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. PMID:25612707
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. PMID:26178115
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.
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.
A Lennard-Jones plus Coulomb potential for Al3+ ions in aqueous solutions
NASA Astrophysics Data System (ADS)
Faro, Tatiana M. C.; Thim, Gilmar P.; Skaf, Munir S.
2010-03-01
We developed a simple pair-additive Lennard-Jones plus Coulomb potential for molecular simulations of the trivalent cation Al3+ in water which accounts reasonably well for the behavior of aluminum aqueous solutions. The model predicts an octahedral first hydration shell containing 6 water molecules and a trigonal second shell with 12 molecules on average, in good agreement with the available experimentally determined structure. The peak positions of the cation-oxygen radial distribution function are only slightly compressed compared to the x-ray structure, the hydration enthalpy is 10% too low, and the cation self-diffusion coefficient and the single-particle second rank reorientational time are in excellent agreement with inelastic neutron scattering and NMR spectroscopy data, respectively. The model also captures the essential vibrational features of the hydrated [Al(H2O)6]3+ complex. It predicts the main O-Al-O bending mode frequency to within ˜5%, but significantly overestimates the frequency of the totally symmetric Al-O stretching mode. Overall, the accuracy of the proposed model is as good as the best available classical potentials, if not better in some aspects, with a much simpler functional form, which makes it an attractive alternative for computer simulations of Al3+ in more complex aqueous and biomolecular systems.
Connectivity in the potential energy landscape for binary Lennard-Jones systems
NASA Astrophysics Data System (ADS)
de Souza, Vanessa K.; Wales, David J.
2009-05-01
Connectivity in the potential energy landscape of a binary Lennard-Jones system can be characterized at the level of cage-breaking. We calculate the number of cage-breaking routes from a given local minimum and determine the branching probabilities at different temperatures, along with correlation factors that represent the repeated reversals of cage-breaking events. The number of reversals increases at lower temperatures and for more fragile systems, while the number of accessible connections decreases. We therefore associate changes in connectivity with super-Arrhenius behavior. Reversals in minimum-to-minimum transitions are common, but often correspond to "non-cage-breaking" processes. We demonstrate that the average waiting time within a minimum shows simple exponential behavior with decreasing temperature. To describe the long-term behavior of the system, we consider reversals and connectivity in terms of the "cage-breaking" processes that are pertinent to diffusion [V. K. de Souza and D. J. Wales, J. Chem. Phys. 129, 164507 (2008)]. These cage-breaking events can be modeled by a correlated random walk. Thus, a full correlation factor can be calculated using short simulations that extend up to two cage-breaking events.
NASA Astrophysics Data System (ADS)
Mamedov, Bahtiyar Akber; Somuncu, Elif
2016-04-01
An efficient analytical method to evaluate the third virial coefficient with Lennard-Jones (12-6) type potential is presented. Proposed approach is particularly suitable for analysis of various properties of three body systems. To conform the correctness of the calculation result, a comparison is given with the literature for NO2, SF6 and C2H2 molecules. Calculation results show that obtained formulae provide higher accuracy and efficiency than the proposed approaches in literature.
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. PMID:26627969
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.
Transport theory for the Lennard-Jones dense fluid
Karkheck, J.; Stell, G.; Xu, J.
1988-11-01
A kinetic theory for a fluid of particles interacting via a pair potential with hard-core plus truncated tail is described and used to derive a transport theory for the Lennard-Jones fluid as well as the square-well fluid. Numerical results for shear viscosity, thermal conductivity, and the self-diffusion coefficient are given for the Lennard-Jones fluid and compared with simulation and experimental results. Our Lennard-Jones theory proves quantitatively useful over a wide range of states.
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.
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.
Taylor, Mark P; Adhikari, Shishir R
2011-07-28
The average conformation of a flexible chain molecule in solution is coupled to the local solvent structure. In a dense solvent, local chain structure often mirrors the pure solvent structure, whereas, in a dilute solvent, the chain can strongly perturb the solvent structure which, in turn, can lead to either chain expansion or compression. Here we use Monte Carlo (MC) simulation to study such solvent effects for a short Lennard-Lones (LJ) chain in monomeric LJ solvent. For an n-site chain molecule in solution these many-body solvent effects can be formally mapped to an n-body solvation potential. We have previously shown that for hard-sphere and square-well chain-in-solvent systems this n-body potential can be decomposed into a set of two-body potentials. Here, we show that this decomposition is also valid for the LJ system. Starting from high precision MC results for the n = 5 LJ chain-in-solvent system, we use a Boltzmann inversion technique to compute numerically exact sets of two-body solvation potentials which map the many-body chain-in-solvent problem to a few-body single-chain problem. We have carried out this mapping across the full solvent phase diagram including the dilute vapor, dense liquid, and supercritical regions and find that these sets of solvation potentials are able to encode the complete range of solvent effects found in the LJ chain-in-solvent system. We also show that these two-site solvation potentials can be used to obtain accurate multi-site intramolecular distribution functions and we discuss the application of these exact short chain potentials to the study of longer chains in solvent. PMID:21806157
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.
The Lennard-Jones melting line and isomorphism
NASA Astrophysics Data System (ADS)
Heyes, D. M.; Brańka, A. C.
2015-12-01
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, X ˜ , 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 X ˜ 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.
Elastic compliances and stiffnesses of the fcc Lennard-Jones solid
NASA Astrophysics Data System (ADS)
Quesnel, D. J.; Rimai, D. S.; Demejo, L. P.
1993-09-01
The isothermal elastic compliances, stiffnesses, and bulk moduli of a Lennard-Jones solid organized into an fcc crystal structure (256 atoms in 43 unit cells) have been calculated as a function of testing temperature (expressed as the mean kinetic energy per atom). Tests conducted in pure shear were used to determine S44 and C44=G100, where 100 refers to crystallographic directions. Tests imposing axial elongation with fixed lateral dimensions established C11 and C12. Axial deformation with zero lateral pressure (a tension test) was used to determine S11, S12, E100 and ν100. This provided an independent set of results for comparison with the dilatational stiffnesses C11 and C12. The bulk modulus K was obtained by independent triaxial tension testing. The stiffnesses, compliances, and moduli were determined by regression analysis and digital filtering applied to combinations of the stress-tensor and strain-tensor data stored at each iteration during the constant-rate deformation experiments. While the cubic fcc Lennard-Jones solid expectedly obeys the Cauchy relations for central-force potentials, it is not isotropic, allowing ν to take on values other than 1/4 as originally proposed by Poisson. The present calculations show ν100=0.347 for the fcc Lennard-Jones solid with a Young's modulus of E100=61.1ɛ/σ3, an initial (as indicated by superscript 0) shear modulus of G0100=57.2ɛ/σ3, and an initial bulk modulus of K0=71.2ɛ/σ3 at zero temperature. The moduli all decreased with increasing temperature. Reuss, Voigt, and Hashin and Shtrikman [J. Mech. Phys. Solids 10, 335 (1962)] bounds on the isotropic elastic properties of polycrystalline aggregates of Lennard-Jones material were also determined. Computed values of the moduli are in reasonable agreement with experimental results for solid argon and crystalline polyethylene.
Scaling of the dynamics of flexible Lennard-Jones chains: Effects of harmonic bonds
NASA Astrophysics Data System (ADS)
Veldhorst, Arno A.; Dyre, Jeppe C.; Schrøder, Thomas B.
2015-11-01
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.
Elastic Lennard-Jones polymers meet clusters: Differences and similarities
NASA Astrophysics Data System (ADS)
Schnabel, Stefan; Bachmann, Michael; Janke, Wolfhard
2009-09-01
We investigate solid-solid and solid-liquid transitions of elastic flexible off-lattice polymers with Lennard-Jones monomer-monomer interaction and anharmonic springs by means of sophisticated variants of multicanonical Monte Carlo methods. We find that the low-temperature behavior depends strongly and nonmonotonically on the system size and exhibits broad similarities to unbound atomic clusters. Particular emphasis is dedicated to the classification of icosahedral and nonicosahedral low-energy polymer morphologies.
Energy landscapes of quantum Lennard-Jones solids.
Chakravarty, Charusita
2011-06-30
To generalize inherent structure analysis to understand structural changes in quantum liquids and solids, differences between classical (V(x)) and quantum-corrected (U(qeff)(x)) energy landscapes are estimated as a function of the de Boer parameter (Λ). Path integral simulations of quantum Lennard-Jones solids are performed at zero pressure and a dimensionless reduced temperature of 0.123, corresponding to an absolute temperature of 4.2K. At constant temperature and pressure, Λ is increased from the classical limit of zero to Λ = 0.28, corresponding to para-H(2). Increasing quantum delocalization effects result in a continuous decrease in density and local order but without a transition to a disordered, liquid state. The inherent structure landscape of bulk systems is strongly dependent on density with the energy and stability of crystalline minima decreasing relative to that of amorphous packing minima as the system is stretched. For Λ ≈ 0.23, the volume fluctuations in quantum solids are sufficient to result in sampling of disordered minima while for Λ = 0.28, the underlying classical inherent structures are completely disordered, indicating that the topography of U(qeff)(x) and V(x) are qualitatively different for such values of Λ. To assess the nature of the quantum-corrected energy landscape, effective pair potentials are defined by u(qeff)(r) = -kT ln g(r) using the pair correlation function (g(r)) of the quantum system in the neighborhood of the first peak. Our results show that as Λ increases, the pair potentials become increasingly softer, shallower, and of increasing range with a shifting of the potential minimum to larger distances. For example, the reduction of the entropy of fusion and melting temperatures of quantum solids with increasing Λ are analogous to the changes in thermodynamics of melting seen in classical solids with increasing range and softness of interactions. The energy landscapes associated with such coarse-grained potentials
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.
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. PMID:16196640
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.
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. PMID:27421400
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.
Equation of State for the Lennard-Jones Fluid
NASA Astrophysics Data System (ADS)
Thol, Monika; Rutkai, Gabor; Köster, Andreas; Lustig, Rolf; Span, Roland; Vrabec, Jadran
2016-06-01
An empirical equation of state correlation is proposed for the Lennard-Jones model fluid. The equation in terms of the Helmholtz energy is based on a large molecular simulation data set and thermal virial coefficients. The underlying data set consists of directly simulated residual Helmholtz energy derivatives with respect to temperature and density in the canonical ensemble. Using these data introduces a new methodology for developing equations of state from molecular simulation. The correlation is valid for temperatures 0.5 < T/Tc < 7 and pressures up to p/pc = 500. Extensive comparisons to simulation data from the literature are made. The accuracy and extrapolation behavior are better than for existing equations of state.
Lennard-Jones fluid-fluid interfaces under shear
NASA Astrophysics Data System (ADS)
Galliero, Guillaume
2010-05-01
Using nonequilibrium molecular dynamics simulations on simple Lennard-Jones binary mixtures, we have studied the behavior of planar fluid-fluid interfaces undergoing shear flow. When the miscibility is low enough, a slip together with a partial depletion have been noticed at the interface between the two fluid phases. The slip length can reach a value equal to some molecular diameters and the corresponding interfacial viscosity can be two times smaller than the value in the bulk. It is shown how the omission of this slip may lead to flow-rate misevaluation when dealing with a multiphase flow in a nanoporous medium even for non polymer fluids. In addition, using the simulation results, a simple relation between interfacial tension and interfacial viscosity is proposed for the monoatomic systems studied in this work. Finally, it is shown that the interfacial viscosity cannot be fully accounted for by estimating the local viscosity deduced from the local thermodynamic properties of the interface.
Computationally Useful Bridge Diagram Series. III. Lennard-Jones Mixtures
Dyer, Kippi M.; Perkyns, John S.; Pettitt, Bernard M.
2002-06-01
The first two orders of bridge diagrams for the f-bond expansion and the h-bond expansion are calculated for a binary mixture of Lennard-Jones spheres. The method used follows the Legendre polynomial integration methods outlined in the first two papers of this series. As for the pure fluid cases, the thermodynamic results which follow from these methods are found to be in reasonable agreement with the simulation result. Analysis of the thermodynamic and structural results in comparison to the best current bridge function approximations indicate that accurate descriptions of higher order mixtures will require methods beyond the current mean field treatments which are of utility in simple fluids. The methods given are unfortunately not computationally convenient at highest order; however, the lower order diagrams are both accessible and give reasonable numerical results.
Computationally useful bridge diagram series. III. Lennard-Jones mixtures
NASA Astrophysics Data System (ADS)
Dyer, Kippi; Perkyns, John; Pettitt, B. Montgomery
2002-06-01
The first two orders of bridge diagrams for the f-bond expansion and the h-bond expansion are calculated for a binary mixture of Lennard-Jones spheres. The method used follows the Legendre polynomial integration methods outlined in the first two papers of this series. As for the pure fluid cases, the thermodynamic results which follow from these methods are found to be in reasonable agreement with the simulation result. Analysis of the thermodynamic and structural results in comparison to the best current bridge function approximations indicate that accurate descriptions of higher order mixtures will require methods beyond the current mean field treatments which are of utility in simple fluids. The methods given are unfortunately not computationally convenient at highest order; however, the lower order diagrams are both accessible and give reasonable numerical results.
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.
Water in the presence of inert Lennard-Jones obstacles
NASA Astrophysics Data System (ADS)
Kurtjak, Mario; Urbic, Tomaz
2014-04-01
Water confined by the presence of a 'sea' of inert obstacles was examined. In the article, freely mobile two-dimensional Mercedes-Benz (MB) water put to a disordered, but fixed, matrix of Lennard-Jones disks was studied by the Monte Carlo computer simulations. For the MB water molecules in the matrix of Lennard-Jones disks, we explored the structures, hydrogen-bond-network formation and thermodynamics as a function of temperature and size and density of matrix particles. We found that the structure of model water is perturbed by the presence of the obstacles. Density of confined water, which was in equilibrium with the bulk water, was smaller than the density of the bulk water and the temperature dependence of the density of absorbed water did not show the density anomaly in the studied temperature range. The behaviour observed as a consequence of confinement is similar to that of increasing temperature, which can for a matrix lead to a process similar to capillary evaporation. At the same occupancy of space, smaller matrix molecules cause higher destruction effect on the absorbed water molecules than the bigger ones. We have also tested the hypothesis that at low matrix densities the obstacles induce an increased ordering and 'hydrogen bonding' of the MB model molecules, relative to pure fluid, while at high densities the obstacles reduce MB water structuring, as they prevent the fluid to form good 'hydrogen-bonding' networks. However, for the size of matrix molecules similar to that of water, we did not observe this effect.
Pressure-energy correlations and thermodynamic scaling in viscous Lennard-Jones liquids
NASA Astrophysics Data System (ADS)
Coslovich, D.; Roland, C. M.
