phys. 137, 084706 (2012)]. The full long-range tails of the potential are accounted for by means of an improved version of the inhomogeneous long-range corrections of Janeček [J. Phys. Chem. B 129, 6264 (2006)] proposed recently by MacDowell and Blas [J. Chem. Phys. 131, 074705 (2008)] valid for spherical as well as for rigid and flexible molecular systems. Three different model systems comprising of 3, 5, and 6 monomers per molecule are considered. The simulations are performed in the canonical ensemble, and the vapor-liquid interfacial tension is evaluated using the test-area method. In addition to the surface tension, we also obtained density profiles, coexistence densities, critical temperature and density, and interfacial thickness as functions of temperature, paying particular attention to the effect of the chain length and rigidity on these properties. According to our results, the main effect of increasing the chain length (at fixed temperature) is to sharpen the vapor-liquid interface and to increase the width of the biphasic coexistence region. As a result, the interfacial thickness decreases and the surface tension increases as the molecular chains get longer. Comparison between predictions for fully flexible and rigid-linear chains, formed by the same number of monomeric units, indicates that the main effects of increasing the flexibility, i.e., passing from a rigid-linear to a fully flexible chain, are: (a) to decrease the difference between the liquid and vapor densities; (b) to decrease the critical temperature and
Precise simulation of the freezing transition of supercritical Lennard-Jones.
Nayhouse, Michael; Amlani, Ankur M; Orkoulas, G
2011-10-21
The fluid-solid transition of the Lennard-Jones model is analyzed along a supercritical isotherm. The analysis is implemented via a simulation method which is based on a modification of the constrained cell model of Hoover and Ree. In the context of hard-sphere freezing, Hoover and Ree simulated the solid phase using a constrained cell model in which each particle is confined within its own Wigner-Seitz cell. Hoover and Ree also proposed a modified cell model by considering the effect of an external field of variable strength. High-field values favor configurations with a single particle per Wigner-Seitz cell and thus stabilize the solid phase. In previous work, a simulation method for freezing transitions, based on constant-pressure simulations of the modified cell model, was developed and tested on a system of hard spheres. In the present work, this method is used to determine the freezing transition of a Lennard-Jones model system on a supercritical isotherm at a reduced temperature of 2. As in the case of hard spheres, constant-pressure simulations of the fully occupied constrained cell model of a system of Lennard-Jones particles indicate a point of mechanical instability at a density which is approximately 70% of the density at close packing. Furthermore, constant-pressure simulations of the modified cell model indicate that as the strength of the field is reduced, the transition from the solid to the fluid is continuous below the mechanical instability point and discontinuous above. The fluid-solid transition of the Lennard-Jones system is obtained by analyzing the field-induced fluid-solid transition of the modified cell model in the high-pressure, zero-field limit. The simulations are implemented under constant pressure using tempering and histogram reweighting techniques. The coexistence pressure and densities are determined through finite-size scaling techniques for first-order phase transitions which are based on analyzing the size-dependent behavior of
Relaxation of surface tension in the liquid-solid interfaces of Lennard-Jones liquids.
Lukyanov, Alex V; Likhtman, Alexei E
2013-11-19
We have established the surface tension relaxation time in the liquid-solid interfaces of Lennard-Jones (LJ) liquids by means of direct measurements in molecular dynamics (MD) simulations. The main result is that the relaxation time is found to be almost independent of the molecular structures and viscosity of the liquids (at 70-fold change) used in our study and lies in such a range that in slow hydrodynamic motion the interfaces are expected to be at equilibrium. The implications of our results for the modeling of dynamic wetting processes and interpretation of dynamic contact angle data are discussed.
Vapour-liquid coexistence of an active Lennard-Jones fluid.
Prymidis, Vasileios; Paliwal, Siddharth; Dijkstra, Marjolein; Filion, Laura
2016-09-28
We study a three-dimensional system of self-propelled Lennard-Jones particles using Brownian dynamics simulations. Using recent theoretical results for active matter, we calculate the pressure and report equations of state for the system. Additionally, we chart the vapour-liquid coexistence and show that the coexistence densities can be well described using simple power laws. Lastly, we demonstrate that our out-of-equilibrium system shows deviations from both the law of rectilinear diameters and the law of corresponding states.
Vapour-liquid coexistence of an active Lennard-Jones fluid
NASA Astrophysics Data System (ADS)
Prymidis, Vasileios; Paliwal, Siddharth; Dijkstra, Marjolein; Filion, Laura
2016-09-01
We study a three-dimensional system of self-propelled Lennard-Jones particles using Brownian dynamics simulations. Using recent theoretical results for active matter, we calculate the pressure and report equations of state for the system. Additionally, we chart the vapour-liquid coexistence and show that the coexistence densities can be well described using simple power laws. Lastly, we demonstrate that our out-of-equilibrium system shows deviations from both the law of rectilinear diameters and the law of corresponding states.
Monte Carlo study of the shear modulus at the surface of a Lennard-Jones crystal
NASA Astrophysics Data System (ADS)
Eerden, J. P. v. d.; Knops, H. J. F.; Roos, A.
1992-01-01
In this paper, we give a microscopic definition of local elastic constants. We apply this to the numerical evaluation of the shear modulus of an interface which is sharp as compared with the interaction range. The algorithm is applied to a study of the (001) face of a face-centered-cubic (fcc) Lennard-Jones crystal. The vanishing of the shear modulus gives an estimate of the melting temperature of the first layer which is well below the bulk triple point. Some theoretical aspects of surface melting are briefly discussed.
Costigliola, Lorenzo; Schrøder, Thomas B; Dyre, Jeppe C
2016-06-21
The recent theoretical prediction by Maimbourg and Kurchan [e-print arXiv:1603.05023 (2016)] that for regular pair-potential systems the virial potential-energy correlation coefficient increases towards unity as the dimension d goes to infinity is investigated for the standard 12-6 Lennard-Jones fluid. This is done by computer simulations for d = 2, 3, 4 going from the critical point along the critical isotherm/isochore to higher density/temperature. In both cases the virial potential-energy correlation coefficient increases significantly. For a given density and temperature relative to the critical point, with increasing number of dimension the Lennard-Jones system conforms better to the hidden-scale-invariance property characterized by high virial potential-energy correlations (a property that leads to the existence of isomorphs in the thermodynamic phase diagram, implying that it becomes effectively one-dimensional in regard to structure and dynamics). The present paper also gives the first numerical demonstration of isomorph invariance of structure and dynamics in four dimensions. Our findings emphasize the need for a universally applicable 1/d expansion in liquid-state theory; we conjecture that the systems known to obey hidden scale invariance in three dimensions are those for which the yet-to-be-developed 1/d expansion converges rapidly.
Urrutia, Ignacio; Paganini, Iván E
2016-05-07
We formulate a straightforward scheme of statistical mechanics for inhomogeneous systems that includes the virial series in powers of the activity for the grand free energy and density distributions. There, cluster integrals formulated for inhomogeneous systems play a main role. We center on second order terms that were analyzed in the case of hard-wall confinement, focusing in planar, spherical, and cylindrical walls. Further analysis was devoted to the Lennard-Jones system and its generalization, the 2k-k potential. For these interaction potentials, the second cluster integral was evaluated analytically. We obtained the fluid-substrate surface tension at second order for the planar, spherical, and cylindrical confinement. Spherical and cylindrical cases were analyzed using a series expansion in the radius including higher order terms. We detected a lnR/R(2) dependence of the surface tension for the standard Lennard-Jones system confined by spherical and cylindrical walls, no matter if particles are inside or outside of the hard walls. The analysis was extended to bending and Gaussian curvatures, where exact expressions were also obtained.
Solubility Limits in Lennard-Jones Mixtures: Effects of Disparate Molecule Geometries
Dyer, Kippi M.; Perkyns, John S.; Pettitt, B. Montgomery
2016-01-01
In order to better understand general effects of the size and energy disparities between macromolecules and solvent molecules in solution, especially for macromolecular constructs self-assembled from smaller molecules, we use the first- and second-order exact bridge diagram extensions of the HNC integral equation theory to investigate single-component, binary, ternary, and quaternary mixtures of Lennard-Jones fluids. For pure fluids, we find that the HNCH3 bridge function integral equation (i.e., exact to third order in density) is necessary to quantitatively predict the pure gas and pure liquid sides of the coexistence region of the phase diagram of the Lennard-Jones fluid. For the mixtures, we find that the HNCH2 bridge function integral equation is sufficient to qualitatively predict solubility in the binary, ternary, and quaternary mixtures, up to the nominal solubility limit. The results, as limiting cases, should be useful to several problems, including accurate phase diagram predictions for complex mixtures, design of self-assembling nanostructures via solvent controls, and the solvent contributions to the conformational behavior of macromolecules in complex fluids. PMID:25621892
Surface tension of short flexible Lennard-Jones chains: Corresponding states behavior.
Galliero, Guillaume
2010-08-21
Molecular dynamics simulations of surface tensions of short flexible Lennard-Jones chains, composed of 2, 3, 4, and 5 segments, have been performed in this work. Using the simulation results, it is shown that the reduced surface tension depends only on the chain length and the reduced temperature. As a consequence, simple three parameters corresponding states using the acentric factor is shown to yield an excellent estimation of the reduced surface tension of the flexible Lennard-Jones chain fluid model. In addition, it has been noticed that the reduced surface tension of this fluid model is a unique function of the coexisting liquid and vapor reduced densities (i.e., there exist a universal Parachor behavior) for all chain lengths tested. When applied to real fluids, this universal behavior holds rather well for a large class of real species which can be nonspherical, nonlinear, and even polar. Only the surface tension of hydrogen-bonding compounds seems to largely deviate from this universal Parachor behavior. These interesting features of the surface tension, written in appropriate scaled forms, can probably be used to improve molecular models, in particular, those on which modern molecular based equations of state rely on.
Solubility Limits in Lennard-Jones Mixtures: Effects of Disparate Molecule Geometries.
Dyer, Kippi M; Perkyns, John S; Pettitt, B Montgomery
2015-07-23
In order to better understand general effects of the size and energy disparities between macromolecules and solvent molecules in solution, especially for macromolecular constructs self-assembled from smaller molecules, we use the first- and second-order exact bridge diagram extensions of the HNC integral equation theory to investigate single-component, binary, ternary, and quaternary mixtures of Lennard-Jones fluids. For pure fluids, we find that the HNCH3 bridge function integral equation (i.e., exact to third order in density) is necessary to quantitatively predict the pure gas and pure liquid sides of the coexistence region of the phase diagram of the Lennard-Jones fluid. For the mixtures, we find that the HNCH2 bridge function integral equation is sufficient to qualitatively predict solubility in the binary, ternary, and quaternary mixtures, up to the nominal solubility limit. The results, as limiting cases, should be useful to several problems, including accurate phase diagram predictions for complex mixtures, design of self-assembling nanostructures via solvent controls, and the solvent contributions to the conformational behavior of macromolecules in complex fluids.
Barbante, Paolo; Frezzotti, Aldo; Gibelli, Livio
2014-12-09
The unsteady evaporation of a thin planar liquid film is studied by molecular dynamics simulations of Lennard-Jones fluid. The obtained results are compared with the predictions of a diffuse interface model in which capillary Korteweg contributions are added to hydrodynamic equations, in order to obtain a unified description of the liquid bulk, liquid-vapor interface and vapor region. Particular care has been taken in constructing a diffuse interface model matching the thermodynamic and transport properties of the Lennard-Jones fluid. The comparison of diffuse interface model and molecular dynamics results shows that, although good agreement is obtained in equilibrium conditions, remarkable deviations of diffuse interface model predictions from the reference molecular dynamics results are observed in the simulation of liquid film evaporation. It is also observed that molecular dynamics results are in good agreement with preliminary results obtained from a composite model which describes the liquid film by a standard hydrodynamic model and the vapor by the Boltzmann equation. The two mathematical model models are connected by kinetic boundary conditions assuming unit evaporation coefficient.
Georgescu, Ionuţ; Brown, Sandra E; Mandelshtam, Vladimir A
2013-04-07
In order to address the issue of whether neon liquid in coexistence with its gas phase can be mapped to a quantum Lennard-Jones (LJ) fluid, we perform a series of simulations using Gibbs ensemble Monte Carlo for a range of de Boer quantum parameters Λ=ℏ/(σ√(mε)). The quantum effects are incorporated by implementing the variational gaussian wavepacket method, which provides an efficient numerical framework for estimating the quantum density at thermal equilibrium. The computed data for the LJ liquid is used to produce its phase diagram as a function of the quantum parameter, 0.065 ≤ Λ ≤ 0.11. These data are then used to fit the experimental phase diagram for neon liquid. The resulting parameters, ε = 35.68 ± 0.03 K and σ = 2.7616 ± 0.0005 Å (Λ = 0.0940), of the LJ pair potential are optimized to best represent liquid neon in coexistence with its gas phase for a range of physically relevant temperatures. This multi-temperature approach towards fitting and assessing a pair-potential is much more consistent than merely fitting a single data point, such as a melting temperature or a second virial coefficient.
Wennberg, Christian L; Murtola, Teemu; Páll, Szilárd; Abraham, Mark J; Hess, Berk; Lindahl, Erik
2015-12-08
Long-range lattice summation techniques such as the particle-mesh Ewald (PME) algorithm for electrostatics have been revolutionary to the precision and accuracy of molecular simulations in general. Despite the performance penalty associated with lattice summation electrostatics, few biomolecular simulations today are performed without it. There are increasingly strong arguments for moving in the same direction for Lennard-Jones (LJ) interactions, and by using geometric approximations of the combination rules in reciprocal space, we have been able to make a very high-performance implementation available in GROMACS. Here, we present a new way to correct for these approximations to achieve exact treatment of Lorentz-Berthelot combination rules within the cutoff, and only a very small approximation error remains outside the cutoff (a part that would be completely ignored without LJ-PME). This not only improves accuracy by almost an order of magnitude but also achieves absolute biomolecular simulation performance that is an order of magnitude faster than any other available lattice summation technique for LJ interactions. The implementation includes both CPU and GPU acceleration, and its combination with improved scaling LJ-PME simulations now provides performance close to the truncated potential methods in GROMACS but with much higher accuracy.
Gordiz, Kiarash; Henry, Asegun
2015-12-17
To date, the established methods that describe thermal interface conductance (TIC) and include mode-level dependence have not included anharmonicity. The current intuition is therefore based on the behavior in the harmonic limit, whereby the extent of overlap in the bulk phonon density of states (DoS) (e.g., frequency overlap) dictates the TIC and more frequency overlap leads to higher TIC. Here, we study over 2,000 interfaces described by the Lennard-Jones potential using equilibrium molecular dynamics simulations, whereby we systematically change the mass and stiffness of each side. We show that the trends in TIC do not generally follow that of the bulk phonon DoS overlap, but instead more closely follow the vibrational power spectrum overlap for the interfacial atoms. We then identify the frequency overlap in the interfacial power spectra as an improved descriptor for understanding the qualitative trends in TIC. Although improved, the results show that the basic intuition of frequency overlap is still insufficient to explain all of the features, as the remaining variations are shown to arise from anharmonicity, which is a critical effect to include in interface calculations above cryogenic temperatures.
NASA Astrophysics Data System (ADS)
Das, Subir K.; Puri, Sanjay; Horbach, Jürgen; Binder, Kurt
2006-03-01
We use molecular dynamics (MD) to simulate an unstable homogeneous mixture of binary fluids (AB), confined in a slit pore of width D . The pore walls are assumed to be flat and structureless and attract one component of the mixture (A) with the same strength. The pairwise interactions between the particles are modeled by the Lennard-Jones potential, with symmetric parameters that lead to a miscibility gap in the bulk. In the thin-film geometry, an interesting interplay occurs between surface enrichment and phase separation. We study the evolution of a mixture with equal amounts of A and B, which is rendered unstable by a temperature quench. We find that A-rich surface enrichment layers form quickly during the early stages of the evolution, causing a depletion of A in the inner regions of the film. These surface-directed concentration profiles propagate from the walls towards the center of the film, resulting in a transient layered structure. This layered state breaks up into a columnar state, which is characterized by the lateral coarsening of cylindrical domains. The qualitative features of this process resemble results from previous studies of diffusive Ginzburg-Landau-type models [S. K. Das, S. Puri, J. Horbach, and K. Binder, Phys. Rev. E 72, 061603 (2005)], but quantitative aspects differ markedly. The relation to spinodal decomposition in a strictly two-dimensional geometry is also discussed.
NASA Astrophysics Data System (ADS)
Gordiz, Kiarash; Henry, Asegun
2015-12-01
To date, the established methods that describe thermal interface conductance (TIC) and include mode-level dependence have not included anharmonicity. The current intuition is therefore based on the behavior in the harmonic limit, whereby the extent of overlap in the bulk phonon density of states (DoS) (e.g., frequency overlap) dictates the TIC and more frequency overlap leads to higher TIC. Here, we study over 2,000 interfaces described by the Lennard-Jones potential using equilibrium molecular dynamics simulations, whereby we systematically change the mass and stiffness of each side. We show that the trends in TIC do not generally follow that of the bulk phonon DoS overlap, but instead more closely follow the vibrational power spectrum overlap for the interfacial atoms. We then identify the frequency overlap in the interfacial power spectra as an improved descriptor for understanding the qualitative trends in TIC. Although improved, the results show that the basic intuition of frequency overlap is still insufficient to explain all of the features, as the remaining variations are shown to arise from anharmonicity, which is a critical effect to include in interface calculations above cryogenic temperatures.
Gordiz, Kiarash; Henry, Asegun
2015-01-01
To date, the established methods that describe thermal interface conductance (TIC) and include mode-level dependence have not included anharmonicity. The current intuition is therefore based on the behavior in the harmonic limit, whereby the extent of overlap in the bulk phonon density of states (DoS) (e.g., frequency overlap) dictates the TIC and more frequency overlap leads to higher TIC. Here, we study over 2,000 interfaces described by the Lennard-Jones potential using equilibrium molecular dynamics simulations, whereby we systematically change the mass and stiffness of each side. We show that the trends in TIC do not generally follow that of the bulk phonon DoS overlap, but instead more closely follow the vibrational power spectrum overlap for the interfacial atoms. We then identify the frequency overlap in the interfacial power spectra as an improved descriptor for understanding the qualitative trends in TIC. Although improved, the results show that the basic intuition of frequency overlap is still insufficient to explain all of the features, as the remaining variations are shown to arise from anharmonicity, which is a critical effect to include in interface calculations above cryogenic temperatures. PMID:26678793
Explicit expression for the Stokes-Einstein relation for pure Lennard-Jones liquids.
Ohtori, Norikazu; Ishii, Yoshiki
2015-01-01
An explicit expression of the Stokes-Einstein (SE) relation in molecular scale has been determined for pure Lennard-Jones (LJ) liquids on the saturated vapor line using a molecular dynamics calculation with the Green-Kubo formula, as Dη(sv)=kTξ(-1)(N/V)(1/3), where D is the self-diffusion coefficient, η(sv) the shear viscosity, k the Boltzmann constant, T the temperature, ξ the constant, and N the particle number included in the system volume V. To this end, the dependence of D and η(sv) on packing fraction, η, and T has been determined so as to complete their scaling equations. The equations for D and η(sv) in these states are m(-1/2)(N/V)(-1/3)(1-η)(4)ε(-1/2)T and m(1/2)(N/V)(2/3)(1-η)(-4)ε(1/2)T(0), respectively, where m and ε are the atomic mass and characteristic parameter of energy used in the LJ potentials, respectively. The equations can well describe the behaviors of D and η(sv) for both the LJ and the real rare-gas liquids. The obtained SE relation justifies the theoretical equation proposed by Eyring and Ree, although the value of ξ is slightly different from that given by them. The difference of the obtained expression from the original SE relation, Dη(sv)=(kT/2π)σ(-1), where σ means the particle size, is the presence of the η(1/3) term, since (N/V)(1/3)=(6/π)(1/3)σ(-1)η(1/3). Since the original SE relation is based on the fluid mechanics for continuum media, allowing the presence of voids in liquids is the origin of the η(1/3) term. Therefore, also from this viewpoint, the present expression is more justifiable in molecular scale than the original SE relation. As a result, the η(1/3) term cancels out the σ dependence from the original SE relation. The present result clearly shows that it is not necessary to attribute the deviation from the original SE relation to any temperature dependence of particle size or to introduce the fractional SE relation for pure LJ liquids. It turned out that the η dependence of both D and
NASA Astrophysics Data System (ADS)
Asano, Yuta; Fuchizaki, Kazuhiro
2017-02-01
The melting curve of the modified Lennard-Jones system, which has been obtained by equating the free energies between the solid and liquid phases, was reinvestigated using the nonequilibrium relaxation method. The latter method satisfactorily reproduced the previous result with much simplified procedures.
Eighth to sixteenth virial coefficients of the Lennard-Jones model.
Feng, Chao; Schultz, Andrew J; Chaudhary, Vipin; Kofke, David A
2015-07-28
We calculated virial coefficients BN, 8 ≤ N ≤ 16, of the Lennard-Jones (LJ) model using both the Mayer-sampling Monte Carlo method and direct generation of configurations, with Wheatley's algorithm for summation of clusters. For N = 8, 24 values are reported, and for N = 9, 12 values are reported, both for temperatures T in the range 0.6 ≤ T ≤ 40.0 (in LJ units). For each N in 10 ≤ N ≤ 16, one to four values are reported for 0.6 ≤ T ≤ 0.9. An approximate functional form for the temperature dependence of BN was developed, and fits of LJ BN(T) based on this form are presented for each coefficient, 4 ≤ N ≤ 9, using new and previously reported data.
Melting in 2D Lennard-Jones Systems: What Type of Phase Transition?
Patashinski, Alexander Z.; Orlik, Rafal; Mitus, Antonio C.; Grzybowski, Bartosz A.; Ratner, Mark A.
2010-12-09
A typical configuration of an equilibrium 2D system of 2500 Lennard-Jones particles at melting is found to be a mosaic of crystallites and amorphous clusters. This mosaic significantly changed at times around the period τ of local vibrations, while most particles retain their nearest neighbors for times much longer than τ. In a system of 2500 particles, we found no phase separation for length scales larger than that of a crystallite. With decreasing density, the number of small amorphous clusters increased, and proliferation and percolation of amorphous matter separated the crystalline-ordered parts so that correlations between local order orientations of remote crystallites disappeared. We suggest that the mosaic is a manifestation of diminished stability of the crystalline structure resulting from competition between attraction and repulsion forces.
Solid-liquid critical behavior of a cylindrically confined Lennard-Jones fluid.
Mochizuki, Kenji; Koga, Kenichiro
2015-07-28
Extensive molecular dynamics simulations have been performed to study the phase behavior of Lennard-Jones particles confined in a quasi-one-dimensional hydrophobic nanopore. We provide unambiguous evidence for a solid-liquid critical point by investigating (i) isotherms in the pressure-volume plane, (ii) the spontaneous solid-liquid phase separation below a certain temperature, (iii) diverging heat capacity and isothermal compressibility as a certain point is approached, (iv) continuous change of dynamical and structural properties above the point, (v) the finite-size scaling analysis of the density distribution below and above the point. The result combined with earlier studies of confined water suggests that the solid-liquid critical point is not uncommon in quasi-one- and quasi-two-dimensional fluids.
Droplet growth during vapor-liquid transition in a 2D Lennard-Jones fluid.
Midya, Jiarul; Das, Subir K
2017-01-14
Results for the kinetics of vapor-liquid phase transition have been presented from the molecular dynamics simulations of a single component two-dimensional Lennard-Jones fluid. The phase diagram for the model, primary prerequisite for this purpose, has been obtained via the Monte Carlo simulations. Our focus is on the region very close to the vapor branch of the coexistence curve. Quenches to such region provide morphology that consists of disconnected circular clusters in the vapor background. We identified that these clusters exhibit diffusive motion and grow via sticky collisions among them. The growth follows power-law behavior with time, exponent of which is found to be in nice agreement with a theoretical prediction.
Properties of the Lennard-Jones dimeric fluid in two dimensions: an integral equation study.
Urbic, Tomaz; Dias, Cristiano L
2014-03-07
The thermodynamic and structural properties of the planar soft-sites dumbbell fluid are examined by Monte Carlo simulations and integral equation theory. The dimers are built of two Lennard-Jones segments. Site-site integral equation theory in two dimensions is used to calculate the site-site radial distribution functions for a range of elongations and densities and the results are compared with Monte Carlo simulations. The critical parameters for selected types of dimers were also estimated. We analyze the influence of the bond length on critical point as well as tested correctness of site-site integral equation theory with different closures. The integral equations can be used to predict the phase diagram of dimers whose molecular parameters are known.
Dynamics of vacancies in two-dimensional Lennard-Jones crystals.
Yao, Zhenwei; de la Cruz, Monica Olvera
2014-12-01
Vacancies represent an important class of crystallographic defects, and their behaviors can be strongly coupled with relevant material properties. In this work, we study the dynamics of generic n-point vacancies in two-dimensional Lennard-Jones crystals in several thermodynamic states. Simulations reveal the spectrum of distinct, size-dependent vacancy dynamics, including the nonmonotonously varying diffusive mobilities of one-, two- and three-point vacancies, and several healing routines of linear vacancies. Specifically, we numerically observe significantly faster diffusion of the two-point vacancy that can be attributed to its rotational degree of freedom. The high mobility of the two-point vacancies opens the possibility of doping two-point vacancies into atomic materials to enhance atomic migration. The rich physics of vacancies revealed in this study may have implications in the engineering of defects in extensive crystalline materials for desired properties.
Determination of new Cu+, Cu2+, and Zn2+ Lennard-Jones ion parameters in acetonitrile.
Torras, Juan; Alemán, Carlos
2013-09-12
We present new Lennard-Jones (LJ) parameters for Cu(+), Cu(2+), and Zn(2+) ion-acetonitrile interactions. The adjustment of ion parameters is made to reproduce simultaneously experimental solvation free energy and structural properties, namely ion-N distance and coordination numbers. Initially, the methodology has been validated deriving parameters for well-studied Na(+) and Cl(-) ions in acetonitrile being compared with experimental and theoretical data. The transferability of parameters is checked by the calculation of thermodynamic and structural properties with three different acetonitrile models. The results obtained for transition metal ions show an overall agreement with reference values. The solvation free energy calculated with new LJ trained parameters using a six-site acetonitrile model, and two older three- and six-site acetonitrile models presents, respectively, percent differences of 0.4, 4.8, and 7.3% when compared with experimental values.
Mesoscopic Hamiltonian for the fluctuations of adsorbed Lennard-Jones liquid films.
Fernández, Eva M; Chacón, Enrique; MacDowell, Luis G; Tarazona, Pedro
2015-06-01
We use Monte Carlo simulations of a Lennard-Jones fluid adsorbed on a short-range planar wall substrate to study the fluctuations in the thickness of the wetting layer, and we get a quantitative and consistent characterization of their mesoscopic Hamiltonian, H[ξ]. We have observed important finite-size effects, which were hampering the analysis of previous results obtained with smaller systems. The results presented here support an appealing simple functional form for H[ξ], close but not exactly equal to the theoretical nonlocal proposal made on the basis a generic density-functional analysis by Parry and coworkers. We have analyzed systems under different wetting conditions, as a proof of principle for a method that provides a quantitative bridge between the molecular interactions and the phenomenology of wetting films at mesoscopic scales.
On the establishment of thermal diffusion in binary Lennard-Jones liquids
NASA Astrophysics Data System (ADS)
Ferrario, M.; Bonella, S.; Ciccotti, G.
2016-10-01
The establishment of thermal diffusion in an Ar-Kr Lennard-Jones mixture is investigated via dynamical non equilibrium molecular dynamics [G. Ciccotti, G. Jacucci, Phys. Rev. Lett. 35, 789 (1975)]. We observe, in particular, the evolution of the density and temperature fields of the system following the onset of the thermal gradient. In stationary conditions, we also compute the Soret coefficient of the mixture. This study confirms that dynamical non equilibrium molecular dynamics is an effective tool to gather information on transient phenomena, even though the full evolution of the mass and energy fluxes associated to the temperature and density fields requires, in this case, a more substantial numerical effort than the one employed here.
New approach to the first-order phase transition of Lennard-Jones fluids.
Muguruma, Chizuru; Okamoto, Yuko; Mikami, Masuhiro
2004-04-22
The multicanonical Monte Carlo method is applied to a bulk Lennard-Jones fluid system to investigate the liquid-solid phase transition. We take the example of a system of 108 argon particles. The multicanonical weight factor we determined turned out to be reliable for the energy range between -7.0 and -4.0 kJ/mol, which corresponds to the temperature range between 60 and 250 K. The expectation values of the thermodynamic quantities obtained from the multicanonical production run by the reweighting techniques exhibit the characteristics of first-order phase transitions between liquid and solid states around 150 K. The present study reveals that the multicanonical algorithm is particularly suitable for analyzing the transition state of the first-order phase transition in detail.
Droplet growth during vapor-liquid transition in a 2D Lennard-Jones fluid
NASA Astrophysics Data System (ADS)
Midya, Jiarul; Das, Subir K.
2017-01-01
Results for the kinetics of vapor-liquid phase transition have been presented from the molecular dynamics simulations of a single component two-dimensional Lennard-Jones fluid. The phase diagram for the model, primary prerequisite for this purpose, has been obtained via the Monte Carlo simulations. Our focus is on the region very close to the vapor branch of the coexistence curve. Quenches to such region provide morphology that consists of disconnected circular clusters in the vapor background. We identified that these clusters exhibit diffusive motion and grow via sticky collisions among them. The growth follows power-law behavior with time, exponent of which is found to be in nice agreement with a theoretical prediction.
Clustering of Lennard-Jones particles in water: temperature and pressure effects.
Ferrara, Gastón; McCarthy, Andrés N; Grigera, J Raúl
2007-09-14
While the hydrophobic effect is, for many systems, one of the most relevant interactions, it may be said that in the case of biological systems this effect becomes of determinant importance. Although the matter has been analyzed extensively, certain aspects are yet to be elucidated. Hence, the study on the behavior of the hydrophobic effect with temperature, and particularly with pressure deserves further investigation; model systems may help us in the task. We have analyzed the behavior of Lennard-Jones particles in water by means of molecular dynamics simulation under different conditions of size, concentration, temperature, and pressure. Following the formation of particle aggregates we can observe an increase of the hydrophobic effect with temperature and a strong weakening of the effect at high pressures. The results agree with the experimental evidence and show the ability of molecular dynamics simulation to account for the behavior of nonpolar substances under different conditions, provided that the intermolecular interactions used are adequate.
Properties of the Lennard-Jones dimeric fluid in two dimensions: An integral equation study
Urbic, Tomaz; Dias, Cristiano L.
2014-03-07
The thermodynamic and structural properties of the planar soft-sites dumbbell fluid are examined by Monte Carlo simulations and integral equation theory. The dimers are built of two Lennard-Jones segments. Site-site integral equation theory in two dimensions is used to calculate the site-site radial distribution functions for a range of elongations and densities and the results are compared with Monte Carlo simulations. The critical parameters for selected types of dimers were also estimated. We analyze the influence of the bond length on critical point as well as tested correctness of site-site integral equation theory with different closures. The integral equations can be used to predict the phase diagram of dimers whose molecular parameters are known.
Dynamics of vacancies in two-dimensional Lennard-Jones crystals
NASA Astrophysics Data System (ADS)
Yao, Zhenwei; Olvera de La Cruz, Monica
2015-03-01
Vacancies represent an important class of crystallographic defects, and their behaviors can be strongly coupled with relevant material properties. We report the rich dynamics of vacancies in two-dimensional Lennard-Jones crystals in several thermodynamic states. Specifically, we numerically observe significantly faster diffusion of the 2-point vacancy with two missing particles in comparison with other types of vacancies; it opens the possibility of doping 2-point vacancies into atomic materials to enhance atomic migration. In addition, the resulting dislocations in the healing of a long vacancy suggest the intimate connection between vacancies and topological defects that may provide an extra dimension in the engineering of defects in extensive crystalline materials for desired properties. We thank the financial support from the U.S. Department of Commerce, National Institute of Standards and Technology, the Office of the Director of Defense Research and Engineering (DDR&E) and the Air Force Office of Scientific Research.
Taghizadeh, Ameneh; Keshavarzi, Ezat Tahmineh
2011-04-07
The aim of this work is to investigate the population inversion of binary asymmetric Lennard-Jones mixtures inside nanoslit pores due to confinement effects for both vapor and liquid phases. For this purpose we have used mean field fundamental measure theory, and the effect of different parameters such as interaction strength and size ratios of the components, confinement size, and thermodynamic state on the population distribution of molecules have been studied. It has been shown that in the case of bulk liquid mixtures, increasing the role of confinement effects can lead to preferential adsorption of the component with larger size and weaker intermolecular interactions into the nanopore in spite of its minority in the bulk which is referred as population inversion. This population inversion phenomenon is terminated by a sudden condensation which, interestingly, involves a simultaneous adsorption and desorption for more and less bulk concentrated species, respectively. We have demonstrated that this condensation phenomenon shifts to higher bulk densities with increasing the role of confinement effects such that in some cases population inversion is observable for the whole range of densities. In consideration of the conditions in which vapor Lennard-Jones mixtures undergo capillary condensation, the population distribution of components in the vapor- and liquidlike phases was studied. It has been shown that variation of parameters such as interaction strength and size ratios, temperature, and confinement size can lead to conditions in which capillary condensation is accompanying with a population inversion phenomenon. In these cases, whereas the composition of vaporlike phases is the same as bulk fluid, liquidlike phases are richer in the component with less bulk concentration.
NASA Astrophysics Data System (ADS)
Bomont, Jean-Marc; Hansen, Jean-Pierre; Pastore, Giorgio
2015-10-01
The structural and thermodynamic behavior of a deeply supercooled Lennard-Jones liquid, and its random first-order transition (RFOT) to an ideal glass is investigated, using a system of two weakly coupled replicas and the hypernetted chain integral equation for the pair structure of this symmetric binary system. A systematic search in the density-temperature plane points to the existence of two glass branches below a density-dependent threshold temperature. The branch of lower free energy exhibits a rapid growth of the structural overlap order parameter upon cooling and may be identified with the ideal glass phase conjectured by several authors for both spin and structural glasses. The RFOT, signaled by a sharp discontinuity of the order parameter, is predicted to be weakly first order from a thermodynamic viewpoint. The transition temperature Tcr increases rapidly with density and approximately obeys a scaling relation valid for a reference system of particles interacting via a purely repulsive 1 /r18 potential.
Excess entropy and crystallization in Stillinger-Weber and Lennard-Jones fluids.
Dhabal, Debdas; Nguyen, Andrew Huy; Singh, Murari; Khatua, Prabir; Molinero, Valeria; Bandyopadhyay, Sanjoy; Chakravarty, Charusita
2015-10-28
Molecular dynamics simulations are used to contrast the supercooling and crystallization behaviour of monatomic liquids that exemplify the transition from simple to anomalous, tetrahedral liquids. As examples of simple fluids, we use the Lennard-Jones (LJ) liquid and a pair-dominated Stillinger-Weber liquid (SW16). As examples of tetrahedral, water-like fluids, we use the Stillinger-Weber model with variable tetrahedrality parameterized for germanium (SW20), silicon (SW21), and water (SW(23.15) or mW model). The thermodynamic response functions show clear qualitative differences between simple and water-like liquids. For simple liquids, the compressibility and the heat capacity remain small on isobaric cooling. The tetrahedral liquids in contrast show a very sharp rise in these two response functions as the lower limit of liquid-phase stability is reached. While the thermal expansivity decreases with temperature but never crosses zero in simple liquids, in all three tetrahedral liquids at the studied pressure, there is a temperature of maximum density below which thermal expansivity is negative. In contrast to the thermodynamic response functions, the excess entropy on isobaric cooling does not show qualitatively different features for simple and water-like liquids; however, the slope and curvature of the entropy-temperature plots reflect the heat capacity trends. Two trajectory-based computational estimation methods for the entropy and the heat capacity are compared for possible structural insights into supercooling, with the entropy obtained from thermodynamic integration. The two-phase thermodynamic estimator for the excess entropy proves to be fairly accurate in comparison to the excess entropy values obtained by thermodynamic integration, for all five Lennard-Jones and Stillinger-Weber liquids. The entropy estimator based on the multiparticle correlation expansion that accounts for both pair and triplet correlations, denoted by S(trip), is also studied. S
Excess entropy and crystallization in Stillinger-Weber and Lennard-Jones fluids
NASA Astrophysics Data System (ADS)
Dhabal, Debdas; Nguyen, Andrew Huy; Singh, Murari; Khatua, Prabir; Molinero, Valeria; Bandyopadhyay, Sanjoy; Chakravarty, Charusita
2015-10-01
Molecular dynamics simulations are used to contrast the supercooling and crystallization behaviour of monatomic liquids that exemplify the transition from simple to anomalous, tetrahedral liquids. As examples of simple fluids, we use the Lennard-Jones (LJ) liquid and a pair-dominated Stillinger-Weber liquid (SW16). As examples of tetrahedral, water-like fluids, we use the Stillinger-Weber model with variable tetrahedrality parameterized for germanium (SW20), silicon (SW21), and water (SW23.15 or mW model). The thermodynamic response functions show clear qualitative differences between simple and water-like liquids. For simple liquids, the compressibility and the heat capacity remain small on isobaric cooling. The tetrahedral liquids in contrast show a very sharp rise in these two response functions as the lower limit of liquid-phase stability is reached. While the thermal expansivity decreases with temperature but never crosses zero in simple liquids, in all three tetrahedral liquids at the studied pressure, there is a temperature of maximum density below which thermal expansivity is negative. In contrast to the thermodynamic response functions, the excess entropy on isobaric cooling does not show qualitatively different features for simple and water-like liquids; however, the slope and curvature of the entropy-temperature plots reflect the heat capacity trends. Two trajectory-based computational estimation methods for the entropy and the heat capacity are compared for possible structural insights into supercooling, with the entropy obtained from thermodynamic integration. The two-phase thermodynamic estimator for the excess entropy proves to be fairly accurate in comparison to the excess entropy values obtained by thermodynamic integration, for all five Lennard-Jones and Stillinger-Weber liquids. The entropy estimator based on the multiparticle correlation expansion that accounts for both pair and triplet correlations, denoted by Strip, is also studied. Strip is a
Excess entropy and crystallization in Stillinger-Weber and Lennard-Jones fluids
Dhabal, Debdas; Chakravarty, Charusita; Nguyen, Andrew Huy; Molinero, Valeria; Singh, Murari; Khatua, Prabir; Bandyopadhyay, Sanjoy
2015-10-28
Molecular dynamics simulations are used to contrast the supercooling and crystallization behaviour of monatomic liquids that exemplify the transition from simple to anomalous, tetrahedral liquids. As examples of simple fluids, we use the Lennard-Jones (LJ) liquid and a pair-dominated Stillinger-Weber liquid (SW{sub 16}). As examples of tetrahedral, water-like fluids, we use the Stillinger-Weber model with variable tetrahedrality parameterized for germanium (SW{sub 20}), silicon (SW{sub 21}), and water (SW{sub 23.15} or mW model). The thermodynamic response functions show clear qualitative differences between simple and water-like liquids. For simple liquids, the compressibility and the heat capacity remain small on isobaric cooling. The tetrahedral liquids in contrast show a very sharp rise in these two response functions as the lower limit of liquid-phase stability is reached. While the thermal expansivity decreases with temperature but never crosses zero in simple liquids, in all three tetrahedral liquids at the studied pressure, there is a temperature of maximum density below which thermal expansivity is negative. In contrast to the thermodynamic response functions, the excess entropy on isobaric cooling does not show qualitatively different features for simple and water-like liquids; however, the slope and curvature of the entropy-temperature plots reflect the heat capacity trends. Two trajectory-based computational estimation methods for the entropy and the heat capacity are compared for possible structural insights into supercooling, with the entropy obtained from thermodynamic integration. The two-phase thermodynamic estimator for the excess entropy proves to be fairly accurate in comparison to the excess entropy values obtained by thermodynamic integration, for all five Lennard-Jones and Stillinger-Weber liquids. The entropy estimator based on the multiparticle correlation expansion that accounts for both pair and triplet correlations, denoted by S{sub trip
Warshavsky, Vadim B.; Song, Xueyu
2008-07-18
Free energies and correlation functions of liquid and solid hard-sphere (HS) mixtures are calculated using the fundamental measure density functional theory. Using the thermodynamic perturbation theory the free energies of solid and liquid Lennard-Jones (LJ) mixtures are obtained from correlation functions of HS systems within a single theoretical approach. The resulting azeotrope- and spindle-type solid-liquid phase diagrams of HS and LJ binary mixtures are in good agreement with the corresponding ones from computer simulations.
Calero, C.; Knorowski, C.; Travesset, A.
2016-03-22
We investigate a general method to calculate the free energy of crystalline solids by considering the harmonic approximation and quasistatically switching the anharmonic contribution. The advantage of this method is that the harmonic approximation provides an already very accurate estimate of the free energy, and therefore the anharmonic term is numerically very small and can be determined to high accuracy. We further show that the anharmonic contribution to the free energy satisfies a number of exact inequalities that place constraints on its magnitude and allows approximate but fast and accurate estimates. The method is implemented into a readily available general software by combining the code HOODLT (Highly Optimized Object Oriented Dynamic Lattice Theory) for the harmonic part and the molecular dynamics (MD) simulation package HOOMD-blue for the anharmonic part. We use the method to calculate the low temperature phase diagram for Lennard-Jones particles. We demonstrate that hcp is the equilibrium phase at low temperature and pressure and obtain the coexistence curve with the fcc phase, which exhibits reentrant behavior. Furthermore, several implications of the method are discussed.
Nucleation of liquid droplets and voids in a stretched Lennard-Jones fcc crystal.
Baidakov, Vladimir G; Tipeev, Azat O
2015-09-28
The method of molecular dynamics simulation has been used to investigate the phase decay of a metastable Lennard-Jones face-centered cubic crystal at positive and negative pressures. It is shown that at high degrees of metastability, crystal decay proceeds through the spontaneous formation and growth of new-phase nuclei. It has been found that there exists a certain boundary temperature. Below this temperature, the crystal phase disintegrates as the result of formation of voids, and above, as a result of formation of liquid droplets. The boundary temperature corresponds to the temperature of cessation of a crystal-liquid phase equilibrium when the melting line comes in contact with the spinodal of the stretched liquid. The results of the simulations are interpreted in the framework of classical nucleation theory. The thermodynamics of phase transitions in solids has been examined with allowance for the elastic energy of stresses arising owing to the difference in the densities of the initial and the forming phases. As a result of the action of elastic forces, at negative pressures, the boundary of the limiting superheating (stretching) of a crystal approaches the spinodal, on which the isothermal bulk modulus of dilatation becomes equal to zero. At the boundary of the limiting superheating (stretching), the shape of liquid droplets and voids is close to the spherical one.
Calero, C; Knorowski, C; Travesset, A
2016-03-28
We investigate a general method to calculate the free energy of crystalline solids by considering the harmonic approximation and quasistatically switching the anharmonic contribution. The advantage of this method is that the harmonic approximation provides an already very accurate estimate of the free energy, and therefore the anharmonic term is numerically very small and can be determined to high accuracy. We further show that the anharmonic contribution to the free energy satisfies a number of exact inequalities that place constraints on its magnitude and allows approximate but fast and accurate estimates. The method is implemented into a readily available general software by combining the code HOODLT (Highly Optimized Object Oriented Dynamic Lattice Theory) for the harmonic part and the molecular dynamics (MD) simulation package HOOMD-blue for the anharmonic part. We use the method to calculate the low temperature phase diagram for Lennard-Jones particles. We demonstrate that hcp is the equilibrium phase at low temperature and pressure and obtain the coexistence curve with the fcc phase, which exhibits reentrant behavior. Several implications of the method are discussed.
Tolman length and rigidity constants of the Lennard-Jones fluid.
Wilhelmsen, Øivind; Bedeaux, Dick; Reguera, David
2015-02-14
It is well-known that the surface tension of small droplets and bubbles deviates significantly from that at the planar interface. In this work, we analyze the leading corrections in the curvature expansion of the surface tension, i.e., the Tolman length and the rigidity constants, using a "hybrid" square gradient theory, where the local Helmholtz energy density is described by an accurate equation of state. We particularize this analysis for the case of the truncated and shifted Lennard-Jones fluid, and are then able to reproduce the surface tensions and Tolman length from recent molecular dynamics simulations within their accuracy. The obtained constants in the curvature expansion depend little on temperature, except in the vicinity of the critical point. When the bubble/droplet radius becomes comparable to the interfacial width at coexistence, the critical bubble/droplet prefers to change its density, rather than to decrease its size, and the curvature expansion is no longer sufficient to describe the change in surface tension. We find that the radius of the bubble/droplet in this region is proportional to the correlation length between fluctuations in the liquid-phase.
Freezing and melting line invariants of the Lennard-Jones system.
Costigliola, Lorenzo; Schrøder, Thomas B; Dyre, Jeppe C
2016-06-07
The invariance of several structural and dynamical properties of the Lennard-Jones (LJ) system along the freezing and melting lines is interpreted in terms of isomorph theory. First the freezing/melting lines of the LJ system are shown to be approximated by isomorphs. Then we show that the invariants observed along the freezing and melting isomorphs are also observed on other isomorphs in the liquid and crystalline phases. The structure is probed by the radial distribution function and the structure factor and dynamics are probed by the mean-square displacement, the intermediate scattering function, and the shear viscosity. Studying these properties with reference to isomorph theory explains why the known single-phase melting criteria hold, e.g., the Hansen-Verlet and the Lindemann criteria, and why the Andrade equation for the viscosity at freezing applies, e.g., for most liquid metals. Our conclusion is that these empirical rules and invariants can all be understood from isomorph theory and that the invariants are not peculiar to the freezing and melting lines, but hold along all isomorphs.
Surface tension of the two center Lennard-Jones plus point dipole fluid.
Werth, Stephan; Horsch, Martin; Hasse, Hans
2016-02-07
Molecular dynamics simulations are used for systematically studying the surface tension of the two center Lennard-Jones plus point dipole (2CLJD) model fluid. In a dimensionless representation, this model fluid has two parameters describing the elongation and the dipole moment. These parameters were varied in the entire range relevant for describing real fluids resulting in a grid of 38 individual models. For each model, the surface tension was determined at temperatures between 60% and 90% of the critical temperature. For completeness, the vapor pressure and the saturated densities were also determined. The latter results agree well with the literature data, whereas for the surface tension, only few data were previously available. From the present results, an empirical correlation for the surface tension of the 2CLJD model as a function of the model parameters is developed. The correlation is used to predict the surface tension of 46 2CLJD molecular models from the literature, which were adjusted to bulk properties, but not to interfacial properties. The results are compared to the experimental data. The molecular models overestimate the surface tension, and deviations between the predictions and experimental data are below 12% on average.
Effect of confinement on the solid-liquid coexistence of Lennard-Jones fluid.
Das, Chandan K; Singh, Jayant K
2013-11-07
The solid-liquid coexistence of a Lennard-Jones fluid confined in slit pores of variable pore size, H, is studied using molecular dynamics simulations. Three-stage pseudo-supercritical transformation path of Grochola [J. Chem. Phys. 120(5), 2122 (2004)] and multiple histogram reweighting are employed for the confined system, for various pore sizes ranging from 20 to 5 molecular diameters, to compute the solid-liquid coexistence. The Gibbs free energy difference is evaluated using thermodynamic integration method by connecting solid-liquid phases under confinement via one or more intermediate states without any first order phase transition among them. Thermodynamic melting temperature is found to oscillate with wall separation, which is in agreement with the behavior seen for kinetic melting temperature evaluated in an earlier study. However, thermodynamic melting temperature for almost all wall separations is higher than the bulk case, which is contrary to the behavior seen for the kinetic melting temperature. The oscillation founds to decay at around H = 12, and beyond that pore size dependency of the shift in melting point is well represented by the Gibbs-Thompson equation.
Effect of confinement on the solid-liquid coexistence of Lennard-Jones Fluid
Das, Chandan K.; Singh, Jayant K.
2013-11-07
The solid-liquid coexistence of a Lennard-Jones fluid confined in slit pores of variable pore size, H, is studied using molecular dynamics simulations. Three-stage pseudo-supercritical transformation path of Grochola [J. Chem. Phys. 120(5), 2122 (2004)] and multiple histogram reweighting are employed for the confined system, for various pore sizes ranging from 20 to 5 molecular diameters, to compute the solid-liquid coexistence. The Gibbs free energy difference is evaluated using thermodynamic integration method by connecting solid-liquid phases under confinement via one or more intermediate states without any first order phase transition among them. Thermodynamic melting temperature is found to oscillate with wall separation, which is in agreement with the behavior seen for kinetic melting temperature evaluated in an earlier study. However, thermodynamic melting temperature for almost all wall separations is higher than the bulk case, which is contrary to the behavior seen for the kinetic melting temperature. The oscillation founds to decay at around H = 12, and beyond that pore size dependency of the shift in melting point is well represented by the Gibbs-Thompson equation.
Nucleation of liquid droplets and voids in a stretched Lennard-Jones fcc crystal
Baidakov, Vladimir G. Tipeev, Azat O.
2015-09-28
The method of molecular dynamics simulation has been used to investigate the phase decay of a metastable Lennard-Jones face-centered cubic crystal at positive and negative pressures. It is shown that at high degrees of metastability, crystal decay proceeds through the spontaneous formation and growth of new-phase nuclei. It has been found that there exists a certain boundary temperature. Below this temperature, the crystal phase disintegrates as the result of formation of voids, and above, as a result of formation of liquid droplets. The boundary temperature corresponds to the temperature of cessation of a crystal–liquid phase equilibrium when the melting line comes in contact with the spinodal of the stretched liquid. The results of the simulations are interpreted in the framework of classical nucleation theory. The thermodynamics of phase transitions in solids has been examined with allowance for the elastic energy of stresses arising owing to the difference in the densities of the initial and the forming phases. As a result of the action of elastic forces, at negative pressures, the boundary of the limiting superheating (stretching) of a crystal approaches the spinodal, on which the isothermal bulk modulus of dilatation becomes equal to zero. At the boundary of the limiting superheating (stretching), the shape of liquid droplets and voids is close to the spherical one.
Local structures in a computer-generated liquid. Two-dimensional Lennard-Jones liquid
NASA Astrophysics Data System (ADS)
Mitus, Antoni C.; Patashinskii, Alexander Z.; Sokolowski, Stefan
1991-06-01
We study the local structures in a 2D Lennard-Jones liquid of 2500 atoms near the melting line ( ϱ ∗ = 0.76 , T ∗ = 0.47 ) with the help of methods of mathematical statistics based on an earlier proposed probabilistic approach. We analyze the local structures in individual configurations and study the time evolution of patterns of matter which is close to the solid hexagonal structure. We conclude that the model liquid displays two types of local structure: hexagonal and “chaotic”. The first one corresponds to the fluctuations of the hexagon with root-mean-square fluctuations ξ of atoms equal to ξ = 0.14-0.16 while the second one can be represented by a strongly fluctuating (ξ = 0.25-0.30) “defect” pattern. We discuss the consequences of the physical picture of the liquid as a locally ordered two-structure system for the methodology of computer simulations and for theories of the 2D liquid phase.
Calero, C.; Knorowski, C.; Travesset, A.
2016-03-22
We investigate a general method to calculate the free energy of crystalline solids by considering the harmonic approximation and quasistatically switching the anharmonic contribution. The advantage of this method is that the harmonic approximation provides an already very accurate estimate of the free energy, and therefore the anharmonic term is numerically very small and can be determined to high accuracy. We further show that the anharmonic contribution to the free energy satisfies a number of exact inequalities that place constraints on its magnitude and allows approximate but fast and accurate estimates. The method is implemented into a readily available generalmore » software by combining the code HOODLT (Highly Optimized Object Oriented Dynamic Lattice Theory) for the harmonic part and the molecular dynamics (MD) simulation package HOOMD-blue for the anharmonic part. We use the method to calculate the low temperature phase diagram for Lennard-Jones particles. We demonstrate that hcp is the equilibrium phase at low temperature and pressure and obtain the coexistence curve with the fcc phase, which exhibits reentrant behavior. Furthermore, several implications of the method are discussed.« less
Single-site Lennard-Jones models via polynomial chaos surrogates of Monte Carlo molecular simulation
NASA Astrophysics Data System (ADS)
Kadoura, Ahmad; Siripatana, Adil; Sun, Shuyu; Knio, Omar; Hoteit, Ibrahim
2016-06-01
In this work, two Polynomial Chaos (PC) surrogates were generated to reproduce Monte Carlo (MC) molecular simulation results of the canonical (single-phase) and the NVT-Gibbs (two-phase) ensembles for a system of normalized structureless Lennard-Jones (LJ) particles. The main advantage of such surrogates, once generated, is the capability of accurately computing the needed thermodynamic quantities in a few seconds, thus efficiently replacing the computationally expensive MC molecular simulations. Benefiting from the tremendous computational time reduction, the PC surrogates were used to conduct large-scale optimization in order to propose single-site LJ models for several simple molecules. Experimental data, a set of supercritical isotherms, and part of the two-phase envelope, of several pure components were used for tuning the LJ parameters (ɛ, σ). Based on the conducted optimization, excellent fit was obtained for different noble gases (Ar, Kr, and Xe) and other small molecules (CH4, N2, and CO). On the other hand, due to the simplicity of the LJ model used, dramatic deviations between simulation and experimental data were observed, especially in the two-phase region, for more complex molecules such as CO2 and C2 H6.
Kadoura, Ahmad; Siripatana, Adil; Sun, Shuyu; Knio, Omar; Hoteit, Ibrahim
2016-06-07
In this work, two Polynomial Chaos (PC) surrogates were generated to reproduce Monte Carlo (MC) molecular simulation results of the canonical (single-phase) and the NVT-Gibbs (two-phase) ensembles for a system of normalized structureless Lennard-Jones (LJ) particles. The main advantage of such surrogates, once generated, is the capability of accurately computing the needed thermodynamic quantities in a few seconds, thus efficiently replacing the computationally expensive MC molecular simulations. Benefiting from the tremendous computational time reduction, the PC surrogates were used to conduct large-scale optimization in order to propose single-site LJ models for several simple molecules. Experimental data, a set of supercritical isotherms, and part of the two-phase envelope, of several pure components were used for tuning the LJ parameters (ε, σ). Based on the conducted optimization, excellent fit was obtained for different noble gases (Ar, Kr, and Xe) and other small molecules (CH4, N2, and CO). On the other hand, due to the simplicity of the LJ model used, dramatic deviations between simulation and experimental data were observed, especially in the two-phase region, for more complex molecules such as CO2 and C2 H6.
Enhancement of the droplet nucleation in a dense supersaturated Lennard-Jones vapor
NASA Astrophysics Data System (ADS)
Zhukhovitskii, D. I.
2016-05-01
The vapor-liquid nucleation in a dense Lennard-Jones system is studied analytically and numerically. A solution of the nucleation kinetic equations, which includes the elementary processes of condensation/evaporation involving the lightest clusters, is obtained, and the nucleation rate is calculated. Based on the equation of state for the cluster vapor, the pre-exponential factor is obtained. The latter diverges as a spinodal is reached, which results in the nucleation enhancement. The work of critical cluster formation is calculated using the previously developed two-parameter model (TPM) of small clusters. A simple expression for the nucleation rate is deduced and it is shown that the work of cluster formation is reduced for a dense vapor. This results in the nucleation enhancement as well. To verify the TPM, a simulation is performed that mimics a steady-state nucleation experiments in the thermal diffusion cloud chamber. The nucleating vapor with and without a carrier gas is simulated using two different thermostats for the monomers and clusters. The TPM proves to match the simulation results of this work and of other studies.
Enhancement of the droplet nucleation in a dense supersaturated Lennard-Jones vapor.
Zhukhovitskii, D I
2016-05-14
The vapor-liquid nucleation in a dense Lennard-Jones system is studied analytically and numerically. A solution of the nucleation kinetic equations, which includes the elementary processes of condensation/evaporation involving the lightest clusters, is obtained, and the nucleation rate is calculated. Based on the equation of state for the cluster vapor, the pre-exponential factor is obtained. The latter diverges as a spinodal is reached, which results in the nucleation enhancement. The work of critical cluster formation is calculated using the previously developed two-parameter model (TPM) of small clusters. A simple expression for the nucleation rate is deduced and it is shown that the work of cluster formation is reduced for a dense vapor. This results in the nucleation enhancement as well. To verify the TPM, a simulation is performed that mimics a steady-state nucleation experiments in the thermal diffusion cloud chamber. The nucleating vapor with and without a carrier gas is simulated using two different thermostats for the monomers and clusters. The TPM proves to match the simulation results of this work and of other studies.
A multiscale transport model for binary Lennard Jones mixtures in slit nanopores
NASA Astrophysics Data System (ADS)
Bhadauria, Ravi; Aluru, N. R.
2016-11-01
We present a quasi-continuum multiscale hydrodynamic transport model for one dimensional isothermal, non-reacting binary mixture confined in slit shaped nanochannels. We focus on species transport equation that includes the viscous dissipation and interspecies diffusion term of the Maxwell-Stefan form. Partial viscosity variation is modeled by van der Waals one fluid approximation and the Local Average Density Method. We use friction boundary conditions where the wall-species friction parameter is computed using a novel species specific Generalized Langevin Equation model. The transport model accuracy is tested by predicting the velocity profiles of Lennard-Jones (LJ) methane-hydrogen and LJ methane-argon mixtures in graphene slit channels of different width. The resultant slip length from the continuum model is found to be invariant of channel width for a fixed mixture molar concentration. The mixtures considered are observed to behave as single species pseudo fluid, with the friction parameter displaying a linear dependence on the molar composition. The proposed model yields atomistic level accuracy with continuum scale efficiency.
May, Helge-Otmar; Mausbach, Peter
2012-03-01
The behavior of thermodynamic response functions and the thermodynamic scalar curvature in the supercritical region have been studied for a Lennard-Jones fluid based on a revised modified Benedict-Webb-Rubin equation of state. Response function extrema are sometimes used to estimate the Widom line, which is characterized by the maxima of the correlation lengths. We calculated the Widom line for the Lennard-Jones fluid without using any response function extrema. Since the volume of the correlation length is proportional to the Riemannian thermodynamic scalar curvature, the locus of the Widom line follows the slope of maximum curvature. We show that the slope of the Widom line follows the slope of the isobaric heat capacity maximum only in the close vicinity of the critical point and that, therefore, the use of response function extrema in this context is problematic. Furthermore, we constructed the vapor-liquid coexistence line for the Lennard-Jones fluid using the fact that the correlation length, and therefore the thermodynamic scalar curvature, must be equal in the two coexisting phases. We compared the resulting phase envelope with those from simulation data where multiple histogram reweighting was used and found striking agreement between the two methods.
Spontaneous cavitation in a Lennard-Jones liquid at negative pressures.
Baidakov, V G; Bobrov, K S
2014-05-14
We report a molecular dynamics (MD) study of homogeneous bubble nucleation in a Lennard-Jones liquid under a negative pressure (cavitation). The rate of bubble nucleation has been determined in the range 2 x 10(-9) < J(*) = Jσ(4)(m/ε)(1/2) < 6 x 10(-6) by the mean lifetime method at temperatures T(*) = kBT/ε = 0.35, 0.4, 0.5, 0.6, 0.7, 0.8, 0.4, 0.5, 0.6, 0.7, 0.8. In molecular dynamics simulation calculations have also been made of the coefficient of bubble size diffusion, the Zeldovich nonequilibrium factor, and the radius of a critical nucleus R*. Different approaches to the determination of the nucleation rate in a stretched liquid have been considered in the framework of classical nucleation theory (CNT). The values of J obtained in MD simulation are by 8-20 orders higher than those predicted by CNT. The work of formation of a critical bubble and the dependence of surface tension γ(R*) at the critical bubble-liquid interface have been determined by data of MD simulation from CNT. The values of γ obtained have been approximated by an extended Tolman formula that takes into account, besides a linear correction, also the quadratic in curvature terms. The Tolman length δ∞ is negative and equals -(0.1-0.2)σ. The coefficient at 1/R*(2) is positive and does not exceed σ(2).
Specifics of freezing of Lennard-Jones fluid confined to molecularly thin layers
NASA Astrophysics Data System (ADS)
Vishnyakov, Aleksey; Neimark, Alexander V.
2003-04-01
Freezing of a Lennard-Jones fluid between solid surfaces was studied using grand canonical Monte Carlo and molecular dynamics simulations. We explored the formation of frozen phases of hexagonal and orthorhombic symmetry in mono-, bi-, and tri-layer structures. The freezing transition, the type of lattice, and translational and orientational ordering were identified on the basis of orientational order parameters, in-plane two-body and three-body translational correlation functions, orientational correlation functions, and analysis of molecular mobilities. We have found that the freezing temperature is a nonmonotonous function of the pore width: orthorhombic bi-layer freezes at lower temperatures than hexagonal monolayer and hexagonal bi-layer. As the pore width increases, the transition from a hexagonal monolayer to an orthorhombic bi-layer occurred via disordered liquidlike and quasi-long-range four-fold ordered bi-layers. The latter, "quadratic" structure is characterized by an algebraically decaying four-fold orientational correlation function. The transition from crystalline hexagonal bi-layer to orthorhombic tri-layer occurs through a bi-layer structure with two uncoupled hexagonal monolayers. The quadratic phase was observed also as an intermediate structure during freezing of a liquidlike bi-layer into an orthorhombic quasi-crystal. The formation of the quadratic phase was associated with step-wise densification of fluid, a sharp increase of the local orientational order parameter, and a significant reduction of fluid mobility. In the process of solidification, the system passed through a sequence of high-density jammed structures, in which the four-fold symmetry developed progressively, as the temperature decreased.
Lundrigan, Sarah E. M.; Saika-Voivod, Ivan
2009-09-14
We perform molecular dynamics (MD) and Monte Carlo computer simulations to test the ability of the recently developed formalism of mean first-passage time (MFPT) [J. Wedekind, R. Strey, and D. Reguera, J. Chem. Phys. 126, 134103 (2007); J. Wedekind and D. Reguera, J. Phys. Chem. B 112, 11060 (2008)] to characterize crystal nucleation in the Lennard-Jones liquid. We find that the nucleation rate, critical embryo size, Zeldovich factor, attachment rate, and the nucleation barrier profile obtained from MFPT all compare very well to the same quantities calculated using other methods. Furthermore, we find that the nucleation rate obtained directly through MD closely matches the prediction of classical nucleation theory.
NASA Astrophysics Data System (ADS)
Lundrigan, Sarah E. M.; Saika-Voivod, Ivan
2009-09-01
We perform molecular dynamics (MD) and Monte Carlo computer simulations to test the ability of the recently developed formalism of mean first-passage time (MFPT) [J. Wedekind, R. Strey, and D. Reguera, J. Chem. Phys. 126, 134103 (2007); J. Wedekind and D. Reguera, J. Phys. Chem. B 112, 11060 (2008)] to characterize crystal nucleation in the Lennard-Jones liquid. We find that the nucleation rate, critical embryo size, Zeldovich factor, attachment rate, and the nucleation barrier profile obtained from MFPT all compare very well to the same quantities calculated using other methods. Furthermore, we find that the nucleation rate obtained directly through MD closely matches the prediction of classical nucleation theory.
NASA Astrophysics Data System (ADS)
Henderson, Der-Ming Duh Douglas; Rowley, Richard L.
Some effects of deviations from the Lorentz-Berthelot (LB) combining rules for LennardJones binary mixtures are studied with a model in which both constituents have the same size and energy interaction parameters but the cross interaction deviates substantially from the LB rules. A single temperature and density and two compositions are studied by molecular dynamics simulations and the recently proposed Duh-Haymet-Henderson (DHH) intergral equation theory. The agreement is satisfactory in both cases. The excess volume and enthalpy of mixing are also studied systematically with the DHH theory. Some interesting phenomena are observed for these no-LB mixtures.
Separdar, L; Davatolhagh, S
2013-02-01
We investigate the static structure and diffusive dynamics of binary Lennard-Jones mixture upon supercooling in the presence of gold nanoparticle within the framework of the mode-coupling theory of the dynamic glass transition in the direct space by means of constant-NVT molecular dynamics simulations. It is found that the presence of gold nanoparticle causes the energy per particle and the pressure of this system to decrease with respect to the bulk binary Lennard-Jones mixture. Furthermore, the presence of nanoparticle has a direct effect on the liquid structure and causes the peaks of the radial distribution functions to become shorter with respect to the bulk binary Lennard-Jones liquid. The dynamics of the liquid at a given density is found to be consistent with the mode-coupling theory (MCT) predictions in a certain range at low temperatures. In accordance with the idealized MCT, the diffusion constants D(T) show a power-law behavior at low temperatures for both types of binary Lennard-Jones (BLJ) particles as well as the gold atoms comprising the nanoparticle. The mode-coupling crossover temperature T(c) is the same for all particle types; however, T(c)=0.4 is reduced with respect to that of the bulk BLJ liquid, and the γ exponent is found to depend on the particle type. The existence of the nanoparticle causes the short-time β-relaxation regime to shorten and the range of validity of the MCT shrinks with respect to the bulk BLJ. It is also found that at intermediate and low temperatures the curves of the mean-squared displacements (MSDs) versus tD(T) fall onto a master curve. The MSDs follow the master curve in an identical time range with the long-time α-relaxation regime of the mode-coupling theory. By obtaining the viscosity, it is observed that the Stokes-Einstein relation remains valid at high and intermediate temperatures but breaks down as the temperatures approach T(c) as a result of the cooperative motion or activated processes.
NASA Astrophysics Data System (ADS)
Maddox, M. W.; Gubbins, K. E.
1997-12-01
A combination of grand canonical Monte Carlo and molecular dynamics simulation techniques are used to study the freezing and melting of Lennard-Jones methane in several different cylindrical pores. Two different types of pore wall are considered; a strongly attractive wall, and a weakly attractive wall, each with pore diameters in the range 1.5-3.5 nm. Freezing point depression is observed in the case of the weakly attractive pores, in agreement with several experimental studies. Freezing point elevation is observed at the walls of the strongly attractive pore, but freezing point depression occurs at the center of such pores, due to geometrical constraints.
Generalized coupling parameter expansion: application to square well and Lennard-Jones fluids.
Sai Venkata Ramana, A
2013-07-28
The coupling parameter expansion in thermodynamic perturbation theory of simple fluids is generalized to include the derivatives of bridge function with respect to coupling parameter. We applied seventh order version of the theory to Square-Well (SW) and Lennard-Jones (LJ) fluids using Sarkisov Bridge function. In both cases, the theory reproduced the radial distribution functions obtained from integral equation theory (IET) and simulations with good accuracy. Also, the method worked inside the liquid-vapor coexistence region where the IETs are known to fail. In the case of SW fluids, the use of Carnahan-Starling expression for Helmholtz free energy density of Hard-Sphere reference system has improved the liquid-vapor phase diagram (LVPD) over that obtained from IET with the same bridge function. The derivatives of the bridge function are seen to have significant effect on the liquid part of the LVPD. For extremely narrow SW fluids, we found that the third order theory is more accurate than the higher order versions. However, considering the convergence of the perturbation series, we concluded that the accuracy of the third order version is a spurious result. We also obtained the surface tension for SW fluids of various ranges. Results of present theory and simulations are in good agreement. In the case of LJ fluids, the equation of state obtained from the present method matched with that obtained from IET with negligible deviation. We also obtained LVPD of LJ fluid from virial and energy routes and found that there is slight inconsistency between the two routes. The applications lead to the following conclusions. In cases where reference system properties are known accurately, the present method gives results which are very much improved over those obtained from the IET with the same bridge function. In cases where reference system data is not available, the method serves as an alternative way of solving the Ornstein-Zernike equation with a given closure relation
Liquid-liquid interfacial properties of a symmetrical Lennard-Jones binary mixture.
Martínez-Ruiz, F J; Moreno-Ventas Bravo, A I; Blas, F J
2015-09-14
We determine the interfacial properties of a symmetrical binary mixture of equal-sized spherical Lennard-Jones molecules, σ11 = σ22, with the same dispersive energy between like species, ϵ11 = ϵ22, but different dispersive energies between unlike species low enough to induce phase separation. We use the extensions of the improved version of the inhomogeneous long-range corrections of Janec̆ek [J. Phys. Chem. B 110, 6264 (2006)], presented recently by MacDowell and Blas [J. Chem. Phys. 131, 074705 (2009)] and Martínez-Ruiz et al. [J. Chem. Phys. 141, 184701 (2014)], to deal with the interaction energy and microscopic components of the pressure tensor. We perform Monte Carlo simulations in the canonical ensemble to obtain the interfacial properties of the symmetrical mixture with different cut-off distances rc and in combination with the inhomogeneous long-range corrections. The pressure tensor is obtained using the mechanical (virial) and thermodynamic route. The liquid-liquid interfacial tension is also evaluated using three different procedures, the Irving-Kirkwood method, the difference between the macroscopic components of the pressure tensor, and the test-area methodology. This allows to check the validity of the recent extensions presented to deal with the contributions due to long-range corrections for intermolecular energy and pressure tensor in the case of binary mixtures that exhibit liquid-liquid immiscibility. In addition to the pressure tensor and the surface tension, we also obtain density profiles and coexistence densities and compositions as functions of pressure, at a given temperature. According to our results, the main effect of increasing the cut-off distance rc is to sharpen the liquid-liquid interface and to increase the width of the biphasic coexistence region. Particularly interesting is the presence of a relative minimum in the total density profiles of the symmetrical mixture. This minimum is related with a desorption of the molecules
Liquid-liquid interfacial properties of a symmetrical Lennard-Jones binary mixture
Martínez-Ruiz, F. J.; Blas, F. J.; Moreno-Ventas Bravo, A. I.
2015-09-14
We determine the interfacial properties of a symmetrical binary mixture of equal-sized spherical Lennard-Jones molecules, σ{sub 11} = σ{sub 22}, with the same dispersive energy between like species, ϵ{sub 11} = ϵ{sub 22}, but different dispersive energies between unlike species low enough to induce phase separation. We use the extensions of the improved version of the inhomogeneous long-range corrections of Janecek [J. Phys. Chem. B 110, 6264 (2006)], presented recently by MacDowell and Blas [J. Chem. Phys. 131, 074705 (2009)] and Martínez-Ruiz et al. [J. Chem. Phys. 141, 184701 (2014)], to deal with the interaction energy and microscopic components of the pressure tensor. We perform Monte Carlo simulations in the canonical ensemble to obtain the interfacial properties of the symmetrical mixture with different cut-off distances r{sub c} and in combination with the inhomogeneous long-range corrections. The pressure tensor is obtained using the mechanical (virial) and thermodynamic route. The liquid-liquid interfacial tension is also evaluated using three different procedures, the Irving-Kirkwood method, the difference between the macroscopic components of the pressure tensor, and the test-area methodology. This allows to check the validity of the recent extensions presented to deal with the contributions due to long-range corrections for intermolecular energy and pressure tensor in the case of binary mixtures that exhibit liquid-liquid immiscibility. In addition to the pressure tensor and the surface tension, we also obtain density profiles and coexistence densities and compositions as functions of pressure, at a given temperature. According to our results, the main effect of increasing the cut-off distance r{sub c} is to sharpen the liquid-liquid interface and to increase the width of the biphasic coexistence region. Particularly interesting is the presence of a relative minimum in the total density profiles of the symmetrical mixture. This minimum is related
Liquid-liquid interfacial properties of a symmetrical Lennard-Jones binary mixture
NASA Astrophysics Data System (ADS)
Martínez-Ruiz, F. J.; Moreno-Ventas Bravo, A. I.; Blas, F. J.
2015-09-01
We determine the interfacial properties of a symmetrical binary mixture of equal-sized spherical Lennard-Jones molecules, σ11 = σ22, with the same dispersive energy between like species, ɛ11 = ɛ22, but different dispersive energies between unlike species low enough to induce phase separation. We use the extensions of the improved version of the inhomogeneous long-range corrections of Janec̆ek [J. Phys. Chem. B 110, 6264 (2006)], presented recently by MacDowell and Blas [J. Chem. Phys. 131, 074705 (2009)] and Martínez-Ruiz et al. [J. Chem. Phys. 141, 184701 (2014)], to deal with the interaction energy and microscopic components of the pressure tensor. We perform Monte Carlo simulations in the canonical ensemble to obtain the interfacial properties of the symmetrical mixture with different cut-off distances rc and in combination with the inhomogeneous long-range corrections. The pressure tensor is obtained using the mechanical (virial) and thermodynamic route. The liquid-liquid interfacial tension is also evaluated using three different procedures, the Irving-Kirkwood method, the difference between the macroscopic components of the pressure tensor, and the test-area methodology. This allows to check the validity of the recent extensions presented to deal with the contributions due to long-range corrections for intermolecular energy and pressure tensor in the case of binary mixtures that exhibit liquid-liquid immiscibility. In addition to the pressure tensor and the surface tension, we also obtain density profiles and coexistence densities and compositions as functions of pressure, at a given temperature. According to our results, the main effect of increasing the cut-off distance rc is to sharpen the liquid-liquid interface and to increase the width of the biphasic coexistence region. Particularly interesting is the presence of a relative minimum in the total density profiles of the symmetrical mixture. This minimum is related with a desorption of the molecules
NASA Astrophysics Data System (ADS)
Duh, Der-Ming; Henderson, Douglas
1996-05-01
The pure Lennard-Jones fluid and various binary mixtures of Lennard-Jones fluids are studied by both molecular dynamics simulation and with a new integral equation which is based on that proposed by Duh and Haymet recently [J. Chem. Phys. 103, 2625 (1995)]. The structural and thermodynamic properties calculated from this integral equation show excellent agreement with simulations for both pure fluids and mixtures under the conditions which we have studied. For mixtures, the effect of deviations from the Lorentz-Berthelot (LB) mixing rules for the interaction parameters between unlike species is studied. Positive deviations from the nonadditivity of the molecular cores leads to an entropy driven tendency for the species to separate. This tendency persists even in the presence of a deviation from the LB rule for the energy parameter which enhances the attraction of the unlike species. On the other hand, in the case of negative deviations from nonadditivity, the tendency for association may be either energy or entropy driven, depending on the size ratio.
Scaling of the viscosity of the Lennard-Jones chain fluid model, argon, and some normal alkanes.
Galliero, Guillaume; Boned, Christian; Fernández, Josefa
2011-02-14
In this work, we have tested the efficiency of two scaling approaches aiming at relating shear viscosity to a single thermodynamic quantity in dense fluids, namely the excess entropy and the thermodynamic scaling methods. Using accurate databases, we have applied these approaches first to a model fluid, the flexible Lennard-Jones chain fluid (from the monomer to the hexadecamer), then to real fluids, such as argon and normal alkanes. To enlarge noticeably the range of thermodynamics conditions for which these scaling methods are applicable, we have shown that the use of the residual viscosity instead of the total viscosity is preferable in the scaling procedures. It has been found that both approaches, using the adequate scaling, are suitable for the Lennard-Jones chain fluid model for a wide range of thermodynamic conditions whatever the chain length when scaling law exponents and prefactors are adjusted for each chain length. Furthermore, these results were found to be well respected by the corresponding real fluids.
Leonardi, Erminia; D'Aguanno, Bruno; Angeli, Celestino
2011-03-21
The thermodiffusive behavior of a Lennard-Jones binary mixture has been studied by using nonequilibrium molecular dynamics. In particular, the dependence of the Soret coefficient, S(T), on the temperature and composition has been investigated, exploring a wide range of temperatures from 1000 K to the condensation temperature of the mixture. In a previous paper the dependence of S(T) on the temperature and the composition was studied for Lennard-Jones binary mixtures presenting mixing/demixing (consolute) phase transition, and the results allowed the formulation of a very simple expression with the computed values of S(T) in the one phase region outside the critical region closely fitted by the function [T - T(c)(x(1))](-1), with T(c)(x(1)) the demixing temperature of the mixture under study. The results of the present work show that the same expression of S(T) can be found for the one phase region outside the evaporation/condensation region but now with T(c) representing the condensation temperature of the mixture under study.
Kulinskii, V L
2010-10-07
We analyze the interrelation between the coexistence curve of the Lennard-Jones fluid and the Ising model in two and three dimensions within the global isomorphism approach proposed earlier [V. L. Kulinskii, J. Phys. Chem. B 114, 2852 (2010)]. In case of two dimensions, we use the exact Onsager result to construct the binodal of the corresponding Lennard-Jones fluid and compare it with the results of the simulations. In the three-dimensional case, we use available numerical results for the Ising model for the corresponding mapping. The possibility to observe the singularity of the binodal diameter is discussed.
NASA Astrophysics Data System (ADS)
Staśkiewicz, B.; Okrasiński, W.
2012-04-01
We propose a simple analytical form of the vapor-liquid equilibrium curve near the critical point for Lennard-Jones fluids. Coexistence densities curves and vapor pressure have been determined using the Van der Waals and Dieterici equation of state. In described method the Bernoulli differential equations, critical exponent theory and some type of Maxwell's criterion have been used. Presented approach has not yet been used to determine analytical form of phase curves as done in this Letter. Lennard-Jones fluids have been considered for analysis. Comparison with experimental data is done. The accuracy of the method is described.
Munaò, Gianmarco; Costa, Dino; Caccamo, Carlo
2016-10-19
Inspired by significant improvements obtained for the performances of the polymer reference interaction site model (PRISM) theory of the fluid phase when coupled with 'molecular closures' (Schweizer and Yethiraj 1993 J. Chem. Phys. 98 9053), we exploit a matrix generalization of this concept, suitable for the more general RISM framework. We report a preliminary test of the formalism, as applied to prototype square-well homonuclear diatomics. As for the structure, comparison with Monte Carlo shows that molecular closures are slightly more predictive than their 'atomic' counterparts, and thermodynamic properties are equally accurate. We also devise an application of molecular closures to models interacting via continuous, soft-core potentials, by using well established prescriptions in liquid state perturbation theories. In the case of Lennard-Jones dimers, our scheme definitely improves over the atomic one, providing semi-quantitative structural results, and quite good estimates of internal energy, pressure and phase coexistence. Our finding paves the way to a systematic employment of molecular closures within the RISM framework to be applied to more complex systems, such as molecules constituted by several non-equivalent interaction sites.
Bomont, Jean-Marc; Hansen, Jean-Pierre; Pastore, Giorgio
2015-10-01
The structural and thermodynamic behavior of a deeply supercooled Lennard-Jones liquid, and its random first-order transition (RFOT) to an ideal glass is investigated, using a system of two weakly coupled replicas and the hypernetted chain integral equation for the pair structure of this symmetric binary system. A systematic search in the density-temperature plane points to the existence of two glass branches below a density-dependent threshold temperature. The branch of lower free energy exhibits a rapid growth of the structural overlap order parameter upon cooling and may be identified with the ideal glass phase conjectured by several authors for both spin and structural glasses. The RFOT, signaled by a sharp discontinuity of the order parameter, is predicted to be weakly first order from a thermodynamic viewpoint. The transition temperature T(cr) increases rapidly with density and approximately obeys a scaling relation valid for a reference system of particles interacting via a purely repulsive 1/r(18) potential.
Peng, L.; Morris, James R; Aga, Rachel
2010-01-01
Large scale simulations of crystal nucleation from the liquid are performed using the Lennard-Jones potential, to determine the time required for nucleation. By considering both transient and finite-size effects, we successfully predict the nucleation time within order of magnitude without any parameter fitting. All necessary parameters are derived from separate, equilibrium simulations. At smaller undercoolings, large system sizes are required, not only to accommodate large critical nuclei, but also to control statistical effects that are controlled by the density of critical nuclei. Two distinct nucleation regions are observed in the simulations, which are dominated by transient time and steady state nucleation time, respectively. At deep undercoolings, we still show consistency between predicted transient times and simulated nucleation times, which suggests that the short nucleation times in simulations are due to a small barrier to nucleation, rather than spinodal transformation that have been previously predicted. We compare with similar, previous results on a model of Al, which does not show such rapid nucleation at low temperatures, and suggest that the differences are due to the behavior of the reduced barrier G*/kBT.
NASA Astrophysics Data System (ADS)
Munaò, Gianmarco; Costa, Dino; Caccamo, Carlo
2016-10-01
Inspired by significant improvements obtained for the performances of the polymer reference interaction site model (PRISM) theory of the fluid phase when coupled with ‘molecular closures’ (Schweizer and Yethiraj 1993 J. Chem. Phys. 98 9053), we exploit a matrix generalization of this concept, suitable for the more general RISM framework. We report a preliminary test of the formalism, as applied to prototype square-well homonuclear diatomics. As for the structure, comparison with Monte Carlo shows that molecular closures are slightly more predictive than their ‘atomic’ counterparts, and thermodynamic properties are equally accurate. We also devise an application of molecular closures to models interacting via continuous, soft-core potentials, by using well established prescriptions in liquid state perturbation theories. In the case of Lennard-Jones dimers, our scheme definitely improves over the atomic one, providing semi-quantitative structural results, and quite good estimates of internal energy, pressure and phase coexistence. Our finding paves the way to a systematic employment of molecular closures within the RISM framework to be applied to more complex systems, such as molecules constituted by several non-equivalent interaction sites.
NASA Astrophysics Data System (ADS)
Tau, M.; Parola, A.; Pini, D.; Reatto, L.
1995-09-01
The hierarchical reference theory (HRT) is applied to the Lennard-Jones fluid below the critical temperature Tc. This study completes a previous one performed above Tc using the same kind of approximate closure for the direct correlation function. Results for several thermodynamic quantities and for the two-particle correlations are reported and compared both with other theories and with simulation data. In the two-phase region the theory correctly yields rigorously flat isotherms; this feature allows a straightforward and accurate determination of the coexistence curve without resorting to the Maxwell construction. In the critical region our analysis is consistent with the previously developed one for T>Tc and displays nontrivial critical exponents. We also study a fluid with the Girifalco model potential for C60. The critical point of the liquid-vapor transition is found at Tc=2138 K and ρc=0.50 nm-3. When the HRT result is supplemented with Verlet's freezing criterion a triple point is found at Tt=1979 K and ρt=0.848 nm-3.
Vorselaars, Bart
2015-03-21
Liquid free energies are computed by integration along a path from a reference system of known free energy, using a strong localization potential. A particular choice of localization pathway is introduced, convenient for use in molecular dynamics codes, and which achieves accurate results without the need to include the identity-swap or relocation Monte Carlo moves used in previous studies. Moreover, an adaptive timestep is introduced to attain the reference system. Furthermore, a center-of-mass correction that is different from previous studies and phase-independent is incorporated. The resulting scheme allows computation of both solid and liquid free energies with only minor differences in simulation protocol. This is used to re-visit solid-liquid equilibrium in a system of short semi-flexible Lennard-Jones chain molecules. The computed melting curve is demonstrated to be consistent with direct co-existence simulations and computed hysteresis loops, provided that an entropic term arising from unsampled solid states is included.
NASA Astrophysics Data System (ADS)
Vorselaars, Bart
2015-03-01
Liquid free energies are computed by integration along a path from a reference system of known free energy, using a strong localization potential. A particular choice of localization pathway is introduced, convenient for use in molecular dynamics codes, and which achieves accurate results without the need to include the identity-swap or relocation Monte Carlo moves used in previous studies. Moreover, an adaptive timestep is introduced to attain the reference system. Furthermore, a center-of-mass correction that is different from previous studies and phase-independent is incorporated. The resulting scheme allows computation of both solid and liquid free energies with only minor differences in simulation protocol. This is used to re-visit solid-liquid equilibrium in a system of short semi-flexible Lennard-Jones chain molecules. The computed melting curve is demonstrated to be consistent with direct co-existence simulations and computed hysteresis loops, provided that an entropic term arising from unsampled solid states is included.
NASA Astrophysics Data System (ADS)
Somasi, Sweta; Khomami, Bamin; Lovett, Ronald
2001-04-01
We introduce a new molecular dynamics simulation path to easily calculate solid-vapor surface free energies. The method is illustrated with explicit calculations of the surface free energies of a face-centered-cubic (fcc) crystal (the [110], [111], and [100] surfaces) and a hexagonal-close-packed (hcp) crystal (the [111] surface) of Lennard-Jones atoms. We verify that, because of the reduced symmetry at interfaces, simulation of the surface structure and free energy requires a large cutoff distance for the range of the pair potential. To estimate when a growing crystal resolves the fcc/hcp structural ambiguity, we observe the binding free energy and dynamics of clusters of adatoms on [111] surfaces of fcc and hcp crystals. A structural distinction only appears when clusters become large enough that their slow translational motion allows a structural relaxation of the crystal's surface. From the observed distribution over cluster structures we deduce thermodynamic parameters that can be used to model the equilibrium between fcc-like clusters and hcp-like clusters on [111] surfaces and the rate of transformation between these.
Georgescu, Ionuţ; Mandelshtam, Vladimir A
2012-10-14
The theory of self-consistent phonons (SCP) was originally developed to address the anharmonic effects in condensed matter systems. The method seeks a harmonic, temperature-dependent Hamiltonian that provides the "best fit" for the physical Hamiltonian, the "best fit" being defined as the one that optimizes the Helmholtz free energy at a fixed temperature. The present developments provide a scalable O(N) unified framework that accounts for anharmonic effects in a many-body system, when it is probed by either thermal (ℏ → 0) or quantum fluctuations (T → 0). In these important limits, the solution of the nonlinear SCP equations can be reached in a manner that requires only the multiplication of 3N × 3N matrices, with no need of diagonalization. For short range potentials, such as Lennard-Jones, the Hessian, and other related matrices are highly sparse, so that the scaling of the matrix multiplications can be reduced from O(N(3)) to ~O(N). We investigate the role of quantum effects by continuously varying the de-Boer quantum delocalization parameter Λ and report the N-Λ (T = 0), and also the classical N-T (Λ = 0) phase diagrams for sizes up to N ~ 10(4). Our results demonstrate that the harmonic approximation becomes inadequate already for such weakly quantum systems as neon clusters, or for classical systems much below the melting temperatures.
Li, Pengfei; Roberts, Benjamin P; Chakravorty, Dhruva K; Merz, Kenneth M
2013-06-11
Metal ions play significant roles in biological systems. Accurate molecular dynamics (MD) simulations on these systems require a validated set of parameters. Although there are more detailed ways to model metal ions, the nonbonded model, which employs a 12-6 Lennard-Jones (LJ) term plus an electrostatic potential is still widely used in MD simulations today due to its simple form. However, LJ parameters have limited transferability due to different combining rules, various water models and diverse simulation methods. Recently, simulations employing a Particle Mesh Ewald (PME) treatment for long-range electrostatics have become more and more popular owing to their speed and accuracy. In the present work we have systematically designed LJ parameters for 24 +2 metal (M(II)) cations to reproduce different experimental properties appropriate for the Lorentz-Berthelot combining rules and PME simulations. We began by testing the transferability of currently available M(II) ion LJ parameters. The results showed that there are differences between simulations employing Ewald summation with other simulation methods and that it was necessary to design new parameters specific for PME based simulations. Employing the thermodynamic integration (TI) method and performing periodic boundary MD simulations employing PME, allowed for the systematic investigation of the LJ parameter space. Hydration free energies (HFEs), the ion-oxygen distance in the first solvation shell (IOD) and coordination numbers (CNs) were obtained for various combinations of the parameters of the LJ potential for four widely used water models (TIP3P, SPC/E, TIP4P and TIP4PEW). Results showed that the three simulated properties were highly correlated. Meanwhile, M(II) ions with the same parameters in different water models produce remarkably different HFEs but similar structural properties. It is difficult to reproduce various experimental values simultaneously because the nonbonded model underestimates the
Johnson, W.R.; Dzuba, V.A.; Safronova, U.I.; Safronova, M.S.
2004-02-01
A finite-field scaling method is applied to evaluate the Lennard-Jones interaction constant C{sub 3} for alkali-metal atoms. The calculations are based on the relativistic single-double approximation in which single and double excitations of Dirac-Hartree-Fock wave functions are included to all orders in perturbation theory.
NASA Astrophysics Data System (ADS)
Shiba, H.; Onuki, A.
We examine the changeover in the particle configurations and the dynamics in dense Lennard-Jones binary mixtures composed of small and large particles. By varying the composition at a low temperature, we realize crystal with defects, polycrystal with small grains, and glass with various degrees of disorder. In particular, we show configurations where small crystalline regions composed of the majority species are enclosed by percolated amorphous layers composed of the two species. We visualize the dynamics of configuration changes using the method of bond breakage and following the particle displacements. In quiescent jammed states, the dynamics is severely slowed down and is highly heterogeneous at any compositions. We apply shear flow by relative motions of boundary layers. Then plastic deformations multiply occur in relatively fragile regions, growing into large-scale shear bands where the strain is highly localized. Such bands appear on short time scales and evolve on l ong time scales with finite lifetimes.
Maddox, M.W.; Gubbins, K.E.
1997-12-01
A combination of grand canonical Monte Carlo and molecular dynamics simulation techniques are used to study the freezing and melting of Lennard-Jones methane in several different cylindrical pores. Two different types of pore wall are considered; a strongly attractive wall, and a weakly attractive wall, each with pore diameters in the range 1.5{endash}3.5 nm. Freezing point depression is observed in the case of the weakly attractive pores, in agreement with several experimental studies. Freezing point elevation is observed at the walls of the strongly attractive pore, but freezing point depression occurs at the center of such pores, due to geometrical constraints. {copyright} {ital 1997 American Institute of Physics.}
Zimmerman, Paul M; Head-Gordon, Martin; Bell, Alexis T
2011-06-14
Quantum mechanics/molecular mechanics (QM/MM) models are an appealing method for performing zeolite simulations. In QM/MM, a small cluster chosen to encompass the active center is described by QM, while the rest of the zeolite is described by MM. In the present study, we demonstrate that the charges and Lennard-Jones parameters on Si and O must be chosen properly for QM/MM calculations of adsorption energies and activation energies to agree closely with full QM calculations. The selection of parameters for Si and O is based on using the ωB97X-D functional for DFT calculations of the QM region, which is effective in capturing the effects of van der Waals interactions. A comparison of the heats of adsorption for a variety of adsorbates and activation energies for the cracking of propane and butane reveals that energies derived from QM/MM calculation carried out with appropriately selected MM parameters agree to within an rms error of ∼1.5 kcal/mol with QM calculations. To avoid reparametrization for new substrates, Lennard-Jones zeolite parameters are chosen to be compatible with existing CHARMM parameters. Transferability of these parameters is demonstrated by tests utilizing the B3LYP density functional and simulations of MFI and FAU zeolites. Moreover, the computational time for QM/MM calculations is considerably lower than that for QM calculations, and the ratio of computational times decreases rapidly with increasing size of the cluster used to represent the zeolite.
Garrido, José Matías; Quinteros-Lama, Héctor; Piñeiro, Manuel M; Mejía, Andrés; Segura, Hugo
2014-07-07
This work focuses on the application of a two-way approach, where Molecular Dynamics (MD) simulations and the Square Gradient Theory (SGT) have been used for describing the phase and interface behavior of binary and ternary Lennard-Jones (LJ) mixtures, along a condition of three-phase equilibrium. The unequivocal correspondence between MD and SGT has been achieved by using the global phase diagram of binary mixtures composed by equally sized Lennard-Jones molecules, from which representative molecular parameters for Type-I, Type-II, and Type-III systems have been determined. The so selected binaries have been used then to scale the behavior of a ternary mixture characterized by complex phase equilibrium patterns. For the case of the theoretical SGT approach applied to the Lennard-Jones equation of state was used for predicting phase equilibrium and interfacial properties. In addition the corresponding MD simulations of these macroscopic properties have been conducted for the LJ potential by using equivalent molecular parameters and conditions than in the theoretical approach. Excellent agreement has been observed between the predictions obtained from theory and simulations. Particularly, our results concerning the characterization of the three phase line of a binary Type-III mixture indicate that the bulk liquid (α) and the bulk gas (G) regions are sharply separated by a bulk liquid region (β) for all the explored temperature, pressure, and concentration conditions. The structural analysis of these bulk phases reveals that a secondary liquid phase (β) perfectly wets the liquid-gas interface (α-G), as previously found for Type-II mixture [A. Mejía and L. F. Vega, J. Chem. Phys. 124, 244505 (2006)]. The exploration along the three-phase line for the ternary mixture shows good agreement between SGT and MD. Particularly, we observed the specific influence of a third component in the phase and interface behavior. From all the previous results, we conclude that the
Sumi, Tomonari; Maruyama, Yutaka; Mitsutake, Ayori; Koga, Kenichiro
2016-06-14
In the conventional classical density functional theory (DFT) for simple fluids, an ideal gas is usually chosen as the reference system because there is a one-to-one correspondence between the external field and the density distribution function, and the exact intrinsic free-energy functional is available for the ideal gas. In this case, the second-order density functional Taylor series expansion of the excess intrinsic free-energy functional provides the hypernetted-chain (HNC) approximation. Recently, it has been shown that the HNC approximation significantly overestimates the solvation free energy (SFE) for an infinitely dilute Lennard-Jones (LJ) solution, especially when the solute particles are several times larger than the solvent particles [T. Miyata and J. Thapa, Chem. Phys. Lett. 604, 122 (2014)]. In the present study, we propose a reference-modified density functional theory as a systematic approach to improve the SFE functional as well as the pair distribution functions. The second-order density functional Taylor series expansion for the excess part of the intrinsic free-energy functional in which a hard-sphere fluid is introduced as the reference system instead of an ideal gas is applied to the LJ pure and infinitely dilute solution systems and is proved to remarkably improve the drawbacks of the HNC approximation. Furthermore, the third-order density functional expansion approximation in which a factorization approximation is applied to the triplet direct correlation function is examined for the LJ systems. We also show that the third-order contribution can yield further refinements for both the pair distribution function and the excess chemical potential for the pure LJ liquids.