2009-01-01
We use molecular dynamics simulation results on viscous binary Lennard-Jones mixtures to examine the correlation between the potential energy and the virial. In accord with a recent proposal [U. R. Pedersen et al., Phys. Rev. Lett. 100, 015701 (2008)], the fluctuations in the two quantities are found to be strongly correlated, exhibiting a proportionality constant, Γ, numerically equal to one-third the slope of an inverse power law approximation to the intermolecular potential function. The correlation is stronger at higher densities, where interatomic separations are in the range where the inverse power law approximation is more accurate. These same liquids conform to thermodynamic scaling of their dynamics, with the scaling exponent equal to Γ. Thus, the properties of strong correlation between energy and pressure and thermodynamic scaling both reflect the ability of an inverse power law representation of the potential to capture interesting features of the dynamics of dense, highly viscous liquids.
NASA Astrophysics Data System (ADS)
Cameron, M. K.
2013-08-01
The large time behavior of a stochastic system with infinitesimally small noise can be described in terms of Freidlin's cycles. We show that if the system is gradient and the potential satisfies certain non-restrictive conditions, the hierarchy of cycles has a structure of a full binary tree, and each cycle is exited via the lowest saddle adjacent to it. Exploiting this property, we propose an algorithm for computing the asymptotic zero-temperature path and building a hierarchy of Freidlin's cycles associated with the transition process between two given local equilibria. This algorithm is suitable for systems with a complex potential energy landscape with numerous minima. We apply it to find the asymptotic zero-temperature path and Freidlin's cycles involved into the transition process between the two lowest minima of the Lennard-Jones cluster of 38 atoms. D. Wales's stochastic network of minima and transition states of this cluster is used as an input.
Molecular Dynamic Study of a Single Dislocation in a Two-Dimensional Lennard Jones System
NASA Astrophysics Data System (ADS)
Robles, Miguel; Mustonen, Ville; Kaski, Kimmo
In this work the motion of a single dislocation in a two-dimensional triangular lattice is studied by using classical Molecular Dynamics method with the Lennard Jones inter-atomic potential. The dislocation motion is investigated with an interactive simulation program developed to track automatically the movement of lattice defects. Constant strain and constant strain-rate deformations were applied to the system. From constant strain simulations a curve of shear stress versus dislocation velocity is obtained, showing a nonlinear power law relation. An equation of motion for the dislocation is proposed and found to be applicable when the movement of dislocation follows a quasi-static process. Numerical simulations at different strain rates show an elastic-to-plastic transition that modifies the dynamics of the dislocation motion.
Density-functional theory of elastic moduli: Hard-sphere and Lennard-Jones crystals
NASA Astrophysics Data System (ADS)
Jarić, Marko V.; Mohanty, Udayan
1988-03-01
We propose a density-functional method for calculating elastic moduli of crystalline solids. The method is based on the second-order Ramakrishnan-Yussouff (RY) expansion of the variational grand-canonical potential around a uniform liquid state. The densities of the strained and unstrained crystal are represented as sums of narrow Gaussians. We express the crystal moduli in terms of the liquid structure factor its first and second derivatives evaluated at the reciprocal-lattice points of the crystal. We evaluate the elastic moduli for fcc hard-sphere and Lennard-Jones crystals using the Percus-Yevick and computer-simulation liquid structure factors, respectively. An indirect comparison with available experimental and theoretical values shows that although our calculated moduli are accurate to an order of magnitude, higher-order terms in the RY expansion might be significant. We find important contributions from density equilibration within the strained unit cell.
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.
Metastable Lennard-Jones fluids. II. Thermal conductivity.
Baidakov, Vladimir G; Protsenko, Sergey P
2014-06-01
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 → ∞. PMID:24908025
Solid-liquid phase equilibrium for binary Lennard-Jones mixtures
NASA Astrophysics Data System (ADS)
Hitchcock, Monica R.; Hall, Carol K.
1999-06-01
Solid-liquid phase diagrams are calculated for binary mixtures of Lennard-Jones spheres using Monte Carlo simulation and the Gibbs-Duhem integration technique of Kofke. We calculate solid-liquid phase diagrams for the model Lennard-Jones mixtures: argon-methane, krypton-methane, and argon-krypton, and compare our simulation results with experimental data and with Cottin and Monson's recent cell theory predictions. The Lennard-Jones model simulation results and the cell theory predictions show qualitative agreement with the experimental phase diagrams. One of the mixtures, argon-krypton, has a different phase diagram than its hard-sphere counterpart, suggesting that attractive interactions are an important consideration in determining solid-liquid phase behavior. We then systematically explore Lennard-Jones parameter space to investigate how solid-liquid phase diagrams change as a function of the Lennard-Jones diameter ratio, σ11/σ22, and well-depth ratio, ɛ11/ɛ22. This culminates in an estimate of the boundaries separating the regions of solid solution, azeotrope, and eutectic solid-liquid phase behavior in the space spanned by σ11/σ22 and ɛ11/ɛ22 for the case σ11/σ22<0.85.
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. PMID:25702023
Systematic investigation of theories of transport in the Lennard-Jones fluid
NASA Astrophysics Data System (ADS)
Dyer, Kippi M.; Pettitt, B. M.; Stell, George
2007-01-01
Three kinetic theories of transport are investigated for the single-species Lennard-Jones model fluid. Transport coefficients, including diffusion, shear, and bulk viscosity, are calculated from these theories for the Lennard-Jones fluid across the fluid regions of the phase diagram. The results are systematically compared against simulation. It is found that for each transport property considered, there is at least one theoretical result based on approximations that have been systematically derived from a first-principles starting point that is quantitatively useful over a wide range of densities and temperatures. To the authors' knowledge, this article constitutes the first such compendium of results for the Lennard-Jones model fluid that has been assembled.
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.
NASA Astrophysics Data System (ADS)
Hoang, Hai; Galliero, Guillaume
2013-12-01
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
2014-02-01
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. PMID:24511981
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.
Thermodynamic stability of soft-core Lennard-Jones fluids and their mixtures
NASA Astrophysics Data System (ADS)
Heyes, D. M.
2010-02-01
Thermodynamic stability of model single component and binary mixture fluids is considered with the Fisher-Ruelle (FR) stability criteria, which apply in the thermodynamic limit, and molecular dynamics (MD) simulation for finite periodic systems. Two soft-core potential forms are considered, ϕ6,1(r)=4[1/(a +r6)2-1/(a +r6)] and ϕ2,3(r)=4[1/(a +r2)6-1/(a+r2)3], where r is the separation between the particle centers. According to FR these are unstable in the thermodynamic limit if a >ac=1/2 and a >ac=(7/32)1/3, respectively. MD simulations with single-component particles show, however, that this transition on typical simulation times is more gradual for finite periodic systems with variation in a on either side of ac. For a
Molecular Dynamics Simulation of the Lennard--Jones Polymers in a Good Solvent
NASA Astrophysics Data System (ADS)
Ciesla, M.; Pawlowicz, J.; Longa, L.
2007-05-01
We carried out united-atom Langevin dynamics simulations of polymer's equilibrium state in a good solvent. Our primary goal was a pedagogical exposition of fundamental equilibrium properties of isolated polymers in dilutions with a model that contains many features of real materials. The polymer was chosen to be a three-dimensional chain of N identical beads (monomers) without internal structure. Each monomer interacted with its two neighbors by a harmonic potential, which modeled a chemical bond. Additionally all monomers within a chain were assumed to interact through the Lennard-Jones (LJ) potential. Interaction with solvent and with other polymers was introduced using Langevin forces. Analyzing internal energy per polymer and radius of gyration as function of temperature we observed a rapid globule to coil phase transition. Also we studied elastic properties of single polymer chain for temperatures below the transition and identified three regions with different elastic behavior. Typical chain lengths in our simulations ranged from 100 to 1000 monomers. The elaborated software package can easily be modified to study {e.g.} the effect of polymer stiffness on thermodynamic behavior.
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. PMID:27434103
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. PMID:24182055
Molecular dynamics study of nanobubbles in the equilibrium Lennard-Jones fluid
NASA Astrophysics Data System (ADS)
Zhukhovitskii, D. I.
2013-10-01
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.
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. PMID:26660062
Freezing and melting equations for the n-6 Lennard-Jones systems
NASA Astrophysics Data System (ADS)
Khrapak, Sergey A.; Ning, Ning
2016-05-01
We generalize previous approach of Khrapak and Morfill [J. Chem. Phys. 134, 094108 (2011)] to construct simple and sufficiently accurate freezing and melting equations for the conventional Lennard-Jones (LJ) system to n-6 LJ systems, using the accurate results for the triple points of these systems published by Sousa et al. [J. Chem. Phys. 136, 174502 (2012)].
Influence of strain on transport in dense Lennard-Jones systems
NASA Astrophysics Data System (ADS)
Petravic, Janka
2004-04-01
We study the shear stress relaxation and temperature dependence of the diffusion coefficient, viscosity, and thermal conductivity along a high-density Lennard-Jones isochore of the reduced density of 1.0, as it crosses the freezing and melting lines, in equilibrium and under constant strain.
Heffelfinger, G.S. ); Swol, F.v. )
1994-05-15
A new approach to calculating diffusivities, both transport as well as equilibrium, is presented. The dual control volume grand canonical molecular dynamics (or DCV-GCMD) method employs two local control volumes for chemical potential control via particle creation/destruction as in grand canonical Monte Carlo (GCMC) simulations. The control volumes are inserted in a standard [ital NVT] molecular dynamics simulation yielding a simulation with stochastic chemical potential control that may be thought of as a hybrid GCMC-MD approach. The geometrical control of the chemical potential enables a steady state chemical potential gradient to be established in the system. By measuring the density profile and flux, Fick's law is used to determine the diffusivity. An example calculation is presented for a simple Lennard-Jones system.
NASA Astrophysics Data System (ADS)
Benjamin, Ronald; Horbach, Jürgen
2015-07-01
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)
Keshavarzi, Ezat; Namdari, Fatemeh; Jildani, Sediqeh Rabiei
2016-04-01
The modified fundamental measure theory has been employed to investigate some well known regularities of bulk fluid for the Lennard-Jones fluid confined in nanoslit pore. The regularities investigated include common compression point, common bulk modulus point, Tait-Murnaghan equation, and the linear regularity between pressure and temperature for each isochore. All these regularities have been investigated for two different components of pressure for confined fluid. Our results show that the common compression and common bulk modulus point remain valid for fluids confined in nanoslit pores of different sizes and with different wall-fluid potentials. The density of the common compression and common bulk modulus point are different from corresponding ones for the bulk fluid. Our observations also show that the Tait-Murnaghan equation and pressure-temperature linear regularity also hold for confined fluid. The sign of the intercept of pressure-temperature regularity is determined by the difference between attraction and repulsion terms in the compressibility factor.
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. PMID:25833595
Crystallization of Lennard-Jones nanodroplets: From near melting to deeply supercooled
NASA Astrophysics Data System (ADS)
Malek, Shahrazad M. A.; Morrow, Gregory P.; Saika-Voivod, Ivan
2015-03-01
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.
Rydberg-London potential for diatomic molecules and unbonded atom pairs.
Cahill, Kevin; Parsegian, V Adrian
2004-12-01
We propose and test a pair potential that is accurate at all relevant distances and simple enough for use in large-scale computer simulations. A combination of the Rydberg potential from spectroscopy and the London inverse-sixth-power energy, the proposed form fits spectroscopically determined potentials better than the Morse, Varnshi, and Hulburt-Hirschfelder potentials and much better than the Lennard-Jones and harmonic potentials. At long distances, it goes smoothly to the London force appropriate for gases and preserves van der Waals's "continuity of the gas and liquid states," which is routinely violated by coefficients assigned to the Lennard-Jones 6-12 form. PMID:15634034
Phase changes in selected Lennard-Jones X13-nYn clusters.
Sabo, Dubravko; Predescu, Cristian; Doll, J D; Freeman, David L
2004-07-01
Detailed studies of the thermodynamic properties of selected binary Lennard-Jones clusters of the type X13-nYn (where n=1, 2, 3) are presented. The total energy, heat capacity, and first derivative of the heat capacity as a function of temperature are calculated by using the classical and path integral Monte Carlo methods combined with the parallel tempering technique. A modification in the phase change phenomena from the presence of impurity atoms and quantum effects is investigated. PMID:15260616
How to quantify solid-liquid phase transition: Lennard-Jones system case study
NASA Astrophysics Data System (ADS)
Klumov, Boris A.; Klumov
2013-12-01
In this paper we analyzed different measures, characterizing the melting of Lennard-Jones solid, and associated with the properties of both the translational and the orientational local order. It has been shown that the most sensitive indicator of melting is the cumulant of the probability distribution function over w 6 bond-order parameter. The criterion of melting based on the indicator is proposed; the criterion can be used for any solids, having fcc/hcp types of symmetry.
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. PMID:25399138
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.
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. PMID:27334147
NASA Astrophysics Data System (ADS)
Costigliola, Lorenzo; Schrøder, Thomas B.; Dyre, Jeppe C.
2016-06-01
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.
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.
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. PMID:25621892
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
Urrutia, Ignacio; Paganini, Iván E
2016-05-01
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. PMID:27155620
NASA Astrophysics Data System (ADS)
Urrutia, Ignacio; Paganini, Iván E.
2016-05-01
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/R2 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.
Georgescu, Ionuţ; Brown, Sandra E; Mandelshtam, Vladimir A
2013-04-01
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. PMID:23574239
Sharapov, Vladimir A; Mandelshtam, Vladimir A
2007-10-18
We consider systems undergoing very-low-temperature solid-solid transitions associated with minima of similar energy but different symmetry, and separated by a high potential barrier. In such cases the well-known "broken-ergodicity" problem is often difficult to overcome, even using the most advanced Monte Carlo (MC) techniques, including the replica exchange method (REM). The methodology that we develop in this paper is suitable for the above specified cases and is numerically accurate and efficient. It is based on a new MC move implemented within the REM framework, in which trial points are generated analytically using an auxiliary harmonic superposition system that mimics well the true system at low temperatures. Due to the new move, the low-temperature random walks are able to frequently switch the relevant potential energy funnels leading to an efficient sampling. Numerically accurate results are obtained for a number of Lennard-Jones clusters, including those that have so far been treated only by the harmonic superposition approximation (HSA). The latter is believed to provide good estimates for low-temperature equilibrium properties but is manifestly uncontrollable and is difficult to validate. The present results provide a good test for the HSA and demonstrate its reliability, particularly for estimation of the solid-solid transition temperatures in most cases considered. PMID:17685597
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
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.
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
Explicit expression for the Stokes-Einstein relation for pure Lennard-Jones liquids
NASA Astrophysics Data System (ADS)
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 D ηsv=k T ξ-1(N/V ) 1 /3 , where D is the self-diffusion coefficient, ηsv 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 ηsv on packing fraction, η , and T has been determined so as to complete their scaling equations. The equations for D and ηsv in these states are m-1 /2(N/V ) -1 /3(1-η ) 4ɛ-1 /2T and m1 /2(N/V ) 2 /3(1-η ) -4ɛ1 /2T0 , respectively, where m and ɛ 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 ηsv 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, D ηsv=(k T /2 π ) σ-1 , where σ means the particle size, is the presence of the η1 /3 term, since (N/V )1 /3=(6/π )1 /3σ-1η1 /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 η1 /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 η1 /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 ηsv is similar to
Modelling of disjoining pressure for Lennard-Jones free thin films
NASA Astrophysics Data System (ADS)
Peng, Tiefeng; Gao, Xuechao; Li, Qibin; Yang, Siyuan; Tang, Qizhong
2016-03-01
Development of disjoining pressure was performed to study the symmetric, Lennard-Jones (LJ) free thin films using molecular modelling. A methodology rooted from film thermodynamics was established to derive the disjoining pressure isotherm (Π ‑ h), which is based on the surface tension at varied film thicknesses and can be viewed as a post-processing technique. The results showed that the disjoining pressure of LJ fluid is purely attractive. Compared with the complicated method reported previously, this methodology is demonstrated to be more convenient and readily applicable for other liquid films (e.g. water, aqueous thin films containing electrolyte or surfactants), meanwhile it can be applied at both low and high temperatures.
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.
On the establishment of thermal diffusion in binary Lennard-Jones liquids
NASA Astrophysics Data System (ADS)
Ferrario, M.; Bonella, S.; Ciccotti, G.
2016-07-01
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.
Phase diagram and universality of the Lennard-Jones gas-liquid system.
Watanabe, Hiroshi; Ito, Nobuyasu; Hu, Chin-Kun
2012-05-28
The gas-liquid phase transition of the three-dimensional Lennard-Jones particles system is studied by molecular dynamics simulations. The gas and liquid densities in the coexisting state are determined with high accuracy. The critical point is determined by the block density analysis of the Binder parameter with the aid of the law of rectilinear diameter. From the critical behavior of the gas-liquid coexisting density, the critical exponent of the order parameter is estimated to be β = 0.3285(7). Surface tension is estimated from interface broadening behavior due to capillary waves. From the critical behavior of the surface tension, the critical exponent of the correlation length is estimated to be ν = 0.63(4). The obtained values of β and ν are consistent with those of the Ising universality class. PMID:22667535
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.
Baidakov, Vladimir G; Bobrov, Konstantin S; Teterin, Aleksey S
2011-08-01
Molecular dynamics simulations have been used to investigate the kinetics of spontaneous cavitation and crystallization in a Lennard-Jones liquid at negative pressures in the temperature range where these processes compete with each other. The nucleation rate has been calculated in NVE and NpT ensembles by the method of mean lifetime and the transition interface sampling method with parallel path swapping. The data obtained have been used to determine in the framework of classical nucleation theory the value of the ratio of the solid-liquid and the liquid-void interfacial free energy for critical crystals and cavities and the values of their volumes at points where the cavitation rate of the liquid is equal to the rate of its crystallization. PMID:21823717
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. PMID:26172722
Dynamics of vacancies in two-dimensional Lennard-Jones crystals
NASA Astrophysics Data System (ADS)
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.
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. PMID:17867756
Properties of the Lennard-Jones dimeric fluid in two dimensions: An integral equation study
Urbic, Tomaz; Dias, Cristiano L.
2014-01-01
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. PMID:24606372
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
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. PMID:27179494
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 (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. PMID:27276951
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. PMID:27036422
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.
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.
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.
Theory of slope-dependent disjoining pressure with application to Lennard-Jones liquid films.
Yi, Taeil; Wong, Harris
2007-09-15
A liquid film of thickness h<100 nm is subject to additional intermolecular forces, which are collectively called disjoining pressure Pi. Since Pi dominates at small film thicknesses, it determines the stability and wettability of thin films. Current theory derived for uniform films gives Pi=Pi(h). This solution has been applied recently to non-uniform films and becomes unbounded near a contact line as h-->0. Consequently, many different effects have been considered to eliminate or circumvent this singularity. We present a mean-field theory of Pi that depends on the slope h(x) as well as the height h of the film. When this theory is implemented for Lennard-Jones liquid films, the new Pi=Pi(h,h(x)) is bounded near a contact line as h-->0. Thus, the singularity in Pi(h) is artificial because it results from extending a theory beyond its range of validity. We also show that the new Pi can capture all three regimes of drop behavior (complete wetting, partial wetting, and pseudo-partial wetting) without altering the signs of the long and short-range interactions. We find that a drop with a precursor film is linearly stable. PMID:17570389
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
Freezing and melting line invariants of the Lennard-Jones system.
Costigliola, Lorenzo; Schrøder, Thomas B; Dyre, Jeppe C
2016-06-01
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. PMID:27186598
NASA Astrophysics Data System (ADS)
Calero, C.; Knorowski, C.; Travesset, A.
2016-03-01
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.
An accurate Van der Waals-type equation of state for the Lennard-Jones fluid
Mecke, M.; Mueller, A.; Winkelmann, J.
1996-03-01
A new equation of state (EOS) is proposed for the Helmholtz energy F of the Lennard-Jones fluid which represents the thermodynamic properties over a wide range of temperatures and densities. The EOS is written in the form of a generalized van der Waals equation, F= F{sub H} + F{sub A}, where F{sub H} is a hard body contribution and FA an attractive dispersion force contribution. The expression for F{sub H} is closely related to the hybrid Barker-Henderson pertubation theory. The construction of FA is accomplished with the Setzmann-Wagner optimization procedure on the basis of virial coefficients and critically assessed computer simulation data. A comparison with the EOS shows improvement in the description of the vapor-liquid coexistence properties, the pvT data, and in peculiar, of the caloric properties. A comparison with the EOS of Kolafa and Nezbeda which appeared after the bulk of this work was finished shows still an improvement in the standard deviations of the pressure and internal energy by about 30%.
NASA Astrophysics Data System (ADS)
McNeil, William J.; Madden, William G.; Haymet, A. D. J.; Rice, Stuart A.
1983-01-01
A recent theory of Haymet, Rice, and Madden (HRM) for the pair and triplet correlation functions is tested at liquid state densities against new molecular dynamics results for the Lennard-Jones (12,6) fluid. The HRM integral equation, based on the Born-Green equation and a topological reduction of the diagrammatic expansion of the triplet correlation function, has been solved for a high temperature state (T*=2.74, ρ*=0.80) and is found to give triplet correlation functions in good agreement with the molecular dynamics results. For a lower-temperature state (T*=0.73, ρ*=0.85), where numerical difficulties have thus far frustrated attempts to obtain a self-consistent solution of the HRM integral equation, direct tests of the HRM closure are made using molecular dynamics pair correlation functions to evaluate the diagrams. Although some striking qualitative features of the triplet correlations are correctly described by the HRM closure for this low-temperature state, the HRM approach is not in quantitative agreement with the molecular dynamics results. Test calculations indicate that the principle source of these errors is the neglect of important higher-order diagrams for the triplet correlation function. A reorganization of the diagrammatic series is suggested which may identify the most important of these neglected diagrams. Additional computer simulation results are also reported for the purely repulsive Weeks-Chandler-Andersen (WCA) ``reference'' fluid and for the underlying hard sphere fluid. The similarity of the pair structures of these fluids, noted by WCA, is also found to hold with high accuracy for the triplet structures. It is suggested that these similarities may be exploited in applying the methods of HRM to the hard sphere fluid.
Klauda, Jeffery B; Wu, Xiongwu; Pastor, Richard W; Brooks, Bernard R
2007-05-01
Molecular dynamics (MD) simulations of heptane/vapor, hexadecane/vapor, water/vapor, hexadecane/water, and dipalmitoylphosphatidylcholine (DPPC) bilayers and monolayers are analyzed to determine the accuracy of treating long-range interactions in interfaces with the isotropic periodic sum (IPS) method. The method and cutoff (rc) dependences of surface tensions, density profiles, water dipole orientation, and electrostatic potential profiles are used as metrics. The water/vapor, heptane/vapor, and hexadecane/vapor interfaces are accurately and efficiently calculated with 2D IPS (rc=10 A). It is demonstrated that 3D IPS is not practical for any of the interfacial systems studied. However, the hybrid method PME/IPS [Particle Mesh Ewald for electrostatics and 3D IPS for Lennard-Jones (LJ) interactions] provides an efficient way to include both types of long-range forces in simulations of large liquid/vacuum and all liquid/liquid interfaces, including lipid monolayers and bilayers. A previously published pressure-based long-range LJ correction yields results similar to those of PME/IPS for liquid/liquid interfaces. The contributions to surface tension of LJ terms arising from interactions beyond 10 A range from 13 dyn/cm for the hexadecane/vapor interface to approximately 3 dyn/cm for hexadecane/water and DPPC bilayers and monolayers. Surface tensions of alkane/vapor, hexadecane/water, and DPPC monolayers based on the CHARMM lipid force fields agree very well with experiment, whereas surface tensions of the TIP3P and TIP4P-Ew water models underestimate experiment by 16 and 11 dyn/cm, respectively. Dipole potential drops (DeltaPsi) are less sensitive to long-range LJ interactions than surface tensions. However, DeltaPsi for the DPPC bilayer (845+/-3 mV proceeding from water to lipid) and water (547+/-2 mV for TIP4P-Ew and 521+/-3 mV for TIP3P) overestimate experiment by factors of 3 and 5, respectively, and represent expected deficiencies in nonpolarizable force fields
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
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
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.
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. PMID:23496514
NASA Astrophysics Data System (ADS)
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 Tc is the same for all particle types; however, Tc=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 Tc as a result of the cooperative motion or activated processes.
Phase and interface behaviors in type-I and type-V Lennard-Jones mixtures: theory and simulations.
Mejía, Andrés; Pàmies, Josep C; Duque, Daniel; Segura, Hugo; Vega, Lourdes F
2005-07-15
Density gradient theory (DGT) and molecular-dynamics (MD) simulations have been used to predict subcritical phase and interface behaviors in type-I and type-V equal-size Lennard-Jones mixtures. Type-I mixtures exhibit a continuum critical line connecting their pure critical components, which implies that their subcritical phase equilibria are gas liquid. Type-V mixtures are characterized by two critical lines and a heteroazeotropic line. One of the two critical lines begins at the more volatile pure component critical point up to an upper critical end point and the other one comes from the less volatile pure component critical point ending at a lower critical end point. The heteroazeotropic line connects both critical end points and is characterized by gas-liquid-liquid equilibria. Therefore, subcritical states of this type exhibit gas-liquid and gas-liquid-liquid equilibria. In order to obtain a correct characterization of the phase and interface behaviors of these types of mixtures and to directly compare DGT and MD results, the global phase diagram of equal-size Lennard-Jones mixtures has been used to define the molecular parameters of these mixtures. According to our results, DGT and MD are two complementary methodologies able to obtain a complete and simultaneous prediction of phase equilibria and their interfacial properties. For the type of mixtures analyzed here, both approaches have shown excellent agreement in their phase equilibrium and interface properties in the full concentration range. PMID:16080742
NASA Astrophysics Data System (ADS)
Ebato, Yuki; Miyata, Tatsuhiko
2016-05-01
Ornstein-Zernike (OZ) integral equation theory is known to overestimate the excess internal energy, Uex, pressure through the virial route, Pv, and excess chemical potential, μex, for one-component Lennard-Jones (LJ) fluids under hypernetted chain (HNC) and Kovalenko-Hirata (KH) approximatons. As one of the bridge correction methods to improve the precision of these thermodynamic quantities, it was shown in our previous paper that the method to apparently adjust σ parameter in the LJ potential is effective [T. Miyata and Y. Ebato, J. Molec. Liquids. 217, 75 (2016)]. In our previous paper, we evaluated the actual variation in the σ parameter by using a fitting procedure to molecular dynamics (MD) results. In this article, we propose an alternative method to determine the actual variation in the σ parameter. The proposed method utilizes a condition that the virial and compressibility pressures coincide with each other. This method can correct OZ theory without a fitting procedure to MD results, and possesses characteristics of keeping a form of HNC and/or KH closure. We calculate the radial distribution function, pressure, excess internal energy, and excess chemical potential for one-component LJ fluids to check the performance of our proposed bridge function. We discuss the precision of these thermodynamic quantities by comparing with MD results. In addition, we also calculate a corrected gas-liquid coexistence curve based on a corrected KH-type closure and compare it with MD results.
NASA Astrophysics Data System (ADS)
Georgescu, IonuÅ£; Mandelshtam, Vladimir A.
2012-10-01
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(N3) 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 ˜ 104. 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.
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. PMID:26565249
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. PMID:27548461
A simple water model in the presence of inert Lennard-Jones obstacles II: the hydrophobic effect
NASA Astrophysics Data System (ADS)
Kurtjak, Mario; Urbic, Tomaz
2015-04-01
Using Monte Carlo computer simulations, hydrophobic effect for a non-polar particle with the diameter of a water molecule was studied in water, confined within a disordered matrix. Freely mobile two-dimensional Mercedes-Benz water was put in a disordered, but fixed, matrix of Lennard-Jones disks. Influence of temperature and matrix properties on the thermodynamic quantities of a non-polar solute solvation was studied. The hydrophobic effect is changed by the presence of the obstacles. Smaller matrix particles change the solute-water structure and thermodynamics drastically, as it was also observed for the properties of pure confined water. The study is bringing new scientific important observations in understanding the role of hydrophobic forces under confinement.
NASA Astrophysics Data System (ADS)
Jung, Jiyun; Lee, Jumin; Kim, Jun Soo
2015-03-01
We present a simulation study on the mechanisms of a phase separation in dilute fluids of Lennard-Jones (LJ) particles as a model of self-interacting molecules. Molecular dynamics (MD) and Brownian dynamics (BD) simulations of the LJ fluids are employed to model the condensation of a liquid droplet in the vapor phase and the mesoscopic aggregation in the solution phase, respectively. With emphasis on the cluster growth at late times well beyond the nucleation stage, we find that the growth mechanisms can be qualitatively different: cluster diffusion and coalescence in the MD simulations and Ostwald ripening in the BD simulations. We also show that the rates of the cluster growth have distinct scaling behaviors during cluster growth. This work suggests that in the solution phase the random Brownian nature of the solute dynamics may lead to the Ostwald ripening that is qualitatively different from the cluster coalescence in the vapor phase.
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.}
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.
Nanoscale Poiseuille flow and effects of modified Lennard-Jones potential function
NASA Astrophysics Data System (ADS)
Toghraie Semiromi, D.; Azimian, A. R.