Ohtori, Norikazu; Ishii, Yoshiki
2015-10-28
Explicit expressions of the self-diffusion coefficient, D(i), and shear viscosity, η(sv), are presented for Lennard-Jones (LJ) binary mixtures in the liquid states along the saturated vapor line. The variables necessary for the expressions were derived from dimensional analysis of the properties: atomic mass, number density, packing fraction, temperature, and the size and energy parameters used in the LJ potential. The unknown dependence of the properties on each variable was determined by molecular dynamics (MD) calculations for an equimolar mixture of Ar and Kr at the temperature of 140 K and density of 1676 kg m(-3). The scaling equations obtained by multiplying all the single-variable dependences can well express D(i) and η(sv) evaluated by the MD simulation for a whole range of compositions and temperatures without any significant coupling between the variables. The equation for Di can also explain the dual atomic-mass dependence, i.e., the average-mass and the individual-mass dependence; the latter accounts for the "isotope effect" on Di. The Stokes-Einstein (SE) relation obtained from these equations is fully consistent with the SE relation for pure LJ liquids and that for infinitely dilute solutions. The main differences from the original SE relation are the presence of dependence on the individual mass and on the individual energy parameter. In addition, the packing-fraction dependence turned out to bridge another gap between the present and original SE relations as well as unifying the SE relation between pure liquids and infinitely dilute solutions.
Ohtori, Norikazu; Ishii, Yoshiki
2015-10-28
Explicit expressions of the self-diffusion coefficient, D{sub i}, and shear viscosity, η{sub sv}, are presented for Lennard-Jones (LJ) binary mixtures in the liquid states along the saturated vapor line. The variables necessary for the expressions were derived from dimensional analysis of the properties: atomic mass, number density, packing fraction, temperature, and the size and energy parameters used in the LJ potential. The unknown dependence of the properties on each variable was determined by molecular dynamics (MD) calculations for an equimolar mixture of Ar and Kr at the temperature of 140 K and density of 1676 kg m{sup −3}. The scaling equations obtained by multiplying all the single-variable dependences can well express D{sub i} and η{sub sv} evaluated by the MD simulation for a whole range of compositions and temperatures without any significant coupling between the variables. The equation for D{sub i} can also explain the dual atomic-mass dependence, i.e., the average-mass and the individual-mass dependence; the latter accounts for the “isotope effect” on D{sub i}. The Stokes-Einstein (SE) relation obtained from these equations is fully consistent with the SE relation for pure LJ liquids and that for infinitely dilute solutions. The main differences from the original SE relation are the presence of dependence on the individual mass and on the individual energy parameter. In addition, the packing-fraction dependence turned out to bridge another gap between the present and original SE relations as well as unifying the SE relation between pure liquids and infinitely dilute solutions.
Kikugawa, Gota; Ando, Shotaro; Suzuki, Jo; Naruke, Yoichi; Nakano, Takeo; Ohara, Taku
2015-01-14
In the present study, molecular dynamics (MD) simulations on the monatomic Lennard-Jones liquid in a periodic boundary system were performed in order to elucidate the effect of the computational domain size and shape on the self-diffusion coefficient measured by the system. So far, the system size dependence in cubic computational domains has been intensively investigated and these studies showed that the diffusion coefficient depends linearly on the inverse of the system size, which is theoretically predicted based on the hydrodynamic interaction. We examined the system size effect not only in the cubic cell systems but also in rectangular cell systems which were created by changing one side length of the cubic cell with the system density kept constant. As a result, the diffusion coefficient in the direction perpendicular to the long side of the rectangular cell significantly increases more or less linearly with the side length. On the other hand, the diffusion coefficient in the direction along the long side is almost constant or slightly decreases. Consequently, anisotropy of the diffusion coefficient emerges in a rectangular cell with periodic boundary conditions even in a bulk liquid simulation. This unexpected result is of critical importance because rectangular fluid systems confined in nanospace, which are present in realistic nanoscale technologies, have been widely studied in recent MD simulations. In order to elucidate the underlying mechanism for this serious system shape effect on the diffusion property, the correlation structures of particle velocities were examined.
NASA Astrophysics Data System (ADS)
Separdar, L.; Davatolhagh, S.
2016-12-01
Molecular dynamics simulations at constant (N , V , T) are used to study the mutual effects of gold nanoparticles on the structure and dynamics of Kob-Andersen binary Lennard-Jones (BLJ) liquid within the framework of mode coupling theory of dynamic glass transition in the reciprocal space. The results show the 'softening' effect of the gold nanoparticles on the liquid dynamics in terms of (i) reducing the mode coupling crossover temperature Tc with respect to that of the bulk BLJ (i.e. BLJ without nanoparticles), (ii) decreasing the time interval of β-relaxation, and (iii) decreasing the exponent γ characterizing the power-law behavior of the α-relaxation time. This softening effect is explained in terms of the van der Waals attraction between the gold atoms comprising the nanoparticle and the BLJ host atoms, such that adsorption of host atoms onto the nanoparticle surface creates more space or free-volume for the other atoms to diffuse. By the same token interactions of purely excluded-volume-type are expected to result in the opposite effect. It is also noted that, much unlike BLJ host particles, the dynamics of gold nanoparticles is much less dependent on the wave-vector and that it exhibits a nearly exponential behavior in the α-relaxation regime.
The role of fcc tetrahedral subunits in the phase behavior of medium sized Lennard-Jones clusters.
Saika-Voivod, Ivan; Poon, Louis; Bowles, Richard K
2010-08-21
The free energy of a 600-atom Lennard-Jones cluster is calculated as a function of surface and bulk crystallinity in order to study the structural transformations that occur in the core of medium sized clusters. Within the order parameter range studied, we find the existence of two free energy minima at temperatures near freezing. One minimum, at low values of both bulk and surface order, belongs to the liquid phase. The second minimum exhibits a highly ordered core with a disordered surface and is related to structures containing a single fcc-tetrahedral subunit, with an edge length of seven atoms (l=7), located in the particle core. At lower temperatures, a third minimum appears at intermediate values of the bulk order parameter which is shown to be related to the formation of multiple l=6 tetrahedra in the core of the cluster. We also use molecular dynamics simulations to follow a series of nucleation events and find that the clusters freeze to structures containing l=5, 6, 7, and 8 sized tetrahedra as well as those containing no tetrahedral units. The structural correlations between bulk and surface order with the size of the tetrahedral units in the cluster core are examined. Finally, the relationships between the formation of fcc tetrahedral subunits in the core, the phase behavior of medium sized clusters and the nucleation of noncrystalline global structures such as icosahedra and decahedra are discussed.
Martínez-Ruiz, F J; Blas, F J; Mendiboure, B; Moreno-Ventas Bravo, A I
2014-11-14
We propose an extension of the improved version of the inhomogeneous long-range corrections of Janeček [J. Phys. Chem. B 110, 6264-6269 (2006)], presented recently by MacDowell and Blas [J. Chem. Phys. 131, 074705 (2009)] to account for the intermolecular potential energy of spherical, rigid, and flexible molecular systems, to deal with the contributions to the microscopic components of the pressure tensor due to the dispersive long-range corrections. We have performed Monte Carlo simulations in the canonical ensemble to obtain the interfacial properties of spherical Lennard-Jones molecules with different cutoff distances, r(c) = 2.5, 3, 4, and 5σ. In addition, we have also considered cutoff distances r(c) = 2.5 and 3σ in combination with the inhomogeneous long-range corrections proposed in this work. The normal and tangential microscopic components of the pressure tensor are obtained using the mechanical or virial route in combination with the recipe of Irving and Kirkwood, while the macroscopic components are calculated using the Volume Perturbation thermodynamic route proposed by de Miguel and Jackson [J. Chem. Phys. 125, 164109 (2006)]. The vapour-liquid interfacial tension is evaluated using three different procedures, the Irving-Kirkwood method, the difference between the macroscopic components of the pressure tensor, and the Test-Area methodology. In addition to the pressure tensor and the surface tension, we also obtain density profiles, coexistence densities, vapour pressure, critical temperature and density, and interfacial thickness as functions of temperature, paying particular attention to the effect of the cutoff distance and the long-range corrections on these properties. According to our results, the main effect of increasing the cutoff distance (at fixed temperature) is to sharpen the vapour-liquid interface, to decrease the vapour pressure, and to increase the width of the biphasic coexistence region. As a result, the interfacial thickness
Martínez-Ruiz, F. J.; Blas, F. J.; Mendiboure, B.; Moreno-Ventas Bravo, A. I.
2014-11-14
We propose an extension of the improved version of the inhomogeneous long-range corrections of Janeček [J. Phys. Chem. B 110, 6264–6269 (2006)], presented recently by MacDowell and Blas [J. Chem. Phys. 131, 074705 (2009)] to account for the intermolecular potential energy of spherical, rigid, and flexible molecular systems, to deal with the contributions to the microscopic components of the pressure tensor due to the dispersive long-range corrections. We have performed Monte Carlo simulations in the canonical ensemble to obtain the interfacial properties of spherical Lennard-Jones molecules with different cutoff distances, r{sub c} = 2.5, 3, 4, and 5σ. In addition, we have also considered cutoff distances r{sub c} = 2.5 and 3σ in combination with the inhomogeneous long-range corrections proposed in this work. The normal and tangential microscopic components of the pressure tensor are obtained using the mechanical or virial route in combination with the recipe of Irving and Kirkwood, while the macroscopic components are calculated using the Volume Perturbation thermodynamic route proposed by de Miguel and Jackson [J. Chem. Phys. 125, 164109 (2006)]. The vapour-liquid interfacial tension is evaluated using three different procedures, the Irving-Kirkwood method, the difference between the macroscopic components of the pressure tensor, and the Test-Area methodology. In addition to the pressure tensor and the surface tension, we also obtain density profiles, coexistence densities, vapour pressure, critical temperature and density, and interfacial thickness as functions of temperature, paying particular attention to the effect of the cutoff distance and the long-range corrections on these properties. According to our results, the main effect of increasing the cutoff distance (at fixed temperature) is to sharpen the vapour-liquid interface, to decrease the vapour pressure, and to increase the width of the biphasic coexistence region. As a result, the interfacial
An EQT-based cDFT approach for a confined Lennard-Jones fluid mixture
Motevaselian, M. H.; Mashayak, S. Y.; Aluru, N. R.
2015-09-28
Empirical potential-based quasi-continuum theory (EQT) provides a route to incorporate atomistic detail into continuum framework such as the Nernst-Planck equation. EQT can also be used to construct a grand potential functional for classical density functional theory (cDFT). The combination of EQT and cDFT provides a simple and fast approach to predict the inhomogeneous density, potential profiles, and thermodynamic properties of confined fluids. We extend the EQT-cDFT approach to confined fluid mixtures and demonstrate it by simulating a mixture of methane and hydrogen inside slit-like channels of graphene. We show that the EQT-cDFT predictions for the structure of the confined fluid mixture compare well with the molecular dynamics simulation results. In addition, our results show that graphene slit nanopores exhibit a selective adsorption of methane over hydrogen.
NASA Astrophysics Data System (ADS)
Salian, Umesh A.
1998-04-01
The cumulated distribution of velocity components of atoms of a cluster in a constant energy classical molecular dynamics simulation is found to fit very well with Maxwellian distribution. This enables, with carefully prepared initial configurations, a cluster as small as containing just four atoms to be viewed to constitute a canonical ensemble in itself. In addition, the statistical distribution of velocity components provides an unambiguous, independent and robust method of obtaining the thermodynamic temperature of an isolated system. The temperature thus obtained differs from the conventionally used kinetic temperature by a fixed factor of (3N-6)/(3N), implications of which are discussed. A new procedure of sampling the configurational energy landscape is introduced, and the "heat capacity" curve computed using this method—which is actually the second moment of the potential energy fluctuations as a function of cluster kinetic energy—exhibits its usefulness by clearly demonstrating the two stage melting of Ar55.
a Theoretical Investigation on 10-12 Potential of Hydrogen-Hydrogen Covalent Bond
NASA Astrophysics Data System (ADS)
Taneri, Sencer
2013-05-01
This is an analytical investigation of well-known 10-12 potential of hydrogen-hydrogen covalent bond. In this research, we will make an elaboration of the well-known 6-12 Lennard-Jones potential in case of this type of bond. Though the results are illustrated in many text books and literature, an analytical analysis for these potentials is missing almost everywhere. The power laws are valid for small radial distances, which are calculated to some extent. The internuclear separation as well as the binding energy of the hydrogen molecule are evaluated with success.
NASA Astrophysics Data System (ADS)
Schaink, H. M.; Hoheisel, C.
1992-12-01
An analytical equation of state for Lennard-Jones mixtures has recently been derived using a perturbation theory with an additive hard sphere mixture (i.e., for the collision diameter d12=(d11+d22)/2) as a reference system. Here we generalize this equation of state using a nonadditive hard sphere mixture as a reference system. Even for Lennard-Jones mixtures that obey the Lorentz-Berthelot mixing rules [σ12=(σ11+σ22)/2 and ɛ12 =√ɛ11ɛ22 ], we find that our generalized theory shows an improvement in the predictions of the excess Gibbs free energy and the excess volume compared to the old version of the theory. For several non-Lorentz-Berthelot mixtures the phase diagrams predicted by the equations of state with recent Gibbs-ensemble Monte Carlo and new molecular dynamics results were compared. In this comparison the van der Waals 1-fluid model as well as an effective hard sphere model were considered. In this work only the fluid-fluid phase behavior was studied. For mixtures characterized by non-Lorentz-Berthelot energy parameters the generalization of the original equation of state gives the best predictions. For a mixture characterized by a relatively large nonadditivity in the repulsion parameters the 1-fluid approximation is best. As a by-product this study yields a generalization of the MIX1 equation of state for mixtures of nonadditive hard spheres with d11≠d22.
Lin, Shueei-Muh; Liauh, Chihng-Tsung; Wang, Wen-Rong; Ho, Shing-Huei
2006-04-01
The role of higher cantilever modes is important to obtain some material contrast. The analysis of AFM subjected to a short-range force can improve greatly the studies of surface topography and interaction energies and interaction forces, especially for chemical and biological materials. When the tip-sample distance is in the order of inter-atomic spacing, the short-range tip-sample force is usually simulated by the Lennard-Jones model. In this study, the analytical method to determine the frequency shift of AFM subjected to the Lennard-Jones force is proposed. The closed-form solution of the partial differential equation with a nonlinear boundary condition is derived and then the corresponding frequency shifts of higher modes can be determined easily. Moreover, the conventional perturbation method is usually used to determine the frequency shift, but only for the first mode. This is because the original continuous beam system is transformed into a discrete lumped-masses model. Although the above disadvantages exist, the lumped-masses model is simple and intuitive. Using the principle of dynamic strain energy, the conventional perturbation method is revised successfully to determine the frequency shifts of higher modes. The assessment of the generalized perturbation method and the proposed method is made. Finally, the effects of several parameters on the first three frequency shifts are investigated.
Adidharma, Hertanto; Tan, Sugata P
2016-07-07
Canonical Monte Carlo simulations on face-centered cubic (FCC) and hexagonal closed packed (HCP) Lennard-Jones (LJ) solids are conducted at very low temperatures (0.10 ≤ T(∗) ≤ 1.20) and high densities (0.96 ≤ ρ(∗) ≤ 1.30). A simple and robust method is introduced to determine whether or not the cutoff distance used in the simulation is large enough to provide accurate thermodynamic properties, which enables us to distinguish the properties of FCC from that of HCP LJ solids with confidence, despite their close similarities. Free-energy expressions derived from the simulation results are also proposed, not only to describe the properties of those individual structures but also the FCC-liquid, FCC-vapor, and FCC-HCP solid phase equilibria.
NASA Astrophysics Data System (ADS)
Abbaspour, Mohsen; Akbarzadeh, Hamed; Salemi, Sirous; Abroodi, Mousarreza
2016-11-01
By considering the anisotropic pressure tensor, two separate equations of state (EoS) as functions of the density, temperature, and carbon nanotube (CNT) diameter have been proposed for the radial and axial directions for the confined Lennard-Jones (LJ) fluid into (11,11), (12,10), and (19,0) CNTs from 120 to 600 K using molecular dynamics (MD) simulations. We have also investigated the effects of the pore size, pore loading, chirality, and temperature on some of the structural and dynamical properties of the confined LJ fluid into (11,11), (12,10), (19,0), and (19,19) CNTs such as the radial density profile and self-diffusion coefficient. We have also determined the EoS for the confined LJ fluid into double and triple walled CNTs.
Oderji, Hassan Yousefi; Ding, Hongbin; Behnejad, Hassan
2011-06-01
The second self-diffusion and viscosity virial coefficients of the Lennard-Jones (LJ) fluid were calculated by a detailed evaluation of the velocity and shear-stress autocorrelation functions using equilibrium molecular dynamics simulations at low and moderate densities. Accurate calculation of these coefficients requires corresponding transport coefficient values with low degrees of uncertainty. These were obtained via very long simulations by increasing the number of particles and by using the knowledge of correlation functions in the Green-Kubo method in conjunction with their corresponding generalized Einstein relations. The values of the self-diffusion and shear viscosity coefficients have been evaluated for systems with reduced densities between 0.0005 and 0.05 and reduced temperatures from 0.7 to 30.0. This provides a new insight into the transport coefficients beyond what can be offered by the Rainwater-Friend theory, which has not been developed for the self-diffusion coefficient.
Polak, W
2008-03-01
Liquid Lennard-Jones clusters of 14 different sizes from N=55-923 atoms were cooled down in Monte Carlo simulations (40 runs for each size) to the reduced temperature T* = 0.05 . Structural analysis and visualization were applied for classification of the internal structure of all 560 final clusters. Small clusters revealed the presence of the multishell icosahedra or regular polyicosahedra. In larger clusters, beginning from N=309 , the noncrystalline atom ordering is often replaced by the formation of defected crystalline clusters in the form of layered face-centered cubic-hexagonal close-packed (fcc-hcp) clusters or defected layered clusters with some additional nonparallel hcp overlayers. The presence of regular polyicosahedral clusters, relatively numerous even at the largest analyzed sizes, is attributed to kinetic effects in structure formation.
NASA Astrophysics Data System (ADS)
Lakrad, Faouzi
2016-03-01
We study the nonlinear vibrations of an AFM system, modeled as a linear mass-spring-damper system, under the Lennard-Jones forces and an imposed harmonic base displacement. The frequency of this latter is very low with respect to the natural fundamental frequency of the system. The invariant slow manifolds of the system are approximated and their bifurcations are investigated. It is shown that two dynamic saddle-node bifurcations, during one period of the base oscillation, of the contact and the noncontact invariant slow manifolds are responsible for triggering the tapping mode. It is also shown that these dynamic bifurcations govern the contact time between the probe and the sample during the tapping mode.
NASA Astrophysics Data System (ADS)
Adidharma, Hertanto; Tan, Sugata P.
2016-07-01
Canonical Monte Carlo simulations on face-centered cubic (FCC) and hexagonal closed packed (HCP) Lennard-Jones (LJ) solids are conducted at very low temperatures (0.10 ≤ T∗ ≤ 1.20) and high densities (0.96 ≤ ρ∗ ≤ 1.30). A simple and robust method is introduced to determine whether or not the cutoff distance used in the simulation is large enough to provide accurate thermodynamic properties, which enables us to distinguish the properties of FCC from that of HCP LJ solids with confidence, despite their close similarities. Free-energy expressions derived from the simulation results are also proposed, not only to describe the properties of those individual structures but also the FCC-liquid, FCC-vapor, and FCC-HCP solid phase equilibria.
Transitioning Model Potentials to Real Systems. II. Application to Molecular Oxygen
2000-09-01
monatomic liquid. This technique was used to obtain interaction potentials of the Lennard - Jones form that accurately describe argon over its entire...a modified Lennard - Jones potential. Simulations using the resulting optimal set of potential parameters of this system predict densities that are...interaction sites centered at the atomic nuclei. The intermolecular interaction is the sum of all site-site interactions described by a modified Lennard
NASA Astrophysics Data System (ADS)
Matsumoto, Akira
2014-12-01
The thermodynamic functions for Lennard-Jones (9,6) gases with a hard core that are evaluated till the third virial coefficients, are investigated at an isobaric process. Some thermodynamic functions are analytically expressed as functions of intensive variables, temperature, and pressure. Some thermodynamic quantities for carbon dioxide are calculated numerically and drawn graphically. In critical states, the heat capacity diverges to infinity at the critical point while the Gibbs free energy, volume, enthalpy, and entropy are continuous at the critical point. In the coexistence of two phases, the boiling temperatures and the enthalpy changes of vaporization are obtained by numerical calculations for 20 substances. The Gibbs free energy indicates a polygonal line; entropy, volume, and enthalpy jump from the liquid to gaseous phase at the boiling point. The heat capacity does not diverge to infinity but shows a finite discrepancy at boiling point. This suggests that a first-order phase transition at the boiling point and a second-order phase transition may occur at the critical point.
Hafskjold, Bjørn
2017-01-01
A binary isotope mixture of Lennard-Jones/spline particles at equilibrium was perturbed by a sudden change in the system's boundary temperatures. The system's response was determined by non-equilibrium molecular dynamics (NEMD). Three transient processes were studied: 1) The propagation of a pressure (shock) wave, 2) heat diffusivity and conduction, and 3) thermal diffusion (the Ludwig-Soret effect). These three processes occur at different time scales, which makes it possible to separate them in one single NEMD run. The system was studied in liquid, supercritical, and dense gas states with various forms and strengths of the thermal perturbation. The results show that heat was initially transported by two separate mechanisms: 1) heat diffusion as described by the transient heat equation and 2) as a consequence of a pressure wave. The pressure wave travelled faster than the speed of sound, generating a shock wave in the system. Local equilibrium was found in the transient phase, even with very strong perturbations and in the shock front. Although the mass separation due to the Ludwig-Soret effect developed much slower than the pressure and temperature fields in the system at large, it was found that the Soret coefficient could be accurately determined from the initial phase of the transient and close to the heat source. This opens the possibility of a new way to analyse results from transient experiments and thereby minimize effects of gravity and convection due to buoyancy.
NASA Astrophysics Data System (ADS)
Lechuga-Sanabria, Fidelmar; Chapela, Gustavo A.; Quintana-H, Jacqueline
2013-10-01
The map of low and high density phases of an idealized system, the infinitely hard zigzag line model with two Lennard-Jones (LJ) sites is presented. LJ sites are added to a previous model composed of the infinitely hard zigzag line shape particles, R.A. Perusqía, J. Peón, J. Quintana, Physica A 345 (1) (2005) 130-142. The attractions and the molecular volume added to this system through the LJ sites create a more realistic model and, as a consequence, a richer phase behavior is obtained. Although the volume of the LJ sites is quite small it is enough to produce solid phases, absent in the original model. On the other hand the smectic phase that was present in the hard system was not found in this case. Two molecular conformations are chosen to provide a comparison with the previous model. The isothermal-isobaric is used to establish the thermodynamic regions of the different molecular self aggregations and to compare them to already published results.
NASA Astrophysics Data System (ADS)
Vogelsang, R.; Hoheisel, C.
1987-02-01
Molecular-dynamics (MD) calculations are reported for three thermodynamic states of a Lennard-Jones fluid. Systems of 2048 particles and 105 integration steps were used. The transverse current autocorrelation function, Ct(k,t), has been determined for wave vectors of the range 0.5<||k||σ<1.5. Ct(k,t) was fitted by hydrodynamic-type functions. The fits returned k-dependent decay times and shear viscosities which showed a systematic behavior as a function of k. Extrapolation to the hydrodynamic region at k=0 gave shear viscosity coefficients in good agreement with direct Green-Kubo results obtained in previous work. The two-exponential model fit for the memory function proposed by other authors does not provide a reasonable description of the MD results, as the fit parameters show no systematic wave-vector dependence, although the Ct(k,t) functions are somewhat better fitted. Similarly, the semiempirical interpolation formula for the decay time based on the viscoelastic concept proposed by Akcasu and Daniels fails to reproduce the correct k dependence for the wavelength range investigated herein.
A new interlayer potential for hexagonal boron nitride
NASA Astrophysics Data System (ADS)
Akıner, Tolga; Mason, Jeremy K.; Ertürk, Hakan
2016-09-01
A new interlayer potential is developed for interlayer interactions of hexagonal boron nitride sheets, and its performance is compared with other potentials in the literature using molecular dynamics simulations. The proposed potential contains Coulombic and Lennard-Jones 6-12 terms, and is calibrated with recent experimental data including the hexagonal boron nitride interlayer distance and elastic constants. The potentials are evaluated by comparing the experimental and simulated values of interlayer distance, density, elastic constants, and thermal conductivity using non-equilibrium molecular dynamics. The proposed potential is found to be in reasonable agreement with experiments, and improves on earlier potentials in several respects. Simulated thermal conductivity values as a function of the number of layers and of temperature suggest that the proposed LJ 6-12 potential has the ability to predict some phonon behaviour during heat transport in the out-of-plane direction.
Fujiwara, K.; Shibahara, M.
2014-07-21
A classical molecular dynamics simulation was conducted for a system composed of fluid molecules between two planar solid surfaces, and whose interactions are described by the 12-6 Lennard-Jones form. This paper presents a general description of the pressure components and interfacial tension at a fluid-solid interface obtained by the perturbative method on the basis of statistical thermodynamics, proposes a method to consider the pressure components tangential to an interface which are affected by interactions with solid atoms, and applies this method to the calculation system. The description of the perturbative method is extended to subsystems, and the local pressure components and interfacial tension at a liquid-solid interface are obtained and examined in one- and two-dimensions. The results are compared with those obtained by two alternative methods: (a) an evaluation of the intermolecular force acting on a plane, and (b) the conventional method based on the virial expression. The accuracy of the numerical results is examined through the comparison of the results obtained by each method. The calculated local pressure components and interfacial tension of the fluid at a liquid-solid interface agreed well with the results of the two alternative methods at each local position in one dimension. In two dimensions, the results showed a characteristic profile of the tangential pressure component which depended on the direction tangential to the liquid-solid interface, which agreed with that obtained by the evaluation of the intermolecular force acting on a plane in the present study. Such good agreement suggests that the perturbative method on the basis of statistical thermodynamics used in this study is valid to obtain the local pressure components and interfacial tension at a liquid-solid interface.
Oh, Inrok; Choi, Saehyun; Jung, YounJoon; Kim, Jun Soo
2015-08-28
Phase separation in a biological cell nucleus occurs in a heterogeneous environment filled with a high density of chromatins and thus it is inevitably influenced by interactions with chromatins. As a model system of nuclear body formation in a cell nucleus filled with chromatins, we simulate the phase separation of a low-density Lennard-Jones (LJ) fluid interacting with a long, condensed polymer chain. The influence of the density variation of LJ particles above and below the phase boundary and the role of attractive interactions between LJ particles and polymer segments are investigated at a fixed value of strong self-interaction between LJ particles. For a density of LJ particles above the phase boundary, phase separation occurs and a dense domain of LJ particles forms irrespective of interactions with the condensed polymer chain whereas its localization relative to the polymer chain is determined by the LJ-polymer attraction strength. Especially, in the case of moderately weak attractions, the domain forms separately from the polymer chain and subsequently associates with the polymer chain. When the density is below the phase boundary, however, the formation of a dense domain is possible only when the LJ-polymer attraction is strong enough, for which the domain grows in direct contact with the interacting polymer chain. In this work, different growth behaviors of LJ particles result from the differences in the density of LJ particles and in the LJ-polymer interaction, and this work suggests that the distinct formation of activity-dependent and activity-independent nuclear bodies (NBs) in a cell nucleus may originate from the differences in the concentrations of body-specific NB components and in their interaction with chromatins.
Baidakov, Vladimir G
2016-02-21
The process of bubble nucleation in a Lennard-Jones (LJ) liquid is studied by molecular dynamics (MD) simulation. The bubble nucleation rate J is determined by the mean life-time method at temperatures above that of the triple point in the region of negative pressures. The results of simulation are compared with classical nucleation theory (CNT) and modified classical nucleation theory (MCNT), in which the work of formation of a critical bubble is determined in the framework of the van der Waals-Cahn-Hilliard gradient theory (GT). It has been found that the values of J obtained in MD simulation systematically exceed the data of CNT, and this excess in the nucleation rate reaches 8-10 orders of magnitude close to the triple point temperature. The results of MCNT are in satisfactory agreement with the data of MD simulation. To describe the properties of vapor-phase nuclei in the framework of GT, an equation of state has been built up which describes stable, metastable and labile regions of LJ fluids. The surface tension of critical bubbles γ has been found from CNT and data of MD simulation as a function of the radius of curvature of the surface of tension R*. The dependence γ(R*) has also been calculated from GT. The Tolman length has been determined, which is negative and in modulus equal to ≈(0.1 - 0.2) σ. The paper discusses the applicability of the Tolman formula to the description of the properties of critical nuclei in nucleation.
Phillips, Carolyn L.; Crozier, Paul S.
2009-08-21
Two-temperature models are used to represent the interaction between atoms and free electrons during thermal transients such as radiation damage, laser heating, and cascade simulations. In this paper, we introduce an energy-conserving version of an inhomogeneous finite reservoir two-temperature model using a Langevin thermostat to communicate energy between the electronic and atomic subsystems. This energy-conserving modification allows the inhomogeneous two-temperature model to be used for longer and larger simulations and simulations of small energy phenomena, without introducing nonphysical energy fluctuations that may affect simulation results. We test this model on the annealing of Frenkel defects. We find that Frenkel defect annealing is largely indifferent to the electronic subsystem, unless the electronic subsystem is very tightly coupled to the atomic subsystem. We also consider radiation damage due to local deposition of heat in two idealized systems. We first consider radiation damage in a large face-centered-cubic Lennard-Jones (LJ) single-component crystal that readily recrystallizes. Second, we consider radiation damage in a large binary glass-forming LJ crystal that retains permanent damage. We find that the electronic subsystem parameters can influence the way heat is transported through the system and have a significant impact on the number of defects after the heat deposition event. We also find that the two idealized systems have different responses to the electronic subsystem. The single-component LJ system anneals most rapidly with an intermediate electron-ion coupling and a high electronic thermal conductivity. If sufficiently damaged, the binary glass-forming LJ system retains the least permanent damage with both a high electron-ion coupling and a high electronic thermal conductivity. In general, we find that the presence of an electronic gas can affect short and long term material annealing.
NASA Astrophysics Data System (ADS)
Fujiwara, K.; Shibahara, M.
2014-07-01
A classical molecular dynamics simulation was conducted for a system composed of fluid molecules between two planar solid surfaces, and whose interactions are described by the 12-6 Lennard-Jones form. This paper presents a general description of the pressure components and interfacial tension at a fluid-solid interface obtained by the perturbative method on the basis of statistical thermodynamics, proposes a method to consider the pressure components tangential to an interface which are affected by interactions with solid atoms, and applies this method to the calculation system. The description of the perturbative method is extended to subsystems, and the local pressure components and interfacial tension at a liquid-solid interface are obtained and examined in one- and two-dimensions. The results are compared with those obtained by two alternative methods: (a) an evaluation of the intermolecular force acting on a plane, and (b) the conventional method based on the virial expression. The accuracy of the numerical results is examined through the comparison of the results obtained by each method. The calculated local pressure components and interfacial tension of the fluid at a liquid-solid interface agreed well with the results of the two alternative methods at each local position in one dimension. In two dimensions, the results showed a characteristic profile of the tangential pressure component which depended on the direction tangential to the liquid-solid interface, which agreed with that obtained by the evaluation of the intermolecular force acting on a plane in the present study. Such good agreement suggests that the perturbative method on the basis of statistical thermodynamics used in this study is valid to obtain the local pressure components and interfacial tension at a liquid-solid interface.
van Westen, Thijs; Oyarzún, Bernardo; Vlugt, Thijs J H; Gross, Joachim
2015-06-28
We develop an equation of state (EoS) for describing isotropic-nematic (IN) phase equilibria of Lennard-Jones (LJ) chain fluids. The EoS is developed by applying a second order Barker-Henderson perturbation theory to a reference fluid of hard chain molecules. The chain molecules consist of tangentially bonded spherical segments and are allowed to be fully flexible, partially flexible (rod-coil), or rigid linear. The hard-chain reference contribution to the EoS is obtained from a Vega-Lago rescaled Onsager theory. For the description of the (attractive) dispersion interactions between molecules, we adopt a segment-segment approach. We show that the perturbation contribution for describing these interactions can be divided into an "isotropic" part, which depends only implicitly on orientational ordering of molecules (through density), and an "anisotropic" part, for which an explicit dependence on orientational ordering is included (through an expansion in the nematic order parameter). The perturbation theory is used to study the effect of chain length, molecular flexibility, and attractive interactions on IN phase equilibria of pure LJ chain fluids. Theoretical results for the IN phase equilibrium of rigid linear LJ 10-mers are compared to results obtained from Monte Carlo simulations in the isobaric-isothermal (NPT) ensemble, and an expanded formulation of the Gibbs-ensemble. Our results show that the anisotropic contribution to the dispersion attractions is irrelevant for LJ chain fluids. Using the isotropic (density-dependent) contribution only (i.e., using a zeroth order expansion of the attractive Helmholtz energy contribution in the nematic order parameter), excellent agreement between theory and simulations is observed. These results suggest that an EoS contribution for describing the attractive part of the dispersion interactions in real LCs can be obtained from conventional theoretical approaches designed for isotropic fluids, such as a Perturbed
Fujiwara, K; Shibahara, M
2014-07-21
A classical molecular dynamics simulation was conducted for a system composed of fluid molecules between two planar solid surfaces, and whose interactions are described by the 12-6 Lennard-Jones form. This paper presents a general description of the pressure components and interfacial tension at a fluid-solid interface obtained by the perturbative method on the basis of statistical thermodynamics, proposes a method to consider the pressure components tangential to an interface which are affected by interactions with solid atoms, and applies this method to the calculation system. The description of the perturbative method is extended to subsystems, and the local pressure components and interfacial tension at a liquid-solid interface are obtained and examined in one- and two-dimensions. The results are compared with those obtained by two alternative methods: (a) an evaluation of the intermolecular force acting on a plane, and (b) the conventional method based on the virial expression. The accuracy of the numerical results is examined through the comparison of the results obtained by each method. The calculated local pressure components and interfacial tension of the fluid at a liquid-solid interface agreed well with the results of the two alternative methods at each local position in one dimension. In two dimensions, the results showed a characteristic profile of the tangential pressure component which depended on the direction tangential to the liquid-solid interface, which agreed with that obtained by the evaluation of the intermolecular force acting on a plane in the present study. Such good agreement suggests that the perturbative method on the basis of statistical thermodynamics used in this study is valid to obtain the local pressure components and interfacial tension at a liquid-solid interface.
NASA Astrophysics Data System (ADS)
Matsumoto, Yoichiro; Matsui, Jun; Ohashi, Hideo
1992-07-01
Rarefied gas flows in various situations are calculated successfully by the direct simulation Monte Carlo method. In the simulation, the Maxwell model, where a gas molecule reflects diffusely with the probability alpha and reflects specularly with the probability 1 - alpha, is widely used for boundary conditions on solid surfaces. However, the value of alpha is determined empirically and varies greatly with conditions such as degree of contamination and temperature of the surface. Rational prediction of the value and analysis of the interaction between gas and solid surface are required. In this paper, the behavior of a gas molecule with collides onto the solid surface is simulated by the molecular dynamics method. The numerical results reveal that the scattering behavior of the gas molecule is neither specular, diffuse, nor Maxwell-type reflection, and that the sticking probability is affected by the initial gas velocity and the potential well depth.
NASA Astrophysics Data System (ADS)
Cezar, Henrique M.; Rondina, Gustavo G.; Da Silva, Juarez L. F.
2017-02-01
A basic requirement for an atom-level understanding of nanoclusters is the knowledge of their atomic structure. This understanding is incomplete if it does not take into account temperature effects, which play a crucial role in phase transitions and changes in the overall stability of the particles. Finite size particles present intricate potential energy surfaces, and rigorous descriptions of temperature effects are best achieved by exploiting extended ensemble algorithms, such as the Parallel Tempering Monte Carlo (PTMC). In this study, we employed the PTMC algorithm, implemented from scratch, to sample configurations of LJn (n =38 , 55, 98, 147) particles at a wide range of temperatures. The heat capacities and phase transitions obtained with our PTMC implementation are consistent with all the expected features for the LJ nanoclusters, e.g., solid to solid and solid to liquid. To identify the known phase transitions and assess the prevalence of various structural motifs available at different temperatures, we propose a combination of a Leader-like clustering algorithm based on a Euclidean metric with the PTMC sampling. This combined approach is further compared with the more computationally demanding bond order analysis, typically employed for this kind of problem. We show that the clustering technique yields the same results in most cases, with the advantage that it requires no previous knowledge of the parameters defining each geometry. Being simple to implement, we believe that this straightforward clustering approach is a valuable data analysis tool that can provide insights into the physics of finite size particles with few to thousand atoms at a relatively low cost.
Fundamental Study of Dense Fluid-Detonation
1983-03-31
equation of state accurately, for sufficiently simple materials. For some "realistic" potentials, such as the Lennard - Jones 6-12 interatomic *potential...continuum calculations are complete. Using an equation of state which describes the Lennard - Jones potential throughout the fluid regions of the phase diagram...reactant and product Hugoniots calculated with the Lennard - Jones equation of state. The well depth and collision diameter are c and a, respectively. The
ON THE EQUATION OF STATE OF COMPRESSED LIQUIDS AND SOLIDS
latter form is used. An analysis of po and G(v,T) for the Lennard - Jones Devonshire free volume theory and the equation of state results obtained by the...the states under consideration. For illustration an analytic fit to the Monte Carlo result for a Lennard - Jones 6-12 potential is presented. A breakdown of Lennard - Jones result for the second virial coefficient is appended.
THERMODYNAMIC AND TRANSPORT PROPERTIES OF RUBIDIUM VAPOR AND CESIUM VAPOR
consideration. It is assumed that the vapors are comprised of alkali atoms whose interactions are the pairwise Lennard - Jones (6 - 12) type. On the basis of...the 2 parameters which occur in the Lennard - Jones potential for interactions between some alkalis and noble gas atoms and the known parameters for the
Ibuki, Kazuyasu; Ueno, Masakatsu
2006-04-07
The validity of a Fokker-Planck-Kramers equation (FPKE) treatment of the rate of diffusion-controlled reaction at short times [K. Ibuki and M. Ueno, J. Chem. Phys. 119, 7054 (2003)] is tested in a supercritical Lennard-Jones fluid over a wide density range by comparing it with the Langevin dynamics and molecular dynamics simulations and other theories. The density n range studied is 0.323n(c)< or =n< or =2.58n(c) and the temperature 1.52T(c), where n(c) and T(c) are the critical density and temperature, respectively. For the rate of bimolecular reactions, the transition between the collision-limited and diffusion-limited regimes is expected to take place in this density range. The simulations show that the rate constant decays with time extensively at high densities, and that the magnitude of decay decreases gradually with decreasing density. The decay profiles of the rate constants obtained by the simulations are reproduced reasonably well by the FPKE treatment in the whole density range studied if a continuous velocity distribution is used in solving the FPKE approximately. If a discontinuous velocity distribution is used instead of the continuous one, the FPKE treatment leads to a rate constant much larger than the simulation results at medium and low densities. The rate constants calculated from the Smoluchowski-Collins-Kimball (SCK) theory based on the diffusion equation are somewhat smaller than the simulation results in medium and low densities when the intrinsic rate constant is chosen to adjust the steady state rate constant in the low density limit to that derived by the kinetic collision theory. The discrepancy is relatively small, so that the SCK theory provides a useful guideline for a qualitative discussion of the density effect on the rate constant.
NASA Astrophysics Data System (ADS)
Mella, Massimo
2008-06-01
In this work, an improved approach for computing cluster dissociation rates using Monte Carlo (MC) simulations is proposed and a discussion is provided on its applicability as a function of environmental variables (e.g., temperature). With an analytical transformation of the integrals required to compute variational transition state theory (vTST) dissociation rates, MC estimates of the expectation value for the Dirac delta δ(qrc-qc) have been made free of the discretization error that is present when a prelimit form for δ is used. As a by-product of this transformation, the statistical error associated with <δ(qrc-qc)> is reduced making this step in the calculation of vTST rates substantially more efficient (by a factor of 4-2500, roughly). The improved MC procedure is subsequently employed to compute the dissociation rate for Lennard-Jones clusters X13-nYn (n=0-3) as a function of temperature (T), composition, and X-Y interaction strength. The X13-nYn family has been previously studied as prototypical set of systems for which it may be possible to select and stabilize structures different from the icosahedral global minimum of X13. It was found that both the dissociation rate and the dissociation mechanism, as suggested by the statistical simulations, present a marked dependence on n, T, and the nature of Y. In particular, it was found that a vacancy is preferentially formed close to a surface impurity when the X-Y interaction is weaker than the X-X one whatever the temperature. Differently, the mechanism was found to depend on T for stronger X-Y interactions, with vacancies being formed opposite to surface impurities at higher temperature. These behaviors are a reflex of the important role played by the surface fluctuations in defining the properties of clusters.
NASA Astrophysics Data System (ADS)
Binder, Kurt; Block, Benjamin J.; Virnau, Peter; Tröster, Andreas
2012-12-01
As a rule, mean-field theories applied to a fluid that can undergo a transition from saturated vapor at density ρυ to a liquid at density ρℓ yield a van der Waals loop. For example, isotherms of the chemical potential μ(T ,ρ) as a function of the density ρ at a fixed temperature T less than the critical temperature Tc exhibit a maximum and a minimum. Metastable and unstable parts of the van der Waals loop can be eliminated by the Maxwell construction. Van der Waals loops and the corresponding double minimum potentials are mean-field artifacts. Simulations at fixed μ =μcoex for ρυ<ρ <ρℓ yield a loop, but for sufficiently large systems this loop does not resemble the van der Waals loop and reflects interfacial effects on phase coexistence due to finite size effects. In contrast to the van der Waals loop, all parts of the loop found in simulations are thermodynamically stable. The successive umbrella sampling algorithm is described as a convenient tool for seeing these effects. It is shown that the maximum of the loop is not the stability limit of a metastable vapor but signifies the droplet evaporation-condensation transition. The descending part of the loop contains information on Tolman-like corrections to the surface tension, rather than describing unstable states.
Makowski, Mariusz; Liwo, Adam; Maksimiak, Katarzyna; Makowska, Joanna; Scheraga, Harold A
2007-03-22
Simple analytical functions consisting of electrostatic, polarization, Lennard-Jones or modified Lennard-Jones, and cavity terms are proposed to express the potentials of mean force analytically for spherical particles interacting in water. The cavity term was expressed either through the molecular-surface area of the solute or by using the Gaussian-overlap model of hydrophobic hydration developed in paper 1 of this series. The analytical expressions were fitted to the potentials of mean force of a methane homodimer, heterodimers composed of a methane molecule, and an ammonium cation or a chloride anion, respectively, and dimers consisting of two chloride anions, two ammonium cations, or a chloride ion and an ammonium cation. The potentials of mean force for these dimers were determined by umbrella-sampling molecular dynamics simulations with the AMBER 7.0 force field with TIP3P water either in our earlier work or in this work. For all systems, the analytical formulas fitted the potentials of mean force very well. However, using the molecular-surface area to express the cavity term provided a good fit only when the nonbonded interactions were expressed by an all-repulsive modified Lennard-Jones potential but also resulted in non-physical values of some of the parameters. Conversely, the use of our new Gaussian-overlap-based expression for the cavity term provided a good fit to the potentials of mean force (PMFs) with Lennard-Jones nonbonded potential, and the values of all parameters were physically reasonable.
NASA Astrophysics Data System (ADS)
Reif, Maria M.; Hünenberger, Philippe H.
2011-04-01
The raw single-ion solvation free energies computed from atomistic (explicit-solvent) simulations are extremely sensitive to the boundary conditions and treatment of electrostatic interactions used during these simulations. However, as shown recently [M. A. Kastenholz and P. H. Hünenberger, J. Chem. Phys. 124, 224501 (2006), 10.1529/biophysj.106.083667; M. M. Reif and P. H. Hünenberger, J. Chem. Phys. 134, 144103 (2010)], the application of appropriate correction terms permits to obtain methodology-independent results. The corrected values are then exclusively characteristic of the underlying molecular model including in particular the ion-solvent van der Waals interaction parameters, determining the effective ion size and the magnitude of its dispersion interactions. In the present study, the comparison of calculated (corrected) hydration free energies with experimental data (along with the consideration of ionic polarizabilities) is used to calibrate new sets of ion-solvent van der Waals (Lennard-Jones) interaction parameters for the alkali (Li+, Na+, K+, Rb+, Cs+) and halide (F-, Cl-, Br-, I-) ions along with either the SPC or the SPC/E water models. The experimental dataset is defined by conventional single-ion hydration free energies [Tissandier et al., J. Phys. Chem. A 102, 7787 (1998), 10.1021/jp982638r; Fawcett, J. Phys. Chem. B 103, 11181] along with three plausible choices for the (experimentally elusive) value of the absolute (intrinsic) hydration free energy of the proton, namely, Δ G_hyd^{ominus }[H+] = -1100, -1075 or -1050 kJ mol-1, resulting in three sets L, M, and H for the SPC water model and three sets LE, ME, and HE for the SPC/E water model (alternative sets can easily be interpolated to intermediate Δ G_hyd^{ominus }[H+] values). The residual sensitivity of the calculated (corrected) hydration free energies on the volume-pressure boundary conditions and on the effective ionic radius entering into the calculation of the correction terms is
A precise phenomonological method is explained for the description of the intermolecular forces of repulsion exemplified for the generalized Lennard ... Jones -potential. Along with the consistent potential parameters the pertinent ’repulsion exponents’ are used for the evaluation of the transport
Reif, Maria M.; Huenenberger, Philippe H.