2010-08-01
Numerical simulation of Poiseuille flow of liquid Argon in a nanochannel using the non-equilibrium molecular dynamics simulation (NEMD) is performed. The nanochannel is a three-dimensional rectangular prism geometry where the concerned numbers of Argon atoms are 2,700, 2,550 and 2,400 at 102, 108 and 120 K. Poiseuille flow is simulated by embedding the fluid particles in a uniform force field. An external driving force, ranging from 1 to 11 PN (Pico Newton), is applied along the flow direction to inlet fluid particles during the simulation. To obtain a more uniform temperature distribution across the channel, local thermostating near the wall are used. Also, the effect of other mixing rules (Lorenthz-Berthelot and Waldman-Kugler rules) on the interface structure are examined by comparing the density profiles near the liquid/solid interfaces for wall temperatures 108 and 133 K for an external force of 7 PN. Using Kong and Waldman-Kugler rules, the molecules near the solid walls were more randomly distributed compared to Lorenthz-Berthelot rule. These mean that the attraction between solid-fluid atoms was weakened by using Kong rule and Waldman-Kugler rule rather than the Lorenthz-Berthelot rule. Also, results show that the mean axial velocity has symmetrical distribution near the channel centerline and an increase in external driving force can increase maximum and average velocity values of fluid. Furthermore, the slip length and slip velocity are functions of the driving forces and they show an arising trend with an increase in inlet driving force and no slip boundary condition is satisfied at very low external force (<1 PN).
NASA Astrophysics Data System (ADS)
Sumi, Tomonari; Maruyama, Yutaka; Mitsutake, Ayori; Koga, Kenichiro
2016-06-01
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{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.
NASA Astrophysics Data System (ADS)
Ohtori, Norikazu; Ishii, Yoshiki
2015-10-01
Explicit expressions of the self-diffusion coefficient, Di, and shear viscosity, ηsv, 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 Di and ηsv 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(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. PMID:26520534
NASA Astrophysics Data System (ADS)
Kikugawa, Gota; Ando, Shotaro; Suzuki, Jo; Naruke, Yoichi; Nakano, Takeo; Ohara, Taku
2015-01-01
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)
Li, Ping; Dong, Yunhong; Zhao, Nanrong; Hou, Zhonghuai
2014-04-01
Distance fluctuation of a single molecule, modeled as an idealized bead-spring chain, dissolved in a Lennard-Jones liquid is studied by using a multidimensional generalized Langevin equation, where the friction kernel ζ(t) is calculated from the kinetic mode coupling theory (MCT). Temporal behavior of the distance autocorrelation function shows three typical regimes of time dependence, starting with a constant, followed by a power law of t-α, and finally an exponential decay. Particular attentions are paid to the time span of the power law regime, which corresponds to anomalous subdiffusion behavior, and the MCT framework enables us to investigate thoroughly how this regime depends on microscopic details such as the bead-to-solvent mass ratio MR, chain spring frequency ω, and the chain length N. Interestingly, the exponent α is robust to be 1/2 against the change of these parameters, although the friction kernel ζ(t) shows nontrivial dependence on time. In addition, we find that the starting time of the power-law region t1 scales with Γ-1, with Γ = 4ω2/ζ0 where ζ0 is the zero-frequency friction which decreases rapidly with increasing bead mass. On the other hand, the ending time t2 is not sensitive to varying ω or ζ0, but it increases with N rapidly before it reaches a constant for N larger than some threshold value. Our work may provide a unified strategy starting from the microscopic level to understand the anomalous subdiffusive behavior regarding large scale conformational change of polymers or proteins.
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.
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
NASA Astrophysics Data System (ADS)
Martínez-Ruiz, F. J.; Blas, F. J.; Mendiboure, B.; Moreno-Ventas Bravo, A. I.
2014-11-01
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, rc = 2.5, 3, 4, and 5σ. In addition, we have also considered cutoff distances rc = 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
NASA Astrophysics Data System (ADS)
Ikeshoji, Tamio; Hafskjold, Bjørn; Hashi, Yuichi; Kawazoe, Yoshiyuki
1996-09-01
Cluster formation of Lennard-Jones particles (65 536 atoms in a unit cell with an overall number density equal to 0.0149) was simulated by molecular dynamics. The temperature was set to decrease linearly with time by various thermostats, starting from a gas state temperature and ending at zero temperature. With the Nosé-Hoover thermostat, it was found that the translational temperature of the clusters suddenly decreased almost to zero when the cluster formation drastically increased around a reduced temperature (T*) of 0.5, while the internal temperature decreased linearly. Using the Andersen thermostat, which could simulate the aggregation of particles in an inert gas, both the internal and translational temperatures decreased almost linearly with time. When these thermostats were used, cluster-cluster and cluster-atom collisions did not give any magic number peaks in the size distribution up to 250 atoms/cluster at any temperature. Careful tracing of the cluster growth of 13-atom clusters showed no difference in reactivity between icosahedral and nonicosahedral clusters. To simulate cooling in a supersonic jet, a thermostat which controlled only the translational temperature was introduced. After the clusters were formed by cooling the system with this thermostat, their internal temperature stayed at T*≊0.5, while the translational temperature decreased linearly to zero with time as it was controlled. A long-time evaporation from these high-temperature clusters gave peaks at 13 and 19 (and less significantly at 23 and 26) which are magic number sizes corresponding to single, double, triple, and quadruple icosahedra, respectively. The internal temperatures of 13- and 19-atom clusters were higher than those of other size clusters. Higher evaporation energy was observed for the clusters of 13, 19, 23, and 26 atoms than for other size clusters after the long-time evaporation, but only the 13-atom clusters had the higher evaporation energy after cooling by the
NASA Astrophysics Data System (ADS)
Miyata, Tatsuhiko; Miyazaki, Sanae
2016-08-01
The accuracy of the temperature derivative of radial distribution function obtained under hypernetted chain (HNC), Kovalenko-Hirata (KH), Percus-Yevick (PY) and Verlet-modified (VM) closure approximations is examined for one-component Lennard-Jones fluid. As relevant thermodynamic quantities, constant-volume heat capacity and thermal pressure coefficient are investigated in terms of their accuracy under the above four approximations. It is found that HNC and KH closures overestimate these quantities, whereas PY closure tends to underestimate them. VM closure predicts rather accurately the quantities. A significant cancellation is observed along the integration for the above quantities under HNC and KH closures, especially at high density state.
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.
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. PMID:21797351
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.
NASA Astrophysics Data System (ADS)
Somasi, Sweta; Khomami, Bamin; Lovett, Ronald
2000-09-01
On a thermodynamic path proposed by Lutsko, Wolf, and Yip, a solid is transformed at fixed density into an ideal gas. The accuracy of molecular dynamics simulation results for the free energy of solids using this path is compromised by the presence of a singularity on the path and by the nonergodic behavior of the ideal gas. We present calculations of the third law free energies of the face-centered-cubic (fcc) and hexagonal-close-packed (hcp) solids of argon (modeled as a Lennard-Jones system) to illustrate how the singularity and the nonergodic dynamics introduce errors. Strategies for removing the singularity and the nonergodic dynamics are presented. Finally, an analytic expansion around the ideal state is developed to provide an alternate route to the free energy of those states for which simulation estimates give large statistical uncertainties. The quantitative errors in these new approaches to the simulation of the free energy of a solid are given.
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.
A new interlayer potential for hexagonal boron nitride.
Akıner, Tolga; Mason, Jeremy K; Ertürk, Hakan
2016-09-28
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. PMID:27452331
NASA Astrophysics Data System (ADS)
van Westen, Thijs; Oyarzún, Bernardo; Vlugt, Thijs J. H.; Gross, Joachim
2015-06-01
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
Baker, Christopher M.; Lopes, Pedro E. M.; Zhu, Xiao; Roux, Benoît; MacKerell, Alexander D.
2010-01-01
Lennard-Jones (LJ) parameters for a variety of model compounds have previously been optimized within the CHARMM Drude polarizable force field to reproduce accurately pure liquid phase thermodynamic properties as well as additional target data. While the polarizable force field resulting from this optimization procedure has been shown to satisfactorily reproduce a wide range of experimental reference data across numerous series of small molecules, a slight but systematic overestimate of the hydration free energies has also been noted. Here, the reproduction of experimental hydration free energies is greatly improved by the introduction of pair-specific LJ parameters between solute heavy atoms and water oxygen atoms that override the standard LJ parameters obtained from combining rules. The changes are small and a systematic protocol is developed for the optimization of pair-specific LJ parameters and applied to the development of pair-specific LJ parameters for alkanes, alcohols and ethers. The resulting parameters not only yield hydration free energies in good agreement with experimental values, but also provide a framework upon which other pair-specific LJ parameters can be added as new compounds are parametrized within the CHARMM Drude polarizable force field. Detailed analysis of the contributions to the hydration free energies reveals that the dispersion interaction is the main source of the systematic errors in the hydration free energies. This information suggests that the systematic error may result from problems with the LJ combining rules and is combined with analysis of the pair-specific LJ parameters obtained in this work to identify a preliminary improved combining rule. PMID:20401166
NASA Astrophysics Data System (ADS)
Baidakov, Vladimir G.
2016-02-01
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.
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)
Nishio, Kengo; Kōga, Junichiro; Yamaguchi, Toshio; Yonezawa, Fumiko
2004-06-01
The purpose of the present paper is to study the freezing procedures of a rare-gas system confined in a nanometer-scale pore as well as the atomic structure of a confined rare-gas solid. To this end, we carry out molecular-dynamics (MD) simulations for Lennard-Jones argon (LJ Ar) confined in an open-ended finite-length pore. Our simulation cell consists of two sections. One section contains a cubic solid with a cylindrical pore, the solid being composed of LJ atoms with interaction parameters appropriate for silica glass. The diameter and length of the cylindrical pore are 10σArAr (3.4 nm) and 20σArAr (6.8 nm), respectively. The other section is a free space into which we insert Ar atoms. The adsorption of Ar atoms into the nanopore proceeds by diffusive mass transfer from the free space. We simulate usual experimental procedures, that is, the pore is first filled with a liquid via capillary condensation, and thereafter the system is cooled. Our results show that, as the temperature is decreased, the freezing of Ar starts from the vicinity of the pore wall. The portion of solidlike Ar atoms increases gradually near the pore wall, while the Ar atoms in the central part of the pore change suddenly from liquidlike to solidlike all at the same time. We find that the structure factor of Ar confined in the pore does not change qualitatively during the freezing process, showing simple-liquid-like behaviors for both the liquid and the solid. This result agrees qualitatively with recently reported x-ray diffraction patterns of confined rare-gas solids. In a bulk LJ Ar system, on the other hand, the atomic structure changes qualitatively during the freezing process. One possible explanation for this difference is that the Ar solid in the pore consists of several different local atomic configurations, each giving distinct contributions to the structure factor of the confined Ar solid. Therefore, analyses beyond the averaged structure are helpful for extending our knowledge
NASA Astrophysics Data System (ADS)
Amon, L. M.; Reinhardt, W. P.
2000-09-01
In this paper four reference states allowing computation of the absolute internal free energies of solid and liquid clusters are introduced and implemented. Three of these are introduced for the first time. Two of these references are useful for highly fluctional liquidlike clusters while the other two are appropriate for more rigid solidlike clusters. These reference states are combined with a finite time variational method to obtain upper and lower bounds to the absolute free energies of clusters of Lennard-Jones (LJ) atoms, LJ4 and LJ55, allowing the efficiency of each of the four reference states to be elucidated. The optimal references are then applied to obtain upper and lower bounds to the internal free energies (the absolute free energy in the cluster center of mass frame) of LJ55 over a series of fixed temperatures including the solid-liquid coexistence regime. The reversible scaling method, recently introduced by de Koning, Antonelli, and Yip, is then used to extend the results over a continuous range of temperatures. Estimation of the rotational free energy allows comparisons to free energies of LJ55 in the nonrotating center of mass frame as estimated by Doye and Wales.
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
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.
Effect of intermolecular potential on compressible Couette flow in slip and transitional regimes
NASA Astrophysics Data System (ADS)
Weaver, Andrew B.; Venkattraman, A.; Alexeenko, Alina A.
2014-10-01
The effect of intermolecular potentials on compressible, planar flow in slip and transitional regimes is investigated using the direct simulation Monte Carlo method. Two intermolecular interaction models, the variable hard sphere (VHS) and the Lennard-Jones (LJ) models, are first compared for subsonic and supersonic Couette flows of argon at temperatures of 40, 273, and 1,000 K, and then for Couette flows in the transitional regime ranging from Knudsen numbers (Kn) of 0.0051 to 1. The binary scattering model for elastic scattering using the Lennard-Jones (LJ) intermolecular potential proposed recently [A. Venkattraman and A. Alexeenko, "Binary scattering model for Lennard-Jones potential: Transport coefficients and collision integrals for non-equilibrium gas flow simulations," Phys. Fluids 24, 027101 (2012)] is shown to accurately reproduce both the theoretical collision frequency in an equilibrium gas as well as the theoretical viscosity variation with temperature. The use of a repulsive-attractive instead of a purely repulsive potential is found to be most important in the continuum and slip regimes as well as in flows with large temperature variations. Differences in shear stress of up to 28% between the VHS and LJ models is observed at Kn=0.0051 and is attributed to differences in collision frequencies, ultimately affecting velocity gradients at the wall. For Kn=1 where the Knudsen layer expands the entire domain, the effect of the larger collision frequency in the LJ model relative to VHS diminishes, and a 7% difference in shear stress is observed.
On Stable Pair Potentials with an Attractive Tail, Remarks on Two Papers by A. G. Basuev
NASA Astrophysics Data System (ADS)
de Lima, Bernardo N. B.; Procacci, Aldo; Yuhjtman, Sergio
2016-04-01
We revisit two old and apparently little known papers by Basuev (Teoret Mat Fiz 37(1):130-134, 1978, Teoret Mat Fiz 39(1):94-105, 1979) and show that the results contained there yield strong improvements on current lower bounds of the convergence radius of the Mayer series for continuous particle systems interacting via a very large class of stable and tempered potentials, which includes the Lennard-Jones type potentials. In particular we analyze the case of the classical Lennard-Jones gas under the light of the Basuev scheme and, using also some new results (Yuhjtman in J Stat Phys 160(6): 1684-1695, 2015) on this model recently obtained by one of us, we provide a new lower bound for the Mayer series convergence radius of the classical Lennard-Jones gas, which improves by a factor of the order 105 on the current best lower bound recently obtained in de Lima and Procacci (J Stat Phys 157(3):422-435, 2014).
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. PMID:27324633
Moučka, Filip; Nezbeda, Ivo; Smith, William R
2013-11-12
It is known that none of the available simple molecular interaction models of aqueous electrolytes based on SPC/E water and their associated force fields are able to reproduce the concentration dependence of important thermodynamic properties of even the simplest electrolyte, NaCl, at ambient conditions over the entire experimentally accessible concentration range [ Mouc̆ka , F. ; Nezbeda , I. ; Smith , W. R. J. Chem. Phys. 2013 , 138 , 154102 ]. This paper explores the possibility of improving their performance by incorporating concentration-dependent experimental data for the total ionic chemical potential and the density into the fitting procedure, in addition to experimental values of solubility and solid chemical potential. We describe a general parameter estimation methodology for a studied class of models that incorporates the aforementioned experimental data. When the entire concentration range is considered, although the resulting force field is a slight improvement over others currently available in the literature, overall quantitative agreement with the experimental data over this range remains unsatisfactory. This indicates an inherent limitation of such simple molecular interaction models and strongly suggests that more complex mathematical forms of such models are required to quantitatively predict the properties of aqueous electrolyte solutions when the entire concentration range is of interest. Our parameter estimation methodology is also applicable to such cases. PMID:26583422
Equilibrium fluctuations of the Lennard-Jones cluster surface
NASA Astrophysics Data System (ADS)
Zhukhovitskii, D. I.