2011-04-14
The raw single-ion solvation free energies computed from atomistic (explicit-solvent) simulations are extremely sensitive to the boundary conditions and treatment of electrostatic interactions used during these simulations. However, as shown recently [M. A. Kastenholz and P. H. Huenenberger, J. Chem. Phys. 124, 224501 (2006); M. M. Reif and P. H. Huenenberger, J. Chem. Phys. 134, 144103 (2010)], the application of appropriate correction terms permits to obtain methodology-independent results. The corrected values are then exclusively characteristic of the underlying molecular model including in particular the ion-solvent van der Waals interaction parameters, determining the effective ion size and the magnitude of its dispersion interactions. In the present study, the comparison of calculated (corrected) hydration free energies with experimental data (along with the consideration of ionic polarizabilities) is used to calibrate new sets of ion-solvent van der Waals (Lennard-Jones) interaction parameters for the alkali (Li{sup +}, Na{sup +}, K{sup +}, Rb{sup +}, Cs{sup +}) and halide (F{sup -}, Cl{sup -}, Br{sup -}, I{sup -}) ions along with either the SPC or the SPC/E water models. The experimental dataset is defined by conventional single-ion hydration free energies [Tissandier et al., J. Phys. Chem. A 102, 7787 (1998); Fawcett, J. Phys. Chem. B 103, 11181] along with three plausible choices for the (experimentally elusive) value of the absolute (intrinsic) hydration free energy of the proton, namely, {Delta}G{sub hyd} {sup O-minus} [H{sup +}]=-1100, -1075 or -1050 kJ mol{sup -1}, resulting in three sets L, M, and H for the SPC water model and three sets L{sub E}, M{sub E}, and H{sub E} for the SPC/E water model (alternative sets can easily be interpolated to intermediate {Delta}G{sub hyd} {sup O-minus} [H{sup +}] values). The residual sensitivity of the calculated (corrected) hydration free energies on the volume-pressure boundary conditions and on the effective
Torres, Edmanuel; DiLabio, Gino A
2013-08-13
Large clusters of noncovalently bonded molecules can only be efficiently modeled by classical mechanics simulations. One prominent challenge associated with this approach is obtaining force-field parameters that accurately describe noncovalent interactions. High-level correlated wave function methods, such as CCSD(T), are capable of correctly predicting noncovalent interactions, and are widely used to produce reference data. However, high-level correlated methods are generally too computationally costly to generate the critical reference data required for good force-field parameter development. In this work we present an approach to generate Lennard-Jones force-field parameters to accurately account for noncovalent interactions. We propose the use of a computational step that is intermediate to CCSD(T) and classical molecular mechanics, that can bridge the accuracy and computational efficiency gap between them, and demonstrate the efficacy of our approach with methane clusters. On the basis of CCSD(T)-level binding energy data for a small set of methane clusters, we develop methane-specific, atom-centered, dispersion-correcting potentials (DCPs) for use with the PBE0 density-functional and 6-31+G(d,p) basis sets. We then use the PBE0-DCP approach to compute a detailed map of the interaction forces associated with the removal of a single methane molecule from a cluster of eight methane molecules and use this map to optimize the Lennard-Jones parameters for methane. The quality of the binding energies obtained by the Lennard-Jones parameters we obtained is assessed on a set of methane clusters containing from 2 to 40 molecules. Our Lennard-Jones parameters, used in combination with the intramolecular parameters of the CHARMM force field, are found to closely reproduce the results of our dispersion-corrected density-functional calculations. The approach outlined can be used to develop Lennard-Jones parameters for any kind of molecular system.
Adsorption of metal atoms at a buckled graphene grain boundary using model potentials
Helgee, Edit E.; Isacsson, Andreas
2016-01-15
Two model potentials have been evaluated with regard to their ability to model adsorption of single metal atoms on a buckled graphene grain boundary. One of the potentials is a Lennard-Jones potential parametrized for gold and carbon, while the other is a bond-order potential parametrized for the interaction between carbon and platinum. Metals are expected to adsorb more strongly to grain boundaries than to pristine graphene due to their enhanced adsorption at point defects resembling those that constitute the grain boundary. Of the two potentials considered here, only the bond-order potential reproduces this behavior and predicts the energy of the adsorbate to be about 0.8 eV lower at the grain boundary than on pristine graphene. The Lennard-Jones potential predicts no significant difference in energy between adsorbates at the boundary and on pristine graphene. These results indicate that the Lennard-Jones potential is not suitable for studies of metal adsorption on defects in graphene, and that bond-order potentials are preferable.
Energy of Cohesion, Compressibility, and the Potential Energy Functions of the Graphite System
NASA Technical Reports Server (NTRS)
Girifalco, L. A.; Lad, R. A.
1956-01-01
The lattice summations of the potential energy of importance in the graphite system have been computed by direct summation assuming a Lennard-Jones 6-12 potential between carbon atoms. From these summations, potential energy curves were constructed for interactions between a carbon atom and a graphite monolayer, between a carbon atom and a graphite surface, between a graphite monolayer and a semi-infinite graphite crystal and between two graphite semi-infinite crystals. Using these curves, the equilibrium distance between two isolated physically interacting carbon atoms was found to be 2.70 a, where a is the carbon-carbon distance in a graphite sheet. The distance between a surface plane and the rest of the crystal was found to be 1.7% greater than the interlayer spacing. Theoretical values of the energy of cohesion and the compressibility were calculated from the potential curve for the interaction between two semi-infinite crystals. They were (delta)E(sub c) = -330 ergs/sq cm and beta =3.18x10(exp -12)sq cm/dyne, respectively. These compared favorably with the experimental values of (delta)E(sub c) = -260 ergs/sq cm and beta = 2.97 X 10(exp -2) sq cm/dyne.
1985-08-01
Best fit Lennard-Jones, Morse, variable exponent , and exponential-3 ’ potentials having well depths %32 meV are derived from the data. These measure- 1...variable exponent , and exponential-3 poten- tials having well depths ot-2 V are derived from the data. These measurements are supported by...the well depth and X the range parameter. The potential minimum is given by ze = 31/6- z iii) Variable exponent potential (VEP) [52] vo0 (z) = D{ [I
A Coarse-Grained Model Based on Morse Potential for Water and n-Alkanes.
Chiu, See-Wing; Scott, H Larry; Jakobsson, Eric
2010-03-09
In order to extend the time and distance scales of molecular dynamics simulations, it is essential to create accurate coarse-grained force fields, in which each particle contains several atoms. Coarse-grained force fields that utilize the Lennard-Jones potential form for pairwise nonbonded interactions have been shown to suffer from serious inaccuracy, notably with respect to describing the behavior of water. In this paper, we describe a coarse-grained force field for water, in which each particle contains four water molecules, based on the Morse potential form. By molecular dynamics simulations, we show that our force field closely replicates important water properties. We also describe a Morse potential force field for alkanes and a simulation method for alkanes in which individual particles may have variable size, providing flexibility in constructing complex molecules comprised partly or solely of alkane groups. We find that, in addition to being more accurate, the Morse potential also provides the ability to take larger time steps than the Lennard-Jones, because the short distance repulsion potential profile is less steep. We suggest that the Morse potential form should be considered as an alternative for the Lennard-Jones form for coarse-grained molecular dynamics simulations.
NASA Astrophysics Data System (ADS)
Tareyeva, E. E.; Ryzhov, V. N.
2016-12-01
We propose an approximation of a direct correlation function corresponding to the linearization with respect to - βϕ( r) of a generalized mean spherical approximation for a hard-core multi-Yukawa system of particles. We use the results to study the behavior of maximums of thermodynamic response functions in the supercritical region of a fluid with a two-term Yukawa potential imitating the Lennard-Jones potential.
NASA Astrophysics Data System (ADS)
Song, W.; Rossky, P. J.; Maroncelli, M.
2003-11-01
We have tested the ability of the OPLS-AA models (optimized potentials for liquid simulations) of alkanes and perfluoroalkanes recently developed by Jorgensen and co-workers to represent the unusual mixing behavior of alkane+perfluoroalkane systems. We find that these all-atom Lennard-Jones (6-12)+Coulomb representations, together with the usual Lorentz-Berthelot combining rules, fail to reproduce the weaker-than-anticipated interactions between these two classes of molecules. Systematic disagreements with experiment are found in the case of second pressure virial coefficients, gas solubilities, and liquid-liquid mixing properties. These discrepancies are not specific to the choice of OPLS-AA potentials, but are rather linked to the failure of the geometric mean combining rule for relating unlike atom interactions. In all cases examined, a reduction in the strength of cross H+F interactions by ˜25% relative to the geometric mean is required in order to achieve reasonable agreement with experiment. Several less commonly used combining rules were also examined. Although some of these rules are able to provide a reasonable description of the interactions among perfluoroalkane and alkane species, they fail to provide a consistent treatment when atoms other than C, H, and F are considered, as is necessary for modeling the interaction of the former molecules with rare-gas atoms.
NASA Astrophysics Data System (ADS)
Zarkova, Lydia P.; Pirgov, Peter S.; Paeva, Gabriela V.; Guerassimov, Nikolay T.; Nefedov, Anatoly P.; Sinel'schikov, Vladimir A.; Usachov, Alexandr D.; Homkin, Mihail A.
1996-12-01
Preliminary results of restoring potentials of interactions Na(3s, 3p)-CO2(X1(Sigma) g+) from measured far wing spectra of sodium resonance line Na-D perturbed by CO2 are presented. The spectra in the range of (Delta) (sigma) approximately equals 10-3500 cm-1 are considered following the quasi-static theory of line broadening by inert gases as continua and due to the A ARLR X and B ARLR X transitions of Na-CO2 quasi-molecules. The reduced absorption coefficient K((sigma) ) at frequency (sigma) equals (sigma) 0 + (Delta) (sigma) is calculated as corresponding to the radiation from molecules with internuclear separation R, where hc(sigma) equals VA,B - VX. As a first approximation, all the three potentials are presented in the shape of a (6,12)-Lennard-Jones potential. The constants C6 and C12 are determined as independent variables by minimization of the sum of squared deviations between measured and calculated K((sigma) ). Four versions of minimization were considered successively: (1) only red wing, (2) only blue wing (3) both blue and red wings with 6 independent variables (C6 and C12), and (4) both wings with fixed C6. The calculated K((Delta) (sigma) ) are compared to the measured ones.
A modified TIP3P water potential for simulation with Ewald summation
NASA Astrophysics Data System (ADS)
Price, Daniel J.; Brooks, Charles L.
2004-11-01
The charges and Lennard-Jones parameters of the TIP3P water potential have been modified to improve its performance under the common condition for molecular dynamics simulations of using Ewald summation in lieu of relatively short nonbonded truncation schemes. These parameters were optimized under the condition that the hydrogen atoms do not have Lennard-Jones parameters, thus making the model independent of the combining rules used for the calculation of nonbonded, heteroatomic interaction energies, and limiting the number of Lennard-Jones calculations required. Under these conditions, this model provides accurate density (ρ=0.997 g/ml) and heat of vaporization (ΔHvap=10.53 kcal/mol) at 25 °C and 1 atm, but also provides improved structure in the second peak of the O-O radial distribution function and improved values for the dielectric constant (ɛ0=89) and the diffusion coefficient (D=4.0×10-5 cm2/s) relative to the original parametrization. Like the original parameterization, however, this model does not show a temperature density maximum. Several similar models are considered with the additional constraint of trying to match the performance of the optimized potentials for liquid simulation atom force field to that obtained when using the simulation conditions under which it was originally designed, but no model was entirely satisfactory in reproducing the relative difference in free energies of hydration between the model compounds, phenol and benzene. Finally, a model that incorporates a long-range correction for truncated Lennard-Jones interactions is presented, which provides a very accurate dielectric constant (ɛ0=76), however, the improvement in this estimate is on the same order as the uncertainty in the calculation.
Jakubov, Tim S; Mainwaring, David E
2007-03-15
A method for the evaluation of quantities that are experimentally inaccessible such as the surface tension at the solid-vacuum interface and the superficial tension of the fluid in contact with the solid is presented. The approach is based on consideration of an equilibrium of a fluid in solid capillary wherein a balance between surface and capillary forces has been replaced by conceptual alternative interfacial and centrifugal forces. This approach involves the simultaneous numerical solution one the special forms of the Gibbs equation for solid-fluid interface and a generalized Kelvin equation derived earlier. The latter equation takes into account interactions between the solid thick cylindrical wall and confined fluid, this body-body interaction potential has been primarily calculated using the Lennard-Jones (6-12) expression for the atom-atom pair potentials and expressed by hypergeometrical functions having good convergences. All numerical calculations shown here have been performed for the model graphite-argon system at 90 K. Finally, an analysis of the accuracy of the proposed method is considered.
Zhang, Minhua; Chen, Lihang; Yang, Huaming; Sha, Xijiang; Ma, Jing
2016-07-01
Gibbs ensemble Monte Carlo simulation with configurational bias was employed to study the vapor-liquid equilibrium (VLE) for pure acetic acid and for a mixture of acetic acid and ethylene. An improved united-atom force field for acetic acid based on a Lennard-Jones functional form was proposed. The Lennard-Jones well depth and size parameters for the carboxyl oxygen and hydroxyl oxygen were determined by fitting the interaction energies of acetic acid dimers to the Lennard-Jones potential function. Four different acetic acid dimers and the proportions of them were considered when the force field was optimized. It was found that the new optimized force field provides a reasonable description of the vapor-liquid phase equilibrium for pure acetic acid and for the mixture of acetic acid and ethylene. Accurate values were obtained for the saturated liquid density of the pure compound (average deviation: 0.84 %) and for the critical points. The new optimized force field demonstrated greater accuracy and reliability in calculations of the solubility of the mixture of acetic acid and ethylene as compared with the results obtained with the original TraPPE-UA force field.
Velaga, Srinath C; Anderson, Brian J
2014-01-16
Gas hydrate deposits are receiving increased attention as potential locations for CO2 sequestration, with CO2 replacing the methane that is recovered as an energy source. In this scenario, it is very important to correctly characterize the cage occupancies of CO2 to correctly assess the sequestration potential as well as the methane recoverability. In order to predict accurate cage occupancies, the guest–host interaction potential must be represented properly. Earlier, these potential parameters were obtained by fitting to experimental equilibrium data and these fitted parameters do not match with those obtained by second virial coefficient or gas viscosity data. Ab initio quantum mechanical calculations provide an independent means to directly obtain accurate intermolecular potentials. A potential energy surface (PES) between H2O and CO2 was computed at the MP2/aug-cc-pVTZ level and corrected for basis set superposition error (BSSE), an error caused due to the lower basis set, by using the half counterpoise method. Intermolecular potentials were obtained by fitting Exponential-6 and Lennard-Jones 6-12 models to the ab initio PES, correcting for many-body interactions. We denoted this model as the “VAS” model. Reference parameters for structure I carbon dioxide hydrate were calculated using the VAS model (site–site ab initio intermolecular potentials) as Δμ(w)(0) = 1206 ± 2 J/mol and ΔH(w)(0) = 1260 ± 12 J/mol. With these reference parameters and the VAS model, pure CO2 hydrate equilibrium pressure was predicted with an average absolute deviation of less than 3.2% from the experimental data. Predictions of the small cage occupancy ranged from 32 to 51%, and the large cage is more than 98% occupied. The intermolecular potentials were also tested by calculating the pure CO2 density and diffusion of CO2 in water using molecular dynamics simulations.
Velocity autocorrelation functions of Lennard-Jones fluids
NASA Technical Reports Server (NTRS)
Tsang, T.; Tang, H.
1977-01-01
By a self-consistent procedure, the velocity autocorrelation functions of both liquid and gaseous argon have been calculated without introducing any arbitrary parameters. The results are in satisfactory agreement with computer experiments. The correlation functions are primarily determined by the nearest-neighbor coordination. Because of the strong hard-core repulsion, the behaviors are more vibratory and damp out quickly at high densities and are more diffusive at lower densities.
Chemical potential calculations in dense liquids using metadynamics
NASA Astrophysics Data System (ADS)
Perego, C.; Giberti, F.; Parrinello, M.
2016-10-01
The calculation of chemical potential has traditionally been a challenge in atomistic simulations. One of the most used approaches is Widom's insertion method in which the chemical potential is calculated by periodically attempting to insert an extra particle in the system. In dense systems this method fails since the insertion probability is very low. In this paper we show that in a homogeneous fluid the insertion probability can be increased using metadynamics. We test our method on a supercooled high density binary Lennard-Jones fluid. We find that we can obtain efficiently converged results even when Widom's method fails.
NASA Astrophysics Data System (ADS)
Sadeghi, F.; Ansari, R.; Darvizeh, M.
2016-06-01
In this research, a continuum-based model is presented to explore potential energy, force distribution and oscillatory motion of ions, and in particular chloride ion, inside carbon nanotubes (CNTs) decorated by functional groups at two ends. To perform this, van der Waals (vdW) interactions between ion and nanotube are modeled by the 6-12 Lennard-Jones (LJ) potential, whereas the electrostatic interactions between ion and functional groups are modeled by the Coulomb potential and the total interactions are analytically derived by summing the vdW and electrostatic interactions. Making the assumption that carbon atoms and charge of functional groups are all uniformly distributed over the nanotube surface and the two ends of nanotube, respectively, a continuum approach is utilized to evaluate the related interactions. Based on the actual force distribution, the equation of motion is also solved numerically to arrive at the time history of displacement and velocity of inner core. With respect to the proposed formulations, comprehensive studies on the variations of potential energy and force distribution are carried out by varying functional group charge and nanotube length. Moreover, the effects of these parameters together with initial conditions on the oscillatory behavior of system are studied and discussed in detail. It is found out that chloride ion escapes more easily from negatively charged CNTs which is followed by uncharged and positively charged ones. It is further shown that the presence of functional groups leads to enhancing the operating frequency of such oscillatory systems especially when the electric charges of ion and functional groups have different signs.
ON THE EQUILIBRIUM STRUCTURE AND THERMODYNAMICS OF SIMPLE LIQUIDS
The equilibrium structure and thermodynamics of a simple liquid is discussed. The particular system considered in our calculations is the Lennard ... Jones liquid in which the intermolecular interaction is the pairwise additive 6- 12 potential. The potential is separated into two parts, a reference
The second virial coefficient and critical point behavior of the Mie Potential
NASA Astrophysics Data System (ADS)
Heyes, D. M.; Rickayzen, G.; Pieprzyk, S.; Brańka, A. C.
2016-08-01
Aspects of the second virial coefficient, b2, of the Mie m : n potential are investigated. The Boyle temperature, T0, is shown to decay monotonically with increasing m and n, while the maximum temperature, Tmax, exhibits a minimum at a value of m which increases as n increases. For the 2n : n special case T0 tends to zero and Tmax approaches the value of 7.81 in the n → ∞ limit which is in quantitative agreement with the expressions derived in Rickayzen and Heyes [J. Chem. Phys. 126, 114504 (2007)] in which it was shown that the 2n : n potential in the n → ∞ limit approaches Baxter's sticky-sphere model. The same approach is used to estimate the n - dependent critical temperature of the 2n : n potential in the large n limit. The ratio of T0 to the critical temperature tends to unity in the infinite n limit for the 2n : n potential. The rate of convergence of expansions of b2 about the high temperature limit is investigated, and they are shown to converge rapidly even at quite low temperatures (e.g., 0.05). In contrast, a low temperature expansion of the Lennard-Jones 12 : 6 potential is shown to be an asymptotic series. Two formulas that resolve b2 into its repulsive and attractive terms are derived. The convergence at high temperature of the Lennard-Jones b2 to the m = 12 inverse power value is slow (e.g., requiring T ≃ 104 just to attain two significant figure accuracy). The behavior of b2 of the ∞ : n and the Sutherland potential special case, n = 6, is explored. By fitting to the exact b2 values, a semiempirical formula is derived for the temperature dependence of b2 of the Lennard-Jones potential which has the correct high and low temperature limits.
The second virial coefficient and critical point behavior of the Mie Potential.
Heyes, D M; Rickayzen, G; Pieprzyk, S; Brańka, A C
2016-08-28
Aspects of the second virial coefficient, b2, of the Mie m : n potential are investigated. The Boyle temperature, T0, is shown to decay monotonically with increasing m and n, while the maximum temperature, Tmax, exhibits a minimum at a value of m which increases as n increases. For the 2n : n special case T0 tends to zero and Tmax approaches the value of 7.81 in the n → ∞ limit which is in quantitative agreement with the expressions derived in Rickayzen and Heyes [J. Chem. Phys. 126, 114504 (2007)] in which it was shown that the 2n : n potential in the n → ∞ limit approaches Baxter's sticky-sphere model. The same approach is used to estimate the n - dependent critical temperature of the 2n : n potential in the large n limit. The ratio of T0 to the critical temperature tends to unity in the infinite n limit for the 2n : n potential. The rate of convergence of expansions of b2 about the high temperature limit is investigated, and they are shown to converge rapidly even at quite low temperatures (e.g., 0.05). In contrast, a low temperature expansion of the Lennard-Jones 12 : 6 potential is shown to be an asymptotic series. Two formulas that resolve b2 into its repulsive and attractive terms are derived. The convergence at high temperature of the Lennard-Jones b2 to the m = 12 inverse power value is slow (e.g., requiring T ≃ 10(4) just to attain two significant figure accuracy). The behavior of b2 of the ∞ : n and the Sutherland potential special case, n = 6, is explored. By fitting to the exact b2 values, a semiempirical formula is derived for the temperature dependence of b2 of the Lennard-Jones potential which has the correct high and low temperature limits.
INTERACTION POTENTIALS FROM THE VELOCITY DEPENDENCE OF TOTAL ATOM-ATOM SCATTERING CROSS SECTIONS,
Lennard - Jones potential, the depth of the interatomic potential well, epsilon and the interatomic separation at the zero of potential energy, sigma was obtained from these measurements. From the experimental epsilon and sigma, a theoretical Q(V) was computed using a partial wave analysis. Good agreement with the experimental data was obtained. In this paper, K-Kr and Li-He are discussed which were studied in the ’low’ velocity region and in the ’’high’’ velocity region, respectively. It is shown that epsilon and sigma may be unambiguously
Accurate calculation of second virial coefficient of the Exp-6 potential and its application
NASA Astrophysics Data System (ADS)
Mamedov, B. A.; Somuncu, E.
2015-02-01
In this study, a new approach to calculate the second virial coefficient of the Exp-6 potential is proposed. Over a wide temperature range, the calculated results of the second virial coefficient determined from Exp-6 potential are comparable with the calculations of second virial coefficient over Lennard-Jones (12-6) potential. As an example of application, the formulas obtained for second virial coefficient are calculated for molecules Kr,Xe,N2,Hg,CH4 and C2H6. The obtained results are in good agreement with the data available in the literature.
A Computational Study of Rare Gas Clusters: Stepping Stones to the Solid State
ERIC Educational Resources Information Center
Glendening, Eric D.; Halpern, Arthur M.
2012-01-01
An upper-level undergraduate or beginning graduate project is described in which students obtain the Lennard-Jones 6-12 potential parameters for Ne[subscript 2] and Ar[subscript 2] from ab initio calculations and use the results to express pairwise interactions between the atoms in clusters containing up to N = 60 atoms. The students use simulated…
THE VISCOSITY OF HELIUM-CESIUM MIXTURES,
The viscosities of helium-cesium mixtures having mole fractions of cesium from zero to unity were evaluated using a Lennard - Jones 6-12 interaction potential for all encounters in the Enskog Chapman expressions for the viscosity of a binary mixture. (Author)
1989-06-01
Lennard - Jones potential energy 6-12-1 atom-atom calculation is used to characterize the structures of these clusters. Experiments and calculations demonstrate that the four different solvent molecules studies can form stable clusters with allylbenzene by coordinating to the Pi-system of allyl substituent in addition to that of the aromatic
PATH INTEGRAL CALCULATION OF THE TWOPARTICLE SLATER SUM FOR HE4,
Lennard - Jones 6-12 potential has been used to describe the interaction. Contributions from exchange were found negligible at 5K and above. Comparisons with the WignerKirkwood expansion are made. The second virial coefficients derived from these results are within two per cent or three per cent of the results obtained from the usual phase shift calculation.
NASA Astrophysics Data System (ADS)
Diraison, M.; Millie, P.; Pommeret, S.; Gustavsson, T.; Mialocq, J.-Cl
1998-01-01
A molecular dynamics simulation study of a coumarin 1 molecule solvated in acetonitrile, in its S 0 and S 1 electronic states, is presented. Three solute-solvent interaction potentials, all containing the same Lennard-Jones component but different electrostatic interactions, have been considered. The structure of the solvent around the large dye solute strongly depends on the electrostatic solute-solvent potential, illustrating the crucial role of the local electric field. An accurate description of the charge distribution of the solute is therefore necessary to describe correctly the solute-solvent structure and the solvation energy.
Note: Modification of the Gay-Berne potential for improved accuracy and speed
NASA Astrophysics Data System (ADS)
Persson, Rasmus A. X.
2012-06-01
A modification of the Gay-Berne (GB) potential is proposed which is about 10% to 20% more speed efficient and statistically more accurate in reproducing the energy of interaction of two linear Lennard-Jones tetratomics when averaged over all orientations. For the special cases of end-to-end and side-by-side configurations, the new potential is equivalent to the GB one. A simple generalization to dissimilar particles of D∞h symmetry is presented but does not retain the superior agreement with respect to its GB counterpart, except at close range.
Revised charge equilibration potential for liquid alkanes.
Davis, Joseph E; Warren, G Lee; Patel, Sandeep
2008-07-17
We present a revised liquid alkane force field based on the charge equilibration formalism for incorporating electrostatic nonadditive effects arising from local polarization. The model is a revision of earlier work by Patel and Brooks, specifically addressing deficiencies in the dihedral potential, electrostatic, and Lennard-Jones (van der Waals) parameters of the force field. We discuss refinement of the alkane backbone torsion potential to match high-level ab initio relative conformational energetics for pentane, hexane, and heptane. We further discuss refinement of the electrostatic and Lennard-Jones (van der Waals) parameters to reproduce the experimental polarizability, liquid density, and vaporization enthalpy of hexane. Finally, we calculate bulk liquid properties including densities, vaporization enthalpies, self-diffusion constants, isothermal compressibilities, constant pressure heat capacities, and NMR T 1 relaxation times for a series of linear alkanes ranging from hexane to pentadecane based on the current revised model. We also compute free energies of hydration for pentane, hexane, and heptane. The revised force field offers a significantly improved overall description of these properties relative to the original parametrization. The current alkane force field represents a platform for ongoing development of a CHARMM (Chemistry at Harvard Molecular Mechanics) polarizable force field for lipids and integral membrane proteins.
Sumpter, Bobby G; Sherrill, David; Sinnokrot, Mutasem O; Marshall, Michael S.; Hohenstein, Edward G.; Walker, Ross; Gould, Ian R
2009-01-01
Several popular force fields, namely, CHARMM, AMBER, OPLS-AA, and MM3, have been tested for their ability to reproduce highly accurate quantum mechani- cal potential energy curves for noncovalent interactions in the benzene dimer, the benzene-CH4 complex, and the benzene-H2S complex. All of the force fields are semi-quantitatively correct, but none of them is consistently reliable quantitatively. Re-optimization of Lennard-Jones parameters and symmetry-adapted perturbation theory analysis for the benzene dimer suggests that better agreement cannot be expected unless more flexible functional forms (particularly for the electrostatic contributions)are employed for the empirical force fields.
The importance of accurate interaction potentials in the melting of argon nanoclusters
NASA Astrophysics Data System (ADS)
Pahl, E.; Calvo, F.; Schwerdtfeger, P.
The melting temperatures of argon clusters ArN (N = 13, 55, 147, 309, 561, and 923) and of bulk argon have been obtained from exchange Monte Carlo simulations and are compared using different two-body interaction potentials, namely the standard Lennard-Jones (LJ), Aziz and extended Lennard-Jones (ELJ) potentials. The latter potential has many advantages: while maintaining the computational efficiency of the commonly used LJ potential, it is as accurate as the Aziz potential but the computer time scales more favorably with increasing cluster size. By applying the ELJ form and extrapolating the cluster data to the infinite system, we are able to extract the melting point of argon already in good agreement with experimental measurements. By considering the additional Axilrod-Teller three-body contribution as well, we calculate a melting temperature of T meltELJ = 84.7 K compared to the experimental value of T meltexp = 83.85 K, whereas the LJ potential underestimates the melting point by more than 7 K. Thus melting temperatures within 1 K accuracy are now feasible.
Solid phase stability of a double-minimum interaction potential system
Suematsu, Ayumi; Yoshimori, Akira Saiki, Masafumi; Matsui, Jun; Odagaki, Takashi
2014-06-28
We study phase stability of a system with double-minimum interaction potential in a wide range of parameters by a thermodynamic perturbation theory. The present double-minimum potential is the Lennard-Jones-Gauss potential, which has a Gaussian pocket as well as a standard Lennard-Jones minimum. As a function of the depth and position of the Gaussian pocket in the potential, we determine the coexistence pressure of crystals (fcc and bcc). We show that the fcc crystallizes even at zero pressure when the position of the Gaussian pocket is coincident with the first or third nearest neighbor site of the fcc crystal. The bcc crystal is more stable than the fcc crystal when the position of the Gaussian pocket is coincident with the second nearest neighbor sites of the bcc crystal. The stable crystal structure is determined by the position of the Gaussian pocket. These results show that we can control the stability of the solid phase by tuning the potential function.
Solid phase stability of a double-minimum interaction potential system
NASA Astrophysics Data System (ADS)
Suematsu, Ayumi; Yoshimori, Akira; Saiki, Masafumi; Matsui, Jun; Odagaki, Takashi
2014-06-01
We study phase stability of a system with double-minimum interaction potential in a wide range of parameters by a thermodynamic perturbation theory. The present double-minimum potential is the Lennard-Jones-Gauss potential, which has a Gaussian pocket as well as a standard Lennard-Jones minimum. As a function of the depth and position of the Gaussian pocket in the potential, we determine the coexistence pressure of crystals (fcc and bcc). We show that the fcc crystallizes even at zero pressure when the position of the Gaussian pocket is coincident with the first or third nearest neighbor site of the fcc crystal. The bcc crystal is more stable than the fcc crystal when the position of the Gaussian pocket is coincident with the second nearest neighbor sites of the bcc crystal. The stable crystal structure is determined by the position of the Gaussian pocket. These results show that we can control the stability of the solid phase by tuning the potential function.
Graph-based analysis of kinetics on multidimensional potential-energy surfaces.
Okushima, T; Niiyama, T; Ikeda, K S; Shimizu, Y
2009-09-01
The aim of this paper is twofold: one is to give a detailed description of an alternative graph-based analysis method, which we call saddle connectivity graph, for analyzing the global topography and the dynamical properties of many-dimensional potential-energy landscapes and the other is to give examples of applications of this method in the analysis of the kinetics of realistic systems. A Dijkstra-type shortest path algorithm is proposed to extract dynamically dominant transition pathways by kinetically defining transition costs. The applicability of this approach is first confirmed by an illustrative example of a low-dimensional random potential. We then show that a coarse-graining procedure tailored for saddle connectivity graphs can be used to obtain the kinetic properties of 13- and 38-atom Lennard-Jones clusters. The coarse-graining method not only reduces the complexity of the graphs, but also, with iterative use, reveals a self-similar hierarchical structure in these clusters. We also propose that the self-similarity is common to many-atom Lennard-Jones clusters.
NASA Astrophysics Data System (ADS)
Nategholeslam, Mostafa; Holland, Bryan W.; Gray, C. G.; Tomberli, Bruno
2011-02-01
We present a method that enables the use of the forward-reverse (FR) method of Kosztin on a broader range of problems in soft matter physics. Our method, which we call the oscillating forward-reverse (OFR) method, adds an oscillatory steering potential to the constant velocity steering potential of the FR method. This enables the calculation of the potential of mean force (PMF) in a single unidirectional oscillatory drift, rather than multiple drifts in both directions as required by the FR method. By following small forward perturbations with small reverse perturbations, the OFR method is able to generate a piecewise reverse path that follows the piecewise forward path much more closely than any practical set of paths used in the FR method. We calculate the PMF for four different systems: a dragged Brownian oscillator, a pair of atoms in a Lennard-Jones liquid, a Na+-Cl- ion pair in an aqueous solution, and a deca-alanine molecule being stretched in an implicit solvent. In all cases, the PMF results are in good agreement with those published previously using various other methods, and, to our knowledge, we give for the first time PMFs calculated by nonequilibrium methods for the Lennard-Jones and Na+-Cl- systems.
NASA Astrophysics Data System (ADS)
Nitschke, Naomi; Atkovska, Kalina; Hub, Jochen S.
2016-09-01
Molecular dynamics simulations are capable of predicting the permeability of lipid membranes for drug-like solutes, but the calculations have remained prohibitively expensive for high-throughput studies. Here, we analyze simple measures for accelerating potential of mean force (PMF) calculations of membrane permeation, namely, (i) using smaller simulation systems, (ii) simulating multiple solutes per system, and (iii) using shorter cutoffs for the Lennard-Jones interactions. We find that PMFs for membrane permeation are remarkably robust against alterations of such parameters, suggesting that accurate PMF calculations are possible at strongly reduced computational cost. In addition, we evaluated the influence of the definition of the membrane center of mass (COM), used to define the transmembrane reaction coordinate. Membrane-COM definitions based on all lipid atoms lead to artifacts due to undulations and, consequently, to PMFs dependent on membrane size. In contrast, COM definitions based on a cylinder around the solute lead to size-independent PMFs, down to systems of only 16 lipids per monolayer. In summary, compared to popular setups that simulate a single solute in a membrane of 128 lipids with a Lennard-Jones cutoff of 1.2 nm, the measures applied here yield a speedup in sampling by factor of ˜40, without reducing the accuracy of the calculated PMF.
Analysis of Atomistic/Continuum Coupling Using Meshless Methods
2008-12-01
potential and a non-linear Lennard - Jones potential, where the harmonic potential is given as: ( )20,2 1 abab H ab rrk −=φ (19) where k is a...constant and r0 is the zero potential distance between two atoms. The Lennard - Jones potential is defined as...analysis shown in figure 2 using a Lennard - Jones potential. The results are shown in figure 4. The results colaberate the above example with
Studying Soft Materials with Soft Potentials -- Fast Monte Carlo Simulations
NASA Astrophysics Data System (ADS)
Zong, Jing; Zhang, Xinghua; Zhang, Pengfei; Yin, Yuhua; Li, Baohui; Wang, Qiang
2010-03-01
The basic idea of fast Monte Carlo (FMC) simulationsfootnotetextQ. Wang and Y. Yin, J. Chem. Phys., 130, 104903 (2009); Q. Wang, Soft Matter, 5, 4564 (2009). is to use soft potentials that allow particle overlapping, instead of hard repulsions (e.g., the Lennard-Jones potential in continuum or the self- and mutual-avoiding walks on a lattice) used in conventional molecular simulations. This gives orders of magnitude faster/better sampling of configurational space. In addition, since soft potentials are commonly used in polymer field theories, using the same Hamiltonian in both FMC simulations and the theories thus allow stringent test of the latter, without any parameter-fitting, to unambiguously and quantitatively reveal the consequences of theoretical approximations. Here we use several systems, ranging from small-molecule liquid crystals to homopolymer solutions and brushes, to demonstrate these great advantages of FMC simulations performed both in continuum and on a lattice.
Fast Off-Lattice Monte Carlo Simulations with Soft Potentials
NASA Astrophysics Data System (ADS)
Zong, Jing; Yang, Delian; Yin, Yuhua; Zhang, Xinghua; Wang, Qiang (David)
2011-03-01
Fast off-lattice Monte Carlo simulations with soft repulsive potentials that allow particle overlapping give orders of magnitude faster/better sampling of the configurational space than conventional molecular simulations with hard-core repulsions (such as the hard-sphere or Lennard-Jones repulsion). Here we present our fast off-lattice Monte Carlo simulations ranging from small-molecule soft spheres and liquid crystals to polymeric systems including homopolymers and rod-coil diblock copolymers. The simulation results are compared with various theories based on the same Hamiltonian as in the simulations (thus without any parameter-fitting) to quantitatively reveal the consequences of approximations in these theories. Q. Wang and Y. Yin, J. Chem. Phys., 130, 104903 (2009).
Near-threshold quantization for potentials with inverse-cube tails
Mueller, Tim-Oliver; Friedrich, Harald
2011-02-15
For potential wells with long-range attractive tails proportional to -1/r{sup 3}, as occur in the resonant dipole-dipole interaction in homonuclear alkali-metal dimers, we present a highly accurate analytical expression for the tail contribution to the quantization function F(E). This quantization function determines the near-threshold bound-state energies via the quantization rule n{sub th}-n=F(E{sub n}). The performance of the quantization function derived in this paper is demonstrated by applying it to a model Lennard-Jones potential and to vibrational bound-state spectra of sodium dimers (Na{sub 2}). These results are compared with those obtained via the semiclassical LeRoy-Bernstein formula which neglects quantum effects that are important in the near-threshold regime.
Numerical solution of the linearized Boltzmann equation for an arbitrary intermolecular potential
Sharipov, Felix Bertoldo, Guilherme
2009-05-20
A numerical procedure to solve the linearized Boltzmann equation with an arbitrary intermolecular potential by the discrete velocity method is elaborated. The equation is written in terms of the kernel, which contains the differential cross section and represents a singularity. As an example, the Lennard-Jones potential is used and the corresponding differential cross section is calculated and tabulated. Then, the kernel is calculated so that to overcome its singularity. Once, the kernel is known and stored it can be used for many kinds of gas flows. In order to test the method, the transport coefficients, i.e. thermal conductivity and viscosity for all noble gases, are calculated and compared with those obtained by the variational method using the Sonine polynomials expansion. The fine agreement between the results obtained by the two different methods shows the feasibility of application of the proposed technique to calculate rarefied gas flows over the whole range of the Knudsen number.
Mie potentials for phase equilibria calculations: application to alkanes and perfluoroalkanes.
Potoff, Jeffrey J; Bernard-Brunel, Damien A
2009-11-05
Transferable united-atom force fields, based on n - 6 Lennard-Jones potentials, are presented for normal alkanes and perfluorocarbons. It is shown that by varying the repulsive exponent the range of the potential can be altered, leading to improved predictions of vapor pressures while also reproducing saturated liquid densities to high accuracy. Histogram-reweighting Monte Carlo simulations in the grand canonical ensemble are used to determine the vapor liquid coexistence curves, vapor pressures, heats of vaporization, and critical points for normal alkanes methane through tetradecane, and perfluorocarbons perfluoromethane through perfluorooctane. For all molecules studied, saturated liquid densities are reproduced to within 1% of experiment. Vapor pressures for normal alkanes and perfluorocarbons were predicted to within 3% and 6% of experiment, respectively. Calculations performed for binary mixture vapor-liquid equilibria for propane + pentane show excellent agreement with experiment, while slight deviations are observed for the ethane + perfluoroethane mixture.
Baer, M.R.; Hobbs, M.L.; McGee, B.C.
1998-11-03
Exponential-13,6 (EXP-13,6) potential pammeters for 750 gases composed of 48 elements were determined and assembled in a database, referred to as the JCZS database, for use with the Jacobs Cowperthwaite Zwisler equation of state (JCZ3-EOS)~l) The EXP- 13,6 force constants were obtained by using literature values of Lennard-Jones (LJ) potential functions, by using corresponding states (CS) theory, by matching pure liquid shock Hugoniot data, and by using molecular volume to determine the approach radii with the well depth estimated from high-pressure isen- tropes. The JCZS database was used to accurately predict detonation velocity, pressure, and temperature for 50 dif- 3 Accurate predictions were also ferent explosives with initial densities ranging from 0.25 glcm3 to 1.97 g/cm . obtained for pure liquid shock Hugoniots, static properties of nitrogen, and gas detonations at high initial pressures.
Zhang, Hui; Sun, Cheng H; Li, Feng; Li, Hong X; Cheng, Hui M
2006-05-18
The potential energies of van der Waals interactions between two multiwalled carbon nanotubes (MWNTs) as well as two carbon nanoparticles (CNPs) were calculated and compared on the basis of the continuum Lennard-Jones model. The well depth of the potential is 1 order of magnitude higher for MWNTs than for CNPs, indicating that MWNTs and CNPs can be separated from each other through polymer-induced steric stabilization. On the basis of this prediction, a novel method for the purification of MWNTs was proposed. The method involves a high-temperature annealing (2600 degrees C, 1 h) followed by an extraction treatment with a selected dispersing agent. While the annealing process evaporates the metal particles, the extraction treatment removes CNPs. The quality of the nanotubes obtained after purification was examined by laser Raman, thermogravimetric analysis, and electron microscopy observations.
A multiscale transport model for Lennard-Jones binary mixtures based on interfacial friction.
Bhadauria, Ravi; Aluru, N R
2016-08-21
We propose a one-dimensional isothermal hydrodynamic transport model for non-reacting binary mixtures in slit shaped nanochannels. The coupled species momentum equations contain viscous dissipation and interspecies friction term of Maxwell-Stefan form. Species partial viscosity variations in the confinement are modeled using the van der Waals one fluid approximation and the local average density method. Species specific macroscopic friction coefficient based Robin boundary conditions are provided to capture the species wall slip effects. The value of this friction coefficient is computed using a species specific generalized Langevin formulation. Gravity driven flow of methane-hydrogen and methane-argon mixtures confined between graphene slit shaped nanochannels are considered as examples. The proposed model yields good quantitative agreement with the velocity profiles obtained from the non-equilibrium molecular dynamics simulations. The mixtures considered are observed to behave as single species pseudo fluid, with the interfacial friction displaying linear dependence on molar composition of the mixture. The results also indicate that the different species have different slip lengths, which remain unchanged with the channel width.
A multiscale transport model for Lennard-Jones binary mixtures based on interfacial friction
NASA Astrophysics Data System (ADS)
Bhadauria, Ravi; Aluru, N. R.
2016-08-01
We propose a one-dimensional isothermal hydrodynamic transport model for non-reacting binary mixtures in slit shaped nanochannels. The coupled species momentum equations contain viscous dissipation and interspecies friction term of Maxwell-Stefan form. Species partial viscosity variations in the confinement are modeled using the van der Waals one fluid approximation and the local average density method. Species specific macroscopic friction coefficient based Robin boundary conditions are provided to capture the species wall slip effects. The value of this friction coefficient is computed using a species specific generalized Langevin formulation. Gravity driven flow of methane-hydrogen and methane-argon mixtures confined between graphene slit shaped nanochannels are considered as examples. The proposed model yields good quantitative agreement with the velocity profiles obtained from the non-equilibrium molecular dynamics simulations. The mixtures considered are observed to behave as single species pseudo fluid, with the interfacial friction displaying linear dependence on molar composition of the mixture. The results also indicate that the different species have different slip lengths, which remain unchanged with the channel width.
Interplay between crystallization and glass transition in binary Lennard-Jones mixtures
NASA Astrophysics Data System (ADS)
Banerjee, Atreyee; Chakrabarty, Suman; Bhattacharyya, Sarika Maitra
2013-09-01
In this work we explore the interplay between crystallization and glass transition in different binary mixtures by changing their inter-species interaction length and also the composition. We find that only those systems which form bcc crystal in the equimolar mixture and whose global structure for larger xA (xA = 0.6, where xA is the mole fraction of the bigger particles) is a mixed fcc + bcc phase, do not crystallize at this higher composition. However, the systems whose equimolar structure is a variant of fcc (NaCl type crystal) and whose global structure at larger xA is a mixed NaCl + fcc phase, crystallize easily to this mixed structure. We find that the stability against crystallization of this "bcc zone" is due to the frustration between the locally preferred structure (LPS) and the mixed bcc + fcc crystal. Our study suggests that when the global structure is a mixed crystal where a single species contributes to both the crystal forms and where the two crystal forms have large difference in some order parameter related to that species then this induces frustration between the LPS and the global structure. This frustration makes the systems good glass former. When xA is further increased (0.70 ⩽ xA < 0.90) the systems show a tendency towards mixed fcc crystal formation. However, the "bcc zone" even for this higher composition is found to be sitting at the bottom of a V shaped phase diagram formed by two different variants of the fcc crystal structure, leading to its stability against crystallization.
Interplay between crystallization and glass transition in binary Lennard-Jones mixtures.
Banerjee, Atreyee; Chakrabarty, Suman; Bhattacharyya, Sarika Maitra
2013-09-14
In this work we explore the interplay between crystallization and glass transition in different binary mixtures by changing their inter-species interaction length and also the composition. We find that only those systems which form bcc crystal in the equimolar mixture and whose global structure for larger x(A) (x(A) = 0.6, where x(A) is the mole fraction of the bigger particles) is a mixed fcc + bcc phase, do not crystallize at this higher composition. However, the systems whose equimolar structure is a variant of fcc (NaCl type crystal) and whose global structure at larger x(A) is a mixed NaCl + fcc phase, crystallize easily to this mixed structure. We find that the stability against crystallization of this "bcc zone" is due to the frustration between the locally preferred structure (LPS) and the mixed bcc + fcc crystal. Our study suggests that when the global structure is a mixed crystal where a single species contributes to both the crystal forms and where the two crystal forms have large difference in some order parameter related to that species then this induces frustration between the LPS and the global structure. This frustration makes the systems good glass former. When x(A) is further increased (0.70 ≤ x(A) < 0.90) the systems show a tendency towards mixed fcc crystal formation. However, the "bcc zone" even for this higher composition is found to be sitting at the bottom of a V shaped phase diagram formed by two different variants of the fcc crystal structure, leading to its stability against crystallization.
NASA Astrophysics Data System (ADS)
Tsuji, Tetsuro; Iseki, Hirotaka; Hanasaki, Itsuo; Kawano, Satoyuki
2016-11-01
Thermophoresis of a nano particle in a fluid is investigated using molecular dynamics simulation. In order to elucidate effective factors on the characteristics of thermophoresis, simple models for both the fluid and the nano particle are considered, namely, the surrounding fluid consists of Lennard-Jones (LJ) particles and the model nano particle is a cluster consisting of several tens of LJ particles. Interaction between the fluid particle and the model nano particle is described by the LJ interaction potential or repulsive interaction potential with the Lorentz-Berthelot mixing rule. As a preliminary result, the effect of mass on thermophoretic force acting on the model nano particle is investigated for both interaction potentials.
High Temperature Properties of the Fcc Metallic Crystals in the Anharmonic Approximation
2001-01-01
interactions were approximated by the Morse and Lennard - Jones pair potential functions. Unfortunately, the parameters of these potentials were...Au) we take as a model of interatomic interactions the (alpha,m) Buckingham, (n,m) Lennard - Jones and (alpha,beta) Morse pair potentials with the
Molecular Dynamics of Propellant Gases. Part 2,
motion of nitrogen gas molecules can be described using the laws of classical mechanics. Lennard - Jones and exponential-6 potentials are used to...of state and perturbation theory. It is found that the Lennard - Jones potential works well at 3000K and that the Hansen perturbation theory could become an effective method for calculating the pressure for real gases.
WICK,COLLIN D.; MARTIN,MARCUS G.; SIEPMANN,J. ILJA
2000-07-12
The Transferable Potentials for Phase Equilibria-United Atom (TraPPE-UA) force field for hydrocarbons is extended to alkenes and alkylbenzenes by introducing the following pseudo-atoms: CH{sub 2}(sp{sup 2}), CH(sp{sup 2}), CH(aro), R-C(aro) for the link to aliphatic side chains, and C(aro) for the link of two benzene rings. In this united-atom force field, the nonbonded interactions of the hydrocarbon pseudo-atoms are solely governed by Lennard-Jones 12-6 potentials, and the Lennard-Jones well depth and size parameters for the new pseudo-atoms were determined by fitting to the single-component vapor-liquid phase equilibria of a few selected model compounds. Configurational-bias Monte Carlo simulations in the NVT version of the Gibbs ensemble were carried out to calculate the single-component vapor-liquid coexistence curves for ethene, propene, 1-butene, trans- and cis-2-butene. 2-methylpropene, 1,5-hexadiene, 1-octene, benzene, toluene, ethylbenzene, propylbenzene, isopropylbenzene, o-, m-, and p-xylene, and naphthalene. The phase diagrams for the binary mixtures of (supercritical) ethene/n-heptane and benzene/n-pentane were determined from simulations in the NpT Gibbs ensemble. Although the TraPPE-UA force field is rather simple and makes use of relatively few different pseudo-atoms, its performance, as judged by comparisons to other popular force fields and available experimental data, is very satisfactory.
ON THE EQUILIBRIUM STRUCTURE OF SIMPLE LIQUIDS
It is shown that the repulsive (not merely the positive) portion of the Lennard - Jones potential quantitatively dominates the equilibrium structure of...the Lennard - Jones liquid. A simple and accurate approximation for the radial distribution function at high densities is presented.
Calculation of the Lattice Frequencies of Alpha and Beta Oxygen.
The optically active lattice frequencies of alpha- and beta-O2 have been calculated using an atom-atom Lennard - Jones potential, with and without the...agreement is obtained between the observed librational frequency and its temperature dependence in beta-O2 and the results calculated using the Lennard - Jones potential... Lennard - Jones atom-atom interaction is a satisfactory model for the potential function in solid oxygen, provided that the packing is such that electronic overlap effects are small. (Author)
Lennard - Jones 6-12 potential with the assumption that the solute interacts with a hard core studded with H atoms. The functional forms of (Gibbs energy) = (heat of solution) - T(entropy of solution) for He, N2, and Ar in symmetrical dimethylhydrazine have been obtained from such correlations, and the method is shown to be useful for similar gas-liquid systems. It is shown that (a) the changes in the solubilities follow the changes in the dipole moments of liquids and (b) the entropy of solution varies linearly with the logarithm of mol fractions of solutes in
NASA Technical Reports Server (NTRS)
Silvaggio, P. M.; Goorvitch, D.; Boese, R. W.
1981-01-01
A theoretical fit has been made to our laboratory measurements of the 2-0 collisionally induced H2 absorption band for temperatures of 122 and 273.3 K and at a density of 20 amagats. A Lennard-Jones 6-12 intermolecular potential and a Birnbaum-Cohen line profile have been used. The fit resulted in a chi-square of 0.2%. Line widths have also been derived as a function of temperature. The lifetimes of the states have been calculated.
NASA Technical Reports Server (NTRS)
Goorvitch, D.; Silvaggio, P. M.; Boese, R. W.
1981-01-01
A theoretical fit has been made to laboratory measurements of the 1-0 collisionally induced H2 absorption band over a temperature range of 100-273 K and for densities up to 22 amagats. Both the Birnbaum-Cohen and the MacTaggert-Hunt line shape profiles were used. In addition, an intermolecular potential of either a Lennard-Jones 6-12 or a Morse-spline-van der Waals has been used for each line shape. The best fit resulted in a chi-square of 5%. Line widths have also been derived as a function of temperature. The lifetimes of the states were calculated.
A new shared-memory programming paradigm for molecular dynamics simulations on the Intel Paragon
D`Azevedo, E.F.; Romine, C.H.
1994-12-01
This report describes the use of shared memory emulation with DOLIB (Distributed Object Library) to simplify parallel programming on the Intel Paragon. A molecular dynamics application is used as an example to illustrate the use of the DOLIB shared memory library. SOTON-PAR, a parallel molecular dynamics code with explicit message-passing using a Lennard-Jones 6-12 potential, is rewritten using DOLIB primitives. The resulting code has no explicit message primitives and resembles a serial code. The new code can perform dynamic load balancing and achieves better performance than the original parallel code with explicit message-passing.
An efficient fully atomistic potential model for dense fluid methane
NASA Astrophysics Data System (ADS)
Jiang, Chuntao; Ouyang, Jie; Zhuang, Xin; Wang, Lihua; Li, Wuming
2016-08-01
A fully atomistic model aimed to obtain a general purpose model for the dense fluid methane is presented. The new optimized potential for liquid simulation (OPLS) model is a rigid five site model which consists of five fixed point charges and five Lennard-Jones centers. The parameters in the potential model are determined by a fit of the experimental data of dense fluid methane using molecular dynamics simulation. The radial distribution function and the diffusion coefficient are successfully calculated for dense fluid methane at various state points. The simulated results are in good agreement with the available experimental data shown in literature. Moreover, the distribution of mean number hydrogen bonds and the distribution of pair-energy are analyzed, which are obtained from the new model and other five reference potential models. Furthermore, the space-time correlation functions for dense fluid methane are also discussed. All the numerical results demonstrate that the new OPLS model could be well utilized to investigate the dense fluid methane.
Computer simulation of acetonitrile and methanol with ab initio-based pair potentials
NASA Astrophysics Data System (ADS)
Hloucha, M.; Sum, A. K.; Sandler, S. I.
2000-10-01
This study address the adequacy of ab initio pair interaction energy potentials for the prediction of macroscopic properties. Recently, Bukowski et al. [J. Phys. Chem. A 103, 7322 (1999)] performed a comprehensive study of the potential energy surfaces for several pairs of molecules using symmetry-adapted perturbation theory. These ab initio energies were then fit to an appropriate site-site potential form. In an attempt to bridge the gap between ab initio interaction energy information and macroscopic properties prediction, we performed Gibbs ensemble Monte Carlo (GEMC) simulations using their developed pair potentials for acetonitrile and methanol. The simulations results show that the phase behavior of acetonitrile is well described by just the pair interaction potential. For methanol, on the other hand, pair interactions are insufficient to properly predict its vapor-liquid phase behavior, and its saturated liquid density. We also explored simplified forms for representing the ab initio interaction energies by refitting a selected range of the data to a site-site Lennard-Jones and to a modified Buckingham (exponential-6) potentials plus Coulombic interactions. These were also used in GEMC simulations in order to evaluate the quality and computational efficiency of these different potential forms. It was found that the phase behavior prediction for acetonitrile and methanol are highly dependent on the details of the interaction potentials developed.
Lennard-Jones fluids in two-dimensional nano-pores. Multi-phase coexistence and fluid structure
NASA Astrophysics Data System (ADS)
Yatsyshin, Petr; Savva, Nikos; Kalliadasis, Serafim
2014-03-01
We present a number of fundamental findings on the wetting behaviour of nano-pores. A popular model for fluid confinement is a one-dimensional (1D) slit pore formed by two parallel planar walls and it exhibits capillary condensation (CC): a first-order phase transition from vapour to capillary-liquid (Kelvin shift). Capping such a pore at one end by a third orthogonal wall forms a prototypical two-dimensional (2D) pore. We show that 2D pores possess a wetting temperature such that below this temperature CC remains of first order, above it becomes a continuous phase transition manifested by a slab of capillary-liquid filling the pore from the capping wall. Continuous CC exhibits hysteresis and can be preceded by a first-order capillary prewetting transition. Additionally, liquid drops can form in the corners of the 2D pore (remnant of 2D wedge prewetting). The three fluid phases, vapour, capillary-liquid slab and corner drops, can coexist at the pore triple point. Our model is based on the statistical mechanics of fluids in the density functional formulation. The fluid-fluid and fluid-substrate interactions are dispersive. We analyze in detail the microscopic fluid structure, isotherms and full phase diagrams. Our findings also suggest novel ways to control wetting of nano-pores. We are grateful to the European Research Council via Advanced Grant No. 247031 for support.
Microcomputer Simulation of Real Gases--Part 2: Thermodynamical Properties.
ERIC Educational Resources Information Center
Sperandeo-Mineo, R. M.; Tripi, G.
1988-01-01
Studies the pressure and energy of particles interacting through a Lennard-Jones potential and correlates thermodynamical properties with system structural characteristics. Analyzes the relationships between computer simulated data and the van der Waals equation. (YP)
Parallel Curriculum Units for Science, Grades 6-12
ERIC Educational Resources Information Center
Leppien, Jann H.; Purcell, Jeanne H.
2011-01-01
Based on the best-selling book "The Parallel Curriculum", this professional development resource gives multifaceted examples of rigorous learning opportunities for science students in Grades 6-12. The four sample units revolve around genetics, the convergence of science and society, the integration of language arts and biology, and the periodic…
Home Economics/Health Grades 6-12. Program Evaluation.
ERIC Educational Resources Information Center
Des Moines Public Schools, IA. Teaching and Learning Div.
Home economics programs are offered to students in grades 6-12 in the Des Moines INdependent Community School District (Iowa). Programs at the middle school level are exploratory, leading to occupational training in family and consumer science, child care, food service, and textile and fashion arts at the high school level. Health education…
A Stress Control Workbook for Youth Grades 6-12.
ERIC Educational Resources Information Center
Trotter, Jennie C.
Stress is an inevitable part of students' lives, but too much stress can have damaging consequences. Ways in which children can respond positively are covered in this stress booklet. Intended for students in grades 6-12, the booklet is divided into 20 lessons on stress. Each lesson features various activities, role plays, exercises, and checklists…
Career and Technology Education Grades 6-12. Program Evaluation.
ERIC Educational Resources Information Center
Des Moines Public Schools, IA. Teaching and Learning Div.
Technology education programs are offered in 10 middle schools, 5 area high schools, 1 alternative high school, and at Central Campus in the Des Moines Independent Community School District. Programs in grades 6-12 consist of hands-on instruction using activities and projects as the medium for teaching modern technologies in the various trades.…
Qin, Sanbo; Zhou, Huan-Xiang
2016-08-25
Chemical potential is a fundamental property for determining thermodynamic equilibria involving exchange of molecules, such as between two phases of molecular systems. Previously, we developed the fast Fourier transform (FFT)-based method for Modeling Atomistic Protein-crowder interactions (FMAP) to calculate excess chemical potentials according to the Widom insertion. Intermolecular interaction energies were expressed as correlation functions and evaluated via FFT. Here, we extend this method to calculate liquid-liquid phase equilibria of macromolecular solutions. Chemical potentials are calculated by FMAP over a wide range of molecular densities, and the condition for coexistence of low- and high-density phases is determined by the Maxwell equal-area rule. When benchmarked on Lennard-Jones fluids, our method produces an accurate phase diagram at 18% of the computational cost of the current best method. Importantly, the gain in computational speed increases dramatically as the molecules become more complex, leading to many orders of magnitude in speed up for atomistically represented proteins. We demonstrate the power of FMAP by reporting the first results for the liquid-liquid coexistence curve of γII-crystallin represented at the all-atom level. Our method may thus open the door to accurate determination of phase equilibria for macromolecular mixtures such as protein-protein mixtures and protein-RNA mixtures, that are known to undergo liquid-liquid phase separation, both in vitro and in vivo.
NASA Astrophysics Data System (ADS)
Kosevich, Yuriy A.; Savin, Alexander V.
2016-10-01
We provide molecular dynamics simulation of heat transport and energy diffusion in one-dimensional molecular chains with different interparticle pair potentials at zero and non-zero temperature. We model the thermal conductivity (TC) and energy diffusion (ED) in the chain of coupled rotators and in the Lennard-Jones chain either without or with the confining parabolic interparticle potential. The considered chains without the confining potential have normal TC and ED at non-zero temperature, while the corresponding chains with the confining potential are characterized by anomalous (diverging with the system length) TC and superdiffusion of energy. Similar effect is produced by the anharmonic quartic confining pair potential. We confirm in such a way that, surprisingly, the confining pair potential makes both heat transport and energy diffusion anomalous in one-dimensional phononic systems. We show that the normal TC is always accompanied by the normal ED in the thermalized anharmonic chains, while the superdiffusion of energy occurs in the thermalized chains with only anomalous heat transport.
Shaik, Majeed S; Liem, Steven Y; Popelier, Paul L A
2010-05-07
We build on previous work [S. Y. Liem and P. L. A. Popelier, J. Chem. Theory Comput. 4, 353 (2008)], where for the first time, a high-rank multipolar electrostatic potential was used in molecular dynamics simulations of liquid water at a wide range of pressures and temperatures, and using a multipolar Ewald summation. Water is represented as a rigid body, with atomic multipole moments defined by quantum chemical topology partitioning its gas phase electron density. The effect of the level of theory on the local structure of liquid water is systematically addressed. Values for Lennard-Jones (LJ) parameters are optimized, for both oxygen and hydrogen atoms, against bulk properties. The best LJ parameters were then used in a set of simulations at 30 different temperatures (1 atm) and another set at 11 different pressures (at 298 K). Inclusion of the hydrogen LJ parameters significantly increases the self-diffusion coefficient. The behavior of bulk properties was studied and the local water structure analyzed by both radial and spatial distribution functions. Comparisons with familiar point-charge potentials, such as TIP3P, TIP4P, TIP5P, and simple point charge, show the benefits of multipole moments.
Soft-core potentials in thermodynamic integration: comparing one- and two-step transformations.
Steinbrecher, Thomas; Joung, InSuk; Case, David A
2011-11-30
Molecular dynamics-based free energy calculations allow the determination of a variety of thermodynamic quantities from computer simulations of small molecules. Thermodynamic integration (TI) calculations can suffer from instabilities during the creation or annihilation of particles. This "singularity" problem can be addressed with "soft-core" potential functions which keep pairwise interaction energies finite for all configurations and provide smooth free energy curves. "One-step" transformations, in which electrostatic and van der Waals forces are simultaneously modified, can be simpler and less expensive than "two-step" transformations in which these properties are changed in separate calculations. Here, we study solvation free energies for molecules of different hydrophobicity using both models. We provide recommended values for the two parameters α(LJ) and β(C) controlling the behavior of the soft-core Lennard-Jones and Coulomb potentials and compare one- and two-step transformations with regard to their suitability for numerical integration. For many types of transformations, the one-step procedure offers a convenient and accurate approach to free energy estimates.
Hermann, Andreas; Krawczyk, Robert P.; Lein, Matthias; Schwerdtfeger, Peter; Hamilton, I. P.; Stewart, James J. P.
2007-07-15
The many-body expansion of the interaction potential between atoms and molecules is analyzed in detail for different types of interactions involving up to seven atoms. Elementary clusters of Ar, Na, Si, and, in particular, Au are studied, using first-principles wave-function- and density-functional-based methods to obtain the individual n-body contributions to the interaction energies. With increasing atom number the many-body expansion converges rapidly only for long-range weak interactions. Large oscillatory behavior is observed for other types of interactions. This is consistent with the fact that Au clusters up to a certain size prefer planar structures over the more compact three-dimensional Lennard-Jones-type structures. Several Au model potentials and semiempirical PM6 theory are investigated for their ability to reproduce the quantum results. We further investigate small water clusters as prototypes of hydrogen-bonded systems. Here, the many-body expansion converges rapidly, reflecting the localized nature of the hydrogen bond and justifying the use of two-body potentials to describe water-water interactions. The question of whether electron correlation contributions can be successfully modeled by a many-body interaction potential is also addressed.
Werhahn, Jasper C.; Akase, Dai; Xantheas, Sotiris S.
2014-08-14
The scaled versions of the newly introduced [S. S. Xantheas and J. C. Werhahn, J. Chem. Phys.141, 064117 (2014)] generalized forms of some popular potential energy functions (PEFs) describing intermolecular interactions – Mie, Lennard-Jones, Morse, and Buckingham exponential-6 – have been used to fit the ab initio relaxed approach paths and fixed approach paths for the halide-water, X^{-}(H_{2}O), X = F, Cl, Br, I, and alkali metal-water, M^{+}(H_{2}O), M = Li, Na, K, Rb, Cs, interactions. The generalized forms of those PEFs have an additional parameter with respect to the original forms and produce fits to the ab initio data that are between one and two orders of magnitude better in the χ^{2} than the original PEFs. They were found to describe both the long-range, minimum and repulsive wall of the respective potential energy surfaces quite accurately. Overall the 4-parameter extended Morse (eM) and generalized Buckingham exponential-6 (gBe-6) potentials were found to best fit the ab initio data for these two classes of ion-water interactions. Finally, the fitted values of the parameter of the (eM) and (gBe-6) PEFs that control the repulsive wall of the potential correlate remarkably well with the ionic radii of the halide and alkali metal ions.
Announcement: Sleep Awareness Week - March 6-12, 2016.
2016-03-04
Sleep Awareness Week, the National Sleep Foundation's annual campaign to educate the public about the importance of sleep in health and safety, will be observed March 6-12, 2016. The American Academy of Sleep Medicine and the Sleep Research Society recommend that adults aged 18-60 years sleep ≥7 hours each night to promote optimal health and well-being. However, 35% of U.S. adults report typically sleeping <7 hours Adults who do not get enough sleep on a regular basis are more likely to suffer from chronic conditions, such as obesity, high blood pressure, diabetes, and poor mental health.
Pair Potential That Reproduces the Shape of Isochrones in Molecular Liquids.
Veldhorst, Arno A; Schrøder, Thomas B; Dyre, Jeppe C
2016-08-18
Many liquids have curves (isomorphs) in their phase diagrams along which structure, dynamics, and some thermodynamic quantities are invariant in reduced units. A substantial part of their phase diagrams is thus effectively one dimensional. The shapes of these isomorphs are described by a material-dependent function of density, h(ρ), which for real liquids is well approximated by a power law, ρ(γ). However, in simulations, a power law is not adequate when density changes are large; typical models, such as Lennard-Jones liquids, show that γ(ρ) ≡ d ln h(ρ)/d ln ρ is a decreasing function of density. This article presents results from computer simulations using a new pair potential that diverges at a nonzero distance and can be tuned to give a more realistic shape of γ(ρ). Our results indicate that the finite size of molecules is an important factor to take into account when modeling liquids over a large density range.
Development of the Transferable Potentials for Phase Equilibria Model for Hydrogen Sulfide.
Shah, Mansi S; Tsapatsis, Michael; Siepmann, J Ilja
2015-06-11
The transferable potentials for phase equilibria force field is extended to hydrogen sulfide. The pure-component and binary vapor-liquid equilibria with methane and carbon dioxide and the liquid-phase relative permittivity are used for the parametrization of the Lennard-Jones (LJ) and Coulomb interactions, and models with three and four interaction sites are considered. For the three-site models, partial point charges are placed on the sites representing the three atoms, while the negative partial charge is moved to an off-atom site for the four-site models. The effect of molecular shape is probed using either only a single LJ interaction site on the sulfur atom or adding sites also on the hydrogen atoms. This procedure results in four distinct models, but only those with three LJ sites can accurately reproduce all properties considered for the parametrization. These two are further assessed for predictions of the liquid-phase structure, the lattice parameters and relative permittivity for the face-centered-cubic solid, and the triple point. An effective balance between LJ interactions and the dipolar and quadrupolar terms of the first-order electrostatic interactions is struck in order to obtain a four-site model that describes the condensed-phase properties and the phase equilibria with high accuracy.
NASA Astrophysics Data System (ADS)
Thuis, H. H. W.; Stolte, S.; Reuss, J.; Van Den Biesen, J. J. H.; Van Den Meijdenberg, C. J. N.
1980-10-01
Three independent sources of information are used to analyze the angle dependent potential for NOAr: (a) the glory structure of the total collision cross section; (b) the relative difference in the total collision cross section for two different orientations of NO in the 2Π 3/2 state; (c) the absolute value of the total collision cross section. The sudden approximation employed for the calculation of the various properties is discussed. For NOAr a fit to the total collision cross section data is obtained on the basis of an extended Maitland—Smith potential containing a Pt anisotropy in the repulsion and a P2 anisotropy in the repulsion and attraction. A comparison is made with the theoretical potential for NOAr recently by Nielson et al. and the extended Lennard-Jones potential employed in the earlier analysis. For NOKr and NOXe similar Maitland—Smith potentials are obtained by assuming the Pt anisotropy parameter for these systems to be equal to that for NOAr. In a separate appendix is analyzed which intermolecular distances are probed through measurements of the anisotropy in the total collision cross section.
NASA Astrophysics Data System (ADS)
Hess, Siegfried; Kröger, Martin
2001-07-01
A short-range polynomial interaction potential is introduced which has both a repulsive core and an attractive part. It is cut off smoothly such that its first and second derivatives vanish at the cutoff distance. The potential therefore enables efficient simulation studies of a model material that exhibits similarities to a full (but computationally expensive) classical Lennard-Jones system. Thermophysical properties of the model are calculated by (nonequilibrium) molecular dynamics computer simulations and compared with analytical results. Among the quantities studied is the pressure as a function of the density for various temperatures. Equations of state for the fluid and the solid are tested. The coexistence of gaseous, (metastable) liquid, and fcc solid phases is found for a range of temperatures. Bulk and shear moduli are computed. The response of the system to a shear deformation with a constant shear rate is analyzed. The liquid shows viscoelastic behavior that can be described with a Maxwell model. The solid behaves as an elastic medium up to a finite deformation and then undergoes a transition to plastic flow, which is stick-slip-like at small shear rates and continuous at higher ones.
NASA Astrophysics Data System (ADS)
Spöler, C.; Klapp, S. H. L.
2004-11-01
Using replica integral equations in the reference hypernetted-chain (RHNC) approximation we calculate vapor-liquid spinodals, chemical potentials, and compressibilities of fluids with angle-averaged dipolar interactions adsorbed to various disordered porous media. Comparison with previous RHNC results for systems with true angle-dependent Stockmayer (dipolar plus Lennard-Jones) interactions [C. Spöler and S. H. L. Klapp, J. Chem. Phys. 118, 3628 (2003); ibid.120, 6734 (2004)] indicate that, for a dilute hard sphere matrix, the angle-averaged fluid-fluid (ff) potential is a reasonable alternative for reduced fluid dipole moments m*2=μ2/(ɛ0σ3)⩽2.0. This range is comparable to that estimated in bulk fluids, for which RHNC results are presented as well. Finally, results for weakly polar matrices suggest that angle-averaged fluid-matrix (fm) interactions can reproduce main features observed for true dipolar (fm) interactions such as the shift of the vapor-liquid spinodals towards lower temperatures and higher densities. However, the effective attraction induced by dipolar (fm) interaction is underestimated rather than overestimated as in the case of angle-averaged ff interactions.
Hughes, Adam P; Thiele, Uwe; Archer, Andrew J
2017-02-14
For a film of liquid on a solid surface, the binding potential g(h) gives the free energy as a function of the film thickness h and also the closely related (structural) disjoining pressure Π=-∂g/∂h. The wetting behaviour of the liquid is encoded in the binding potential and the equilibrium film thickness corresponds to the value at the minimum of g(h). Here, the method we developed in the work of Hughes et al. [J. Chem. Phys. 142, 074702 (2015)], and applied with a simple discrete lattice-gas model, is used with continuum density functional theory (DFT) to calculate the binding potential for a Lennard-Jones fluid and other simple liquids. The DFT used is based on fundamental measure theory and so incorporates the influence of the layered packing of molecules at the surface and the corresponding oscillatory density profile. The binding potential is frequently input in mesoscale models from which liquid drop shapes and even dynamics can be calculated. Here we show that the equilibrium droplet profiles calculated using the mesoscale theory are in good agreement with the profiles calculated directly from the microscopic DFT. For liquids composed of particles where the range of the attraction is much less than the diameter of the particles, we find that at low temperatures g(h) decays in an oscillatory fashion with increasing h, leading to highly structured terraced liquid droplets.
NASA Astrophysics Data System (ADS)
Hughes, Adam P.; Thiele, Uwe; Archer, Andrew J.
2017-02-01
For a film of liquid on a solid surface, the binding potential g(h) gives the free energy as a function of the film thickness h and also the closely related (structural) disjoining pressure Π =-∂g /∂h . The wetting behaviour of the liquid is encoded in the binding potential and the equilibrium film thickness corresponds to the value at the minimum of g(h). Here, the method we developed in the work of Hughes et al. [J. Chem. Phys. 142, 074702 (2015)], and applied with a simple discrete lattice-gas model, is used with continuum density functional theory (DFT) to calculate the binding potential for a Lennard-Jones fluid and other simple liquids. The DFT used is based on fundamental measure theory and so incorporates the influence of the layered packing of molecules at the surface and the corresponding oscillatory density profile. The binding potential is frequently input in mesoscale models from which liquid drop shapes and even dynamics can be calculated. Here we show that the equilibrium droplet profiles calculated using the mesoscale theory are in good agreement with the profiles calculated directly from the microscopic DFT. For liquids composed of particles where the range of the attraction is much less than the diameter of the particles, we find that at low temperatures g(h) decays in an oscillatory fashion with increasing h, leading to highly structured terraced liquid droplets.
Paz-Borbón, Lauro Oliver; Mortimer-Jones, Thomas V; Johnston, Roy L; Posada-Amarillas, Alvaro; Barcaro, Giovanni; Fortunelli, Alessandro
2007-10-14
The energetics of 98 atom bimetallic Pd-Pt clusters are studied using a combination of: a genetic algorithm technique (to explore vast areas of the configurational space); a basin-hopping atom-exchange routine (to search for lowest-energy homotops at fixed composition); and a shell optimisation approach (to search for high symmetry isomers). The interatomic interactions between Pd and Pt are modelled by the Gupta many-body empirical potential. For most compositions, the putative global minima are found to have structures based on defective Marks decahedra, but in the composition range from Pd46Pt52 to Pd63Pt35, the Leary tetrahedron (LT)--a structure previously identified for 98 atom Lennard-Jones clusters--is consistently found as the most stable structure. Based on the excess energy stability criterion, Pd56Pt42 represents the most stable cluster across the entire composition range. This structure, a Td-symmetry LT, exhibits multi-layer segregation with an innermost core of Pd atoms, an intermediate layer of Pt atoms and an outermost Pd surface shell (Pd-Pt-Pd). The stability of the Leary tetrahedron is compared against other low-energy competing structural motifs: the Marks decahedron (Dh-M), a "quasi" tetrahedron (a closed-packed structure) and two other closed-packed structures. The stability of LT structures is rationalized in terms of their spherical shape and the large number of nearest neighbours.
Keasler, Samuel J; Charan, Sophia M; Wick, Collin D; Economou, Ioannis G; Siepmann, J Ilja
2012-09-13
While the transferable potentials for phase equilibria-united atom (TraPPE-UA) force field has generally been successful at providing parameters that are highly transferable between different molecules, the polarity and polarizability of a given functional group can be significantly perturbed in small cyclic structures, which limits the transferability of parameters obtained for linear molecules. This has motivated us to develop a version of the TraPPE-UA force field specifically for five- and six-membered cyclic alkanes and ethers. The Lennard-Jones parameters for the methylene group obtained from cyclic alkanes are transferred to the ethers for each ring size, and those for the oxygen atom are common to all compounds for a given ring size. However, the partial charges are molecule specific and parametrized using liquid-phase dielectric constants. This model yields accurate saturated liquid densities and vapor pressures, critical temperatures and densities, normal boiling points, heat capacities, and isothermal compressibilities for the following molecules: cyclopentane, tetrahydrofuran, 1,3-dioxolane, cyclohexane, oxane, 1,4-dioxane, 1,3-dioxane, and 1,3,5-trioxane. The azeotropic behavior and separation factor for the binary mixtures of 1,3-dioxolane/cyclohexane and ethanol/1,4-dioxane are qualitively reproduced.
Lattice model theory of the equation of state covering the gas, liquid, and solid phases
NASA Technical Reports Server (NTRS)
Bonavito, N. L.; Tanaka, T.; Chan, E. M.; Horiguchi, T.; Foreman, J. C.
1975-01-01
The three stable states of matter and the corresponding phase transitions were obtained with a single model. Patterned after Lennard-Jones and Devonshires's theory, a simple cubic lattice model containing two fcc sublattices (alpha and beta) is adopted. The interatomic potential is taken to be the Lennard-Jones (6-12) potential. Employing the cluster variation method, the Weiss and the pair approximations on the lattice gas failed to give the correct phase diagrams. Hybrid approximations were devised to describe the lattice term in the free energy. A lattice vibration term corresponding to a free volume correction is included semi-phenomenologically. The combinations of the lattice part and the free volume part yield the three states and the proper phase diagrams. To determine the coexistence regions, the equalities of the pressure and Gibbs free energy per molecule of the coexisting phases were utilized. The ordered branch of the free energy gives rise to the solid phase while the disordered branch yields the gas and liquid phases. It is observed that the triple point and the critical point quantities, the phase diagrams and the coexistence regions plotted are in good agreement with the experimental values and graphs for argon.
[Oral hygiene customs in 6-12 year old schoolchildren].
Hernández-Martínez, César Tadeo; Medina-Solís, Carlo Eduardo; Robles-Bermeo, Norma Leticia; Mendoza-Rodríguez, Martha; Veras-Hernández, Miriam; De la Rosa-Santillana, Rubén; Escoffié-Ramírez, Mauricio; Márquez-Rodríguez, Sonia
2014-01-01
OBJECTIVE. To characterize utilization of oral hygiene devices and customs in schoolchildren. MATERIAL AND METHODS. We performed a cross-sectional study in 1,404 schoolchildren (6- 12 year olds) from 14 public schools in Pachuca, Hidalgo, México, using a questionnaire for sociodemographic variables and 1) Tooth brushing frequency (<1/d vs. at least 1/d), 2) Use of toothpaste (not always vs. always), 3) Flossing (never, does not know vs. at least 1/week), 4) Use of mouthwash (never, does not know vs. at least 1/week). Analyses were performed with nonparametric tests. RESULTS. Mean age was 8.97 ± 1.99 years; 50.1% were male. Prevalence of utilization of oral hygiene devices and associated customs were 85.5% tooth brushing, 90.9% toothpaste, 19.4% flossing, and 28.2% mouthwash. Only 11.8% of participants reported utilization in all 4 categories. We observed differences (p < 0.05) across sexes only in the use of toothpaste, as women used it more often. Differences across age were observed (p < 0.05) for tooth brushing (younger children brushed more often) and flossing (older children flossed more often). CONCLUSIONS. Tooth brushing was the oral hygiene practice more often performed in this sample, with other frequencies being relatively low. There were differences by age and sex across some variables.
Pérez-Sánchez, G; González-Salgado, D; Piñeiro, M M; Vega, C
2013-02-28
In this work the solid-fluid equilibrium for carbon dioxide (CO2) has been evaluated using Monte Carlo simulations. In particular the melting curve of the solid phase denoted as I, or dry ice, was computed for pressures up to 1000 MPa. Four different models, widely used in computer simulations of CO2 were considered in the calculations. All of them are rigid non-polarizable models consisting of three Lennard-Jones interaction sites located on the positions of the atoms of the molecule, plus three partial charges. It will be shown that although these models predict similar vapor-liquid equilibria their predictions for the fluid-solid equilibria are quite different. Thus the prediction of the entire phase diagram is a severe test for any potential model. It has been found that the Transferable Potentials for Phase Equilibria (TraPPE) model yields the best description of the triple point properties and melting curve of carbon dioxide. It is shown that the ability of a certain model to predict the melting curve of carbon dioxide is related to the value of the quadrupole moment of the model. Models with low quadrupole moment tend to yield melting temperatures too low, whereas the model with the highest quadrupole moment yields the best predictions. That reinforces the idea that not only is the quadrupole needed to provide a reasonable description of the properties in the fluid phase, but also it is absolutely necessary to describe the properties of the solid phase.
Generalized Potential Energy Finite Elements for Modeling Molecular Nanostructures.
Chatzieleftheriou, Stavros; Adendorff, Matthew R; Lagaros, Nikos D
2016-10-24
The potential energy of molecules and nanostructures is commonly calculated in the molecular mechanics formalism by superimposing bonded and nonbonded atomic energy terms, i.e. bonds between two atoms, bond angles involving three atoms, dihedral angles involving four atoms, nonbonded terms expressing the Coulomb and Lennard-Jones interactions, etc. In this work a new, generalized numerical simulation is presented for studying the mechanical behavior of three-dimensional nanostructures at the atomic scale. The energy gradient and Hessian matrix of such assemblies are usually computed numerically; a potential energy finite element model is proposed herein where these two components are expressed analytically. In particular, generalized finite elements are developed that express the interactions among atoms in a manner equivalent to that invoked in simulations performed based on the molecular dynamics method. Thus, the global tangent stiffness matrix for any nanostructure is formed as an assembly of the generalized finite elements and is directly equivalent to the Hessian matrix of the potential energy. The advantages of the proposed model are identified in terms of both accuracy and computational efficiency. In the case of popular force fields (e.g., CHARMM), the computation of the Hessian matrix by implementing the proposed method is of the same order as that of the gradient. This analysis can be used to minimize the potential energy of molecular systems under nodal loads in order to derive constitutive laws for molecular systems where the entropy and solvent effects are neglected and can be approximated as solids, such as double stranded DNA nanostructures. In this context, the sequence dependent stretch modulus for some typical base pairs step is calculated.
Fritsche, Miriam; Pandey, Ras B; Farmer, Barry L; Heermann, Dieter W
2012-01-01
Histone proteins are not only important due to their vital role in cellular processes such as DNA compaction, replication and repair but also show intriguing structural properties that might be exploited for bioengineering purposes such as the development of nano-materials. Based on their biological and technological implications, it is interesting to investigate the structural properties of proteins as a function of temperature. In this work, we study the spatial response dynamics of the histone H2AX, consisting of 143 residues, by a coarse-grained bond fluctuating model for a broad range of normalized temperatures. A knowledge-based interaction matrix is used as input for the residue-residue Lennard-Jones potential.We find a variety of equilibrium structures including global globular configurations at low normalized temperature (T* = 0.014), combination of segmental globules and elongated chains (T* = 0.016,0.017), predominantly elongated chains (T* = 0.019,0.020), as well as universal SAW conformations at high normalized temperature (T* ≥ 0.023). The radius of gyration of the protein exhibits a non-monotonic temperature dependence with a maximum at a characteristic temperature (T(c)* = 0.019) where a crossover occurs from a positive (stretching at T* ≤ T(c)*) to negative (contraction at T* ≥ T(c)*) thermal response on increasing T*.
Rai, Neeraj; Siepmann, J Ilja
2007-09-13
The explicit hydrogen version of the transferable potentials for phase equilibria (TraPPE-EH) force field is extended to benzene, pyridine, pyrimidine, pyrazine, pyridazine, thiophene, furan, pyrrole, thiazole, oxazole, isoxazole, imidazole, and pyrazole. While the Lennard-Jones parameters for carbon, hydrogen (two types), nitrogen (two types), oxygen, and sulfur are transferable for all 13 compounds, the partial charges are specific for each compound. The benzene dimer energies for sandwich, T-shape, and parallel-displaced configurations obtained for the TraPPE-EH force field compare favorably with high-level electronic structure calculations. Gibbs ensemble Monte Carlo simulations were carried out to compute the single-component vapor-liquid equilibria for benzene, pyridine, three diazenes, and eight five-membered heterocycles. The agreement with experimental data is excellent with the liquid densities and vapor pressures reproduced within 1 and 5%, respectively. The critical temperatures and normal boiling points are predicted with mean deviations of 0.8 and 1.6%, respectively.
NASA Astrophysics Data System (ADS)
Fritsche, Miriam; Heermann, Dieter; Pandey, Ras; Farmer, Barry
2012-02-01
Using a coarse-grained bond fluctuating model, we investigate structure and dynamics of two histones, H2AX (143 residues) and H3.1 (136 residues) as a function of temperature (T). A knowledged based contact matrix is used as an input for a phenomenological residue-residue interaction in a generalized Lennard-Jones potential. Metropolis algorithm is used to execute stochastic movement of each residue. A number of local and global physical quantities are analyzed. Despite unique energy and mobility profiles of its residues in a specific sequence, the histone H3.1 appears to undergo a structural transformation from a random coil to a globular conformation on reducing the temperature. The radius of gyration of the histone H2AX, in contrast, exhibits a non-monotonic dependence on temperature with a maximum at a characteristic temperature (Tc) where crossover occurs from a positive (stretching below Tc) to negative (contraction above Tc) thermal response on increasing T. Multi-scale structures of the proteins are examined by a detailed analysis of their structure functions.
Lennnard Jones Potential for Mesoscopic System
NASA Astrophysics Data System (ADS)
Taruna, Jutri
2005-11-01
The liquid-gas phase transition of a Lennard Jones system of N=500 particles is studied via Molecular Dynamics simulations. Rather than displaying a positive isothermal compressibility --- as is demanded of stable systems in the thermodynamic limit --- the system develops a ``Van der Waals loop'', namely, a region with negative isothermal compressibility. We use various observables as well as state-of-the-art computer renderings to elucidate the nature of this behavior.
NASA Astrophysics Data System (ADS)
Bourasseau, Emeric; Haboudou, Mehalia; Boutin, Anne; Fuchs, Alain H.; Ungerer, Philippe
2003-02-01
In this study, we propose a new global procedure to perform optimization of semiempirical intermolecular potential parameters on the basis of a large reference database. To obtain transferable parameters, we used the original method proposed by Ungerer [Ungerer et al., J. Chem. Phys. 112, 5499 (2000)], based on the minimization of a dimensionless error criterion. This method allows the simultaneous optimization of several parameters from a large set of reference data. However, the computational cost of such a method limits its application, because it implies the calculation of an important number of partial derivatives, calculated by finite differences between the results of several different simulations. In this work, we propose a new method to evaluate partial derivatives, in order to reduce the computing time and to obtain more consistent derivatives. This method is based on the analysis of statistical fluctuations during a single simulation. To predict equilibrium properties of olefins, we optimize the Lennard-Jones potential parameters of the unsaturated hydrocarbon groups using the anisotropic united atoms description. The resulting parameters are consistent with those previously determined for linear and branched alkanes. Test simulations have been performed at temperatures ranging from 150 to 510 K for several α-olefins (ethylene, propene, 1-butene, 1-pentene, 1-hexene, 1-octene), several β-olefins (trans-2-butene, cis-2-butene, trans-2-pentene), isobutene, and butadiene. Equilibrium properties are well predicted, and critical properties can be evaluated with a good accuracy, despite the fact that most of the results constitute pure predictions. It is concluded that the AUA potential, due to a relevant physical meaning, can be transferred to a large range of olefins with good success.
NASA Astrophysics Data System (ADS)
Koperski, J.
1996-11-01
A0 +( 3Π) → X0 +( 1Σ +) andB1( 3Σ +) → X0 +( 1Σ +) fluorescence spectra of HgAr van der Waals molecules were previously produced in a pulsed supersonic molecular beam crossed with a pulsed dye-laser beam, following excitation of single vibronic levels. The dispersed fluorescence displayed characteristic Condon internal diffraction (CID) patterns consisting of bound-free reflection type, continuous spectra, and also bound-bound discrete features. An analysis of the A O+ → X0 + and B1 → X O+ bound-bound spectra indicates that a Morese function is an adequate representatation of the X0 + potential energy (PE) curve below the dissociation limit. In simulation of the A O+ → X0 + bound-free spectra of the Morse, Lennard-Jones ( n - 6) and Maitland-Smith functions were tested, and the Maitland-Smith potential was found to be a good representation of the repulsive wall of the X0 + PE curve above the dissociation limit over the internuclear separation range R = 2.8-3.5 Å.
40 CFR 721.524 - Alcohols, C6-12, ethoxylated, reaction product with maleic anhydride.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 40 Protection of Environment 32 2013-07-01 2013-07-01 false Alcohols, C6-12, ethoxylated, reaction... New Uses for Specific Chemical Substances § 721.524 Alcohols, C6-12, ethoxylated, reaction product... chemical substance identified generically as alcohols, C6-12, ethoxylated, reaction product with...
40 CFR 721.524 - Alcohols, C6-12, ethoxylated, reaction product with maleic anhydride.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 40 Protection of Environment 31 2014-07-01 2014-07-01 false Alcohols, C6-12, ethoxylated, reaction... New Uses for Specific Chemical Substances § 721.524 Alcohols, C6-12, ethoxylated, reaction product... chemical substance identified generically as alcohols, C6-12, ethoxylated, reaction product with...
40 CFR 721.524 - Alcohols, C6-12, ethoxylated, reaction product with maleic anhydride.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 40 Protection of Environment 31 2011-07-01 2011-07-01 false Alcohols, C6-12, ethoxylated, reaction... New Uses for Specific Chemical Substances § 721.524 Alcohols, C6-12, ethoxylated, reaction product... chemical substance identified generically as alcohols, C6-12, ethoxylated, reaction product with...
40 CFR 721.524 - Alcohols, C6-12, ethoxylated, reaction product with maleic anhydride.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 40 Protection of Environment 30 2010-07-01 2010-07-01 false Alcohols, C6-12, ethoxylated, reaction... New Uses for Specific Chemical Substances § 721.524 Alcohols, C6-12, ethoxylated, reaction product... chemical substance identified generically as alcohols, C6-12, ethoxylated, reaction product with...
40 CFR 721.524 - Alcohols, C6-12, ethoxylated, reaction product with maleic anhydride.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 40 Protection of Environment 32 2012-07-01 2012-07-01 false Alcohols, C6-12, ethoxylated, reaction... New Uses for Specific Chemical Substances § 721.524 Alcohols, C6-12, ethoxylated, reaction product... chemical substance identified generically as alcohols, C6-12, ethoxylated, reaction product with...
Intermolecular potential parameters and combining rules determined from viscosity data
Bastien, Lucas A.J.; Price, Phillip N.; Brown, Nancy J.
2010-05-07
The Law of Corresponding States has been demonstrated for a number of pure substances and binary mixtures, and provides evidence that the transport properties viscosity and diffusion can be determined from a molecular shape function, often taken to be a Lennard-Jones 12-6 potential, that requires two scaling parameters: a well depth {var_epsilon}{sub ij} and a collision diameter {sigma}{sub ij}, both of which depend on the interacting species i and j. We obtain estimates for {var_epsilon}{sub ij} and {sigma}{sub ij} of interacting species by finding the values that provide the best fit to viscosity data for binary mixtures, and compare these to calculated parameters using several 'combining rules' that have been suggested for determining parameter values for binary collisions from parameter values that describe collisions of like molecules. Different combining rules give different values for {sigma}{sub ij} and {var_epsilon}{sub ij} and for some mixtures the differences between these values and the best-fit parameter values are rather large. There is a curve in ({var_epsilon}{sub ij}, {sigma}{sub ij}) space such that parameter values on the curve generate a calculated viscosity in good agreement with measurements for a pure gas or a binary mixture. The various combining rules produce couples of parameters {var_epsilon}{sub ij}, {sigma}{sub ij} that lie close to the curve and therefore generate predicted mixture viscosities in satisfactory agreement with experiment. Although the combining rules were found to underpredict the viscosity in most of the cases, Kong's rule was found to work better than the others, but none of the combining rules consistently yields parameter values near the best-fit values, suggesting that improved rules could be developed.
He-broadening and shift coefficients of water vapor lines in infrared spectral region
NASA Astrophysics Data System (ADS)
Petrova, T. M.; Solodov, A. M.; Solodov, A. A.; Deichuli, V. M.; Starikov, V. I.
2015-11-01
The water vapor line broadening and shift coefficients in the ν1+ν2, ν2+ν3, ν1+ν3, 2ν3, 2ν1, 2ν2+ν3, and ν1+2ν2 vibrational bands induced by helium pressure were measured using a Bruker IFS 125HR spectrometer. The vibrational bands 2ν3 and ν1+2ν2 were investigated for the first time. The interaction potential used in the calculations of broadening and shift coefficients was chosen as the sum of pair potentials, which were modeled by the Lennard-Jones (6-12) potentials. The vibrational and rotational contributions to this potential were obtained by use of the intermolecular potential parameters and intramolecular parameters of H2O molecule. The calculated values of the broadening and shift coefficients were compared with the experimental data.
Calculation of chemical potentials of chain molecules by the incremental gauge cell method.
Rasmussen, Christopher J; Vishnyakov, Aleksey; Neimark, Alexander V
2011-12-07
The gauge cell Monte Carlo method is extended to calculations of the incremental chemical potentials and free energies of linear chain molecules. The method was applied to chains of Lennard-Jones beads with stiff harmonic bonds up to 500 monomers in length. We show that the suggested method quantitatively reproduces the modified Widom particle insertion method of Kumar et al. [S. K. Kumar, I. Szleifer, and A. Z. Panagiotopoulos, Phys. Rev. Lett. 66(22), 2935 (1991)], and is by an order of magnitude more efficient for long chains in terms of the computational time required for the same accuracy of chemical potential calculations. The chain increment ansatz, which suggests that the incremental chemical potential is independent of the chain length, was tested at different temperatures. We confirmed that the ansatz holds only for coils above the θ temperature. Special attention is paid to the effects of the magnitude of adsorption potential and temperature on the behavior of single chains in confinements that are comparable in size with the free chain radius of gyration. At sufficiently low temperatures, the dependence of the incremental chemical potential on the chain length in wetting pores is superficially similar to a capillary condensation isotherm, reflecting monolayer formation following by pore volume filling, as the chain length increases. We find that the incremental gauge cell method is an accurate and efficient technique for calculations of the free energies of chain molecules in bulk systems and nanoconfinements alike. The suggested method may find practical applications, such as modeling polymer partitioning on porous substrates and dynamics of chain translocation into nanopores.
Calculation of chemical potentials of chain molecules by the incremental gauge cell method
NASA Astrophysics Data System (ADS)
Rasmussen, Christopher J.; Vishnyakov, Aleksey; Neimark, Alexander V.
2011-12-01
The gauge cell Monte Carlo method is extended to calculations of the incremental chemical potentials and free energies of linear chain molecules. The method was applied to chains of Lennard-Jones beads with stiff harmonic bonds up to 500 monomers in length. We show that the suggested method quantitatively reproduces the modified Widom particle insertion method of Kumar et al. [S. K. Kumar, I. Szleifer, and A. Z. Panagiotopoulos, Phys. Rev. Lett. 66(22), 2935 (1991)], 10.1103/PhysRevLett.66.2935, and is by an order of magnitude more efficient for long chains in terms of the computational time required for the same accuracy of chemical potential calculations. The chain increment ansatz, which suggests that the incremental chemical potential is independent of the chain length, was tested at different temperatures. We confirmed that the ansatz holds only for coils above the θ temperature. Special attention is paid to the effects of the magnitude of adsorption potential and temperature on the behavior of single chains in confinements that are comparable in size with the free chain radius of gyration. At sufficiently low temperatures, the dependence of the incremental chemical potential on the chain length in wetting pores is superficially similar to a capillary condensation isotherm, reflecting monolayer formation following by pore volume filling, as the chain length increases. We find that the incremental gauge cell method is an accurate and efficient technique for calculations of the free energies of chain molecules in bulk systems and nanoconfinements alike. The suggested method may find practical applications, such as modeling polymer partitioning on porous substrates and dynamics of chain translocation into nanopores.