2008-11-01
Spectra of the cluster surface equilibrium fluctuations are treated by decomposition into the bulk and net capillary ones. The bulk fluctuations without capillary ones are simulated by the surface of a cluster truncated by a sphere. The bulk fluctuation spectrum is shown to be generated primarily by the discontinuity in the spatial distribution of cluster internal particles. The net capillary fluctuation slice spectrum is obtained in molecular dynamics simulation by subtraction of the bulk fluctuation spectrum from the total one. This net spectrum is in the best agreement with a theoretical estimation if we assume the intrinsic surface tension to be independent of the wave number. The wave number cutoff is brought in balance with the intrinsic surface tension and excess surface area induced by the capillary fluctuations. It is shown that the ratio of the ordinary surface tension to the intrinsic one can be considered as a universal constant independent of the temperature and cluster size.
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. PMID:24328234
Classical scattering in strongly attractive potentials
NASA Astrophysics Data System (ADS)
Khrapak, S. A.
2014-03-01
Scattering in central attractive potentials is investigated systematically, in the limit of strong interaction, when large-angle scattering dominates. In particular, three important model interactions (Lennard-Jones, Yukawa, and exponential), which are qualitatively different from each other, are studied in detail. It is shown that for each of these interactions the dependence of the scattering angle on the properly normalized impact parameter exhibits a quasiuniversal behavior. This implies simple scaling of the transport cross sections with energy in the considered limit. Accurate fits for the momentum transfer cross section are suggested. Applications of the obtained results are discussed.
Classical scattering in strongly attractive potentials.
Khrapak, S A
2014-03-01
Scattering in central attractive potentials is investigated systematically, in the limit of strong interaction, when large-angle scattering dominates. In particular, three important model interactions (Lennard-Jones, Yukawa, and exponential), which are qualitatively different from each other, are studied in detail. It is shown that for each of these interactions the dependence of the scattering angle on the properly normalized impact parameter exhibits a quasiuniversal behavior. This implies simple scaling of the transport cross sections with energy in the considered limit. Accurate fits for the momentum transfer cross section are suggested. Applications of the obtained results are discussed. PMID:24730827
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.
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. PMID:27586933
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…
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.
NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface
NASA Astrophysics Data System (ADS)
Ingebrigtsen, Trond S.; Toxvaerd, Søren; Heilmann, Ole J.; Schrøder, Thomas B.; Dyre, Jeppe C.
2011-09-01
An algorithm is derived for computer simulation of geodesics on the constant-potential-energy hypersurface of a system of N classical particles. First, a basic time-reversible geodesic algorithm is derived by discretizing the geodesic stationarity condition and implementing the constant-potential-energy constraint via standard Lagrangian multipliers. The basic NVU algorithm is tested by single-precision computer simulations of the Lennard-Jones liquid. Excellent numerical stability is obtained if the force cutoff is smoothed and the two initial configurations have identical potential energy within machine precision. Nevertheless, just as for NVE algorithms, stabilizers are needed for very long runs in order to compensate for the accumulation of numerical errors that eventually lead to "entropic drift" of the potential energy towards higher values. A modification of the basic NVU algorithm is introduced that ensures potential-energy and step-length conservation; center-of-mass drift is also eliminated. Analytical arguments confirmed by simulations demonstrate that the modified NVU algorithm is absolutely stable. Finally, we present simulations showing that the NVU algorithm and the standard leap-frog NVE algorithm have identical radial distribution functions for the Lennard-Jones liquid.
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.
Graph-based analysis of kinetics on multidimensional potential-energy surfaces
NASA Astrophysics Data System (ADS)
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.
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. PMID:19905185
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.
Effects of interatomic potentials on mechanical deformation of glasses
NASA Astrophysics Data System (ADS)
Chen, Wei-Ren; Iwashita, Takuya; Egami, Takeshi
2013-03-01
Apparently glasses behave like an elastic solid, which shows a linear relationship between stress and strain in mechanical deformation. However the understanding of the mechanical response of glasses remains elusive because of structural disorder. Mechanical deformation of monatomic model glasses was studied using athermal quasi-static shear (AQS) simulation and with three different potentials. As the interatomic potentials we employed the 12-6 Lennard-Jones (LJ) potential, modified Johnson (mJ) potential, and Dzugutov (Dz) potential, respectively. For mJ and Dz glasses the shear modulus keeps constant below a critical strain, below which it decreases rapidly or discontinuously with strain. Such changes in shear modulus were mostly related to the change in local topology of atomic connectivity or anelasticity. In contrast LJ glass shows a gradual decrease in shear modulus in a continuous manner. The results indicated that the difference arises from the nature of the potentials if the topology of atomic connectivity can be clearly defined.
Visualizing the orientational dependence of an intermolecular potential
NASA Astrophysics Data System (ADS)
Sweetman, Adam; Rashid, Mohammad A.; Jarvis, Samuel P.; Dunn, Janette L.; Rahe, Philipp; Moriarty, Philip
2016-02-01
Scanning probe microscopy can now be used to map the properties of single molecules with intramolecular precision by functionalization of the apex of the scanning probe tip with a single atom or molecule. Here we report on the mapping of the three-dimensional potential between fullerene (C60) molecules in different relative orientations, with sub-Angstrom resolution, using dynamic force microscopy (DFM). We introduce a visualization method which is capable of directly imaging the variation in equilibrium binding energy of different molecular orientations. We model the interaction using both a simple approach based around analytical Lennard-Jones potentials, and with dispersion-force-corrected density functional theory (DFT), and show that the positional variation in the binding energy between the molecules is dominated by the onset of repulsive interactions. Our modelling suggests that variations in the dispersion interaction are masked by repulsive interactions even at displacements significantly larger than the equilibrium intermolecular separation.
Kuszewski, J; Gronenborn, A M; Clore, G M
1996-06-01
A new conformational database potential involving dihedral angle relationships in databases of high-resolution highly refined protein crystal structures is presented as a method for improving the quality of structures generated from NMR data. The rationale for this procedure is based on the observation that uncertainties in the description of the nonbonded contacts present a key limiting factor in the attainable accuracy of protein NMR structures and that the nonbonded interaction terms presently used have poor discriminatory power between high- and low-probability local conformations. The idea behind the conformational database potential is to restrict sampling during simulated annealing refinement to conformations that are likely to be energetically possible by effectively limiting the choices of dihedral angles to those that are known to be physically realizable. In this manner, the variability in the structures produced by this method is primarily a function of the experimental restraints, rather than an artifact of a poor nonbonded interaction model. We tested this approach with the experimental NMR data (comprising an average of about 30 restraints per residue and consisting of interproton distances, torsion angles, 3JHN alpha coupling constants, and 13C chemical shifts) used previously to calculate the solution structure of reduced human thioredoxin (Qin J, Clore GM, Gronenborn AM, 1994, Structure 2:503-522). Incorporation of the conformational database potential into the target function used for refinement (which also includes terms for the experimental restraints, covalent geometry, and nonbonded interactions in the form of either a repulsive, repulsive-attractive, or 6-12 Lennard-Jones potential) results in a significant improvement in various quantitative measures of quality (Ramachandran plot, side-chain torsion angles, overall packing). This is achieved without compromising the agreement with the experimental restraints and the deviations from
Correlation of fragility with mechanical moduli in double-well potential for glass-forming liquid
NASA Astrophysics Data System (ADS)
Cao, Wan Qiang
2012-02-01
The shoving model and the Vogel-Fulcher relation are employed to derive correlation of the fragility with the mechanical moduli for glass-forming simple liquids. The result shows that a liquid with smaller fragility will have larger ratio of K∞/G∞ in dilute liquid system. Based on radial distribution function with the Lennard-Jones potential modified by the Gaussian potential with a second minimum, fragility of the supercooled simple liquid is derived from the correlation between viscosity and shear modulus via configurational entropy. The results demonstrate that the fragility is determined by two parts: thermodynamic components and mechanical moduli. For a weak Gaussian potential liquid, the fragility is proportional to the Tg, while for a strong one, the fragility is inversely proportional to the Tg, and the Gaussian potential will increase fragility.
Li, Arvin H.-T.; Chao, S.D.
2006-01-15
To verify the recently calculated intermolecular interaction potentials of the methane dimer within the density functional theory using the (Perdew) local density approximation (LDA) [Chen et al., Phys. Rev. A 69, 034701 (2004)], we have performed a parallel series of calculations using the LDA/6-311++G (3df, 3pd) level of theory with selected exchange functionals (B, G96, MPW, O, PBE, PW91, S, and XA). None of the above calculated intermolecular interaction potentials from the local density approximation reproduce the results reported in the commented paper. In addition, we point out the inappropriateness of using the Lennard-Jones function to model the long-range parts of the calculated intermolecular interaction potentials, as suggested positively by Chen et al.
NASA Astrophysics Data System (ADS)
Wu, Lei; Liu, Haihu; Zhang, Yonghao; Reese, Jason M.
2015-08-01
The Boltzmann equation with an arbitrary intermolecular potential is solved by the fast spectral method. As examples, noble gases described by the Lennard-Jones potential are considered. The accuracy of the method is assessed by comparing both transport coefficients with variational solutions and mass/heat flow rates in Poiseuille/thermal transpiration flows with results from the discrete velocity method. The fast spectral method is then applied to Fourier and Couette flows between two parallel plates, and the influence of the intermolecular potential on various flow properties is investigated. It is found that for gas flows with the same rarefaction parameter, differences in the heat flux in Fourier flow and the shear stress in Couette flow are small. However, differences in other quantities such as density, temperature, and velocity can be very large.
NASA Astrophysics Data System (ADS)
Sierra-Suarez, Jonatan A.; Majumdar, Shubhaditya; McGaughey, Alan J. H.; Malen, Jonathan A.; Higgs, C. Fred
2016-04-01
This work formulates a rough surface contact model that accounts for adhesion through a Morse potential and plasticity through the Kogut-Etsion finite element-based approximation. Compared to the commonly used Lennard-Jones (LJ) potential, the Morse potential provides a more accurate and generalized description for modeling covalent materials and surface interactions. An extension of this contact model to describe composite layered surfaces is presented and implemented to study a self-assembled monolayer (SAM) grown on a gold substrate placed in contact with a second gold substrate. Based on a comparison with prior experimental measurements of the thermal conductance of this SAM junction [Majumdar et al., Nano Lett. 15, 2985-2991 (2015)], the more general Morse potential-based contact model provides a better prediction of the percentage contact area than an equivalent LJ potential-based model.
Influence of the interatomic potential on the structure of dislocations in a monolayer
NASA Astrophysics Data System (ADS)
Joós, B.; Ren, Q.; Duesbery, M. S.
1994-02-01
Using atomic relaxation techniques, dislocation dipoles of various sizes and orientations have been studied for monolayers with the Lennard-Jones potential (LJP) and nearest-neighbour piecewise linear force (PLF) interactions. In the LJP system the lower energy vacancy dipoles have over a wide range of angles an energy which is mainly a function of the vacancy content of the dipole. There is a competition between the elastic forces and the topological constraints which favour a five-fold coordinate vacancy (FCV) at the centre of each core. For the short range PLF system the lattice usually compresses upon the introduction of a dislocation, a consequence of the soft core of the interaction potential, and interstitial dipoles are lower in energy. For the long range LJP system the dislocations are mobile whereas for the PLF system they are pinned. The relevance of these results to existing theories of melting are discussed.
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.
Poiseuille flow of Lennard-Jones fluids in narrow slit pores
NASA Astrophysics Data System (ADS)
Travis, Karl P.; Gubbins, Keith E.
2000-01-01
We present results from nonequilibrium molecular dynamics (NEMD) simulations of simple fluids undergoing planar Poiseuille flow in a slit pore only a few molecular diameters in width. The calculations reported in this publication build on previous results by including the effects of attractive forces and studying the flow at narrower pore widths. Our aims are: (1) to examine the role of attractive forces in determining hydrodynamic properties, (2) to provide clearer evidence for the existence of a non-Markovian generalization of Newtons law, (3) to examine the slip-stick boundary conditions in more detail by using a high spatial resolution of the streaming velocity profiles, (4) to investigate the significance of the recently proposed cross-coupling coefficient on the temperature profiles. The presence of attractive interactions gives rise to interesting packing effects, but otherwise, does not significantly alter the spatial dependence of hydrodynamic quantities. We find the strongest evidence to date that Newton's Law breaks down for very narrow pores; the shear viscosity exhibits singularities. We suggest a method to test the validity of the non-Markovian generalization of Newton's Law. No-slip boundary conditions are found to apply, even at these microscopic length scales, provided one takes into account the finite size of the wall atoms. The effects of any strain rate induced coupling to the heat flow are found to be insignificant.
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. PMID:27544095
NASA Astrophysics Data System (ADS)
Xu, H.; Wittmer, J. P.; Polińska, P.; Baschnagel, J.
2012-10-01
The truncation of a pair potential at a distance rc is well known to imply, in general, an impulsive correction to the pressure and other moments of the first derivatives of the potential. That, depending on rc, the truncation may also be of relevance to higher derivatives is shown theoretically for the Born contributions to the elastic moduli obtained using the stress-fluctuation formalism in d dimensions. Focusing on isotropic liquids for which the shear modulus G must vanish by construction, the predicted corrections are tested numerically for binary mixtures and polydisperse Lennard-Jones beads in, respectively, d=3 and 2 dimensions. Both models being glass formers, we comment briefly on the temperature (T) dependence of the (corrected) shear modulus G(T) around the glass transition temperature Tg.