NASA Astrophysics Data System (ADS)
Gamache, R. R.; Lynch, R.; Neshyba, S. P.
1998-05-01
Calculations of the halfwidth and line shift of water vapor perturbed by N2, O2, CO2 and H2 based on a complex implementation of the formalism of Robert and Bonamy are made. The potentials employ the leading terms of the electrostatic potential, a Lennard-Jones (6-12) atom-atom potential, and the induction and dispersion components of the isotropic potential. The dynamics of the collisions are correct to second order in time. The results are compared with measurements and very good agreement is observed for both halfwidths and line shifts. A new feature in this approach is that the real and imaginary components of the S matrix affect both the halfwidth and the line shift. It is shown here that the imaginary parts of the S matrix strongly affect the calculated halfwidths for some of the systems considered.
Neimark, Alexander V; Vishnyakov, Aleksey
2005-06-15
We present a modification of the gauge cell Monte Carlo simulation method [A. V. Neimark and A. Vishnyakov, Phys. Rev. E 62, 4611 (2000)] designed for chemical potential calculations in small confined inhomogeneous systems. To measure the chemical potential, the system under study is set in chemical equilibrium with the gauge cell, which represents a finite volume reservoir of ideal particles. The system and the gauge cell are immersed into the thermal bath of a given temperature. The size of the gauge cell controls the level of density fluctuations in the system. The chemical potential is rigorously calculated from the equilibrium distribution of particles between the system cell and the gauge cell and does not depend on the gauge cell size. This scheme, which we call a mesoscopic canonical ensemble, bridges the gap between the canonical and the grand canonical ensembles, which are known to be inconsistent for small systems. The ideal gas gauge cell method is illustrated with Monte Carlo simulations of Lennard-Jones fluid confined to spherical pores of different sizes. Special attention is paid to the case of extreme confinement of several molecular diameters in cross section where the inconsistency between the canonical ensemble and the grand canonical ensemble is most pronounced. For sufficiently large systems, the chemical potential can be reliably determined from the mean density in the gauge cell as it was implied in the original gauge cell method. The method is applied to study the transition from supercritical adsorption to subcritical capillary condensation, which is observed in nanoporous materials as the pore size increases.
Nanoparticle interaction potentials constructed by multiscale computation.
Lee, Cheng K; Hua, Chi C
2010-06-14
The van der Waals (vdW) potentials governing macroscopic objects have long been formulated in the context of classical theories, such as Hamaker's microscopic theory and Lifshitz's continuum theory. This work addresses the possibility of constructing the vdW interaction potentials of nanoparticle species using multiscale simulation schemes. Amorphous silica nanoparticles were considered as a benchmark example for which a series of (SiO(2))(n) (n being an integer) has been systematically surveyed as the potential candidates of the packing units that reproduce known bulk material properties in atomistic molecular dynamics simulations. This strategy led to the identification of spherical Si(6)O(12) molecules, later utilized as the elementary coarse-grained (CG) particles to compute the pair interaction potentials of silica nanoparticles ranging from 0.62 to 100 nm in diameter. The model nanoparticles so built may, in turn, serve as the children CG particles to construct nanoparticles assuming arbitrary sizes and shapes. Major observations are as follows. The pair interaction potentials for all the investigated spherical silica nanoparticles can be cast into a semiempirical, generalized Lennard-Jones 2alpha-alpha potential (alpha being a size-dependent, large integral number). In its reduced form, we discuss the implied universalities for the vdW potentials governing a certain range of amorphous nanoparticle species as well as how thermodynamic transferability can be fulfilled automatically. In view of future applications with colloidal suspensions, we briefly evaluated the vdW potential in the presence of a "screening" medium mimicking the effects of electrical double layers or grafting materials atop the nanoparticle core. The general observations shed new light on strategies to attain a microscopic control over interparticle attractions. In future perspectives, the proposed multiscale computation scheme shall help bridge the current gap between the modeling of
In silico prediction of drug solubility: 4. Will simple potentials suffice?
Lüder, Kai; Lindfors, Lennart; Westergren, Jan; Nordholm, Sture; Persson, Rasmus; Pedersen, Mikaela
2009-09-01
In view of the extreme importance of reliable computational prediction of aqueous drug solubility, we have established a Monte Carlo simulation procedure which appears, in principle, to yield reliable solubilities even for complex drug molecules. A theory based on judicious application of linear response and mean field approximations has been found to reproduce the computationally demanding free energy determinations by simulation while at the same time offering mechanistic insight. The focus here is on the suitability of the model of both drug and solvent, i.e., the force fields. The optimized potentials for liquid simulations all atom (OPLS-AA) force field, either intact or combined with partial charges determined either by semiempirical AM1/CM1A calculations or taken from the condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASS) force field has been used. The results illustrate the crucial role of the force field in determining drug solubilities. The errors in interaction energies obtained by the simple force fields tested here are still found to be too large for our purpose but if a component of this error is systematic and readily removed by empirical adjustment the results are significantly improved. In fact, consistent use of the OPLS-AA Lennard-Jones force field parameters with partial charges from the COMPASS force field will in this way produce good predictions of amorphous drug solubility within 1 day on a standard desktop PC. This is shown here by the results of extensive new simulations for a total of 47 drug molecules which were also improved by increasing the water box in the hydration simulations from 500 to 2000 water molecules.
Interatomic potentials and solvation parameters from protein engineering data for buried residues
Lomize, Andrei L.; Reibarkh, Mikhail Y.; Pogozheva, Irina D.
2002-01-01
Van der Waals (vdW) interaction energies between different atom types, energies of hydrogen bonds (H-bonds), and atomic solvation parameters (ASPs) have been derived from the published thermodynamic stabilities of 106 mutants with available crystal structures by use of an originally designed model for the calculation of free-energy differences. The set of mutants included substitutions of uncharged, inflexible, water-inaccessible residues in α-helices and β-sheets of T4, human, and hen lysozymes and HI ribonuclease. The determined energies of vdW interactions and H-bonds were smaller than in molecular mechanics and followed the "like dissolves like" rule, as expected in condensed media but not in vacuum. The depths of modified Lennard-Jones potentials were −0.34, −0.12, and −0.06 kcal/mole for similar atom types (polar–polar, aromatic–aromatic, and aliphatic–aliphatic interactions, respectively) and −0.10, −0.08, −0.06, −0.02, and nearly 0 kcal/mole for different types (sulfur–polar, sulfur–aromatic, sulfur–aliphatic, aliphatic–aromatic, and carbon–polar, respectively), whereas the depths of H-bond potentials were −1.5 to −1.8 kcal/mole. The obtained solvation parameters, that is, transfer energies from water to the protein interior, were 19, 7, −1, −21, and −66 cal/moleÅ2 for aliphatic carbon, aromatic carbon, sulfur, nitrogen, and oxygen, respectively, which is close to the cyclohexane scale for aliphatic and aromatic groups but intermediate between octanol and cyclohexane for others. An analysis of additional replacements at the water–protein interface indicates that vdW interactions between protein atoms are reduced when they occur across water. PMID:12142453
Dynamical phases of attractive particles sliding on a structured surface
NASA Astrophysics Data System (ADS)
Hasnain, J.; Jungblut, S.; Dellago, C.
2015-05-01
Inspired by experiments on quartz crystal microbalance setups, we study the mobility of a monolayer of Lennard-Jones particles driven over a hexagonal external potential. We pay special attention to the changes in the dynamical phases that arise when the lattice constant of the external substrate potential and the Lennard-Jones interaction are mismatched. We find that if the average particle separation is such that the particles repel each other, or interact harmonically, the qualitative behavior of the system is akin to that of a monolayer of purely repulsive Yukawa particles. On the other hand, if the particles typically attract each other, the ensuing dynamical states are determined entirely by the relative strength of the Lennard-Jones interaction with respect to that of the external potential.
Vörtler, Horst L; Schäfer, Katja; Smith, William R
2008-04-17
We study the simulation cell size dependence of chemical potential isotherms in subcritical square-well fluids by means of series of canonical ensemble Monte Carlo simulations with increasing numbers of particles, for both three-dimensional bulk systems and two-dimensional planar layers, using Widom-like particle insertion methods. By estimating the corresponding vapor/liquid coexistence densities using a Maxwell-like equal area rule for the subcritical chemical potential isotherms, we are able to study the influence of system size not only on chemical potentials but also on the coexistence properties. The chemical potential versus density isotherms show van der Waals-like loops in the subcritical vapor/liquid coexistence range that exhibit distinct finite size effects for both two- and three-dimensional fluids. Generally, in agreement with recent findings for related studies of Lennard-Jones fluids, the loops shrink with increasing number of particles. In contrast to the subcritical isotherms themselves, the equilibrium vapor/liquid densities show only a weak system size dependence and agree quantitatively with the best-known literature values for three-dimensional fluids. This allows our approach to be used to accurately predict the phase coexistence properties. Our resulting phase equilibrium results for two-dimensional square-well fluids are new. Knowledge concerning finite size effects of square-well systems is important not only for the simulation of thermodynamic properties of simple fluids, but also for the simulation of models of more complex fluids (such as aqueous or polymer fluids) involving square-well interactions.
Maeda, Kouji; Asakuma, Yusuke; Fukui, Keisuke
2008-01-28
Directional crystallization from a binary mixture was performed by pseudo-NpT ensemble molecular dynamics. The initial crystal phase having a face-centered-cubic (fcc) structure grew toward the whole cell according to the temperature gradient in the universal cell. The growing crystal phase was not planar even though the solute molecules grew in two-dimensional coordinates because the solvent molecules disturbed the crystallization of the solute molecules at the diffusive crystal-solution interface. This represented the essential phenomenon of solute distribution during crystallization. Consequently, the growing crystal phase still contained solvent molecules having a liquid structure. The time change of the solute composition in the early phase of crystal growth showed an increase in solute composition as the time step proceeded. The resulting solute composition in this early phase was considered at different temperature gradients in the universal cell and it increased as the temperature of the initial crystal-solution interface increased. A new distribution coefficient model was proposed as a function of the difference between the local solute composition and bulk solute composition in the solution around the crystal-solution interface. The impurity-solvent distribution coefficient could be represented by the new model for faster growth of the lower temperature's initial interface. As regards a better distribution coefficient, there was found to be a very dilute solution phase over the crystal phase. The new variable "distribution rate" instead of the ambiguous variable "growth rate" was considered as a function of temperature gradient in the universal cell.
Orientation of C{sub 70} molecules in peapods as a function of the nanotube diameter
Chorro, Matthieu; Delhey, Axel; Launois, Pascale; Noe, Laure; Monthioux, Marc
2007-01-15
Encapsulated C{sub 70} molecules packed in single-walled carbon nanotubes display different orientations depending on the nanotube radius. We present x-ray scattering data obtained on a powder of nanotubes filled with C{sub 70} molecules. Analytical expressions for calculating the diffraction diagram taking into account fullerene orientations are developed. The comparison between calculations and experiments allows us to conclude that the change from the lying to standing orientation--corresponding to the molecule long axis parallel and perpendicular to the tube axis, respectively--takes place when nanotubes reach a diameter of about 1.42 nm. Energy calculations are performed using a Lennard-Jones (6-12) potential, leading to a calculated reorientation diameter in good agreement with that determined experimentally.
NASA Technical Reports Server (NTRS)
Gamache, Robert R.; Fischer, Jonathan
2001-01-01
Pressure-broadened half-widths and pressure-induced line shifts for the two most important bands of water vapor in the 0.7-micron region are determined using the complex Robert-Bonamy (CRB) formalism. The calculations are made with nitrogen and oxygen as the perturbing gas from which values for air as the perturbing gas are determined. The intermolecular potential is taken as a sum of electrostatic contributions and Lennard-Jones (6-12) atom-atom, and isotropic induction and dispersion components. The dynamics of the collision process are correct to second order in time. The calculated values are compared with published measurements and agreement is observed for both half-widths and line shifts. The temperature dependence of the half-width, which is necessary for reduction of remotely sensed data, is determined.
Proposal for a material with negative thermal expansion
NASA Astrophysics Data System (ADS)
Abdullah, Mikrajuddin
2016-09-01
I propose a model of a material that exhibits negative thermal expansion (NTE) properties and criteria for the occurrence of linear and volumetric NTE. I derived the criteria for an arbitrary force between rigid units in the material. These criteria are also discussed specifically for the Lennard-Jones (6-12) potential and in more detail for metal-organic framework (MOF) materials comprising rigid units connected by organic linkers. Qualitatively, the model predictions can explain some observed results. Surprisingly, the model can produce equations for the transition temperature from NTE to positive thermal expansion (PTE), Tc ≈ T0 - 50 K, which is exactly the same as the temperature at which the glass transition begins to occur in most polymers, i.e., Tc ≈ Tg - 50 K.
A high performance communications and memory caching scheme for molecular dynamics on the CM-5
Beazley, D.M.; Lomdahl, P.S.; Gronbech-Jensen, N.; Tamayo, P.
1993-09-15
In this paper, we provide a brief overview of our general molecular dynamics algorithm and focus on several performance enhancements that have allowed us to achieve high performance on the CM-5. Our use of the CM-5 vector units (VUs) to calculate forces is described along with a memory caching scheme that speeds up the force calculation by as much as 50%. In addition, we discuss a method used to speed up the communication aspects of our algorithm by more than 35%. Lastly, recent timing and scaling results are presented. Our code has been implemented in ANSI C with explicit calls to the CMMD message-passing library. To use the VUs we have written our force calculation in CDPEAC (a C interface to the VU assembler language, DPEAC). We also assume that particles interact according to the Lennard-Jones 6--12 (LJ) potential.
Isolating the non-polar contributions to the intermolecular potential for water-alkane interactions
NASA Astrophysics Data System (ADS)
Ballal, Deepti; Venkataraman, Pradeep; Fouad, Wael A.; Cox, Kenneth R.; Chapman, Walter G.
2014-08-01
Intermolecular potential models for water and alkanes describe pure component properties fairly well, but fail to reproduce properties of water-alkane mixtures. Understanding interactions between water and non-polar molecules like alkanes is important not only for the hydrocarbon industry but has implications to biological processes as well. Although non-polar solutes in water have been widely studied, much less work has focused on water in non-polar solvents. In this study we calculate the solubility of water in different alkanes (methane to dodecane) at ambient conditions where the water content in alkanes is very low so that the non-polar water-alkane interactions determine solubility. Only the alkane-rich phase is simulated since the fugacity of water in the water rich phase is calculated from an accurate equation of state. Using the SPC/E model for water and TraPPE model for alkanes along with Lorentz-Berthelot mixing rules for the cross parameters produces a water solubility that is an order of magnitude lower than the experimental value. It is found that an effective water Lennard-Jones energy ɛW/k = 220 K is required to match the experimental water solubility in TraPPE alkanes. This number is much higher than used in most simulation water models (SPC/E—ɛW/k = 78.2 K). It is surprising that the interaction energy obtained here is also higher than the water-alkane interaction energy predicted by studies on solubility of alkanes in water. The reason for this high water-alkane interaction energy is not completely understood. Some factors that might contribute to the large interaction energy, such as polarizability of alkanes, octupole moment of methane, and clustering of water at low concentrations in alkanes, are examined. It is found that, though important, these factors do not completely explain the anomalously strong attraction between alkanes and water observed experimentally.
Isolating the non-polar contributions to the intermolecular potential for water-alkane interactions.
Ballal, Deepti; Venkataraman, Pradeep; Fouad, Wael A; Cox, Kenneth R; Chapman, Walter G
2014-08-14
Intermolecular potential models for water and alkanes describe pure component properties fairly well, but fail to reproduce properties of water-alkane mixtures. Understanding interactions between water and non-polar molecules like alkanes is important not only for the hydrocarbon industry but has implications to biological processes as well. Although non-polar solutes in water have been widely studied, much less work has focused on water in non-polar solvents. In this study we calculate the solubility of water in different alkanes (methane to dodecane) at ambient conditions where the water content in alkanes is very low so that the non-polar water-alkane interactions determine solubility. Only the alkane-rich phase is simulated since the fugacity of water in the water rich phase is calculated from an accurate equation of state. Using the SPC/E model for water and TraPPE model for alkanes along with Lorentz-Berthelot mixing rules for the cross parameters produces a water solubility that is an order of magnitude lower than the experimental value. It is found that an effective water Lennard-Jones energy ε(W)/k = 220 K is required to match the experimental water solubility in TraPPE alkanes. This number is much higher than used in most simulation water models (SPC/E-ε(W)/k = 78.2 K). It is surprising that the interaction energy obtained here is also higher than the water-alkane interaction energy predicted by studies on solubility of alkanes in water. The reason for this high water-alkane interaction energy is not completely understood. Some factors that might contribute to the large interaction energy, such as polarizability of alkanes, octupole moment of methane, and clustering of water at low concentrations in alkanes, are examined. It is found that, though important, these factors do not completely explain the anomalously strong attraction between alkanes and water observed experimentally.
NASA Astrophysics Data System (ADS)
Koperski, J.; Czajkowski, M.
2002-04-01
First-time observed D1(1Π)v‧=10→X0+(1Σ) fluorescence in ZnAr, and A0+(3Π)v‧=4→X0+ and D1(1Π)v‧=7,8→X0+ fluorescence in CdAr van der Waals (vdW) molecules were produced in a continuous supersonic molecular beam crossed with a pulsed dye-laser beam, following excitation of single vibronic levels. The dispersed fluorescence spectra displayed characteristic Condon internal diffraction (CID) patterns consisting of bound-free, reflection type, continuous spectra, and, in certain cases, bound-bound discrete features. An analysis of the A0+→X0+ and D1→X0+ bound-bound spectra indicates that Morse functions are adequate representations of the X0+ potential energy (PE) curves below their dissociation limits. In simulation of the A0+→X0+ and D1→X0+ bound-free spectra, the Morse, Lennard-Jones L-J(n-6), and Maitland-Smith M-S(n0,n1) functions were tested, and the respective M-S(11.3, 9.0) and M-S(10.6, 7.0) potentials were found to be good representations for the repulsive walls of the X0+ PE curves of ZnAr and CdAr, respectively, over the short range, R=2.45-4.38 Å (ZnAr) and R=2.85-4.31 Å (CdAr), of internuclear separations.
Capillary condensation of a binary mixture in slit-like pores.
Bucior, Katarzyna; Patrykiejew, Andrzej; Pizio, Orest; Sokołowski, Stefan
2003-03-15
We investigate the capillary condensation of two model fluid mixtures in slit-like pores, which exhibit different demixing properties in the bulk phase. The interactions between adsorbate particles are modeled by using Lennard-Jones (12,6) potentials and the adsorbing potentials are of the Lennard-Jones (9,3) type. The calculations are performed for different pore widths and at different concentrations of the bulk gas, by means of density functional theory. We evaluate the capillary phase diagrams and discuss their dependence on the parameters of the model. Our calculations indicate that a binary mixture confined to a slit-like pore may exhibit rich phase behavior.
Modified Jeans Instability for Dust Grains in a Plasma
Delzanno, G.L.; Lapenta, G.
2005-05-06
An investigation of the properties of linear stability is conducted for a system consisting of particles having mass m and charge q, interacting through the gravitational and electrostatic force (Jeans instability). However, in light of recent works showing that dust particles in a plasma can have a Lennard-Jones-like shielding potential, a new set of equations has been derived, where the electrostatic interaction among the dust particles is Lennard-Jones-like instead of Coulomb-like. A new condition for the gravitational instability is derived, showing a broader spectrum of unstable modes with faster growth rates.
Chapela, Gustavo A; del Río, Fernando; Alejandre, José
2013-02-07
The liquid-vapor phase diagrams of equal size diameter σ binary mixtures of screened potentials have been reported for several ranges of interaction using Monte Carlo simulation methods [J. B. Caballero, A. M. Puertas, A. Ferńandez-Barbero, F. J. de las Nieves, J. M. Romero-Enrique, and L. F. Rull, J. Chem. Phys. 124, 054909 (2006); A. Fortini, A.-P. Hynninen, and M. Dijkstra, J. Chem. Phys. 125, 094502 (2006)]. Both works report controversial results about the stability of the phase diagram with the inverse Debye screening length κ. Caballero found stability for values of κσ up to 20 while Fortini reported stability for κσ up to 20 while Fortini reported stability for κσ ≤ 4. In this work a spinodal decomposition process where the liquid and vapor phases coexist through an interface in a slab geometry is used to obtain the phase equilibrium and surface properties using a discontinuous molecular dynamics simulations for mixtures of equal size particles carrying opposite charge and interacting with a mixture of attractive and repulsive Yukawa potentials at different values of κσ. An crude estimation of the triple point temperatures is also reported. The isothermal-isobaric method was also used to determine the phase stability using one phase simulations. We found that liquid-vapor coexistence is stable for values of κσ > 20 and that the critical temperatures have a maximum value at around κσ = 10, in agreement with Caballero et al. calculations. There also exists a controversy about the liquid-vapor envelope stability of the pure component attractive Yukawa model which is also discussed in the text. In addition, details about the equivalence between continuous and discontinuous molecular dynamics simulations are given, in the Appendix, for Yukawa and Lennard-Jones potentials.
NASA Astrophysics Data System (ADS)
Chapela, Gustavo A.; del Río, Fernando; Alejandre, José
2013-02-01
The liquid-vapor phase diagrams of equal size diameter σ binary mixtures of screened potentials have been reported for several ranges of interaction using Monte Carlo simulation methods [J. B. Caballero, A. M. Puertas, A. Ferńandez-Barbero, F. J. de las Nieves, J. M. Romero-Enrique, and L. F. Rull, J. Chem. Phys. 124, 054909 (2006), 10.1063/1.2159481; A. Fortini, A.-P. Hynninen, and M. Dijkstra, J. Chem. Phys. 125, 094502 (2006), 10.1063/1.2335453]. Both works report controversial results about the stability of the phase diagram with the inverse Debye screening length κ. Caballero found stability for values of κσ up to 20 while Fortini reported stability for κσ up to 20 while Fortini reported stability for κσ ⩽ 4. In this work a spinodal decomposition process where the liquid and vapor phases coexist through an interface in a slab geometry is used to obtain the phase equilibrium and surface properties using a discontinuous molecular dynamics simulations for mixtures of equal size particles carrying opposite charge and interacting with a mixture of attractive and repulsive Yukawa potentials at different values of κσ. An crude estimation of the triple point temperatures is also reported. The isothermal-isobaric method was also used to determine the phase stability using one phase simulations. We found that liquid-vapor coexistence is stable for values of κσ > 20 and that the critical temperatures have a maximum value at around κσ = 10, in agreement with Caballero et al. calculations. There also exists a controversy about the liquid-vapor envelope stability of the pure component attractive Yukawa model which is also discussed in the text. In addition, details about the equivalence between continuous and discontinuous molecular dynamics simulations are given, in the Appendix, for Yukawa and Lennard-Jones potentials.
NASA Astrophysics Data System (ADS)
Koperski, J.; Atkinson, J. B.; Krause, L.
2001-06-01
We present an analysis of the A0+(63P1)→X0+(61S0) bound-bound and bound-free fluorescence spectrum, and of the A0+(63P1)←X0+(61S0) and B1(63P1)←X0+(61S0) bound-bound excitation spectrum of the HgKr van der Waals molecule. The A→X fluorescence spectrum, which was observed for the first time, as well as the excitation spectra were recorded using a pulsed supersonic molecular beam crossed with a pulsed dye laser beam. An analysis of the A(v‧)←X(v″), B(v‧)←X(v″), and A(v‧=8)→X(v″) bound-bound bands indicates that a Morse function combined with a long-range approximation represents the interatomic potential energy curve of the A, B, and X states below the dissociation limit. In the simulation of the A(v‧=8)→X bound-free spectrum the Morse, Lennard-Jones (n-6), and Maitland-Smith (n0, n1) functions were tested, and the Maitland-Smith (11.39, 10.50) potential was found to be a good representation of the repulsive part of the X-state PE curve above the dissociation limit, over the internuclear separation range R=2.85-3.55 Å. The spectroscopic characteristics for the A, B, and X states obtained in this work are compared with other available experimental and theoretical results.
Su, Pin-Chih; Johnson, Michael E.
2015-01-01
Thermodynamic integration (TI) can provide accurate binding free energy insights in a lead optimization program, but its high computational expense has limited its usage. In the effort of developing an efficient and accurate TI protocol for FabI inhibitors lead optimization program, we carefully compared TI with different Amber molecular dynamics (MD) engines (sander and pmemd), MD simulation lengths, the number of intermediate states and transformation steps, and the Lennard-Jones and Coulomb Softcore potentials parameters in the one-step TI, using eleven benzimidazole inhibitors in complex with Francisella tularensis enoyl acyl reductase (FtFabI). To our knowledge, this is the first study to extensively test the new AMBER MD engine, pmemd, on TI and compare the parameters of the Softcore potentials in the one-step TI in a protein-ligand binding system. The best performing model, the one-step pmemd TI, using 6 intermediate states and 1 ns MD simulations, provides better agreement with experimental results (RMSD = 0.52 kcal/mol) than the best performing implicit solvent method, QM/MM-GBSA from our previous study (RMSD = 3.00 kcal/mol), while maintaining similar efficiency. Briefly, we show the optimized TI protocol to be highly accurate and affordable for the FtFabI system. This approach can be implemented in a larger scale benzimidazole scaffold lead optimization against FtFabI. Lastly, the TI results here also provide structure-activity relationship insights, and suggest the para-halogen in benzimidazole compounds might form a weak halogen bond with FabI, which is a well-known halogen bond favoring enzyme. PMID:26666582
Su, Pin-Chih; Johnson, Michael E
2016-04-05
Thermodynamic integration (TI) can provide accurate binding free energy insights in a lead optimization program, but its high computational expense has limited its usage. In the effort of developing an efficient and accurate TI protocol for FabI inhibitors lead optimization program, we carefully compared TI with different Amber molecular dynamics (MD) engines (sander and pmemd), MD simulation lengths, the number of intermediate states and transformation steps, and the Lennard-Jones and Coulomb Softcore potentials parameters in the one-step TI, using eleven benzimidazole inhibitors in complex with Francisella tularensis enoyl acyl reductase (FtFabI). To our knowledge, this is the first study to extensively test the new AMBER MD engine, pmemd, on TI and compare the parameters of the Softcore potentials in the one-step TI in a protein-ligand binding system. The best performing model, the one-step pmemd TI, using 6 intermediate states and 1 ns MD simulations, provides better agreement with experimental results (RMSD = 0.52 kcal/mol) than the best performing implicit solvent method, QM/MM-GBSA from our previous study (RMSD = 3.00 kcal/mol), while maintaining similar efficiency. Briefly, we show the optimized TI protocol to be highly accurate and affordable for the FtFabI system. This approach can be implemented in a larger scale benzimidazole scaffold lead optimization against FtFabI. Lastly, the TI results here also provide structure-activity relationship insights, and suggest the parahalogen in benzimidazole compounds might form a weak halogen bond with FabI, which is a well-known halogen bond favoring enzyme.
Teaching Global Awareness with Simulations and Games. Grades 6-12. Global Awareness Series.
ERIC Educational Resources Information Center
Lamy, Steven L.; And Others
This teaching guide contains 15 simulation/games for students in grades 6-12 on the topic of global awareness. The overall objective is to help students understand various global concepts and social studies content. Specifically, it gives students the chance to experience and understand international/intercultural situations which involve people…
Improving the Precollegiate Curriculum on Latin America, Grades 6-12. Final Performance Report.
ERIC Educational Resources Information Center
Wirth, John D.
The Latin America Project, which developed print and nonprint materials for use in grades 6-12, is described. The two-year effort was conducted in five phases: survey of existing materials; the development of curriculum units; review of curriculum by teachers attending summer institutes; field testing and evaluation; and dissemination. Titles of…
Teens on Target Violence Prevention Curriculum for Grades 6-12.
ERIC Educational Resources Information Center
Becker, Marla G.; Calhoun, Deane
This curriculum is designed to help schools implement programs to prevent violence among students in grades 6-12. It is a six-session, school based curriculum intended for adolescents who are living in communities experiencing high rates of violence. It is facilitated by trained Teens on Target (TNT) members/peer educators, young people who are…
Health Problems in the Classroom 6-12: An A-Z Reference Guide for Educators.
ERIC Educational Resources Information Center
Huffman, Dolores M.; Fontaine, Karen Lee; Price, Bernadette K.
This guide provides a resource for middle and high school teachers, teacher aides, administrators, and educators, covering health problems that affect students in grades 6-12. The handbook alphabetically lists the most current health concerns for this age group. Part 1, "Health Issues in the Classroom," includes (1) "Health,…
West Nile virus activity--United States, October 6-12, 2004.
2004-10-15
During October 6-12, a total of 86 cases of human West Nile virus (WNV) illness were reported from 18 states (Arizona, Florida, Illinois, Kansas, Louisiana, Michigan, Minnesota, Missouri, Nevada, New Jersey, New Mexico, North Dakota, Ohio, Oklahoma, Pennsylvania, Tennessee, Texas, and Utah).
More Novels and Plays: Thirty Creative Teaching Guides for Grades 6-12.
ERIC Educational Resources Information Center
Worthington, Janet E.; Somers, Albert B.
This companion volume to "Novels and Plays" contains 30 detailed teaching guides for some of the best literature commonly taught in grades 6-12. Twenty of the guides are new to this edition and the others have been updated with fresh related readings, extension resources, and revised questions and activities. Guides are organized according to the…
Teaching Global Awareness Using the Media. Grades 6-12, Global Awareness Series.
ERIC Educational Resources Information Center
Lamy, Steven L.; And Others
This teaching guide on global awareness contains 15 media-related activities for students in grades 6-12. The objective is to help students see how the media affect their opinions and the roles the media plays in world affairs. The activities are divided into five sections. The first section contains a general survey of the students' knowledge of…
ERIC Educational Resources Information Center
What Works Clearinghouse, 2011
2011-01-01
The "University of Chicago School Mathematics Project ("UCSMP") 6-12 Curriculum" is a series of yearlong courses--(1) Transition Mathematics; (2) Algebra; (3) Geometry; (4) Advanced Algebra; (5) Functions, Statistics, and Trigonometry; and (6) Precalculus and Discrete Mathematics--emphasizing problem solving, real-world applications, and the use…
Language Arts Grades 6-12 Program Evaluation, 1996-97.
ERIC Educational Resources Information Center
Wadden, Jerry M.
The Language Arts 6-12 Program of the Des Moines Independent Community School District (Iowa) is directed by its mission statement to provide a quality educational program to a diverse community of students where all are expected to learn. The Language Arts supervisor is responsible for supervising and coordinating all aspects of the middle and…
Measurement of Fluorine Atom Concentrations and Reaction Rates in Chemical Laser Systems.
1982-09-01
Lindholm-Foley theory, using available ab initio and experimentally-derived fluorine atom-rare gas interaction potentials, as well as semiempirical Lennard ... Jones potentials. Good agreement is obtained for broadening by argon and for the temperature dependence of broadening by helium.
From Dimer to Crystal: Calculating the Cohesive Energy of Rare Gas Solids
ERIC Educational Resources Information Center
Halpern, Arthur M.
2012-01-01
An upper-level undergraduate project is described in which students perform high-level ab initio computational scans of the potential energy curves for Ne[subscript 2] and Ar[subscript 2] and obtain the respective Lennard-Jones (LJ) potential parameters [sigma] and [epsilon] for the dimers. Using this information, along with the summation of…
A Computer Simulation of Detonation within an Energetic Molecular Crystal.
1986-07-11
desired condition or time. A nonhomogeneous crystal of diatomic molecules was monitored to discover the atomic interactions during detonation. A Lennard ... Jones potential equation was used to represent the exothermic reaction between diatomic hydrogen and chlorine molecules. This is the first project to
Microcomputer Simulation of Real Gases--Part 1.
ERIC Educational Resources Information Center
Sperandeo-Mineo, R. M.; Tripi, G.
1987-01-01
Describes some simple computer programs designed to simulate the molecular dynamics of two-dimensional systems with a Lennard-Jones interaction potential. Discusses the use of the software in introductory physics courses at the high school and college level. (TW)
2007-11-02
of the individual components or the mixture. Three-dimensional supercritical oxygen vaporization into gaseous oxygen and helium using two-site Lennard ... Jones potentials for the oxygen has been modeled and both the disappearance of surface tension above the critical point and the modification of the
Water vapor continuum in the millimeter spectral region
NASA Astrophysics Data System (ADS)
Ma, Q.; Tipping, R. H.
1990-12-01
A theory is presented for the calculation of the continuous absorption of water molecules in the millimeter spectral region. Using only the known rotational constants, dipole moment, and reasonable values of two Lennard-Jones potential parameters, both the absolute magnitude and temperature dependence of the absorption coefficient are in agreement with empirical results.
An alternative model for estimating liquid diffusion coefficients requiring no viscosity data
NASA Technical Reports Server (NTRS)
Morales, Wilfredo
1993-01-01
An equation, based on the free volume of a liquid solvent, was derived via dimensional analysis, to predict binary diffusion coefficients. The equation assumed that interaction between the solute and liquid solvent molecules followed a Lennard-Jones potential. The equation was compared to other diffusivity equations and was found to give good results over the temperature range examined.
NASA Astrophysics Data System (ADS)
Zarkova, L.; Hohm, U.; Damyanova, M.
2006-09-01
Reference tables of second pVT-virial coefficients B(T ), viscosity η(T ), and self-diffusion ρD(T ) are given for all neat alkanes CnH2n+2, n <6, for temperatures T ⩽1200K starting at 100K for CH4, 150K for C2H6, and 180K for C3H8, n-C4H10, i-C4H10, n-C5H12, i-C5H12, and C(CH3)4. Restricting ourselves to low densities the thermophysical properties are calculated by means of an isotropic (n-6) Lennard-Jones temperature dependent potential (LJTDP). In this model the potential well depth ɛeff(T ) and the separation at minimum energy Rm(eff)(T) are explicitly temperature dependent, whereas the repulsive term n >12 is independent of T. The LJTDP has been used before in order to construct reference tables of thermophysical properties of neat gases [Zarkova and Hohm, J. Phys. Chem. Ref. Data 31, 183 (2002)] and binary mixtures [Zarkova, Hohm, and Damyanova, J. Phys. Chem. Ref. Data 32, 1591 (2003)]. However, those studies were restricted to atoms and globularly shaped nondipolar molecules. Here the approach is extended to elongated, not necessarily spherically symmetric, and in part slightly dipolar molecules. As in previous works the potential parameters ɛ(eff)(T), Rm(eff)(T), and n are determined by minimizing the root-mean-square deviation between calculated and experimentally obtained thermophysical properties B(T ), η(T ), ρD(T ), and the second acoustic virial coefficient β(T ) normalized to their experimental error. In extension of our previous efforts we present a thorough statistical analysis of the experimental input data which gives us the possibility to select primary data which could be used to build up a database.
Electronic properties and carrier mobilities of 6,6,12-graphyne nanoribbons
Ding, Heyu; Huang, Yuanhe; Bai, Hongcun
2015-07-15
Structures, stabilities, electronic properties and carrier mobilities of 6,6,12-graphyne nanoribbons (GyNRs) with armchair and zigzag edges are investigated using the self-consistent field crystal orbital method based on density functional theory. It is found that the 1D GyNRs are more stable than the 2D 6,6,12-graphyne sheet in the view of the Gibbs free energy. The stabilities of these GyNRs decrease as their widths increase. The calculated band structures show that all these GyNRs are semiconductors and that dependence of band gaps on the ribbon width is different from different types of the GyNRs. The carrier mobility was calculated based on the deformation theory and effective mass approach. It is found that the carrier mobilities of these GyNRs can reach the order of 10{sup 5} cm{sup 2} V {sup –1}s{sup –1} at room temperature and are comparable to those of graphene NRs. Moreover, change of the mobilities with change of the ribbon width is quite different from different types of the GyNRs.
Meaningful, Authentic and Place-Based Informal Science Education for 6-12 Students
NASA Astrophysics Data System (ADS)
Ito, E.; Dalbotten, D. M.
2014-12-01
American Indians are underrepresented in STEM and especially in Earth sciences. They have the lowest high school graduation rate and highest unemployment. On the other hand, tribes are in search of qualified young people to work in geo- and hydro-technical fields to manage reservations' natural resources. Dalbotten and her collaborators at the Fond du Lac Band of Lake Superior Chippewa and local 6-12 teachers ran a place-based but non-themed informal monthly science camps (gidakiimanaaniwigamig) for 7 years starting 2003. Camps were held on reservation and some activities focused on observing seasonal changes. The students enjoyed coming to the camps but the camp activities went largely unnoticed by the reservation itself. For the last 5 years, we and the same cast of characters from the gidakiimanaaniwigamig camps ran a very place-based, research-based camp program, manoomin. The research was focused on manoomin (wild rice) which is a culturally important plant and food that grows in local lakes and wetlands. Manmade changes in hydrology, toxic metals from mining, and changing weather patterns due to climate change threaten this precious resource. Our plan was for 6-12 students to investigate the past, the present and the future conditions of manoomin on and around the reservation. It became clear by 3rd year that the research project, as conceived, was overly ambitious and could not be completed at the level we hoped in a camp setting (6 weekend camps = 6 full days per year). However, students felt that they were involved in research that was beneficial to their reservation, reported gaining self-confidence to pursue a career in science, and stated a desired to obtain a college degree. They also became aware of STEM employment opportunities on reservation that they could aim for. The camps also fostered a trusting relationship between researchers at Fond du Lac resource managers and the U. of MN. Based on these experiences, we proposed a new format for these
An Experimental Trial of Adaptive Programming in Drug Court: Outcomes at 6, 12 and 18 Months
Marlowe, Douglas B.; Festinger, David S.; Dugosh, Karen L.; Benasutti, Kathleen M.; Fox, Gloria; Harron, Ashley
2013-01-01
Objectives Test whether an adaptive program improves outcomes in drug court by adjusting the schedule of court hearings and clinical case-management sessions pursuant to a priori performance criteria. Methods Consenting participants in a misdemeanor drug court were randomly assigned to the adaptive program (n = 62) or to a baseline-matching condition (n = 63) in which they attended court hearings based on the results of a criminal risk assessment. Outcome measures were re-arrest rates at 18 months post-entry to the drug court and urine drug test results and structured interview results at 6 and 12 months post-entry. Results Although previously published analyses revealed significantly fewer positive drug tests for participants in the adaptive condition during the first 18 weeks of drug court, current analyses indicate the effects converged during the ensuing year. Between-group differences in new arrest rates, urine drug test results and self-reported psychosocial problems were small and non-statistically significant at 6, 12 and 18 months post-entry. A non-significant trend (p = .10) suggests there may have been a small residual impact (Cramer's ν = .15) on new misdemeanor arrests after 18 months. Conclusions Adaptive programming shows promise for enhancing short-term outcomes in drug courts; however, additional efforts are needed to extend the effects beyond the first 4 to 6 months of enrollment. PMID:25346652
Ishihara, Toru; Sugasawa, Shigemi; Matsuda, Yusuke; Mizuno, Masao
2016-11-16
The aim of this cross-sectional study was to evaluate the relationships between cognitively engaging exercise (i.e., game-based and coordination exercises), executive functions (i.e., inhibitory control and working memory), and physical fitness. Forty junior tennis players (6-12 years old), who regularly participated in tennis lessons (2.55 years, SD = 1.61) prior to the study, were investigated. All participants completed evaluations of executive functions (inhibitory control and working memory) at rest. The duration of each lessons' instructional activities, including coordination training, game-based exercise, rallying, and non-physical activity (explanations and breaks), was recorded. Physical fitness was evaluated using the Tennis Field Test. A longer duration of game-based exercise was positively correlated with inhibitory control and physical fitness. Coordination training was associated with improved working memory. Non-physical activity was inversely correlated with inhibitory control, working memory, and physical fitness. The results suggest that game-based tennis lessons have beneficial effects on inhibitory control and physical fitness levels, and a longer duration of coordination training is associated with better working memory. The present study indicates that shortened non-physical activity time within a sports setting is associated with the development of executive functions and physical fitness.
Whole-grain food consumption in Singaporean children aged 6-12 years.
Neo, Jia En; Binte Mohamed Salleh, Saihah; Toh, Yun Xuan; How, Kesslyn Yan Ling; Tee, Mervin; Mann, Kay; Hopkins, Sinead; Thielecke, Frank; Seal, Chris J; Brownlee, Iain A
2016-01-01
Public health bodies in many countries are attempting to increase population-wide habitual consumption of whole grains. Limited data on dietary habits exist in Singaporean children. The present study therefore aimed to assess whole grain consumption patterns in Singaporean children and compare these with dietary intake, physical activity and health parameters. Dietary intake (assessed by duplicate, multipass, 24-h food recalls), physical activity (by questionnaire) and anthropometric measurements were collected from a cross-section of 561 Singaporean children aged 6-12 years. Intake of whole grains was evaluated using estimates of portion size and international food composition data. Only 38·3 % of participants reported consuming whole grains during the dietary data collection days. Median intake of whole grains in consumers was 15·3 (interquartile range 5·4-34·8) g/d. The most commonly consumed whole-grain food groups were rice (29·5 %), wholemeal bread (28·9 %) and ready-to-eat breakfast cereals (18·8 %). A significantly lower proportion of Malay children (seven out of fifty-eight; P < 0·0001) consumed whole grains than children of other ethnicities. Only 6 % of all children consumed the amount of whole grains most commonly associated with improved health outcomes (48 g/d). There was no relationship between whole grain consumption patterns and BMI, waist circumference or physical activity but higher whole grain intake was associated with increased fruit, vegetable and dairy product consumption (P < 0·001). These findings demonstrate that consumption of whole grain foods is low at a population level and infrequent in Singaporean children. Future drives to increase whole-grain food consumption in this population are likely to require input from multiple stakeholders.
Interaction of endokinin A/B and (Mpa(6))-γ2-MSH-6-12 in pain regulation in mice.
Zhou, Lanxia; Yang, Qing; He, Chunbo; Wei, Chunnan; Yang, Yinliang; Dong, Shouliang
2015-10-01
The present study focused on the interactive effects of (Mpa(6))-γ2-MSH-6-12 (Mpa, spinal level) and endokinin A/B (EKA/B, supraspinal level) on pain regulation in mice. EKA/B (30 pmol) only weakened 100 pmol Mpa-induced hyperalgesia at 5 min, but could enhance it during 20-30 min. However, EKA/B (100 pmol) antagonized all dose levels of Mpa significantly at 5 min and blocked them completely at 10 min. EKA/B (3 nmol) co-injected with Mpa presented marked analgesia at 5 min and enduring hyperalgesia within 20-60 min. To investigate the underlying mechanisms between Mpa and EKA/B, SR140333B and SR142801 (NK1 and NK3 receptor antagonists, respectively) were utilized. SR140333B had no influence on Mpa, while SR142801 potentiated it during 20-30 min. Whereas, SR140333B and SR142801 could block the co-administration of Mpa and EKA/B (30 pmol) separately at 5 min and 30 min. These phenomena might attribute to that these two antagonists promoted the antagonism of EKA/B (30 pmol) at the early stage, while antagonized EKA/B preferentially in the latter period. SR140333B weakened the analgesia of EKA/B (3 nmol), but produced no effect on Mpa. However, SR140333B failed to affect the co-injection of Mpa and EKA/B, which implied that EKA/B cooperated with Mpa prior to SR140333B. These results could potentially help to better understand the interaction of NK and MrgC receptors in pain regulation in mice.
Müller, Erich A; Mejía, Andrés
2011-11-10
Canonical ensemble molecular dynamics (MD) simulations are reported which compute both the vapor-liquid equilibrium properties (vapor pressure and liquid and vapor densities) and the interfacial properties (density profiles, interfacial tensions, entropy and enthalpy of surface formation) of four long-chained n-alkanes: n-decane (n-C(10)), n-eicosane (n-C(20)), n-hexacontane (n-C(60)), and n-decacontane (n-C(100)). Three of the most commonly employed united-atom (UA) force fields for alkanes (SKS: Smit, B.; Karaborni, S.; Siepmann, J. I. J. Chem. Phys. 1995,102, 2126-2140; J. Chem. Phys. 1998,109, 352; NERD: Nath, S. K.; Escobedo, F. A.; de Pablo, J. J. J. Chem. Phys. 1998, 108, 9905-9911; and TraPPE: Martin M. G.; Siepmann, J. I. J. Phys. Chem. B1998, 102, 2569-2577.) are critically appraised. The computed results have been compared to the available experimental data and those fitted using the square gradient theory (SGT). In the latter approach, the Lennard-Jones chain equation of state (EoS), appropriately parametrized for long hydrocarbons, is used to model the homogeneous bulk phase Helmholtz energy. The MD results for phase equilibria of n-decane and n-eicosane exhibit sensible agreement both to the experimental data and EoS correlation for all potentials tested, with the TraPPE potential showing the lowest deviations. However, as the molecular chain increases to n-hexacontane and n-decacontane, the reliability of the UA potentials decreases, showing notorious subpredictions of both saturated liquid density and vapor pressure. Based on the recommended data and EoS results for the heaviest hydrocarbons, it is possible to attest, that in this extreme, the TraPPE potential shows the lowest liquid density deviations. The low absolute values of the vapor pressure preclude the discrimination among the three UA potentials studied. On the other hand, interfacial properties are very sensitive to the type of UA potential thus allowing a differentiation of the
Hwang, Kao-Pin; Hsu, Yu-Lung; Hsieh, Tsung-Hsueh; Lin, Hsiao-Chuan; Yen, Ting-Yu; Wei, Hsiu-Mei; Lin, Hung-Chih; Chen, An-Chyi; Chow, Julie Chi; Huang, Li-Min
2014-05-01
This prospective study aimed to investigate the immune responses and safety of an influenza vaccine in vaccine-naïve infants aged 6-12 months, and was conducted from November 2010 to May 2011. Fifty-nine infants aged 6-12 months received two doses of trivalent inactivated influenza vaccine 4 weeks apart. Hemagglutination inhibition titers were measured 4 weeks after the two doses of study vaccine. Based on the assumption that a hemagglutination inhibition titer of 1:40 or greater against the antigen would be protective in adults, two doses of the study vaccine generated a protective immune response of 63.2% against influenza A(H1N1), 82.5% against influenza A(H3N2) and 38.6% against influenza B viruses in infants aged 6-12 months. The geometric mean fold rises against influenza type A and B viruses also met the European Medicines Agency criteria for flu vaccines. The solicited events within 7 days after vaccination were mild in intensity. No deaths or adverse events such as optic neuritis, cranial neuropathy, and brachial neuropathy or Guillain-Barre syndrome were reported. Two doses of inactivated influenza vaccine were well tolerated and induced a protective immune response against influenza in infants aged 6-12 months.