Lubna, Nusrat; Kamath, Ganesh; Potoff, Jeffrey J; Rai, Neeraj; Siepmann, J Ilja
2005-12-22
An extension of the transferable potentials for phase equilibria united-atom (TraPPE-UA) force field to thiol, sulfide, and disulfide functionalities and thiophene is presented. In the TraPPE-UA force field, nonbonded interactions are governed by a Lennard-Jones plus fixed point charge functional form. Partial charges are determined through a CHELPG analysis of electrostatic potential energy surfaces derived from ab initio calculations at the HF/6-31g+(d,p) level. The Lennard-Jones well depth and size parameters for four new interaction sites, S (thiols), S(sulfides), S(disulfides), and S(thiophene), were determined by fitting simulation data to pure-component vapor-equilibrium data for methanethiol, dimethyl sulfide, dimethyl disulfide, and thiophene, respectively. Configurational-bias Monte Carlo simulations in the grand canonical ensemble combined with histogram-reweighting methods were used to calculate the vapor-liquid coexistence curves for methanethiol, ethanethiol, 2-methyl-1-propanethiol, 2-methyl-2-propanethiol, 2-butanethiol, pentanethiol, octanethiol, dimethyl sulfide, diethyl sulfide, ethylmethyl sulfide, dimethyl disulfide, diethyl disulfide, and thiophene. Excellent agreement with experiment is achieved, with unsigned errors of less than 1% for saturated liquid densities and less than 3% for critical temperatures. The normal boiling points were predicted to within 1% of experiment in most cases, although for certain molecules (pentanethiol) deviations as large as 5% were found. Additional calculations were performed to determine the pressure-composition behavior of ethanethiol+n-butane at 373.15 K and the temperature-composition behavior of 1-propanethiol+n-hexane at 1.01 bar. In each case, a good reproduction of experimental vapor-liquid equilibrium separation factors is achieved; both of the coexistence curves are somewhat shifted because of overprediction of the pure-component vapor pressures. PMID:16375402
NASA Astrophysics Data System (ADS)
Molinari, Vincenzo; Mostacci, Domiziano
2015-10-01
He-4 is known to become superfluid at very low temperatures. This effect is now generally accepted to be connected with BEC (Bose-Einstein Condensation). The dispersion relation of pressure waves in superfluid He-4 has been determined at 1.1 °K by Yarnell et al., and exhibits a non monotonic behavior-with a maximum and a minimum-usually explained in terms of excitations called rotons, introduced by Landau. In the present work an attempt is made to describe the phenomenon within the Bohmian interpretation of QM. To this end, the effects of the intermolecular potential, taken to be essentially of the Lennard-Jones type modified to account for molecule finiteness, are included as a Vlasov-type self-consistent field. A dispersion relation is found, that is in quite good agreement with Yarnell's curve.
Statistical systems with nonintegrable interaction potentials
NASA Astrophysics Data System (ADS)
Yukalov, V. I.
2016-07-01
Statistical systems composed of atoms interacting with each other trough nonintegrable interaction potentials are considered. Examples of these potentials are hard-core potentials and long-range potentials, for instance, the Lennard-Jones and dipolar potentials. The treatment of such potentials is known to confront several problems, e.g., the impossibility of using the standard mean-field approximations, such as Hartree and Hartree-Fock approximations, the impossibility of directly introducing coherent states, the difficulty in breaking the global gauge symmetry, which is required for describing Bose-Einstein condensed and superfluid systems, the absence of a correctly defined Fourier transform, which hampers the description of uniform matter as well as the use of local-density approximation for nonuniform systems. A novel iterative procedure for describing such systems is developed, starting from a correlated mean-field approximation, allowing for a systematic derivation of higher orders, and meeting no problems listed above. The procedure is applicable to arbitrary systems, whether equilibrium or nonequilibrium. The specification for equilibrium systems is presented. The method of extrapolating the expressions for observable quantities from weak coupling to strong coupling is described.
Statistical systems with nonintegrable interaction potentials.
Yukalov, V I
2016-07-01
Statistical systems composed of atoms interacting with each other trough nonintegrable interaction potentials are considered. Examples of these potentials are hard-core potentials and long-range potentials, for instance, the Lennard-Jones and dipolar potentials. The treatment of such potentials is known to confront several problems, e.g., the impossibility of using the standard mean-field approximations, such as Hartree and Hartree-Fock approximations, the impossibility of directly introducing coherent states, the difficulty in breaking the global gauge symmetry, which is required for describing Bose-Einstein condensed and superfluid systems, the absence of a correctly defined Fourier transform, which hampers the description of uniform matter as well as the use of local-density approximation for nonuniform systems. A novel iterative procedure for describing such systems is developed, starting from a correlated mean-field approximation, allowing for a systematic derivation of higher orders, and meeting no problems listed above. The procedure is applicable to arbitrary systems, whether equilibrium or nonequilibrium. The specification for equilibrium systems is presented. The method of extrapolating the expressions for observable quantities from weak coupling to strong coupling is described. PMID:27575076
46 CFR 12.01-6-12.01-7 - [Reserved
Code of Federal Regulations, 2010 CFR
2010-10-01
... 46 Shipping 1 2010-10-01 2010-10-01 false 12.01-6-12.01-7 Section 12.01-6-12.01-7 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY MERCHANT MARINE OFFICERS AND SEAMEN REQUIREMENTS FOR RATING ENDORSEMENTS General §§ 12.01-6-12.01-7...
36 CFR 6.12 - Prohibited acts and penalties.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 36 Parks, Forests, and Public Property 1 2010-07-01 2010-07-01 false Prohibited acts and penalties. 6.12 Section 6.12 Parks, Forests, and Public Property NATIONAL PARK SERVICE, DEPARTMENT OF THE INTERIOR SOLID WASTE DISPOSAL SITES IN UNITS OF THE NATIONAL PARK SYSTEM § 6.12 Prohibited acts and penalties. (a) The following are prohibited:...
Molecular Multipole Potential Energy Functions for Water.
Tan, Ming-Liang; Tran, Kelly N; Pickard, Frank C; Simmonett, Andrew C; Brooks, Bernard R; Ichiye, Toshiko
2016-03-01
Water is the most common liquid on this planet, with many unique properties that make it essential for life as we know it. These properties must arise from features in the charge distribution of a water molecule, so it is essential to capture these features in potential energy functions for water to reproduce its liquid state properties in computer simulations. Recently, models that utilize a multipole expansion located on a single site in the water molecule, or "molecular multipole models", have been shown to rival and even surpass site models with up to five sites in reproducing both the electrostatic potential around a molecule and a variety of liquid state properties in simulations. However, despite decades of work using multipoles, confusion still remains about how to truncate the multipole expansions efficiently and accurately. This is particularly important when using molecular multipole expansions to describe water molecules in the liquid state, where the short-range interactions must be accurate, because the higher order multipoles of a water molecule are large. Here, truncation schemes designed for a recent efficient algorithm for multipoles in molecular dynamics simulations are assessed for how well they reproduce results for a simple three-site model of water when the multipole moments and Lennard-Jones parameters of that model are used. In addition, the multipole analysis indicates that site models that do not account for out-of-plane electron density overestimate the stability of a non-hydrogen-bonded conformation, leading to serious consequences for the simulated liquid. PMID:26562223
A New Shared-Memory Programming Paradigm for Molecular Dynamics Simulations on the Intel Paragon
D'Azevedo, E.F.
1995-01-01
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.
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.
NASA Astrophysics Data System (ADS)
Somer, Frank
2005-03-01
Results of recent molecular dynamics simulations of a two-dimensional glass forming system are presented. The system's inherent structures are investigated over a wide range of temperature and cooling rate and compared to previous results for three-dimensional liquids and glasses. A method for analyzing the regions of the energy landscape sampled under various conditions is introduced and used to characterize the glass transition. Connections with inherent-structures theory, mode-coupling theory, and spatially inhomogeneous dynamics are discussed.
Anisotropic united-atoms (AUA) potential for alcohols.
Pérez-Pellitero, Javier; Bourasseau, Emeric; Demachy, Isabelle; Ridard, Jacqueline; Ungerer, Philippe; Mackie, Allan D
2008-08-14
An anisotropic united-atom (AUA4) intermolecular potential has been derived for the family of alkanols by first optimizing a set of charges to reproduce the electrostatic potential of the isolated molecules of methanol and ethanol and then by adjusting the parameters of the OH group to fit selected equilibrium properties. In particular, the proposed potential includes additional extra-atomic charges in order to improve the matching to the electrostatic field. Gibbs ensemble Monte Carlo simulations were performed to determine the phase equilibria, while the critical region was explored by means of grand canonical Monte Carlo simulations combined with histogram reweighting techniques. In order to increase the transferability of the model, only the parameters of the Lennard-Jones OH group have been fitted, the parameters of the other AUA groups are taken from previous works. Nevertheless, a good level of agreement was obtained for all compounds considered in this work. In particular, excellent results were obtained for the Henry constants calculation of different gases in alkanols. PMID:18646801
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.
Formulation of wide-ranging embedded-atom-type potentials: the role of mechanical stability
NASA Astrophysics Data System (ADS)
Pechenik, Eugene; Kelson, Itzhak; Makov, Guy
2013-01-01
Wide-ranging inter-atomic potentials are necessary for modeling many problems in material physics that involve multiple atomic environments and phases. The domains of thermodynamic and mechanical stability of embedded-atom-type potentials are examined for the cubic phases. It is shown that the choice of the pair potential is critical in determining the domain of stability of embedded-atom-type potentials. In particular, the Lennard-Jones embedded-atom potential is shown not to stabilize the bcc phase. A simple four-parameter universal equation of state-based embedded-atom potential is shown to have a domain of stability for all the cubic phases and to reproduce the high-pressure equation of state. A model phase diagram for the three cubic phases is presented. This potential is fitted to 17 elemental systems and found to be able to reproduce both the elastic constants and the ground state crystalline structure. For elements with a low degree of elastic anisotropy, this potential can also reproduce the high-pressure behavior.
NASA Astrophysics Data System (ADS)
Ziegenhain, Gerolf; Hartmaier, Alexander; Urbassek, Herbert M.
2009-09-01
Molecular-dynamics simulation can give atomistic information on the processes occurring in nanoindentation experiments. In particular, the nucleation of dislocation loops, their growth, interaction and motion can be studied. We investigate how realistic the interatomic potentials underlying the simulations have to be in order to describe these complex processes. Specifically we investigate nanoindentation into a Cu single crystal. We compare simulations based on a realistic many-body interaction potential of the embedded-atom-method type with two simple pair potentials, a Lennard-Jones and a Morse potential. We find that qualitatively many aspects of nanoindentation are fairly well reproduced by the simple pair potentials: elastic regime, critical stress and indentation depth for yielding, dependence on the crystal orientation, and even the level of the hardness. The quantitative deficits of the pair potential predictions can be traced back: (i) to the fact that the pair potentials are unable in principle to model the elastic anisotropy of cubic crystals and (ii) as the major drawback of pair potentials we identify the gross underestimation of the stable stacking fault energy. As a consequence these potentials predict the formation of too large dislocation loops, the too rapid expansion of partials, too little cross slip and in consequence a severe overestimation of work hardening.
The Potential Field of Carbon Bodies as a Basis for Sorption Properties of Barrier Gas Systems
NASA Astrophysics Data System (ADS)
Bubenchikov, A. M.; Bubenchikov, M. A.; Potekaev, A. I.; Libin, É. E.; Khudobina, Yu. P.
2015-11-01
A modification of the Lennard-Jones potential allowed us, via integration over the volume of the bodies of different shapes, to determine the integral action (potential energy barrier) generated by the distributed force centers. The body generating the potential barrier was a carbon plate and the test particles overcoming this barrier were atoms or molecules of a number of gases (hydrogen, helium and methane). When considering the transit of particles (gas atoms or molecules) over this barrier, use was made of the energy barrier wave theory and the potential of a continuous body was used as a barrier. In so doing, the Schrödinger equation was integrated numerically for the molecular density. This integration yielded the expected wave pattern of the process of transit and reflection of the molecules, so a phase averaging procedure had to be applied. By varying the parameters of the layer containing force centers - field sources, the dimensions and density of the carbon plate possessing high selectivity towards separation of gas mixture containing helium, hydrogen and methane were determined. The data obtained provide an interpretation of the sorption properties of barrier carbon systems capable of filtering or separating gases.
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. PMID:27327881
Systematic and Simulation-Free Coarse-Graining of Polymer Melts using Soft Potentials
NASA Astrophysics Data System (ADS)
Yang, Delian; Wang, Qiang
2014-03-01
Full atomistic simulations of multi-chain systems are not feasible at present due to their formidable computational requirements. Molecular simulations with coarse-grained models have to be used instead, where each segment represents, for example, the center-of-mass of a group of atoms or real monomers. While atoms interact with hard excluded-volume interactions (e.g., the Lennard-Jones potential) and cannot overlap, the coarse-grained segments can certainly overlap and should therefore interact with soft potentials that allow complete particle overlapping. Coarse-grained models, however, reduce the chain conformational entropy, which plays an essential role in the behavior of polymeric systems. In this work, we use integral-equation theories, instead of molecular simulations, to perform both the structure-based and relative-entropy-based coarse-graining of homopolymer melts, and systematically examine how the coarse-grained soft potential varies with N (the number of segments on each chain) and how well the coarse-grained models reproduce both the structural and thermodynamic properties of the original system. This provides us with a quantitative basis for choosing small N-values that can still capture the chain conformational entropy, a characteristics of polymers.
Optimization of intermolecular potential parameters for the CO2/H2O mixture.
Orozco, Gustavo A; Economou, Ioannis G; Panagiotopoulos, Athanassios Z
2014-10-01
Monte Carlo simulations in the Gibbs ensemble were used to obtain optimized intermolecular potential parameters to describe the phase behavior of the mixture CO2/H2O, over a range of temperatures and pressures relevant for carbon capture and sequestration processes. Commonly used fixed-point-charge force fields that include Lennard-Jones 12-6 (LJ) or exponential-6 (Exp-6) terms were used to describe CO2 and H2O intermolecular interactions. For force fields based on the LJ functional form, changes of the unlike interactions produced higher variations in the H2O-rich phase than in the CO2-rich phase. A major finding of the present study is that for these potentials, no combination of unlike interaction parameters is able to adequately represent properties of both phases. Changes to the partial charges of H2O were found to produce significant variations in both phases and are able to fit experimental data in both phases, at the cost of inaccuracies for the pure H2O properties. By contrast, for the Exp-6 case, optimization of a single parameter, the oxygen-oxygen unlike-pair interaction, was found sufficient to give accurate predictions of the solubilities in both phases while preserving accuracy in the pure component properties. These models are thus recommended for future molecular simulation studies of CO2/H2O mixtures. PMID:25198539
Nurisso, Alessandra; Bravo, Juan; Carrupt, Pierre-Alain; Daina, Antoine
2012-05-25
GOLD is a molecular docking software widely used in drug design. In the initial steps of docking, it creates a list of hydrophobic fitting points inside protein cavities that steer the positioning of ligand hydrophobic moieties. These points are generated based on the Lennard-Jones potential between a carbon probe and each atom of the residues delimitating the binding site. To thoroughly describe hydrophobic regions in protein pockets and properly guide ligand hydrophobic moieties toward favorable areas, an in-house tool, the MLP filter, was developed and herein applied. This strategy only retains GOLD hydrophobic fitting points that match the rigorous definition of hydrophobicity given by the molecular lipophilicity potential (MLP), a molecular interaction field that relies on an atomic fragmental system based on 1-octanol/water experimental partition coefficients (log P(oct)). MLP computations in the binding sites of crystallographic protein structures revealed that a significant number of points considered hydrophobic by GOLD were actually polar according to the MLP definition of hydrophobicity. To examine the impact of this new tool, ligand-protein complexes from the Astex Diverse Set and the PDB bind core database were redocked with and without the use of the MLP filter. Reliable docking results were obtained by using the MLP filter that increased the quality of docking in nonpolar cavities and outperformed the standard GOLD docking approach. PMID:22462609
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.
Folman, M.; Fastow, M.; Kozirovski, Y.