Second virial coefficient and mechanical moduli of metallic glasses
NASA Astrophysics Data System (ADS)
Cao, Wan Qiang
2013-10-01
The relationship between the bulk, shear moduli and second virial coefficient of amorphous materials is derived according to their dependences with the radial distribution function. Lennard-Jones-Gaussian potential is used to investigate the relationship between second virial coefficient and temperature, where Lennard-Jones potential represents interactions with the nearest neighbor atoms, and Gaussian potential is responsible for the multi-atom interactions including the next nearest neighbor atoms and heterogeneous structures for a metallic glass. The results show that deep potential well formed by Gaussian potential causes a large second virial coefficient at low temperatures, which is very obvious for the larger fragility glasses. The quadratic form relationship of shear modulus and compositions is proposed, and confirmed by the experimental results of PdxNi100-x-20P20 alloy.
NASA Astrophysics Data System (ADS)
Rabochiy, Pyotr; Lubchenko, Vassiliy
2012-02-01
We establish, via classical density functional theory, that the crossover to activated transport in liquids takes place when the depth of the metastable minimum in the free energy corresponding to long-lived aperiodic structures reaches a certain near universal value. We show that the particle vibrational displacement is strongly correlated with this depth in a broad range of pressure and temperature, thus providing basis for a Lindemann-like criterion for the onset of activated transport in liquids. The configurational entropy at the crossover temperature Tcr, too, is found to be nearly system-independent, consistent with the random first order transition theory. We show that to reproduce existing data for the pressure dependence of Tcr, the liquid must increase its coordination with pressure. Upon increasing pressure at fixed coordination, the liquid's fragility is predicted to exhibit re-entrant behavior. This prediction is consistent with glycerol data but is in contrast with data in several organic liquids and polymers, whose fragility monotonically decreases with pressure in the so far accessed pressure range. Allowing for increase in coordination with pressure mitigates the disagreement, owing to the resulting decrease in the thermal expansivity. Finally, we rationalize the correlation between the isobaric and isochoric fragilities put forth by Casalini and Roland [Phys. Rev. E 72, 031503 (2005), 10.1103/PhysRevE.72.031503] and make predictions on the limiting behavior of the fragility at high pressure.
Surface Modification in Control SiO2 Fiber Fracture.
1981-10-01
assuming the Lennard - Jones potential . The results show that the potential due to the dispersion forces falls obB if rapidly with the distance from...A. susceptibility for crack propagation. Gases containing straight or branched chain hydrocarbons are expected to reduce the absorption potential ...fracture strength. Most optical- fibers currently in service have a composition that varies continuously from a Ucore of mixed GeO2 - Sio2 composit
Determination of arm fat area and arm muscle area norms in children 6-12 years of age in Bursa.
Günay, U; Sapan, N; Salih, C; Doğruyol, H
1990-01-01
Since arm fat area and arm muscle area measurements are said to assess the calorie and protein reserves in the body more accurately than triceps skinfold thickness measurements, we decided to use this system on 1497 girls and 1651 boys who were pupils in elementary schools in Bursa. From the data obtained, percentile norms for the children aged between 6-12 were calculated and percentile curves were drawn. The data that we collected can be used in future nutritional surveys.
The impact of bonded interactions on the ground-state geometries of a small flexible polymer
NASA Astrophysics Data System (ADS)
Koci, Tomas; Qi, Kai; Bachmann, Michael
2016-10-01
Bonded interactions in coarse-grained models of elastic polymers are commonly represented by the finitely extensible nonlinear elastic (FENE) potential. In this study, we perform parallel multicanonical Monte Carlo simulations to examine the impact of an additional Lennard-Jones term in the bonded potential on the geometry of ground-state structures of a short polymer. Employing microcanonical inflection point analysis and conformational analysis, we construct a hyper-phase diagram and identify ground-state structures with two distinct geometries.
COMPUTER ’EXPERIMENTS’ ON CLASSICAL FLUIDS. II. EQUILIBRIUM CORRELATION FUNCTIONS,
Lennard - Jones potential. The behaviour of the correlation function at large distance, and that of its Fourier transform at large wave number are discussed in detail and shown to be related to the existence of a strong repulsion in the potential. A simple hard sphere model is shown to reproduce very well the Fourier transform of those correlations functions at high density, the only parameter of the model being the diameter a of the hard spheres.
NASA Astrophysics Data System (ADS)
Cuadros, F.; Mulero, A.; Faundez, C. A.
The Lennard-Jones attractive and repulsive contributions of intermolecular forces (as separated in the Weeks-Chandler-Andersen (WCA) theory) to the pressure and chemical potential of coexisting vapour and liquid phases are obtained by using an equation of state recently proposed by us. Some comments are given about the computer simulation results obtained by Plackov and Sadus (1997, Fluid Phase Equilib., 134, 77) using the McQuarrie-Katz separation of the intermolecular potential.
Molecular dynamic simulation of Copper and Platinum nanoparticles Poiseuille flow in a nanochannels
NASA Astrophysics Data System (ADS)
Toghraie, Davood; Mokhtari, Majid; Afrand, Masoud
2016-10-01
In this paper, simulation of Poiseuille flow within nanochannel containing Copper and Platinum particles has been performed using molecular dynamic (MD). In this simulation LAMMPS code is used to simulate three-dimensional Poiseuille flow. The atomic interaction is governed by the modified Lennard-Jones potential. To study the wall effects on the surface tension and density profile, we placed two solid walls, one at the bottom boundary and the other at the top boundary. For solid-liquid interactions, the modified Lennard-Jones potential function was used. Velocity profiles and distribution of temperature and density have been obtained, and agglutination of nanoparticles has been discussed. It has also shown that with more particles, less time is required for the particles to fuse or agglutinate. Also, we can conclude that the agglutination time in nanochannel with Copper particles is faster that in Platinum nanoparticles. Finally, it is demonstrated that using nanoparticles raises thermal conduction in the channel.
Transferability of a coarse-grained atactic polystyrene model: the non-bonded potential effect.
Xiao, Qiang; Guo, Hongxia
2016-11-02
In this paper, we construct an efficient and simple coarse grained (CG) model for atactic polystyrene (PS) by using a 1 : 1 mapping scheme at 463 K and 1 atm pressure and derive the corresponding bonded and non-bonded potentials in the CG force field (FF) via a direct Boltzmann inversion approach and a combined structure-based and thermodynamic quantities-based CG method, respectively. For computational considerations, the non-bonded interaction between CG particles is described by Lennard-Jones (LJ) type potentials, and both the radial distribution function (RDF) and the bulk density of the atomistic simulations are taken as target properties in the parameterization of the two LJ parameters. To shed light on the choice of LJ forms of CG non-bonded potentials when designing the CG models, a series of CG models with different LJ potentials are constructed and compared in order to understand how the quality of a CG model in reproducing the structure and thermodynamic properties of chemically realistic systems is affected by the choice of non-bonded potentials. We find that with our structural and thermodynamics combined CG method to construct the CG FF at a single thermodynamic state point without any temperature dependent LJ potential correction and/or pressure optimization, the resulting CG models possess good temperature transferability in a wide range of temperatures 300-600 K, where both the target properties and several other static properties (such as thermal expansion coefficient and mean-square radius of gyration) are generally reproduced. Furthermore, the non-bonded LJ potential influences the density response of CG models to the temperature change, i.e., CG models with harder LJ potentials show better temperature transferability than the softer ones. Meanwhile, the derived Tg increases with increasing LJ repulsion strength while thermal expansion coefficients in both melt and glass states are lowered as the LJ potential hardens. With regard to the
Some comments on the second virial coefficient of semiflexible polymers.
Ida, Daichi; Yoshizaki, Takenao
2008-10-28
A Monte Carlo study is made of the mean-square radius of gyration S(2) and second virial coefficient A(2) for the two freely rotating chains with the Lennard-Jones (LJ) 6-12 potential and the hard-sphere (HS) one in the range of the bond angle theta from 109 degrees (typical flexible chain) to 175 degrees (typical semiflexible or stiff chain) and in the range of the number n of bonds from 6 to 1000. It is shown that a value may be properly assigned to the collision diameter of the HS potential so that S(2) of the chain with the HS potential agrees well with that of the chain with the LJ one whose parameter values correspond to a good-solvent condition irrespective of the chain stiffness. It is then found that A(2) of the latter chain becomes remarkably smaller than that of the former as the chain stiffness is increased. The result implies that the binary-cluster approximation does not seem to work well for typical semiflexible and stiff polymers.
Theoretical calculation of heat capacity by using third virial coefficient
NASA Astrophysics Data System (ADS)
Mamedov, Bahtiyar Akber; Somuncu, Elif
2017-02-01
We have presented a new formula to determine the heat capacity for real gaseous. This formula is a simple and more accurate analytical approximation for heat capacity using third virial coefficient over Lennard-Jones (12-6) potential. The calculation results of heat capacity show a good agreement with the data in the literature. The consistency of results demonstrates that the proposed formula is applicable to real gaseous.
Computer simulation of surface and film processes
NASA Technical Reports Server (NTRS)
Tiller, W. A.
1981-01-01
A molecular dynamics technique based upon Lennard-Jones type pair interactions is used to investigate time-dependent as well as equilibrium properties. The case study deals with systems containing Si and O atoms. In this case a more involved potential energy function (PEF) is employed and the system is simulated via a Monte-Carlo procedure. This furnishes the equilibrium properties of the system at its interfaces and surfaces as well as in the bulk.
Collision integrals for isotopic hydrogen molecules.
NASA Technical Reports Server (NTRS)
Brown, N. J.; Munn, R. J.
1972-01-01
The study was undertaken to determine the effects of reduced mass and differences in asymmetry on the collision integrals and thermal diffusion factors of isotopic hydrogen systems. Each system selected for study consisted of two diatoms, one in the j = 0 rotation state and the other in the j = 1 state. The molecules interacted with a Lennard-Jones type potential modified to include angular terms. A set of cross sections and collision integrals were obtained for each system.
Maxwellian distribution in non-classical regime
NASA Astrophysics Data System (ADS)
Mohazzabi, Pirooz; L. Helvey, Shannon; McCumber, Jeremy
2002-12-01
A molecular dynamics investigation shows that the assumption of molecular chaos remains valid in the non-classical regime. Consequently, the velocity distribution function of an extremely dense system of spinless particles relaxes into Maxwellian, even in the presence of arbitrary interactions between the particles of the system. Systems with densities exceeding 30 times solid densities are investigated using a soft Lennard-Jones interparticle potential energy function.
Plurality of inherent states in equiatomic solid solutions
NASA Astrophysics Data System (ADS)
Demkowicz, M. J.
2017-03-01
We show that single-crystal, equiatomic solid solutions of Lennard-Jones particles have a plurality of inherent states: mechanically stable configurations with identical lattice site occupancies, yet distinct potential-energy minima. External loading triggers transitions between inherent states via localized shear transformations. A plurality of inherent states and mechanically activated transitions between them make equiatomic solid solutions an unusual form of matter: one that is crystalline like single-component metals, yet exhibits localized shear transformations like metallic glasses.
Identification of structure in condensed matter with the topological cluster classification
NASA Astrophysics Data System (ADS)
Malins, Alex; Williams, Stephen R.; Eggers, Jens; Royall, C. Patrick
2013-12-01
We describe the topological cluster classification (TCC) algorithm. The TCC detects local structures with bond topologies similar to isolated clusters which minimise the potential energy for a number of monatomic and binary simple liquids with m ⩽ 13 particles. We detail a modified Voronoi bond detection method that optimizes the cluster detection. The method to identify each cluster is outlined, and a test example of Lennard-Jones liquid and crystal phases is considered and critically examined.
The second virial coefficients of some halogenated ethanes
NASA Astrophysics Data System (ADS)
Kohler, Friedrich; van Nhu, Nguyen
The second virial coefficients of 1,1-difluoroethane, 1,1,1-trifluoroethane, 1,1,1,2-tetrafluoroethane and 1-chloro-1,1-difluoroethane have been calculated on the basis of two-centre-Lennard-Jones + superimposed dipole model potentials and compared with experimental results. These can be explained taking into account the reduced dipole moments and the angle between dipole moment and molecular axis.
Vibrational properties of noncovalently oligothiophene-functionalized graphene nanomaterials
NASA Astrophysics Data System (ADS)
Boutahir, M.; Rahmani, A. H.; Chadli, H.; Rahmani, A.
2016-10-01
In this paper, the non resonant Raman spectra of hybrid nanostructures obtained by confinement of oligothiophene derivatives in two sheets of graphene are calculated in the framework of spectral moments method, together with a bond-polarizability model. Minimum energy calculations are performed, using a convenient Lennard-Jones expression of the van der Waals intermolecular potential, to derive the optimum configurations of oligothiophene with graphene. Parallel configuration of thiophene molecules with respect to the graphene plane was considered.
NASA Astrophysics Data System (ADS)
Bondarenko, Natalya V.; Nedolya, Anatoliy V.
2017-02-01
The energy of the isolated iron-nickel nanocluster was calculated by molecular mechanics method using Lennard-Jones potential. The cluster included a carbon atom that drifted from an inside octahedral interstice to a tetrahedral interstice in
Multiscale Modeling of Semiconductor Nanostructures
2011-11-23
Van der Waals Interaction between Two Crossed Carbon Nanotubes [A. I. Zhbanov, E. G. Pogorelov, and Y.-C. Chang, ACS nano , 4(10),5937-45 (2010...The analytical expressions for the van der Waals potential energy and force between two crossed carbon nanotubes are presented. The Lennard-Jones...emitters, and the anode current are also obtained. 6. Universal curves for van der Waals interaction between single-wall carbon nanotubes [Evgeny G
Soddemann, Thomas; Dünweg, Burkhard; Kremer, Kurt
2003-10-01
We discuss dissipative particle dynamics as a thermostat to molecular dynamics, and highlight some of its virtues: (i) universal applicability irrespective of the interatomic potential; (ii) correct and unscreened reproduction of hydrodynamic correlations; (iii) stabilization of the numerical integration of the equations of motion; and (iv) the avoidance of a profile bias in boundary-driven nonequilibrium simulations of shear flow. Numerical results on a repulsive Lennard-Jones fluid illustrate our arguments.
New look at thermodynamics of gas and at clusterization
NASA Astrophysics Data System (ADS)
Maslov, V. P.
2008-12-01
In the paper, by using the example of a rigorous formulation and rigorous proof of the Maxwell distribution, estimates for the distribution in dependence of the parameter N (the number of particles) are established. Further, the problem concerning the creation of dimers in classical gas is regarded as an analog of Bose condensation, and estimates for the lower level of the analog of Bose condensation are proved. The relationship between this level and the theory of “capture” in the scattering problem corresponding to interaction in the form of Lennard-Jones potential is clarified. The equation of state of a nonideal gas as a result of pairwise interaction of particles in the Lennard-Jones and Kihara models is derived. New quantum equations for the transfer of neutral gas consisting of particles with evenly and oddly many neutrons in capillaries and nanotubes are also presented.
NASA Astrophysics Data System (ADS)
von Rudorff, Guido Falk; Wehmeyer, Christoph; Sebastiani, Daniel
2014-06-01
We adapt a swarm-intelligence-based optimization method (the artificial bee colony algorithm, ABC) to enhance its parallel scaling properties and to improve the escaping behavior from deep local minima. Specifically, we apply the approach to the geometry optimization of Lennard-Jones clusters. We illustrate the performance and the scaling properties of the parallelization scheme for several system sizes (5-20 particles). Our main findings are specific recommendations for ranges of the parameters of the ABC algorithm which yield maximal performance for Lennard-Jones clusters and Morse clusters. The suggested parameter ranges for these different interaction potentials turn out to be very similar; thus, we believe that our reported values are fairly general for the ABC algorithm applied to chemical optimization problems.
Nonlinear dynamics of bi-layered graphene sheet, double-walled carbon nanotube and nanotube bundle
NASA Astrophysics Data System (ADS)
Gajbhiye, Sachin O.; Singh, S. P.
2016-05-01
Due to strong van der Waals (vdW) interactions, the graphene sheets and nanotubes stick to each other and form clusters of these corresponding nanostructures, viz. bi-layered graphene sheet (BLGS), double-walled carbon nanotube (DWCNT) and nanotube bundle (NB) or ropes. This research work is concerned with the study of nonlinear dynamics of BLGS, DWCNT and NB due to nonlinear interlayer vdW forces using multiscale atomistic finite element method. The energy between two adjacent carbon atoms is represented by the multibody interatomic Tersoff-Brenner potential, whereas the nonlinear interlayer vdW forces are represented by Lennard-Jones 6-12 potential function. The equivalent nonlinear material model of carbon-carbon bond is used to model it based on its force-deflection relation. Newmark's algorithm is used to solve the nonlinear matrix equation governing the motion of the BLGS, DWCNT and NB. An impulse and harmonic excitations are used to excite these nanostructures under cantilevered, bridged and clamped boundary conditions. The frequency responses of these nanostructures are computed, and the dominant resonant frequencies are identified. Along with the forced vibration of these structures, the eigenvalue extraction problem of armchair and zigzag NB is also considered. The natural frequencies and corresponding mode shapes are extracted for the different length and boundary conditions of the nanotube bundle.
Simulation optimization of spherical non-polar guest recognition by deep-cavity cavitands.
Wanjari, Piyush P; Gibb, Bruce C; Ashbaugh, Henry S
2013-12-21
Biomimetic deep-cavity cavitand hosts possess unique recognition and encapsulation properties that make them capable of selectively binding a range of non-polar guests within their hydrophobic pocket. Adamantane based derivatives which snuggly fit within the pocket of octa-acid deep cavity cavitands exhibit some of the strongest host binding. Here we explore the roles of guest size and attractiveness on optimizing guest binding to form 1:1 complexes with octa-acid cavitands in water. Specifically we simulate the water-mediated interactions of the cavitand with adamantane and a range of simple Lennard-Jones guests of varying diameter and attractive well-depth. Initial simulations performed with methane indicate hydrated methanes preferentially reside within the host pocket, although these guests frequently trade places with water and other methanes in bulk solution. The interaction strength of hydrophobic guests increases with increasing size from sizes slightly smaller than methane to Lennard-Jones guests comparable in size to adamantane. Over this guest size range the preferential guest binding location migrates from the bottom of the host pocket upwards. For guests larger than adamantane, however, binding becomes less favorable as the minimum in the potential-of-mean force shifts to the cavitand face around the portal. For a fixed guest diameter, the Lennard-Jones well-depth is found to systematically shift the guest-host potential-of-mean force to lower free energies, however, the optimal guest size is found to be insensitive to increasing well-depth. Ultimately our simulations show that adamantane lies within the optimal range of guest sizes with significant attractive interactions to match the most tightly bound Lennard-Jones guests studied.
Ab initio parameterization of YFF1, a universal force field for drug-design applications.
Yakovenko, Olexandr Ya; Li, Yvonne Y; Oliferenko, Alexander A; Vashchenko, Ganna M; Bdzhola, Volodymyr G; Jones, Steven J M
2012-02-01
The YFF1 is a new universal molecular mechanic force field designed for drug discovery purposes. The electrostatic part of YFF1 has already been parameterized to reproduce ab initio calculated dipole and quadrupole moments. Now we report a parameterization of the van der Waals interactions (vdW) for the same atom types that were previously defined. The 6-12 Lennard-Jones potential terms were parameterized against homodimerization energies calculated at the MP2/6-31 G level of theory. The Boys-Bernardi counterpoise correction was employed to account for the basis-set superposition error. As a source of structural information we used about 2,400 neutral compounds from the ZINC2007 database. About 6,600 homodimeric configurations were generated from this dataset. A special "closure" procedure was designed to accelerate the parameters fitting. As a result, dimerization energies of small organic compounds are reproduced with an average unsigned error of 1.1 kcal mol(-1). Although the primary goal of this work was to parameterize nonbonded interactions, bonded parameters were also derived, by fitting to PM6 semiempirically optimized geometries of approximately 20,000 compounds.
NASA Astrophysics Data System (ADS)
Gamache, Robert R.
2001-07-01
For the first time the half-width within the complex Robert-Bonamy (CRB) formalism is calculated without making the mean relative thermal velocity approximation. The application is to the nitrogen-broadened half-width of the 500.4-GHz transition (342 32←341 33) of the ground vibrational state of ozone. For each state of the perturber, the optical cross sections are determined at a number of velocities with the intermolecular potential taken as a sum of electrostatic contributions and Lennard-Jones (6-12) atom-atom components. The dynamics of the collision process are correct to second order in time. Using a nonlinear least-squares fitting method, the optical cross sections are fit to a double power law, which allows the velocity integral for the half-width to be done analytically. The results are compared with the mean relative thermal velocity complex Robert-Bonamy calculations and with measurement. The temperature dependence of the half-width, which is necessary for reduction of remotely sensed data, is determined from both methods and compared with experiment.
Oscillatory characteristics of metallic nanoparticles inside lipid nanotubes
NASA Astrophysics Data System (ADS)
Sadeghi, Fatemeh; Ansari, Reza; Darvizeh, Mansour
2015-12-01
This study is concerned with the oscillatory behavior of metallic nanoparticles, and in particular silver and gold nanoparticles, inside lipid nanotubes (LNTs) using the continuum approximation along with the 6-12 Lennard-Jones (LJ) potential function. The nanoparticle is modeled as a dense sphere and the LNT is assumed to be comprised of six layers including two head groups, two intermediate layers and two tail groups. To evaluate van der Waals (vdW) interactions, analytical expressions are first derived through undertaking surface and volume integrals which are then validated by a fully numerical scheme based on the differential quadrature (DQ) technique. Using the actual force distribution between the two interacting molecules, the equation of motion is directly solved utilizing the Runge-Kutta numerical integration scheme to arrive at the time history of displacement and velocity of the inner core. Also, a semi-analytical expression incorporating both geometrical parameters and initial conditions is introduced for the precise evaluation of oscillation frequency. A comprehensive study is conducted to gain an insight into the influences of nanoparticle radius, LNT length, head and tail group thicknesses and initial conditions on the oscillatory behavior of the metallic nanoparticles inside LNTs. It is found that the escape velocity and oscillation frequency of silver nanoparticles are higher than those of gold ones. It is further shown that the oscillation frequency is less affected by the tail group thickness when compared to the head group thickness.
NASA Astrophysics Data System (ADS)
Colmont, Jean-Marcel; Priem, Dominique; Wlodarczak, Georges; Gamache, Robert R.
1999-02-01
In this paper we report the results of both an experimental and theoretical study of the halfwidths of two transitions of water vapor. Measurements on the lines of the H216O and H218O isotopomers located at 325.1 and 203.4 GHz, respectively, were carried out in the temperature range 300-393 K, with N2and O2as perturbing gases. The foreign-broadening coefficients and their temperature-dependence parameters were determined assuming a Voigt profile and the usual temperature dependence for the halfwidth. The retrieved values are compared to values calculated using the complex semiclassical formalism of Robert and Bonamy. The assumed intermolecular potential is a combination of electrostatic and atom-atom components. This last contribution is defined as the sum of pairwise Lennard-Jones 6-12 interactions between the atoms of H2O and the atoms of the perturbing molecules expanded to eighth order. Also calculated are the pressure-induced shifts of the spectral lines for temperatures from 200 to 400 K. Calculated and experimental results are in good agreement, within ±3.2%, except for the N2-broadening temperature coefficients, for which there are discrepancies as high as 23%. Air-broadening parameters are determined following the classical relation: γ (air) = 0.79γ (N2) + 0.21γ (O2).
Pang, Yuan-Ping
2015-02-06
1-4 interaction scaling factors are used in AMBER forcefields to reduce the exaggeration of short-range repulsion caused by the 6-12 Lennard-Jones potential and a nonpolarizable charge model and to obtain better agreements of small-molecule conformational energies with experimental data. However, the effects of these scaling factors on protein secondary structure conformations have not been investigated until now. This article reports the finding that the 1-4 interactions among the protein backbone atoms separated by three consecutive covalent bonds are more repulsive in the α-helix conformation than in two β-strand conformations. Therefore, the 1-4 interaction scaling factors of protein backbone torsions ϕ and ψ control the conformational equilibrium between α-helix and β-strand. Molecular dynamics simulations confirm that reducing the ϕ and ψ scaling factors readily converts the α-helix conformation of AcO-(AAQAA)3-NH2 to a β-strand conformation, and the reverse occurs when these scaling factors are increased. These results suggest that the ϕ and ψ scaling factors can be used to generate the α-helix or β-strand conformation in situ and to control the propensities of a forcefield for adopting secondary structure elements.
Energy behaviour for DNA translocation through graphene nanopores.
Alshehri, Mansoor H; Cox, Barry J; Hill, James M
2015-12-21
Nanoparticles have considerable promise for many applications in electronics, energy storage, bioscience and biotechnologies. Here we use applied mathematical modelling to exploit the basic principles of mechanics and the 6-12 Lennard-Jones potential function together with the continuum approach, which assumes that a discrete atomic structure can be replaced by an average constant atomic surface density of atoms that is assumed to be smeared over each molecule. We identify a circular hole in a graphene sheet as a nanopore and we consider the molecular interaction energy for both single-strand and double-strand DNA molecules assumed to move through the circular hole in a graphene sheet to determine the radius b of the hole that gives the minimum energy. By minimizing the interaction energy, we observe that the single-strand DNA and double-strand DNA molecules penetrate through a graphene nanopore when the pore radii b> 7.8Å and b> 12.7Å, respectively. Our results can be adopted to offer new applications in the atomic surface processes and electronic sensing.
NASA Astrophysics Data System (ADS)
Alshehri, Mansoor H.; Cox, Barry J.; Hill, James M.
2013-11-01
Here we use classical applied mathematical modeling to determine surface binding energies between both single-strand and double-strand DNA molecules interacting with a graphene sheet. We adopt basic mechanical principles to exploit the 6-12 Lennard-Jones potential function and the continuum approximation, which assumes that intermolecular interactions can be approximated by average atomic line or surface densities. The minimum binding energy occurs when the single-strand DNA molecule is centred 20.2 Å from the surface of the graphene and the double-strand DNA molecule is centred 20.3 Å from the surface, noting that these close values apply for the case when the axis of the helix is perpendicular to the surface of graphene. For the case when the axis of the helix is parallel to the surface, the minimum binding energy occurs when the axis of the single-strand molecule is 8.3 Å from the surface, and the double-strand molecule has axis 13.3 Å from the surface. For arbitrary tilted axis, we determine the optimal angles Ω of the axis of the helix, which give the minimum values of the binding energies, and we observe that the optimal angles tend to occur in the intervals Ω ∈ ( π /4 ,π/2) and Ω ∈ ( π /7 ,π/5) for the single and double-strand DNA molecules, respectively.
Holan, Vladimir; Javorkova, Eliska; Trosan, Peter
2013-01-01
The injured or otherwise damaged cornea is healed by limbal stem cells (LSC). If the limbus where LSC reside is also damaged or nonfunctional, the cornea cannot heal properly and this defect leads to impaired vision that can result in blindness. The only way to treat total LSC deficiency is by transplantation of limbal tissue or a transfer of LSC. Recently, mesenchymal stem cells (MSC) have been shown as another promising source of stem cells for corneal healing and regeneration. Here, we describe a protocol for the use of polyamide 6/12 nanofiber scaffolds for the growth of MSC and LSC, and for their transfer onto a mechanically damaged ocular surface in the experimental mouse model.
Quantifying Non-Equilibrium in Hypersonic Flows Using Entropy Generation
2007-03-01
Lennard - Jones model is offered as an alternative to Sutherland?s Law for calculating viscosity and thermal conductivity. The two are compared, and parameters offering a good fit for these flows are suggested for the Lennard - Jones
Role of side-chain interactions on the formation of α -helices in model peptides
NASA Astrophysics Data System (ADS)
Mahmoudinobar, Farbod; Dias, Cristiano L.; Zangi, Ronen
2015-03-01
The role played by side-chain interactions on the formation of α -helices is studied using extensive all-atom molecular dynamics simulations of polyalanine-like peptides in explicit TIP4P water. The peptide is described by the OPLS-AA force field except for the Lennard-Jones interaction between Cβ-Cβ atoms, which is modified systematically. We identify values of the Lennard-Jones parameter that promote α -helix formation. To rationalize these results, potentials of mean force (PMF) between methane-like molecules that mimic side chains in our polyalanine-like peptides are computed. These PMF exhibit a complex distance dependence where global and local minima are separated by an energy barrier. We show that α -helix propensity correlates with values of these PMF at distances corresponding to Cβ-Cβ of i -i +3 and other nearest neighbors in the α -helix. In particular, the set of Lennard-Jones parameters that promote α -helices is characterized by PMF that exhibit a global minimum at distances corresponding to i -i +3 neighbors in α -helices. Implications of these results are discussed.
Madan, B; Lee, B
1994-08-01
The free energies of cavity formation in water with and without hydrogen bonding potential were computed from the results of a set of Monte Carlo simulation calculations on pure liquid TIP4P water model and on the same model but with the electrostatic charges turned off (Lennard-Jones liquid). The free energies of cavity formation in the Lennard-Jones liquids are higher than or approximately equal to those in TIP4P water, depending, respectively, on whether the Lennard-Jones size parameter sigma is set equal to 3.15 A, which is the value of sigma for TIP4P water, or to 2.8 A, which is the commonly assumed value for the oxygen-oxygen distance between two hydrogen-bonded water molecules. This result indicates that changes in the hydrogen-bonded structure of water and/or in the orientational degree of freedom of water are not essential features in the production of the large free energy change upon cavity formation.
Role of side-chain interactions on the formation of α-helices in model peptides.
Mahmoudinobar, Farbod; Dias, Cristiano L; Zangi, Ronen
2015-03-01
The role played by side-chain interactions on the formation of α-helices is studied using extensive all-atom molecular dynamics simulations of polyalanine-like peptides in explicit TIP4P water. The peptide is described by the OPLS-AA force field except for the Lennard-Jones interaction between Cβ-Cβ atoms, which is modified systematically. We identify values of the Lennard-Jones parameter that promote α-helix formation. To rationalize these results, potentials of mean force (PMF) between methane-like molecules that mimic side chains in our polyalanine-like peptides are computed. These PMF exhibit a complex distance dependence where global and local minima are separated by an energy barrier. We show that α-helix propensity correlates with values of these PMF at distances corresponding to Cβ-Cβ of i-i+3 and other nearest neighbors in the α-helix. In particular, the set of Lennard-Jones parameters that promote α-helices is characterized by PMF that exhibit a global minimum at distances corresponding to i-i+3 neighbors in α-helices. Implications of these results are discussed.
Intermolecular interactions and the thermodynamic properties of supercritical fluids
NASA Astrophysics Data System (ADS)
Yigzawe, Tesfaye M.; Sadus, Richard J.
2013-05-01
The role of different contributions to intermolecular interactions on the thermodynamic properties of supercritical fluids is investigated. Molecular dynamics simulation results are reported for the energy, pressure, thermal pressure coefficient, thermal expansion coefficient, isothermal and adiabatic compressibilities, isobaric and isochoric heat capacities, Joule-Thomson coefficient, and speed of sound of fluids interacting via both the Lennard-Jones and Weeks-Chandler-Andersen potentials. These properties were obtained for a wide range of temperatures, pressures, and densities. For each thermodynamic property, an excess value is determined to distinguish between attraction and repulsion. It is found that the contributions of intermolecular interactions have varying effects depending on the thermodynamic property. The maxima exhibited by the isochoric and isobaric heat capacities, isothermal compressibilities, and thermal expansion coefficient are attributed to interactions in the Lennard-Jones well. Repulsion is required to obtain physically realistic speeds of sound and both repulsion and attraction are necessary to observe a Joule-Thomson inversion curve. Significantly, both maxima and minima are observed for the isobaric and isochoric heat capacities of the supercritical Lennard-Jones fluid. It is postulated that the loci of these maxima and minima converge to a common point via the same power law relationship as the phase coexistence curve with an exponent of β = 0.32. This provides an explanation for the terminal isobaric heat capacity maximum in supercritical fluids.
Assessment of food habits in children aged 6-12 years and the risk of caries.
Doichinova, Liliya; Bakardjiev, Peter; Peneva, Milena
2015-01-02
Food is necessary for the proper growth and development of children. The excessive intake of low-molecular carbohydrates constitutes a serious health issue, which has an unfavourable impact on the dental health status. The aim of this study was to assess the food habits in healthy children aged 6-12 years and the effect on their oral risk profile. The study included 100 children. The assessment of their nutrition was done with the help of a seven-day reproduction of the food intake and a survey used to determine their underlying food habits and preferences. The results revealed unbalanced nutrition of the children and increased intake of simple sugar, which will increase the risk of development of dental caries. The observed high levels of DMFT (number of decayed, missing and filled teeth) in 54% of the children is a logical result of the frequent intake of sugary foods and beverages for a long period of time, as this will increase the acid production by microorganisms in dental plaque, which is one of the leading etiologic factors for the development of caries. It is necessary for dentists to administer control over the carbohydrate intake and the food habits of children, as well as to encourage non-cariogenic diet in order to keep their good oral health.
Bhattacharjee, Apurba K; Skanchy, David J; Jennings, Barton; Hudson, Thomas H; Brendle, James J; Werbovetz, Karl A
2002-06-01
Several indolo[2,1-b]quinazoline-6,12-dione (tryptanthrin) derivatives exhibited remarkable activity at concentrations below 100 ng/mL when tested against in vitro Leishmania donovani amastigotes. The in vitro toxicity studies indicate that the compounds are fairly well tolerated in both macrophage and neuronal lines. An analysis based on qualitative and quantitative structure-activity relationship studies between in vitro antileishmanial activity and molecular electronic structure of 27 analogues of indolo[2,1-b]quinazoline-6,12-dione is presented here by using a combination of semi-empirical AM1 quantum chemical, cyclic voltammetry and a pharmacophore generation (CATALYST) methods. A modest to good correlation is observed between activity and a few calculated molecular properties such as molecular density, octanol-water partition coefficient, molecular orbital energies, and redox potentials. Electron transfer seems to be a plausible path in the mechanism of action of the compounds. A pharmacophore generated by using the 3-D QSAR of CATALYST produced a fairly accurate predictive model of antileishmanial activity of the tryptanthrins. The validity of the pharmacophore model extends to structurally different class of compounds that could open new frontiers for study. The carbonyl group of the five- and six-membered rings in the indolo[2,1-b]quinazoline-6,12-dione skeleton and the electron transfer ability to the carbonyl atom appear to be crucial for activity.
NASA Astrophysics Data System (ADS)
Kolmogorov, Aleksey N.
The main topics of this dissertation are the development of empirical interaction potentials and the study of electronic and mechanical properties of sp2-bonded carbon nanostructures. First, we investigate the weak interlayer binding in graphitic structures. We argue that although the absolute cohesion is not properly described in the local DFT approximations, the variation in the binding energy under interlayer shifts appears to be much more sound than previously suspected. We combine this result with experimental data to introduce a new empirical potential, which describes the variation in the interlayer binding with the relative alignment (registry) of the layers. Lacking a registry dependence, the commonly used Lennard-Jones potential significantly underestimates the variation in energy. We use our potential to study interwall sliding in nested nanotubes. We find that the well-defined geometry and extreme structural anisotropy of a multiwalled carbon nanotube can bring qualitatively new features to its nanometer-scale tribology. Efficient cancellation of registration-dependent interactions in incommensurate tubes (and also, surprisingly, certain axial commensurate tubes) can induce extremely small and nonextensive shear strengths. This result suggests the use of multiwalled carbon nanotubes as nanoscale bearings. We also apply our potential to look at the alignment of nanotubes on a graphitic substrate. We discover that the interaction of a one-dimensional tube with a two-dimensional substrate then leads to an unusual registry phenomenon not visible in standard layer-on-layer growth: the system develops favorable orientations which clearly are incommensurate. This effect could be used for nanotube separation by their helical angle. Next, we study the effect of doping in carbon nanostructures. Using a self-consistent tight-binding model we examine the radial distribution of charge in a bromine-doped double-walled carbon nanotube system. Our results confirm
Zhang, Shulan; Wu, Ziyan; Luo, Jing; Ding, Xuefeng; Hu, Chaojun; Li, Ping; Deng, Chuiwen; Zhang, Fengchun; Qian, Jiaming; Li, Yongzhe
2015-01-01
Abstract The need for reliable biomarkers for distinguishing Crohn disease (CD) from ulcerative colitis (UC) is increasing. This study aimed at evaluating the diagnostic potential of anti-GP2 antibodies as a biomarker in Chinese patients with CD. In addition, a variety of autoantibodies, including anti-saccharomyces cerevisiae antibodies (ASCA), perinuclear anti-neutrophil cytoplasmic antibodies (PANCA), anti-intestinal goblet cell autoantibodies (GAB), and anti-pancreatic autoantibodies (PAB), were evaluated. A total of 91 subjects were prospectively enrolled in this study, including 35 patients with CD, 35 patients with UC, 13 patients with non-IBD gastrointestinal diseases as disease controls (non-IBD DC), and 8 healthy controls (HC). The diagnosis of IBD was determined based on the Lennard-Jones criteria, and the clinical phenotypes of the IBD patients were determined based on the Montreal Classification. Anti-GP2 IgG antibodies were significantly elevated in patients with CD, compared with patients with UC (P = 0.0038), HC (P = 0.0055), and non-IBD DC (P = 0.0063). The prevalence of anti-GP2 IgG, anti-GP2 IgA and anti-GP2 IgA, or IgG antibodies in patients with CD was 40.0%, 37.1%, and 54.3%, respectively, which were higher than those in non-IBD DC (anti-GP2 IgG, 15.4%; anti-GP2 IgA, 7.7%; and anti-GP2 IgA or IgG, 23.1%) and those in patients with UC (anti-GP2 IgG, 11.4%; anti-GP2 IgA, 2.9%; and anti-GP2 IgA or IgG, 14.3%). For distinguishing CD from UC, the sensitivity, specificity, positive predictive value (PPV) and positive likelihood ratios (LR+) were 40%, 88.6%, 77.8%, and 3.51 for anti-GP2 IgG, 37.1%, 97.1%, 92.9%, and 13.0 for anti-GP2 IgA, and 54.3%, 85.3%, 79.2%, and 3.69 for anti-GP2 IgA or IgG. For CD diagnosis, the combination of anti-GP2 antibodies with ASCA IgA increased the sensitivity to 68.6% with moderate loss of specificity to 74.3%. Spearman's rank of order revealed a significantly positive correlation of anti-GP2 IgG with
Carbon nanotube oscillators for applications as nanothermometers
NASA Astrophysics Data System (ADS)
Rahmat, Fainida; Thamwattana, Ngamta; Hill, James M.
2010-10-01
Nanostructures such as carbon nanotubes have a broad range of potential applications such as nanomotors, nano-oscillators and electromechanical nanothermometers, and a proper understanding of the molecular interaction between nanostructures is fundamentally important for these applications. In this paper, we determine the molecular interaction potential of interacting carbon nanotubes for two configurations. The first is a shuttle configuration involving a short outer tube sliding on a fixed inner tube, and the second involves a telescopic configuration for which an inner tube moves both in the region between two outer tubes and through the tubes themselves. For the first configuration we examine two cases of semi-infinite and finite inner carbon nanotubes. We employ the continuum approximation and the 6-12 Lennard-Jones potential for non-bonded molecules to determine the molecular interaction potential and the resulting van der Waals force, and we evaluate the resulting surface integrals numerically. We also investigate the acceptance condition and suction energy for the first configuration. Our results show that for the shuttle configuration with a semi-infinite inner tube, the suction energy is maximum when the difference between the outer and inner tubes radii is approximately 3.4 Å, which is the ideal inter-wall spacing between graphene sheets. For the finite inner tube, the potential energy is dependent on both the inner and outer tube lengths as well as on the inter-wall spacing. In terms of the oscillating frequency, the critical issue is the length of the moving outer tube, and the shorter the length, the higher the frequency. Further, for the telescopic configuration with two semi-infinite outer nanotubes of different radii, we find that the interaction energy also depends on the difference of the tube radii. For two outer nanotubes of equal radii we observe that the shorter the distance between the two outer nanotubes, the higher the magnitude of the
Nilchian, Firoozeh; Shakibaei, Fereshteh; Jarah, Zeinab Taghi
2017-03-01
This study was aimed to evaluate the impact of visual pedagogy in dental check-ups and preventive practices among children with autism aged 6-12. In this randomized double-blind clinical trial, the cooperation of 40 children with autism age 6-12. The selected children were equally divided into two groups of case and control (n = 20). The obtained data were analyzed by statistical tests, including Chi square and independent t test. The results of Cochran showed a significant increase in children's cooperation with regard to fluoride therapy in the case group by repeating the visit and training sessions (p ≤ 0.001). The findings of this study demonstrated, visual pedagogy was merely effective in the case of fluoride therapy in the case group.
NASA Astrophysics Data System (ADS)
Tan, Hong-bo; Song, Xiu-qing; Yan, Hong; Xin, Hong-xing
2017-02-01
Novel 3-(2-naphthoyl)-6,12-diphenyl-3,9-diazatetraasterane (3, Tetraethyl 3-(2-naphthoyl)-6,12-diphenyl-3,9-diazapentacyclo [6.4.0.02,7.04,11.05,10]dodecane-1,5,7,11-tetracarboxylate) was prepared by naphthoylation of 3,9-diazatetraasterane (2). The target compound was isolated and unambiguously confirmed by NMR spectra, high-resolution mass spectrometry, and single-crystal X-ray diffraction analysis. In order to discuss the spatial effects on the NMR of 3 by the naphthoyl group, spectra analysis (1D-NMR and 2D-NMR) of 2 and 3 was conducted in details by the shifts and assignments of signals. Single-crystal X-ray diffraction assists to explain the molecular asymmetry of 3 and elucidates the effects of naphthoyl group on the geometry of the central cage of 3,9-diazatetraasterane.
ERIC Educational Resources Information Center
DiIorio, Colleen K.; Pluhar, Erika I.; Pines, Kathy; Jennings, Tanya
2006-01-01
In this article, we describe the Set the P.A.C.E.! (Parents And Children Empowered) curriculum designed for mothers of children 6-12 years of age. The development of the curriculum was part of a research study to test an intervention to enhance the mother's role in promoting resilience among 6- to 12-year-old children and to reduce the risk of…
Vásquez, Solange; García, Andrés Gerardi; Lugo, Raquel Salazar
2004-01-01
A biochemical and anthropometrical study of 175 children (6-12 years old) from Chacopata, Sucre State was done (December--January, 1997). The children were evaluated by combined anthropometrical indicators (OMS), clinical, nutritional and biochemical tests. The results showed 81.71% well-nourished children, 4.57% obese children and 13.72% with some degree of undernutrition: 3.43% acute undernourished and 10.29% chronic undernourished. Total seric proteins including fractions: albumin, alfa-1 alfa-2, beta and gamma globulins as well as total globulins and albumin/globulin indexes were at the normal reference range for children (6-12 years old). A significative increase in alfa-1 globulin (0.18+/-0.08 g/dl; 8-9 years old group) and decrease of alfa-2 globulin (0.71+/-0.11 g/dl; 10-12 year old group) was observed. Biochemical results associated with nutritional condition showed normal values, moreover, this biochemical index decreased in the undernourished group. A significant decrease of the seric beta globulin in the undernourished children (0.72+/-0,12 g/dl) with respect to the well-nourished children (0.79+/-0.15) was found. In children (6-12 years old) from Chacopata, compensated chronic undernourishement is prevalent.
Van der Waals interaction between two crossed carbon nanotubes.
Zhbanov, Alexander I; Pogorelov, Evgeny G; Chang, Yia-Chung
2010-10-26
The analytical expressions for the van der Waals potential energy and force between two crossed carbon nanotubes are presented. The Lennard-Jones potential between pairs of carbon atoms and the smeared-out approximation suggested by L. A. Girifalco (J. Phys. Chem. 1992, 96, 858) were used. The exact formula is expressed in terms of rational and elliptical functions. The potential and force for carbon nanotubes were calculated. The uniform potential curves for single- and multiwall nanotubes were plotted. The equilibrium distance, maximal attractive force, and potential energy have been evaluated.
Modeling of blood vessel constriction in 2-D case using molecular dynamics method
NASA Astrophysics Data System (ADS)
A. S., M. Rendi; Suprijadi, Viridi, S.
2014-03-01
Blood vessel constriction is simulated with particle-based method using a molecular dynamics authoring software known as Molecular Workbench (WM). Blood flow and vessel wall, the only components considered in constructing a blood vessel, are all represented in particle form with interaction potentials: Lennard-Jones potential, push-pull spring potential, and bending spring potential. Influence of medium or blood plasma is accommodated in plasma viscosity through Stokes drag force. It has been observed that pressure p is increased as constriction c is increased. Leakage of blood vessel starts at 80% constriction, which shows existence of maximum pressure that can be overcome by vessel wall.
Effective protein-protein interaction from structure factor data of a lysozyme solution
Abramo, M. C.; Caccamo, C.; Costa, D.; Ruberto, R.; Wanderlingh, U.; Cavero, M.; Pellicane, G.
2013-08-07
We report the determination of an effective protein-protein central potential for a lysozyme solution, obtained from the direct inversion of the total structure factor of the system, as extracted from small angle neutron scattering. The inversion scheme rests on a hypernetted-chain relationship between the effective potential and the structural functions, and is preliminarily tested for the case of a Lennard-Jones interaction. The characteristics of our potential are discussed in comparison with current models of effective interactions in complex fluids. The phase behavior predictions are also investigated.
NASA Astrophysics Data System (ADS)
Sadeghi, F.; Ansari, R.; Darvizeh, M.