1997-03-05
In our recent investigation of the IR spectrum of CO physically adsorbed on C{sub 60} films, two well-resolved absorption bands at 2135 and 2128 cm{sup -1} were found, suggesting that the molecule is adsorbed on two different sites. To determine the nature of these adsorption sites, calculations of adsorption potentials and spectral shifts for the CO/C{sub 60} system were performed. The calculations were done for the fcc (100), fcc (111) hcp (001), and hcp (111) surface planes. In the calculations the 6-exponential and the Lennard-Jones potentials were used. A number of adsorption sites were chosen. These included the void space between four, three, and two neighboring C{sub 60} molecules and the center of the hexagon and the pentagon on the C{sub 60} surface. The calculated potentials and spectral shifts clearly indicate that adsorption sites in the voids between the C{sub 60} molecules are energetically preferred over sites on top of single C{sub 60} molecules. Comparison is made between results obtained with the two potentials and with results obtained previously with the two other carbon allotropes: graphite and diamond. 11 refs., 4 figs., 3 tabs.
Using a Checking Account. Grades 6-12.
ERIC Educational Resources Information Center
Trey, Frances
Instructions and exercises on the use of checking accounts are provided for students in grades 6-12. The following topics are included: (1) reasons for opening a checking account; (2) how to open a checking account; (3) how to fill out deposit slips; (4) the elements of a check and how to write a check correctly; (5) checking account rules; (6)…
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…
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…
36 CFR 6.12 - Prohibited acts and penalties.
Code of Federal Regulations, 2013 CFR
2013-07-01
... (4) Operating a solid waste disposal site in violation of 40 CFR Parts 257 or 258, or in violation of... INTERIOR SOLID WASTE DISPOSAL SITES IN UNITS OF THE NATIONAL PARK SYSTEM § 6.12 Prohibited acts and penalties. (a) The following are prohibited: (1) Operating a solid waste disposal site without a...
Van der Waals correlation between two 4He monolayers on the opposite sides of graphene
NASA Astrophysics Data System (ADS)
Kwon, Yongkyung
2015-06-01
Path-integral Monte Carlo calculations have been performed to study the correlation between two 4He monolayers adsorbed on opposite sides of a graphene sheet. Here, the 4He-substrate interaction is described by the pairwise sum of the 4He-C interatomic potentials. We employ two different anisotropic 4He-C pair potentials proposed to fit the helium scattering data on a graphite surface, namely, a 6-12 Lennard-Jones potential and a Yukawa-6 potential. With the Lennard-Jones substrate potential, we do not observe any noticeable correlation between two oppositeside 4He monolayers, which is consistent with the prediction of the previous theoretical studies based on the same substrate potential. When the Yukawa-6 substrate potential is used, however, two incommensurate triangular solids, which are realized at the first-layer completion density of 0.12 Å -2, are found to favor an AA stacking order, two triangular lattices on top of each other, over an AB stacking. Finally, the effects of this interlayer correlation on the formation of stable mobile vacancies are discussed.
Lopes, Juliana Fedoce; Rocha, Willian R; Dos Santos, Hélio F; De Almeida, Wagner B
2008-04-28
In this work, a systematic study of the interaction of neutral cisplatin ([Pt(NH(3))(2)Cl(2)]) and their charged aquated species ([Pt(NH(3))(2)Cl(H(2)O)](+) and [Pt(NH(3))(2)(H(2)O)(2)](2+)) with water was carried out. The potential energy surface (PES) was analyzed by considering 35 spatial orientations for the interacting species. The calculations were performed at various levels of theory including Moller-Plesset fourth order perturbation theory and density functional theory (DFT-B3LYP) using extended basis sets. Lennard-Jones (12-6) plus Coulomb classical potential was also used to assess the repulsion-dispersion and electrostatic contributions. The effect of atomic charges on the interaction energies is discussed using Mulliken, charges from electrostatic potential grid method and natural bond orbital schemes. The outcomes show that the electrostatic term plays a primary role on the calculation of interaction energies, with the absolute values of atomic charges from different approaches significantly affecting the overall interaction. Unusual results were revealed by basis set superposition error calculations for the structures located on the platinum-water PES. PMID:18447507
NASA Astrophysics Data System (ADS)
Rizzi, F.; Jones, R. E.; Debusschere, B. J.; Knio, O. M.
2013-05-01
This article extends the uncertainty quantification analysis introduced in Paper I for molecular dynamics (MD) simulations of concentration driven ionic flow through a silica nanopore. Attention is now focused on characterizing, for a fixed pore diameter of D = 21 Å, the sensitivity of the system to the Lennard-Jones energy parameters, \\varepsilon _{Na^+} and \\varepsilon _{Cl^-}, defining the depth of the potential well for the two ions Na+ and Cl-, respectively. A forward propagation analysis is applied to map the uncertainty in these parameters to the MD predictions of the ionic fluxes. Polynomial chaos expansions and Bayesian inference are exploited to isolate the effect of the intrinsic noise, stemming from thermal fluctuations of the atoms, and properly quantify the impact of parametric uncertainty on the target MD predictions. A Bayes factor analysis is then used to determine the most suitable regression model to represent the MD noisy data. The study shows that the response surface of the Na+ conductance can be effectively inferred despite the substantial noise level, whereas the noise partially hides the underlying trend in the Cl- conductance data over the studied range. Finally, the dependence of the conductances on the uncertain potential parameters is analyzed in terms of correlations with key bulk transport coefficients, namely, viscosity and collective diffusivities, computed using Green-Kubo time correlations.
Hess, S; Kröger, M
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. PMID:11461234
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.
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. PMID:22900670
A Redox Economical Synthesis of Bioactive 6,12-Guaianolides
Wen, Bo; Hexum, Joseph K.; Widen, John C.
2013-01-01
Syntheses of two 6,12-guaianolide analogs are reported within. The scope of the tandem allylboration/lactonization chemistry is expanded to provide a functionalized alleneyne-containing α-methylene butyrolactone that undergoes a Rh(I)-catalyzed cyclocarbonylation reaction to afford a 5-7-5 ring system. The resulting cycloadducts bear a structural resemblance to other NF-κB inhibitors such as cumambrin A and indeed were shown to inhibit NF-κB signaling and cancer cell growth. PMID:23662902
[CrIII8MII6]12+ Coordination Cubes (MII=Cu, Co)**
Sanz, Sergio; O'Connor, Helen M; Pineda, Eufemio Moreno; Pedersen, Kasper S; Nichol, Gary S; Mønsted, Ole; Weihe, Høgni; Piligkos, Stergios; McInnes, Eric J L; Lusby, Paul J; Brechin, Euan K
2015-01-01
[CrIII8MII6]12+ (MII=Cu, Co) coordination cubes were constructed from a simple [CrIIIL3] metalloligand and a “naked” MII salt. The flexibility in the design proffers the potential to tune the physical properties, as all the constituent parts of the cage can be changed without structural alteration. Computational techniques (known in theoretical nuclear physics as statistical spectroscopy) in tandem with EPR spectroscopy are used to interpret the magnetic behavior. PMID:25891167
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. PMID:17713943
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 (), combination of segmental globules and elongated chains (), predominantly elongated chains (), as well as universal SAW conformations at high normalized temperature (). The radius of gyration of the protein exhibits a non-monotonic temperature dependence with a maximum at a characteristic temperature () where a crossover occurs from a positive (stretching at ) to negative (contraction at ) thermal response on increasing . PMID:22442661
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.
Pigment Spectra and Intermolecular Interaction Potentials in Glasses and Proteins
Renge, I.; van Grondelle, R.; Dekker, J. P.
2007-01-01
A model is proposed for chromophore optical spectra in solids over a wide range of temperatures and pressures. Inhomogeneous band shapes and their pressure dependence, as well as baric shift coefficients of spectral lines, selected by the frequency, were derived using Lennard-Jones potentials of the ground and excited states. Quadratic electron-phonon coupling constants, describing the thermal shift and broadening of zero-phonon lines, were also calculated. Experimentally, thermal shift and broadening of spectral holes were studied between 5 and 40 K for a synthetic pigment, chlorin, embedded in polymer hosts. The baric effects on holes were determined by applying hydrostatic He gas pressure up to 200 bar, at 6 K. Absorption spectra of pheophytin a, chlorophyll a, and β-carotene in polymers and plant photosystem II CP47 complex were measured between 5 (or 77) and 300 K, and subject to Voigtian deconvolution. A narrowing of inhomogeneous bandwidth with increasing temperature, predicted on the basis of hole behavior, was observed as the shrinking of Gaussian spectral component. The Lorentzian broadening was ascribed to optical dephasing up to 300 K in transitions with weak to moderate linear electron-phonon coupling strength. The thermal broadening is purely Gaussian in multiphonon transitions (S2 band of β-carotene, Soret bands of tetrapyrrolic pigments), and the Lorentz process appears to be suppressed, indicating a lack of exponential dephasing. Density, polarity, polarizability, compressibility, and other local parameters of the pigment binding sites in biologically relevant systems can be deduced from spectroscopic data, provided that sufficient background information is available. PMID:17557783
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.
Calculating excess chemical potentials using dynamic simulations in the fourth dimension
Pomes, R.; Eisenmesser, E.; Post, C.B.; Roux, B.
1999-08-01
A general method for computing excess chemical potentials is presented. The excess chemical potential of a solute or ligand molecule is estimated from the potential of mean-force (PMF) calculated along a nonphysical fourth spatial dimension, {ital w}, into which the molecule is gradually inserted or from which it is gradually abstracted. According to this {open_quotes}4D-PMF{close_quotes} (four dimensional) scheme, the free energy difference between two limiting states defines the excess chemical potential: At w={plus_minus}{infinity}, the molecule is not interacting with the rest of the system, whereas at w=0, it is fully interacting. Use of a fourth dimension avoids the numerical instability in the equations of motion encountered upon growing or shrinking solute atoms in conventional free energy perturbation simulations performed in three dimensions, while benefiting from the efficient sampling of configurational space afforded by PMF calculations. The applicability and usefulness of the method are illustrated with calculations of the hydration free energy of simple Lennard-Jones (LJ) solutes, a water molecule, and camphor, using molecular dynamics simulations and umbrella sampling. Physical insight into the nature of the PMF profiles is gained from a continuum treatment of short- and long-range interactions. The short-range barrier for dissolution of a LJ solute in the added dimension provides an apparent surface tension of the solute. An approximation to the long-range behavior of the PMF profiles is made in terms of a continuum treatment of LJ dispersion and electrostatic interactions. Such an analysis saves the need for configurational sampling in the long-range limit of the fourth dimension. The 4D-PMF method of calculating excess chemical potentials should be useful for neutral solute and ligand molecules with a wide range of sizes, shapes, and polarities. {copyright} {ital 1999 American Institute of Physics.}
Wang, Jiyao; Deng, Yuqing; Roux, Benoît
2006-01-01
The absolute (standard) binding free energy of eight FK506-related ligands to FKBP12 is calculated using free energy perturbation molecular dynamics (FEP/MD) simulations with explicit solvent. A number of features are implemented to improve the accuracy and enhance the convergence of the calculations. First, the absolute binding free energy is decomposed into sequential steps during which the ligand-surrounding interactions as well as various biasing potentials restraining the translation, orientation, and conformation of the ligand are turned “on” and “off.” Second, sampling of the ligand conformation is enforced by a restraining potential based on the root mean-square deviation relative to the bound state conformation. The effect of all the restraining potentials is rigorously unbiased, and it is shown explicitly that the final results are independent of all artificial restraints. Third, the repulsive and dispersive free energy contribution arising from the Lennard-Jones interactions of the ligand with its surrounding (protein and solvent) is calculated using the Weeks-Chandler-Andersen separation. This separation also improves convergence of the FEP/MD calculations. Fourth, to decrease the computational cost, only a small number of atoms in the vicinity of the binding site are simulated explicitly, while all the influence of the remaining atoms is incorporated implicitly using the generalized solvent boundary potential (GSBP) method. With GSBP, the size of the simulated FKBP12/ligand systems is significantly reduced, from ∼25,000 to 2500. The computations are very efficient and the statistical error is small (∼1 kcal/mol). The calculated binding free energies are generally in good agreement with available experimental data and previous calculations (within ∼2 kcal/mol). The present results indicate that a strategy based on FEP/MD simulations of a reduced GSBP atomic model sampled with conformational, translational, and orientational restraining
40 CFR 721.524 - Alcohols, C6-12, ethoxylated, reaction product with maleic anhydride.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 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 maleic... 40 Protection of Environment 31 2014-07-01 2014-07-01 false Alcohols, C6-12, ethoxylated,...
40 CFR 721.524 - Alcohols, C6-12, ethoxylated, reaction product with maleic anhydride.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 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 maleic... 40 Protection of Environment 32 2012-07-01 2012-07-01 false Alcohols, C6-12, ethoxylated,...
40 CFR 721.524 - Alcohols, C6-12, ethoxylated, reaction product with maleic anhydride.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 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 maleic... 40 Protection of Environment 31 2011-07-01 2011-07-01 false Alcohols, C6-12, ethoxylated,...
40 CFR 721.524 - Alcohols, C6-12, ethoxylated, reaction product with maleic anhydride.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 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 maleic... 40 Protection of Environment 32 2013-07-01 2013-07-01 false Alcohols, C6-12, ethoxylated,...
40 CFR 721.524 - Alcohols, C6-12, ethoxylated, reaction product with maleic anhydride.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 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 maleic... 40 Protection of Environment 30 2010-07-01 2010-07-01 false Alcohols, C6-12, ethoxylated,...
41 CFR 51-6.12 - Specification changes and similar actions.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 41 Public Contracts and Property Management 1 2010-07-01 2010-07-01 true Specification changes and similar actions. 51-6.12 Section 51-6.12 Public Contracts and Property Management Other Provisions Relating to Public Contracts COMMITTEE FOR PURCHASE FROM PEOPLE WHO ARE BLIND OR SEVERELY DISABLED 6-PROCUREMENT PROCEDURES § 51-6.12...
NASA Astrophysics Data System (ADS)
Loeffler, Troy D.; Chen, Bin
2013-12-01
The aggregation-volume-bias Monte Carlo method was employed to study surface-induced nucleation of Lennard-Jonesium on an implicit surface below the melting point. It was found that surfaces catalyze not only the formation of the droplets (where the nucleation free energy barriers were shown to decrease with increasing surface interaction strength), but also the transition of these droplets into crystal structures due to the surface-induced layering effects. However, this only occurs under suitable interaction strength. When surface attraction is too strong, crystallization is actually inhibited due to the spread of the particles across the surface and corresponding formation of two-dimensional clusters. The simulation results were also used to examine the bulk-droplet based classical nucleation theory for surface-induced nucleation, particularly the additional contact angle term used to describe both the nucleation free energy barrier heights and the critical cluster sizes compared to its homogeneous nucleation formalism. Similar to what has been found previously for homogeneous nucleation, the theory does poorly toward the high-supersaturation region when the critical clusters are small and fractal, but the theoretical predictions on both barrier heights and critical cluster sizes improve rapidly with the decrease of the supersaturation.