2016-02-01
Research concerning the fabrication of nano-oscillators with operating frequency in the gigahertz (GHz) range has become a focal point in recent years. In this paper, a new type of GHz oscillators is introduced based on a C60 fullerene inside a cyclic peptide nanotube (CPN). To study the dynamic behavior of such nano-oscillators, using the continuum approximation in conjunction with the 6-12 Lennard-Jones (LJ) potential function, analytical expressions are derived to determine the van der Waals (vdW) potential energy and interaction force between the two interacting molecules. Employing Newton's second law, the equation of motion is solved numerically to arrive at the telescopic oscillatory motion of a C60 fullerene inside CPNs. It is shown that the fullerene molecule exhibits different kinds of oscillation inside peptide nanotubes which are sensitive to the system parameters. Furthermore, for the precise evaluation of the oscillation frequency, a novel semi-analytical expression is proposed based on the conservation of the mechanical energy principle. Numerical results are presented to comprehensively study the effects of the number of peptide units and initial conditions (initial separation distance and velocity) on the oscillatory behavior of C60 -CPN oscillators. It is found out that for peptide nanotubes comprised of one unit, the maximum achievable frequency is obtained when the inner core oscillates with respect to its preferred positions located outside the tube, while for other numbers of peptide units, such frequency is obtained when the inner core oscillates with respect to the preferred positions situated in the space between the two first or the two last units. It is further found out that four peptide units are sufficient to obtain the optimal frequency.
A description of phase equilibria in nonideal systems with the use of integral equation theory
NASA Astrophysics Data System (ADS)
D'Yakonov, S. G.; Klinov, A. V.; D'Yakonov, G. S.
2009-06-01
Integral equation theory for partial distribution functions was used to consider a method for calculations of vapor-liquid phase equilibrium conditions in binary Lennard-Jones systems with substantial deviations from the Berthelot-Lorentz mixing rules. Possible sources of errors in pressure and chemical potential values and methods for refining the results were analyzed. The required accuracy of calculations can be reached using two parameters only, one in the closure to the Ornstein-Zernike equation and the other in the equation for the chemical potential. These parameters are determined independently from two thermodynamic equations.
Time-dependent perturbation theory for inelastic scattering
NASA Astrophysics Data System (ADS)
Cross, R. J.
1982-08-01
We show by numerical integration that the first-order, time-dependent, Magnus approximation agrees with the first-order, exponential, distorted-wave approximation to within a few percent, provided that the trajectory used for the time-dependent calculation is characterized by the arithmetic mean of the initial and final velocities and the arithmetic mean of the initial and final orbital angular momenta. Calculations are done for rotational energy transfer from an exponentially repulsive potential characteristic of He+H2 and for a Lennard-Jones potential characteristic of Ar+N2.
A Wang-Landau study of the phase transitions in a flexible homopolymer
NASA Astrophysics Data System (ADS)
Seaton, D. T.; Wüst, T.; Landau, D. P.
2009-04-01
Using Wang-Landau sampling we study the characteristic behavior of a flexible homopolymer (off-lattice) for chain lengths up to N=300. The Hamiltonian consists of a Lennard-Jones potential between all monomers, and an additional FENE potential between bonded monomers. From the resultant density of states, we calculate thermodynamic properties for a wide range of temperatures, including low temperatures that are inaccessible to traditional Monte Carlo algorithms. Peaks in the specific heat and radius of gyration indicate the coil-globule and solid-liquid transitions. With a careful implementation of the algorithm, we find no evidence of a liquid-liquid transition.
A calculation of the diffusion energies for adatoms on surfaces of F.C.C. metals
NASA Technical Reports Server (NTRS)
Halicioglu, T.; Pound, G. M.
1979-01-01
The activation energies for diffusion were determined for gold, platinum and iridium adatoms on plane and plane PT surfaces and were found to be in good agreement with the measurements reported by Bassett and Webber. The Lennard-Jones pair potentials were used to model the interatomic forces, and relaxation of the substrate atoms in near proximity to the adatom was considered in detail. The present calculations clarify the mechanism of the observed two-dimensional diffusion of platinum and iridium atoms on a plane PT surface. The results are compared with those obtained using Morse potential functions and different relaxation techniques.
Oscillations of spherical fullerenes interacting with graphene sheet
NASA Astrophysics Data System (ADS)
Ghavanloo, Esmaeal; Fazelzadeh, S. Ahmad
2017-01-01
In the present study, the oscillations of spherical fullerenes in the vicinity of a fully constrained graphene sheet are investigated. Using the continuous approximation and Lennard-Jones potential, the van der Waals (vdW) potential energy and interaction forces are obtained. The equation of motion is derived and directly solved based on the actual force distribution between the fullerene molecules and the graphene sheet. Numerical results are obtained and shown that the oscillation is sensitive to the size of the fullerene as well as the distance between the center of the fullerene and the graphene sheet.
Jankunas, Justin; Bertsche, Benjamin; Osterwalder, Andreas; Jachymski, Krzysztof; Hapka, Michał
2014-06-28
Two isotopic chemical reactions, Ne{sup *} + NH{sub 3}, and Ne{sup *} + ND{sub 3}, have been studied at low collision energies by means of a merged beams technique. Partial cross sections have been recorded for the two reactive channels, namely, Ne{sup *} + NH{sub 3} → Ne + NH{sub 3}{sup +} + e{sup −}, and Ne{sup *} + NH{sub 3} → Ne + NH{sub 2}{sup +}+ H + e{sup −}, by detecting the NH{sub 3}{sup +} and NH{sub 2}{sup +} product ions, respectively. The cross sections for both reactions were found to increase with decreasing collision energy, E{sub coll}, in the range 8 μeV < E{sub coll} < 20 meV. The measured rate constant exhibits a curvature in a log(k)-log(E{sub coll}) plot from which it is concluded that the Langevin capture model does not properly describe the Ne{sup *} + NH{sub 3} reaction in the entire range of collision energies covered here. Calculations based on multichannel quantum defect theory were performed to reproduce and interpret the experimental results. Good agreement was obtained by including long range van der Waals interactions combined with a 6-12 Lennard-Jones potential. The branching ratio between the two reactive channels, Γ=([NH{sub 2}{sup +}])/([NH{sub 2}{sup +}]+[NH{sub 3}{sup +}]) , is relatively constant, Γ ≈ 0.3, in the entire collision energy range studied here. Possible reasons for this observation are discussed and rationalized in terms of relative time scales of the reactant approach and the molecular rotation. Isotopic differences between the Ne{sup *} + NH{sub 3} and Ne{sup *} + ND{sub 3} reactions are small, as suggested by nearly equal branching ratios and cross sections for the two reactions.
NASA Technical Reports Server (NTRS)
Pearson, W. E.
1974-01-01
The viscosity and thermal conductivity of nitrogen gas for the temperature range 5 K - 135 K have been computed from the second Chapman-Enskog approximation. Quantum effects, which become appreciable at the lower temperatures, are included by utilizing collision integrals based on quantum theory. A Lennard-Jones (12-6) potential was assumed. The computations yield viscosities about 20 percent lower than those predicted for the high end of this temperature range by the method of corresponding states, but the agreement is excellent when the computed values are compared with existing experimental data.
Solid-liquid phase transition in argon
NASA Technical Reports Server (NTRS)
Tsang, T.; Tang, H. T.
1978-01-01
Starting from the Lennard-Jones interatomic potential, a modified cell theory has been used to describe the solid-liquid phase transition in argon. The cell-size variations may be evaluated by a self-consistent condition. With the inclusion of cell-size variations, the transition temperature, the solid and liquid densities, and the liquid-phase radial-distribution functions have been calculated. These ab initio results are in satisfactory agreement with molecular-dynamics calculations as well as experimental data on argon.
On the Pyrazine and Pyrazine-Pyrimidine Dimers.
1986-06-01
Lennard - Jones -hydrogen-bonding (LJ-HB) potential energy calculations. The pyrazine isotopic hetero- and homo-dimers possess nearly identical spectra with the exception that the perpendicular dimer features are displaced to the red by approx. 11 cm. Exchange or exciton interactions in this system are vanishingly small (less than 1/cm). The geometrics suggested by the isotopically substituted pyrazine dimer spectra are the same as those found for the pyrazine-h sub 4 homo-dimer: a parallel planar hydrogen bonded and a perpendicular dimer. The pyrazine-h sub 4 and pyrazine-h
1993-04-01
Lennard - Jones (LJ) spheres in contact, of varying diameter (4 or 5 A), and containing a univalent charge (cation or anion) on one site so to probe possible effects of the ionic charge sign. Following equilibration, the collective solvent response to a sudden charge transfer between the spherical sites is followed, and described in terms of the response function C(t), describing the difference in the solvent-induced electrostatic potential between the initial and final solute states. In all cases, the C(t) curves exhibit a very rapid (50-100 fs) initial decay component
EQUATIONS OF STATE IN LIQUIDS.
Lennard - Jones and Devonshire cell model for calculating the energy of cold compression used in the solid part of the partition function. This potential is used to determine the frequency of oscillation in an Einstein solid or to determine the total classical partition function. Part II examines the basic physical concepts of the liquid state and proposes an alternative to the Eyring hole theory based on the mobility of atoms trapped between two partially separated layers. Some predictions based on this model are compared with experimental data.
Strain accommodation in inelastic deformation of glasses
Murali, P.; Ramamurty, U.; Shenoy, Vijay B.
2007-01-01
Motivated by recent experiments on metallic glasses, we examine the micromechanisms of strain accommodation including crystallization and void formation during inelastic deformation of glasses by employing molecular statics simulations. Our atomistic simulations with Lennard-Jones-like potentials suggests that a softer short range interaction between atoms favors crystallization. Compressive hydrostatic strain in the presence of a shear strain promotes crystallization whereas a tensile hydrostatic strain is found to induce voids. The deformation subsequent to the onset of crystallization includes partial reamorphization and recrystallization, suggesting important atomistic mechanisms of plastic dissipation in glasses.
Determining pressure-temperature phase diagrams of materials
NASA Astrophysics Data System (ADS)
Baldock, Robert J. N.; Pártay, Lívia B.; Bartók, Albert P.; Payne, Michael C.; Csányi, Gábor
2016-05-01
We extend the nested sampling algorithm to simulate materials under periodic boundary and constant pressure conditions, and show how it can be used to determine the complete equilibrium phase diagram for a given potential energy function, efficiently and in a highly automated fashion. The only inputs required are the composition and the desired pressure and temperature ranges, in particular, solid-solid phase transitions are recovered without any a priori knowledge about the structure of solid phases. We benchmark and showcase the algorithm on the periodic Lennard-Jones system, aluminum, and NiTi.
Stability of Double-Walled Carbon Nanotubes Revisited
NASA Astrophysics Data System (ADS)
Semenyuk, N. P.
2016-01-01
An approach to the stability analysis of orthotropic two-layer shells with mechanical and electrical properties of carbon nanotubes is proposed. Van der Waals forces act between the layers. The parameters of the continuum between the layers are obtained using the Lennard-Jones potential. The governing system of equations is written for rates of sixteen variables. The loading and boundary conditions are specified for each layer separately. Numerical results are obtained using the discrete orthogonalization method. The stability of single- and double-walled nanotubes is analyzed. Numerical results are summarized in tables and analyzed
NASA Astrophysics Data System (ADS)
Yatsyshin, P.; Parry, A. O.; Kalliadasis, S.
2016-07-01
We study continuous interfacial transitions, analagous to two-dimensional complete wetting, associated with the first-order prewetting line, which can occur on steps, patterned walls, grooves and wedges, and which are sensitive to both the range of the intermolecular forces and interfacial fluctuation effects. These transitions compete with wetting, filling and condensation producing very rich phase diagrams even for relatively simple prototypical geometries. Using microscopic classical density functional theory to model systems with realistic Lennard-Jones fluid-fluid and fluid-substrate intermolecular potentials, we compute mean-field fluid density profiles, adsorption isotherms and phase diagrams for a variety of confining geometries.
Theory of warm ionized gases: equation of state and kinetic Schottky anomaly.
Capolupo, A; Giampaolo, S M; Illuminati, F
2013-10-01
Based on accurate Lennard-Jones-type interaction potentials, we derive a closed set of state equations for the description of warm atomic gases in the presence of ionization processes. The specific heat is predicted to exhibit peaks in correspondence to single and multiple ionizations. Such kinetic analog in atomic gases of the Schottky anomaly in solids is enhanced at intermediate and low atomic densities. The case of adiabatic compression of noble gases is analyzed in detail and the implications on sonoluminescence are discussed. In particular, the predicted plasma electron density in a sonoluminescent bubble turns out to be in good agreement with the value measured in recent experiments.
Application the particle method in problems of mechanics deformable media
NASA Astrophysics Data System (ADS)
Berezhnoi, D. V.; Gabsalikova, N. F.; Miheev, V. V.
2016-11-01
The work implemented method of deformation of ground-based particle method, which is a collection of mineral grains, which are linked to some system of forces on the contact areas between the mineral particles. Two-parameter potential Lennard-Jones and it is modified version were selected for describing the behavior of ground. Some model problems of straining layer of ground in the gravity field was decided. The calculations were performed on a heterogeneous computing cluster, on each of the seven components that were installed on three GPU AMD Radeon HD 7970.
Trillion-atom molecular dynamics becomes a reality
Kadau, Kai; Germann, Timothy C
2008-01-01
By utilizing the molecular dynamics code SPaSM on Livermore's BlueGene/L architecture, consisting of 212 992 IBM PowerPC440 700 MHz processors, a molecular dynamics simulation was run with one trillion atoms. To demonstrate the practicality and future potential of such ultra large-scale simulations, the onset of the mechanical shear instability occurring in a system of Lennard-Jones particles arranged in a simple cubic lattice was simulated. The evolution of the instability was analyzed on-the-fly using the in-house developed massively parallel graphical object-rendering code MD{_}render.
Thermophysical properties of CF4/O2 and SF6/O2 gas mixtures
NASA Astrophysics Data System (ADS)
Damyanova, M.; Hohm, U.; Balabanova, E.; Barton, D.
2016-03-01
Fitting formulae are presented for the calculation of the second interaction virial coefficients, mixture viscosities and binary diffusion coefficients for CF4/O2 and SF6/O2 gas mixtures in the temperature range between 200 K and 1000 K. The data recommended are obtained from the isotropic (n-6) Lennard-Jones intermolecular interaction potentials of the pure substances by using the Hohm-Zarkova-Damyanova mixing rules. In general, a good agreement is observed between our results and the experimental and theoretical data found in the literature.
NASA Astrophysics Data System (ADS)
Titov, S. V.; Tovbin, Yu. K.
2016-11-01
A molecular model developed earlier for a polar fluid within the lattice gas model is supplemented by considering the vibrational motions of molecules using water as an example. A combination of point dipole and Lennard-Jones potentials from SPC parametrization is chosen as the force field model for the molecule. The main thermodynamic properties of liquid water (density, internal energy, and entropy) are studied as functions of temperature. There is qualitative agreement between the calculation results and the experimental data. Ways of refining the molecular theory are discussed.
Garzon, I.L.; Jellinek, J.
1991-12-31
The meltinglike phenomenon in Ni{sub n}, n = 19,20,55, clusters is studied using microcanonical molecular dynamics simulations. The interaction between the atoms in the clusters is modelled by a size-dependent Gupta-like potential that incorporates many-body effects. The clusters display the ``usual`` stages in their meltinglike transition, which characterize also Lennard-Jones (e.g., noble gas) and ionic clusters. In addition, Ni{sub 20} passes through a so-called premelting stage found earlier also for Ni{sub 14}. 11 ref., 3 figs.
Garzon, I.L. . Inst. de Fisica); Jellinek, J. )
1991-01-01
The meltinglike phenomenon in Ni{sub n}, n = 19,20,55, clusters is studied using microcanonical molecular dynamics simulations. The interaction between the atoms in the clusters is modelled by a size-dependent Gupta-like potential that incorporates many-body effects. The clusters display the usual'' stages in their meltinglike transition, which characterize also Lennard-Jones (e.g., noble gas) and ionic clusters. In addition, Ni{sub 20} passes through a so-called premelting stage found earlier also for Ni{sub 14}. 11 ref., 3 figs.
Modeling of gamma/gamma-prime phase equilibrium in the nickel-aluminum system
NASA Technical Reports Server (NTRS)
Sanchez, J. M.; Barefoot, J. R.; Jarrett, R. N.; Tien, J. K.
1984-01-01
A theoretical model is proposed for the determination of phase equilibrium in alloys, taking into consideration dissimilar lattice parameters. Volume-dependent pair interactions are introduced by means of phenomenological Lennard-Jones potentials and the configurational entropy of the system is treated in the tetrahedron approximation of the cluster variation method. The model is applied to the superalloy-relevant, nickel-rich, gamma/gamma-prime phase region of the Ni-Al phase diagram. The model predicts reasonable values for the lattice parameters and the enthalpy of formation as a function of composition, and the calculated phase diagram closely approximates the experimental diagram.
Capillary condensation in pores with rough walls: a density functional approach.
Bryk, P; Rzysko, W; Malijevsky, Al; Sokołowski, S
2007-09-01
The effect of surface roughness of slit-like pore walls on the capillary condensation of a spherical particles and short chains is studied. The gas molecules interact with the substrate by a Lennard-Jones (9,3) potential. The rough layer at each pore wall has a variable thickness and density and consists of a disordered quenched matrix of spherical particles. The system is described in the framework of a density functional approach and using computer simulations. The contribution due to attractive van der Waals interactions between adsorbate molecules is described by using first-order mean spherical approximation and mean-field approximation.
Negative Poisson's ratio materials via isotropic interactions.
Rechtsman, Mikael C; Stillinger, Frank H; Torquato, Salvatore
2008-08-22
We show that under tension a classical many-body system with only isotropic pair interactions in a crystalline state can, counterintuitively, have a negative Poisson's ratio, or auxetic behavior. We derive the conditions under which the triangular lattice in two dimensions and lattices with cubic symmetry in three dimensions exhibit a negative Poisson's ratio. In the former case, the simple Lennard-Jones potential can give rise to auxetic behavior. In the latter case, a negative Poisson's ratio can be exhibited even when the material is constrained to be elastically isotropic.
Percolation of clusters with a residence time in the bond definition: Integral equation theory.
Zarragoicoechea, Guillermo J; Pugnaloni, Luis A; Lado, Fred; Lomba, Enrique; Vericat, Fernando
2005-03-01
We consider the clustering and percolation of continuum systems whose particles interact via the Lennard-Jones pair potential. A cluster definition is used according to which two particles are considered directly connected (bonded) at time t if they remain within a distance d, the connectivity distance, during at least a time of duration tau, the residence time. An integral equation for the corresponding pair connectedness function, recently proposed by two of the authors [Phys. Rev. E 61, R6067 (2000)], is solved using the orthogonal polynomial approach developed by another of the authors [Phys. Rev. E 55, 426 (1997)]. We compare our results with those obtained by molecular dynamics simulations.
Chen, Zhijie; Weseliński, Łukasz J; Adil, Karim; Belmabkhout, Youssef; Shkurenko, Aleksander; Jiang, Hao; Bhatt, Prashant M; Guillerm, Vincent; Dauzon, Emilie; Xue, Dong-Xu; O'Keeffe, Michael; Eddaoudi, Mohamed
2017-03-01
Highly connected and edge-transitive nets are of prime importance in crystal chemistry and are regarded as ideal blueprints for the rational design and construction of metal-organic frameworks (MOFs). We report the design and synthesis of highly connected MOFs based on reticulation of the sole two edge-transitive nets with a vertex figure as double six-membered-ring (d6R) building unit, namely the (4,12)-coordinated shp net (square and hexagonal-prism) and the (6,12)-coordinated alb net (aluminum diboride, hexagonal-prism and trigonal-prism). Decidedly, the combination of our recently isolated 12-connected (12-c) rare-earth (RE) nonanuclear [RE9(μ3-OH)12(μ3-O)2(O2C-)12] carboxylate-based cluster, points of extension matching the 12 vertices of hexagonal-prism d6R, with 4-connected (4-c) square porphyrinic tetracarboxylate ligand led to the formation of the targeted RE-shp-MOF. This is the first time that RE-MOFs based on 12-c molecular building blocks (MBBs), d6R building units, have been deliberately targeted and successfully isolated, paving the way for the long-awaited (6,12)-c MOF with alb topology. Indeed, combination of a custom-designed hexacarboxylate ligand with RE salts led to the formation of the first related alb-MOF, RE-alb-MOF. Intuitively, we successfully transplanted the alb topology to another chemical system and constructed the first indium-based alb-MOF, In-alb-MOF, by employing trinuclear [In3(μ3-O)(O2C-)6] as the requisite 6-connected trigonal-prism and purposely made a dodecacarboxylate ligand as a compatible 12-c MBB. Prominently, the dodecacarboxylate ligand was employed to transplant shp topology into copper-based MOFs by employing the copper paddlewheel [Cu2(O2C-)4] as the complementary square building unit, affording the first Cu-shp-MOF. We revealed that highly connected edge-transitive nets such shp and alb are ideal for topological transplantation and deliberate construction of related MOFs based on minimal edge-transitive nets.
Gao Bing; Liu Zhifeng
2004-11-01
The structures of hydrated sulfate clusters, SO{sub 4}{sup 2-}(H{sub 2}O){sub n} with n=6-12, are obtained by density functional theory calculations. For SO{sub 4}{sup 2-}(H{sub 2}O){sub 12}, two structures with symmetric distribution of H{sub 2}O molecules around the sulfate group are favored in energy. The structures for the smaller clusters, SO{sub 4}{sup 2-}(H{sub 2}O){sub n} with n=6-11, are obtained by taking away one H{sub 2}O molecule successively from the two symmetric SO{sub 4}{sup 2-}(H{sub 2}O){sub 12} isomers. The hydrogen bonding between the sulfate O atoms and H{sub 2}O molecules are strong. So are the hydrogen bonds among H{sub 2}O molecules, which are facilitated by the structure of the polyatomic sulfate group. The solvation energy is quite large (often exceeding 15 kcal/mol). The patterns for structural and energy changes as the cluster size increases are very different from the well studied hydrated halide ions, although the competition between solute-solvent and solvent-solvent interactions is again an important factor. Ab initio molecular dynamics simulations also show 'crowding' effects in the first solvation of SO{sub 4}{sup 2-}(H{sub 2}O){sub 12} at raised temperature.
Ishihara, Toru; Sugasawa, Shigemi; Matsuda, Yusuke; Mizuno, Masao
2017-03-06
This study evaluated the effects of two different types of tennis lessons-those involving a technique-based approach (TBA) and those involving a game-based approach (PLAY+STAY [P+S])-on the executive functions (EFs) of junior tennis players. Eighty-one tennis players (6-12 years old) were recruited and assigned to one of three groups: TBA, P+S, or watching TV (CONT). Subjects completed evaluations of EFs (inhibitory control, working memory, and cognitive flexibility) before and after 50min programs. The overall score for EFs improved significantly for both the P+S and TBA groups but not for the CONT group; indeed the CONT group showed no improvement in overall EFs. Furthermore, the overall EF score improved more for P+S participants than for those in TBA. Looking at components of EFs, the pattern for inhibitory control reflected the pattern for the overall EF index: Improvement in the P+S and TBA groups but not in the CONT group. Only the P+S group improved in working memory. Thus, playing tennis and practicing isolated tennis skills both improved EFs of junior players more than did watching TV, and game-based tennis lessons seem to hold more promise for improving EFs than drills of tennis skills.
AIREBO-M: A reactive model for hydrocarbons at extreme pressures
O’Connor, Thomas C. Robbins, Mark O.; Andzelm, Jan
2015-01-14
The Adaptive Intermolecular Reactive Empirical Bond Order potential (AIREBO) for hydrocarbons has been widely used to study dynamic bonding processes under ambient conditions. However, its intermolecular interactions are modeled by a Lennard-Jones (LJ) potential whose unphysically divergent power-law repulsion causes AIREBO to fail when applied to systems at high pressure. We present a modified potential, AIREBO-M, where we have replaced the singular Lennard-Jones potential with a Morse potential. We optimize the new functional form to improve intermolecular steric repulsions, while preserving the ambient thermodynamics of the original potentials as much as possible. The potential is fit to experimental measurements of the layer spacing of graphite up to 14 GPa and first principles calculations of steric interactions between small alkanes. To validate AIREBO-M’s accuracy and transferability, we apply it to a graphite bilayer and orthorhombic polyethylene. AIREBO-M gives bilayer compression consistent with quantum calculations, and it accurately reproduces the quasistatic and shock compression of orthorhombic polyethlyene up to at least 40 GPa.
Hanson, Nicholas Buck; Kachin, Kevin; Berger, Jan
2016-01-01
Background Obesity is the leading cause of preventable death costing the health care system billions of dollars. Combining self-monitoring technology with personalized behavior change strategies results in clinically significant weight loss. However, there is a lack of real-world outcomes in commercial weight-loss program research. Objective Retrofit is a personalized weight management and disease-prevention solution. This study aimed to report Retrofit’s weight-loss outcomes at 6, 12, and 24 months and characterize behaviors, age, and sex of high-performing participants who achieved weight loss of 10% or greater at 12 months. Methods A retrospective analysis was performed from 2011 to 2014 using 2720 participants enrolled in a Retrofit weight-loss program. Participants had a starting body mass index (BMI) of >25 kg/m² and were at least 18 years of age. Weight measurements were assessed at 6, 12, and 24 months in the program to evaluate change in body weight, BMI, and percentage of participants who achieved 5% or greater weight loss. A secondary analysis characterized high-performing participants who lost ≥10% of their starting weight (n=238). Characterized behaviors were evaluated, including self-monitoring through weigh-ins, number of days wearing an activity tracker, daily step count average, and engagement through coaching conversations via Web-based messages, and number of coaching sessions attended. Results Average weight loss at 6 months was −5.55% for male and −4.86% for female participants. Male and female participants had an average weight loss of −6.28% and −5.37% at 12 months, respectively. Average weight loss at 24 months was −5.03% and −3.15% for males and females, respectively. Behaviors of high-performing participants were assessed at 12 months. Number of weigh-ins were greater in high-performing male (197.3 times vs 165.4 times, P=.001) and female participants (222 times vs 167 times, P<.001) compared with remaining participants
NASA Technical Reports Server (NTRS)
Richards, P. G.; Buonsanto, M. J.; Reinisch, B. W.; Holt, J.; Fennelly, J. A.; Scali, J. L.; Comfort, R. H.; Germany, G. A.; Spann, J.; Brittnacher, M.
1999-01-01
Measurements from a network of digisondes and an incoherent scatter radar In Eastern North American For January 6-12, 1997 have been compared with the Field Line Interhemispheric Plasma (FLIP) model which now includes the effects of electric field convective. With the exception of Bermuda, the model reproduces the daytime electron density very well most of the time. As is typical behavior for winter solar minimum on magnetically undisturbed nights, the measurements at Millstone Hill show high electron temperatures before midnight followed by a rapid decay, which is accompanied by a pronounced density enhancement in the early morning hours. The FLIP model reproduces the nighttime density enhancement well, provided the model is constrained to follow the topside electron temperature and the flux tube is full. Similar density enhancements are seen at Goose Bay, Wallops Island and Bermuda. However, the peak height variation and auroral images indicate the density enhancements at Goose Bay are most likely due to particle precipitation. Contrary to previously published work we find that the nighttime density variation at Millstone Hill is driven by the temperature behavior and not the other way around. Thus, in both the data and model, the overall nighttime density is lowered and the enhancement does not occur if the temperature remains high all night. Our calculations show that convections of plasma from higher magnetic latitudes does not cause the observed density maximum but it may enhance the density maximum if over-full flux tubes are convected over the station. On the other had, convection of flux tubes with high temperatures and depleted densities may prevent the density maximum from occurring. Despite the success in modeling the nighttime density enhancements, there remain two unresolved problems. First, the measured density decays much faster than the modeled density near sunset at Millstone Hill and Goose Bay though not at lower latitude stations. Second, we
Sacrey, Lori-Ann R; Karl, Jenni M; Whishaw, Ian Q
2012-06-01
The reach-to-eat movement, transport of a hand to grasp an object that is withdrawn and placed in the mouth, is amongst the earliest developing functional movements of human infants. The present longitudinal study is the first description of the maturation of hand-rotation, hand shaping, and accuracy associated with the advance and withdrawal phases of the movement. Eight infants, aged 6-12 months, and eight adults, were video recorded as they reached for familiar objects or food items. Hand, arm, and trunk movements were assessed frame-by-frame with the Skilled Reaching Rating Scale, previously developed for the assessment of adult reaching, and supplementary kinematic analysis. Reach-to-eat maturation was characterized by three changes. First, for advance, a simple open hand transport gradually matured to a movement associated with pronation and hand shaping of the digits for precision grasping. Second, for withdrawal to the mouth, a direct withdrawal movement gradually became associated with hand supination that oriented the target object to the mouth. Third, associated with the maturation of rotational movements, inaccurate and fragmented hand transport and withdrawal movements developed into precise targeting of the hand-to-object and object-to-mouth. Across the age range, there was a decrease in bimanual reaching and an increase in right handed reaching. The results are discussed in relation to the idea that the maturation of the reach-to-eat movement involves the development of rotational and shaping movements of the hand and visual and somatosensory guidance of a preferred hand.
±J Ising model on mixed Archimedean lattices: (33,42), (32,4,3,4), (3,122), (4,6,12)
NASA Astrophysics Data System (ADS)
Lebrecht, W.; Valdés, J. F.
2013-10-01
This paper addresses the problem of finding analytical expressions describing the ground state properties of mixed Archimedean lattices over which a generalized Edwards-Anderson model (±J Ising model) is defined. A local frustration analysis is performed based on representative cells for (33,42), (32,4,3,4), (3,122) and (4,6,12) lattices, following the notation proposed by Grünbaum and Shephard. The concentration of ferromagnetic (F) bonds x is used as the independent variable in the analysis (1-x is the concentration for antiferromagnetic (A) bonds), where x spans the range [0.00,1.00]. The presence of A bonds brings frustration, whose clear manifestation is when bonds around the minimum possible circuit of bonds (plaquette) cannot be simultaneously satisfied. The distribution of curved (frustrated) plaquettes within the representative cell is determinant for the evaluation of the parameters of interest such as average frustration segment, energy per bond, and fractional content of unfrustrated bonds. Two methods are developed to cope with this analysis: one based on the direct probability of a plaquette being curved; the other one is based on the consideration of the different ways bonds contribute to the particular plaquette configuration. Exact numerical simulations on a large number of randomly generated samples associated to (33,42) and (32,4,3,4) lattices allow to validate the previously described theoretical analysis. It is found that the first method presents slight advantages over the second one. However, both methods give an excellent description for most of the range for x. The small deviations at specific intervals of x for each lattice are relevant to the self-imposed limitations of both methods due to practical reasons. A particular discussion for the point x=0.50 for each one of the four lattices also sheds light on the general trends of the properties described here.
Heat conduction in diatomic chains with correlated disorder
NASA Astrophysics Data System (ADS)
Savin, Alexander V.; Zolotarevskiy, Vadim; Gendelman, Oleg V.
2017-01-01
The paper considers heat transport in diatomic one-dimensional lattices, containing equal amounts of particles with different masses. Ordering of the particles in the chain is governed by single correlation parameter - the probability for two neighboring particles to have the same mass. As this parameter grows from zero to unity, the structure of the chain varies from regular staggering chain to completely random configuration, and then - to very long clusters of particles with equal masses. Therefore, this correlation parameter allows a control of typical cluster size in the chain. In order to explore different regimes of the heat transport, two interatomic potentials are considered. The first one is an infinite potential wall, corresponding to instantaneous elastic collisions between the neighboring particles. In homogeneous chains such interaction leads to an anomalous heat transport. The other one is classical Lennard-Jones interatomic potential, which leads to a normal heat transport. The simulations demonstrate that the correlated disorder of the particle arrangement does not change the convergence properties of the heat conduction coefficient, but essentially modifies its value. For the collision potential, one observes essential growth of the coefficient for fixed chain length as the limit of large homogeneous clusters is approached. The thermal transport in these models remains superdiffusive. In the Lennard-Jones chain the effect of correlation appears to be not monotonous in the limit of low temperatures. This behavior stems from the competition between formation of long clusters mentioned above, and Anderson localization close to the staggering ordered state.
Gröne, A; Alldinger, S; Baumgärtner, W
2000-10-02
Canine distemper virus infection in dogs is commonly associated with demyelinating central nervous system lesions. Investigations on viral protein expression by studying mRNA and protein distribution together with the characterization of CD4 and CD8 inflammatory cells and MHC class II up-regulation revealed a biphasic disease process. To further investigate the cellular interactions in the different plaque types the cerebella of 14 dogs with confirmed distemper infection were investigated for expression of interleukin (IL)-1beta, -6, -12 and tumor necrosis factor-alpha (TNF) by immunohistochemistry using rabbit polyclonal anti-cytokine antibodies. T-cells and astrocytes were identified with rabbit anti CD3- and GFAP-monoclonal and polyclonal antibodies, respectively; and microglia/macrophages were characterized by their ability to bind lectin from Bandeiraea simplicifolia (BS-1). To further name the cytokine expressing cells immunoenzymatic double staining using DAB and New Fuchsin was performed. White matter lesions were classified according to histopathological criteria into acute, subacute and chronic. Canine distemper virus nucleoprotein antigen was demonstrated in nearly all plaques, except in older plaques where virus was not present within the plaque but adjacent to the lesion. IL-1 expression was observed to varying degrees in all types of lesions. Most often IL-1 was present in CD3 and BS-1 positive cells in the brain parenchyma in earlier plaques and comprising perivascular cuffs found in chronic plaques. IL-6 expression was present in all lesions, and followed a similar distribution pattern as IL-1. IL-12 displayed very often a granular extracellular pattern of immunoreactivity, especially in the brain parenchyma, and was found only in individual perivascular cells. TNF staining, predominantly found in astrocytes, was present in lesions of various types; however, staining appeared to be stronger in acute lesions and decreased in chronic plaques. In the
Manjunath, Bhanu; Suman, G; Hemanth, T; Shivaraj, N S; Murthy, N S
2016-01-01
In India, endemic goitre is present in sub-Himalayan region and in pockets in states of Andhra Pradesh, Karnataka and Gujarat. Being a public health problem amenable for prevention, the assessment of prevalence of endemic goitre in an area helps in understanding whether the preventive strategies under National Iodine Deficiency Disorder Control Program (NIDDCP) have any impact on the control of endemic goitre. Hence, the current study was carried out to determine the prevalence, distribution and factors associated with iodine deficiency goitre among 6-12-year-old children in a rural area in south Karnataka. A cross-sectional study was conducted among 838 children, using a questionnaire adopted from Iodized Salt Program Assessment Tool and the tools prescribed by WHO for goitre survey. The prevalence of goitre in the study area was 21.9% (95% CI 19.2-24.8). There was higher prevalence of goitre among those having salt iodine <15 ppm than those with >15 ppm (P = 0.01; OR 1.59; 95% CI 1.10-2.29). In 10% of the children, urinary iodine excretion (UIE) was assessed and prevalence was higher among those with <100 μg/l of UIE than those with normal UIE, which was not statistically significant (P = 0.8, OR 1.36; 95% CI 0.62-2.96). Multiple logistic regression revealed that gender (P = 0.002; OR 1.7; 95% CI 1.21-2.35) was an independent variable associated with goitre. The study area was found to be moderately endemic for goitre based on the WHO criteria. Higher prevalence of goitre was found to be still associated with consumption of low iodized salt (<15 ppm) necessitating emphasis on monitoring of salt iodine levels in the study area. Though NIDDCP is being implemented since five decades in India, the burden of iodine deficiency disorders (IDDs) is still high demanding further impetus to the monitoring systems of the programme.
Simplicity of condensed matter at its core: Generic definition of a Roskilde-simple system
Schrøder, Thomas B. Dyre, Jeppe C.
2014-11-28
The isomorph theory is reformulated by defining Roskilde-simple systems by the property that the order of the potential energies of configurations at one density is maintained when these are scaled uniformly to a different density. If the potential energy as a function of all particle coordinates is denoted by U(R), this requirement translates into U(R{sub a}) < U(R{sub b}) ⇒ U(λR{sub a}) < U(λR{sub b}). Isomorphs remain curves in the thermodynamic phase diagram along which structure, dynamics, and excess entropy are invariant, implying that the phase diagram is effectively one-dimensional with respect to many reduced-unit properties. In contrast to the original formulation of the isomorph theory, however, the density-scaling exponent is not exclusively a function of density and the isochoric heat capacity is not an exact isomorph invariant. A prediction is given for the latter quantity's variation along the isomorphs. Molecular dynamics simulations of the Lennard-Jones and Lennard-Jones Gaussian systems validate the new approach.
Computer simulation of nucleation in a gas-saturated liquid.
Protsenko, S P; Baidakov, V G; Teterin, A S; Zhdanov, E R
2007-03-07
Molecular dynamics methods have been used to investigate the kinetics of the liquid-gas phase transition in a two-component Lennard-Jones system at negative pressures and elastic stretches of the liquid to values close to spinodal ones. The molecular dynamics system consists of 2048 interacting particles with parameters of the Lennard-Jones potential for argon and neon. Density dependences of pressure and internal energy have been calculated for stable and metastable states of the mixture at a temperature T* approximately 0.7+/-0.01 and three values of the concentration. The location of mechanical and the diffusion spinodals has been determined. It has been established that a gas-saturated mixture retains its stability against finite variations of state variables up to stretches close to the values near the diffusion spinodal. The statistic laws of the process of destruction of the metastable state have been investigated. The lifetimes of the metastable phase have been determined. It is shown that owing to the small height of the potential barrier that separates the microheterogeneous from the homogeneous state a system of finite size has a possibility to make the reverse transition from the microheterogeneous into the homogeneous state. The lifetimes of the system in the microheterogeneous state, as well as the expectation times of the occurrence of a critical nucleus, are described by Poissonian distributions.
Onset of simple liquid behaviour in modified water models
NASA Astrophysics Data System (ADS)
Prasad, Saurav; Chakravarty, Charusita
2014-04-01
The transition to simple liquid behaviour is studied in a set of modified hybrid water models where the potential energy contribution of the Lennard-Jones dispersion-repulsion contribution is progressively enhanced relative to the electrostatic contribution. Characteristics of simple liquid behaviour that indicate the extent to which a given system can be mapped onto an inverse power law fluid are examined, including configurational energy-virial correlations, functional form of temperature dependence of the excess entropy along isochores, and thermodynamic and excess entropy scaling of diffusivities. As the Lennard-Jones contribution to the potential energy function increases, the strength of the configurational energy-virial correlations increases. The Rosenfeld-Tarazona temperature dependence of the excess entropy is found to hold for the range of state points studied here for all the hybrid models, regardless of the degree of correlating character. Thermodynamic scaling is found to hold for weakly polar fluids with a moderate degree of energy-virial correlations. Rosenfeld-scaling of transport properties is found not to be necessarily linked with the strength of energy-virial correlations but may hold for systems with poor thermodynamic scaling if diffusivities and excess entropies show correlated departures from the isomorph-invariant behaviour characteristic of approximate inverse power law fluids. The state-point dependence of the configurational energy-virial correlation coefficient and the implications for thermodynamic and excess entropy scalings are considered.
NASA Astrophysics Data System (ADS)
Wemhoff, A. P.; Carey, V. P.
2006-03-01
A simple surface tension estimation technique is described that is based solely upon the characteristics of the density profile in the interfacial region and the physical properties of the molecules in the fluid. This method, denoted free energy integration (FEI), links interfacial tension to known interfacial region density profile characteristics obtained via experiment or simulation. The general FEI methodology is provided here, and specific relations are derived for a methodology that incorporates the Redlich-Kwong fluid model. The Redlich-Kwong based FEI method was used to predict interfacial tension using the density profile characteristics of molecular dynamics (MD) simulations of argon using the Lennard-Jones potential, diatomic nitrogen using the two-center Lennard-Jones potential, and water using the extended simple point-charge (SPC/E) model. These results for argon compare favorably to values calculated by the traditional virial approach, known values from the literature using the finite-size scaling technique, and ASHRAE recommended values. In addition, the FEI predictions agree well with ASHRAE values and predictions using the virial method for nitrogen for the simulated range of temperatures in this study, and for water for reduced temperatures above 0.7. In addition, the FEI method results agree well with other established theoretical techniques for predictions of the surface tension of sulfur hexafluoride close to the critical point.
Onset of simple liquid behaviour in modified water models
Prasad, Saurav; Chakravarty, Charusita
2014-04-28
The transition to simple liquid behaviour is studied in a set of modified hybrid water models where the potential energy contribution of the Lennard-Jones dispersion-repulsion contribution is progressively enhanced relative to the electrostatic contribution. Characteristics of simple liquid behaviour that indicate the extent to which a given system can be mapped onto an inverse power law fluid are examined, including configurational energy-virial correlations, functional form of temperature dependence of the excess entropy along isochores, and thermodynamic and excess entropy scaling of diffusivities. As the Lennard-Jones contribution to the potential energy function increases, the strength of the configurational energy-virial correlations increases. The Rosenfeld-Tarazona temperature dependence of the excess entropy is found to hold for the range of state points studied here for all the hybrid models, regardless of the degree of correlating character. Thermodynamic scaling is found to hold for weakly polar fluids with a moderate degree of energy-virial correlations. Rosenfeld-scaling of transport properties is found not to be necessarily linked with the strength of energy-virial correlations but may hold for systems with poor thermodynamic scaling if diffusivities and excess entropies show correlated departures from the isomorph-invariant behaviour characteristic of approximate inverse power law fluids. The state-point dependence of the configurational energy-virial correlation coefficient and the implications for thermodynamic and excess entropy scalings are considered.
Simplicity of condensed matter at its core: generic definition of a Roskilde-simple system.
Schrøder, Thomas B; Dyre, Jeppe C
2014-11-28
The isomorph theory is reformulated by defining Roskilde-simple systems by the property that the order of the potential energies of configurations at one density is maintained when these are scaled uniformly to a different density. If the potential energy as a function of all particle coordinates is denoted by U(R), this requirement translates into U(Ra) < U(Rb) ⇒ U(λRa) < U(λRb). Isomorphs remain curves in the thermodynamic phase diagram along which structure, dynamics, and excess entropy are invariant, implying that the phase diagram is effectively one-dimensional with respect to many reduced-unit properties. In contrast to the original formulation of the isomorph theory, however, the density-scaling exponent is not exclusively a function of density and the isochoric heat capacity is not an exact isomorph invariant. A prediction is given for the latter quantity's variation along the isomorphs. Molecular dynamics simulations of the Lennard-Jones and Lennard-Jones Gaussian systems validate the new approach.
Neyt, Jean-Claude; Wender, Aurélie; Lachet, Véronique; Malfreyt, Patrice
2011-08-04
We report Monte Carlo simulations of the liquid-vapor interface of SO(2), O(2), N(2), and Ar to reproduce the dependence of the surface tension with the temperature. Whereas the coexisting densities, critical temperature, density, and pressure are very well reproduced by the two-phase simulations showing the same accuracy as the calculations performed using the Gibbs ensemble Monte Carlo technique (GEMC), the performance of the prediction of the variation of the surface tension with the temperature depends on the magnitude of the electrostatic and repulsive-dispersive interactions. The surface tension of SO(2) is very well reproduced, whereas the prediction of this property is less satisfactory for O(2) and N(2), for which the average intermolecular electrostatic interactions are several orders smaller than the dispersion interactions. For argon, we observe significant deviations from experiments. The representation of the surface tension of argon in reduced units shows that our calculations are in line with the existing surface tensions of the Lennard-Jones fluid in the literature. This underlines the difficulty of reproducing the temperature dependence of the surface tension of argon with interactions only modeled by the Lennard-Jones pair potential.
Assessment of high-fidelity collision models in the direct simulation Monte Carlo method
NASA Astrophysics Data System (ADS)
Weaver, Andrew B.
Advances in computer technology over the decades has allowed for more complex physics to be modeled in the DSMC method. Beginning with the first paper on DSMC in 1963, 30,000 collision events per hour were simulated using a simple hard sphere model. Today, more than 10 billion collision events can be simulated per hour for the same problem. Many new and more physically realistic collision models such as the Lennard-Jones potential and the forced harmonic oscillator model have been introduced into DSMC. However, the fact that computer resources are more readily available and higher-fidelity models have been developed does not necessitate their usage. It is important to understand how such high-fidelity models affect the output quantities of interest in engineering applications. The effect of elastic and inelastic collision models on compressible Couette flow, ground-state atomic oxygen transport properties, and normal shock waves have therefore been investigated. Recommendations for variable soft sphere and Lennard-Jones model parameters are made based on a critical review of recent ab-initio calculations and experimental measurements of transport properties.
Kadoura, Ahmad; Sun, Shuyu Salama, Amgad
2014-08-01
Accurate determination of thermodynamic properties of petroleum reservoir fluids is of great interest to many applications, especially in petroleum engineering and chemical engineering. Molecular simulation has many appealing features, especially its requirement of fewer tuned parameters but yet better predicting capability; however it is well known that molecular simulation is very CPU expensive, as compared to equation of state approaches. We have recently introduced an efficient thermodynamically consistent technique to regenerate rapidly Monte Carlo Markov Chains (MCMCs) at different thermodynamic conditions from the existing data points that have been pre-computed with expensive classical simulation. This technique can speed up the simulation more than a million times, making the regenerated molecular simulation almost as fast as equation of state approaches. In this paper, this technique is first briefly reviewed and then numerically investigated in its capability of predicting ensemble averages of primary quantities at different neighboring thermodynamic conditions to the original simulated MCMCs. Moreover, this extrapolation technique is extended to predict second derivative properties (e.g. heat capacity and fluid compressibility). The method works by reweighting and reconstructing generated MCMCs in canonical ensemble for Lennard-Jones particles. In this paper, system's potential energy, pressure, isochoric heat capacity and isothermal compressibility along isochors, isotherms and paths of changing temperature and density from the original simulated points were extrapolated. Finally, an optimized set of Lennard-Jones parameters (ε, σ) for single site models were proposed for methane, nitrogen and carbon monoxide.
Thermodynamic response functions of fluids: A microscopic approach based on NpT Monte Carlo
NASA Astrophysics Data System (ADS)
Piñeiro, Manuel M.; Cerdeiriña, Claudio A.; Medeiros, Milton
2008-07-01
On the basis of NpT Monte Carlo simulations, a detailed analysis on the microscopic origins of some specific features of thermodynamic response functions of fluids is performed. Specifically, the residual isobaric heat capacity Cpres, the isobaric thermal expansivity αp, and the isothermal compressibility κT for Lennard-Jones methane and optimized potential for liquid simulations (OPLS) methanol have been determined via standard techniques. For the former, data along the liquid, gas, and supercritical regions are presented, while a wide temperature range at a single supercritical pressure is covered for the latter. They have been obtained by computing the various pairwise fluctuations contributing to each property. Attention is mainly focused on isothermal and isobaric maxima found for both Cpres and αp, which have been rationalized at a molecular level using qualitative arguments. It is encountered that maxima emerge as a natural consequence of the destruction of fluid structure as temperature is increased or as pressure is decreased. The results for Lennard-Jones methane reveal the competition of energetic and volumetric effects, while those for OPLS methanol evidence that hydrogen-bonding is dominant as energetic effects are concerned. Further discussion on previous results and alternative approaches using equations of state as well as on closely related topics such as "maxima and critical phenomena" is included.