Nanoparticle interaction potentials constructed by multiscale computation
NASA Astrophysics Data System (ADS)
Lee, Cheng K.; Hua, Chi C.
2010-06-01
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 (SiO2)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 Si6O12 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 2α-α potential (α 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 polymer chains and
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
Molecular-dynamics simulations of stress relaxation in metals and polymers
NASA Astrophysics Data System (ADS)
Blonski, Slawomir; Brostow, Witold; Kubát, Josef
1994-03-01
Molecular-dynamics simulations of stress relaxation have been performed for models of metals and polymers. A method that employs coupling between the simulation cell and an applied stress as well as an external thermal bath has been used. Two-dimensional models of the materials are defined with interactions described by the Lennard-Jones (Mie 6-12) and harmonic potentials. A special method is employed to generate chains in dense polymeric systems. In agreement with experiments, simulated stress-relaxation curves are similar for metals and polymers. At the same time, there exists an essential difference in the stress-strain behavior of the two kinds of simulated materials. During the relaxation, trajectories of the particles in different materials display a common feature: There exist domains in which movement of the particles is highly correlated. Thus, the simulation results support the cooperative theory of stress relaxation.
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.
Benjamin, Ronald; Horbach, Jürgen
2012-07-28
A method is proposed to compute the interfacial free energy of a Lennard-Jones system in contact with a structured wall by molecular dynamics simulation. Both the bulk liquid and bulk face-centered-cubic crystal phase along the (111) orientation are considered. Our approach is based on a thermodynamic integration scheme where first the bulk Lennard-Jones system is reversibly transformed to a state where it interacts with a structureless flat wall. In a second step, the flat structureless wall is reversibly transformed into an atomistic wall with crystalline structure. The dependence of the interfacial free energy on various parameters such as the wall potential, the density and orientation of the wall is investigated. The conditions are indicated under which a Lennard-Jones crystal partially wets a flat wall. PMID:22852644
Bridge function of the repulsive Weeks-Chandler-Andersen (WCA) fluid
NASA Astrophysics Data System (ADS)
Tomazic, Daniel; Hoffgaard, Franziska; Kast, Stefan M.
2014-01-01
The bridge function of a simple liquid is calculated for the repulsive part of the Weeks-Chandler-Andersen (WCA) separation of the Lennard-Jones potential. We employ explicit molecular dynamics simulations of the potential of mean force between constrained dimers in order to extract bridge data near zero separation and illustrate the difference to full Lennard-Jones results. We compare direct, reciprocal space and iterative, real space inversions of the Ornstein-Zernike equation. Bridge functions for various thermodynamic states are analyzed as to their parametric dependence on the renormalized indirect correlation function, which has consequences for the analytic representation of the free energy functional.
41 CFR 51-6.12 - Specification changes and similar actions.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 41 Public Contracts and Property Management 1 2011-07-01 2009-07-01 true Specification changes and similar actions. 51-6.12 Section 51-6.12 Public Contracts and Property Management Other Provisions... Procurement List, including a change that involves the assignment of a new national stock number or...
Su, Pin-Chih; Johnson, Michael E
2016-04-01
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 parahalogen in benzimidazole compounds might form a weak halogen bond with FabI, which is a well-known halogen bond favoring enzyme. PMID:26666582
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…
Makowski, Mariusz; Liwo, Adam; Sobolewski, Emil; Scheraga, Harold A
2011-05-19
A new model of side-chain-side-chain interactions for charged side-chains of amino acids, to be used in the UNRES force-field, has been developed, in which a side chain consists of a nonpolar and a charged site. The interaction energy between the nonpolar sites is composed of a Gay-Berne and a cavity term; the interaction energy between the charged sites consists of a Lennard-Jones term, a Coulombic term, a generalized-Born term, and a cavity term, while the interaction energy between the nonpolar and charged sites is composed of a Gay-Berne and a polarization term. We parametrized the energy function for the models of all six pairs of natural like-charged amino-acid side chains, namely propionate-propionate (for the aspartic acid-aspartic acid pair), butyrate-butyrate (for the glutamic acid-glutamic acid pair), propionate-butyrate (for the aspartic acid-glutamic acid pair), pentylamine cation-pentylamine cation (for the lysine-lysine pair), 1-butylguanidine cation-1-butylguanidine cation (for the arginine-arginine pair), and pentylamine cation-1-butylguanidine cation (for the lysine-arginine pair). By using umbrella-sampling molecular dynamics simulations in explicit TIP3P water, we determined the potentials of mean force of the above-mentioned pairs as functions of distance and orientation and fitted analytical expressions to them. The positions and depths of the contact minima and the positions and heights of the desolvation maxima, including their dependence on the orientation of the molecules were well represented by analytical expressions for all systems. The values of the parameters of all the energy components are physically reasonable, which justifies use of such potentials in coarse-grain protein-folding simulations. PMID:21500792
Makowski, Mariusz; Liwo, Adam; Sobolewski, Emil; Scheraga, Harold A.
2011-01-01
A new model of side-chain – side-chain interactions for charged side-chains of amino acids, to be used in the UNRES force-field, has been developed, in which a side chain consists of a nonpolar and a charged site. The interaction energy between the nonpolar sites is composed of a Gay-Berne and a cavity term; the interaction energy between the charged sites consists of a Lennard-Jones term, a Coulombic term, a Generalized-Born term, and a cavity term, while the interaction energy between the nonpolar and charged sites is composed of a Gay-Berne and a polarization term. We parameterized the energy function for the models of all six pairs of natural like-charged amino-acid side chains, namely propionate-propionate (for the aspartic acid-aspartic acid pair), butyrate-butyrate (for the glutamic acid-glutamic acid pair), propionate-butyrate (for the aspartic acid-glutamic acid pair), pentylamine cation-pentylamine cation (for the lysine-lysine pair), 1-butylguanidine cation-1-butylguanidine cation (for the arginine-arginine pair), and pentylamine cation-1-butylguanidine cation (for the lysine-arginine pair). By using umbrella-sampling molecular dynamics simulations in explicit TIP3P water, we determined the potentials of mean force of the above-mentioned pairs as functions of distance and orientation and fitted analytical expressions to them. The positions and depths of the contact minima and the positions and heights of the desolvation maxima, including their dependence on the orientation of the molecules were well represented by analytical expressions for all systems. The values of the parameters of all the energy components are physically reasonable, which justifies use of such potentials in coarse-grain protein-folding simulations. PMID:21500792
A Polarizable and Transferable PHAST N2 Potential for Use in Materials Simulation.
Cioce, Christian R; McLaughlin, Keith; Belof, Jonathan L; Space, Brian
2013-12-10
A polarizable and transferable intermolecular potential energy function, potentials with high accuracy, speed, and transferability (PHAST), has been developed from first principles for molecular nitrogen to be used in the modeling of heterogeneous processes such as materials sorption and separations. A five-site (van der Waals and point charge) anisotropic model, that includes many-body polarization, is proposed. It is parametrized to reproduce high-level electronic structure calculations (CCSD(T) using Dunning-type basis sets extrapolated to the CBS limit) for a representative set of dimer potential energy curves. Thus it provides a relatively simple yet robust and broadly applicable representation of nitrogen. Two versions are developed, differing by the type of mixing rules applied to unlike Lennard-Jones potential sites. It is shown that the Waldman-Hagler mixing rules are more accurate than Lorentz-Berthelot. The resulting potentials are demonstrated to be effective in modeling neat nitrogen but are designed to also be useful in modeling N2 interactions in a large array of environments such as metal-organic frameworks and zeolites and at interfaces. In such settings, capturing anisotropic forces and interactions with (open and coordinated) metals and charged/polar environments is essential. In developing the potential, it was found that adding a seemingly redundant dimer orientation, slip-parallel (S), improved the transferability of the potential energy surface (PES). Notably, one of the solid phases of nitrogen was not as accurately represented energetically without including S in the representative set. Liquid simulations, however, were unaffected and worked equally well for both potentials. This suggests that accounting for a wide variety of configurations is critical in designing a potential that is intended for use in heterogeneous environments where many orientations, including those not commonly explored in the bulk, are possible. Testing and
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.
The calculation of elastic constants from displacement fluctuations
NASA Astrophysics Data System (ADS)
Meyers, M. T.; Rickman, J. M.; Delph, T. J.
2005-09-01
We present a methodology for the accurate and efficient extraction of elastic constants in homogeneous solids via the calculation of the atomic displacement correlation function. This approach is validated for cubic solids parametrized by both Lennard-Jones and embedded-atom method potentials. Finally, we also discuss the extension of this method to obtain the elastic properties of inhomogeneous solids.
Green's function Monte Carlo calculation for the ground state of helium trimers
Cabral, F.; Kalos, M.H.
1981-02-01
The ground state energy of weakly bound boson trimers interacting via Lennard-Jones (12,6) pair potentials is calculated using a Monte Carlo Green's Function Method. Threshold coupling constants for self binding are obtained by extrapolation to zero binding.
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…
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…
40 CFR 721.10559 - Morpholine, 4-C6-12 acyl derivs.
Code of Federal Regulations, 2013 CFR
2013-07-01
... subject to reporting. (1) The chemical substance identified as morpholine, 4-C6-12 acyl derivs. (PMN P-06...) through (h) are applicable to manufacturers, importers, and processors of this substance. (2) Limitations... SUBSTANCES CONTROL ACT SIGNIFICANT NEW USES OF CHEMICAL SUBSTANCES Significant New Uses for Specific...
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…
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, Illness, and…
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…
NASA Astrophysics Data System (ADS)
Bresme, Fernando; Abascal, José L. F.; Lomba, Enrique
1996-12-01
Structure and thermodynamics of fluids made of particles that interact via a central force model potential are studied by means of Monte Carlo simulations and integral equation theories. The Hamiltonian has two terms, an intramolecular component represented by a harmonic oscillatorlike potential and an intermolecular interaction of the Lennard-Jones type. The potential does not fulfill the steric saturation condition so it leads to a polydisperse system. First, we investigate the association (clustering) and thermodynamic properties as a function of the potential parameters, such as the intramolecular potential depth, force constant, and bond length. It is shown that the atomic hypernetted chain (HNC) integral equation provides a correct description of the model as compared with simulation results. The calculation of the HNC pseudospinodal curve indicates that the stability boundaries between the vapor and liquid phases are strongly dependent on the bond length and suggests that there might be a direct gas-solid transition for certain elongations. On the other hand, we have assessed the ability of the model to describe the thermodynamics and structure of diatomic liquids such as N2 and halogens. To this end we have devised a procedure to model the intramolecular potential depth to reproduce the complete association limit (i.e., an average number of bonds per particle equal to one). This constraint is imposed on the Ornstein-Zernike integral equation in a straightforward numerical way. The structure of the resulting fluid is compared with results from molecular theories. An excellent agreement between the HNC results for the associating fluid and the reference interaction site model (RISM)-HNC computations for the atom-atom model of the same fluid is obtained. There is also a remarkable coincidence between the simulation results for the molecular and the associating liquids, despite the polydisperse character of the latter. The stability boundaries in the complete
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.
Anderson, Brian J; Bazant, Martin Z; Tester, Jefferson W; Trout, Bernhardt L
2005-04-28
We present the application of a mathematical method reported earlier by which the van der Waals-Platteeuw statistical mechanical model with the Lennard-Jones and Devonshire approximation can be posed as an integral equation with the unknown function being the intermolecular potential between the guest molecules and the host molecules. This method allows us to solve for the potential directly for hydrates for which the Langmuir constants are computed, either from experimental data or from ab initio data. Given the assumptions made in the van der Waals-Platteeuw model with the spherical-cell approximation, there are an infinite number of solutions; however, the only solution without cusps is a unique central-well solution in which the potential is at a finite minimum at the center to the cage. From this central-well solution, we have found the potential well depths and volumes of negative energy for 16 single-component hydrate systems: ethane (C2H6), cyclopropane (C3H6), methane (CH4), argon (Ar), and chlorodifluoromethane (R-22) in structure I; and ethane (C2H6), cyclopropane (C3H6), propane (C3H8), isobutane (C4H10), methane (CH4), argon (Ar), trichlorofluoromethane (R-11), dichlorodifluoromethane (R-12), bromotrifluoromethane (R-13B1), chloroform (CHCl3), and 1,1,1,2-tetrafluoroethane (R-134a) in structure II. This method and the calculated cell potentials were validated by predicting existing mixed hydrate phase equilibrium data without any fitting parameters and calculating mixture phase diagrams for methane, ethane, isobutane, and cyclopropane mixtures. Several structural transitions that have been determined experimentally as well as some structural transitions that have not been examined experimentally were also predicted. In the methane-cyclopropane hydrate system, a structural transition from structure I to structure II and back to structure I is predicted to occur outside of the known structure II range for the cyclopropane hydrate. Quintuple (L
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.
Vibrational and thermodynamic properties of α-, β-, γ-, and 6, 6, 12-graphyne structures.
Perkgöz, Nihan Kosku; Sevik, Cem
2014-05-01
Electronic, vibrational, and thermodynamic properties of different graphyne structures, namely α-, β-, γ-, and 6, 6, 12-graphyne, are investigated through first principles-based quasi-harmonic approximation by using phonon dispersions predicted from density-functional perturbation theory. Similar to graphene, graphyne was shown to exhibit a structure with extraordinary electronic features, mechanical hardness, thermal resistance, and very high conductivity from different calculation methods. Hence, characterizing its phonon dispersions and vibrational and thermodynamic properties in a systematic way is of great importance for both understanding its fundamental molecular properties and also figuring out its phase stability issues at different temperatures. Thus, in this research work, thermodynamic stability of different graphyne allotropes is assessed by investigating vibrational properties, lattice thermal expansion coefficients, and Gibbs free energy. According to our results, although the imaginary vibrational frequencies exist for β-graphyne, there is no such a negative behavior for α-, γ-, and 6, 6, 12-graphyne structures. In general, the Grüneisen parameters and linear thermal expansion coefficients of these structures are calculated to be rather more negative when compared to those of the graphene structure. In addition, the predicted difference between the binding energies per atom for the structures of graphene and graphyne points out that graphyne networks have relatively lower phase stability in comparison with the graphene structures. PMID:24737253
Weiss, Vinícius Almir; Faoro, Helisson; Tadra-Sfeir, Michelle Zibbetti; Raittz, Roberto Tadeu; de Souza, Emanuel Maltempi; Monteiro, Rose Adele; Cardoso, Rodrigo Luis Alves; Wassem, Roseli; Chubatsu, Leda Satie; Huergo, Luciano Fernandes; Müller-Santos, Marcelo; Steffens, Maria Berenice Reynaud; Rigo, Liu Un; Pedrosa, Fábio de Oliveira
2012-01-01
Herbaspirillum lusitanum strain P6-12 (DSM 17154) is, so far, the only species of Herbaspirillum isolated from plant root nodules. Here we report a draft genome sequence of this organism. PMID:22815451
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