Density functional for ternary non-additive hard sphere mixtures.
Schmidt, Matthias
2011-10-19
Based on fundamental measure theory, a Helmholtz free energy density functional for three-component mixtures of hard spheres with general, non-additive interaction distances is constructed. The functional constitutes a generalization of the previously given theory for binary non-additive mixtures. The diagrammatic structure of the spatial integrals in both functionals is of star-like (or tree-like) topology. The ternary diagrams possess a higher degree of complexity than the binary diagrams. Results for partial pair correlation functions, obtained via the Ornstein-Zernike route from the second functional derivatives of the excess free energy functional, agree well with Monte Carlo simulation data. PMID:21946780
Density Fluctuations of Hard-Sphere Fluids in Narrow Confinement
NASA Astrophysics Data System (ADS)
Nygârd, Kim; Sarman, Sten; Hyltegren, Kristin; Chodankar, Shirish; Perret, Edith; Buitenhuis, Johan; van der Veen, J. Friso; Kjellander, Roland
2016-01-01
Spatial confinement induces microscopic ordering of fluids, which in turn alters many of their dynamic and thermodynamic properties. However, the isothermal compressibility has hitherto been largely overlooked in the literature, despite its obvious connection to the underlying microscopic structure and density fluctuations in confined geometries. Here, we address this issue by probing density profiles and structure factors of hard-sphere fluids in various narrow slits, using x-ray scattering from colloid-filled nanofluidic containers and integral-equation-based statistical mechanics at the level of pair distributions for inhomogeneous fluids. Most importantly, we demonstrate that density fluctuations and isothermal compressibilities in confined fluids can be obtained experimentally from the long-wavelength limit of the structure factor, providing a formally exact and experimentally accessible connection between microscopic structure and macroscopic, thermodynamic properties. Our approach will thus, for example, allow direct experimental verification of theoretically predicted enhanced density fluctuations in liquids near solvophobic interfaces.
Density Functional Approximation for Non-Hard Sphere Fluids Subjected to External Fields
NASA Astrophysics Data System (ADS)
Zhou, Shiqi
A theoretical way is proposed, by which any hard sphere density functional approximation (DFA) can be applied to non-hard sphere fluids for the calculation of density profile in the framework of density functional theory (DFT). Used as examples, the present formalism is combined respectively with two recently proposed hard sphere DFAs to predict the density profile of Lennard-Jones (LJ) fluid, hard core square well (SW) fluid and penetrable potenial fluid subjected to diverse external fields. Extensive comparison between theoretical predictions and corresponding simulation results shows that the present theoretical way, when combined with an accurate hard sphere DFA, can perform well for calculating the density profile of the non-uniform fluids of the above mentioned potentials. Concretely speaking, for LJ and hard core SW fluid, even a less accurate FEDFA is sufficient, while for extreme potential such as the penetrable potenial, a more accurate adjustable parameter free version of LTDFA is needed to combine with the present theoretical way to predict density profile satisfactorily. The advantage of the proposed theoretical way is that the resultant DFA is applicable to both subcritical and supercritical temperature cases, thereby overcoming the disadvantages of previous two categories of DFT approach.
Equilibrium Sampling of Hard Spheres up to the Jamming Density and Beyond
NASA Astrophysics Data System (ADS)
Berthier, Ludovic; Coslovich, Daniele; Ninarello, Andrea; Ozawa, Misaki
2016-06-01
We implement and optimize a particle-swap Monte Carlo algorithm that allows us to thermalize a polydisperse system of hard spheres up to unprecedentedly large volume fractions, where previous algorithms and experiments fail to equilibrate. We show that no glass singularity intervenes before the jamming density, which we independently determine through two distinct nonequilibrium protocols. We demonstrate that equilibrium fluid and nonequilibrium jammed states can have the same density, showing that the jamming transition cannot be the end point of the fluid branch.
Equilibrium Sampling of Hard Spheres up to the Jamming Density and Beyond.
Berthier, Ludovic; Coslovich, Daniele; Ninarello, Andrea; Ozawa, Misaki
2016-06-10
We implement and optimize a particle-swap Monte Carlo algorithm that allows us to thermalize a polydisperse system of hard spheres up to unprecedentedly large volume fractions, where previous algorithms and experiments fail to equilibrate. We show that no glass singularity intervenes before the jamming density, which we independently determine through two distinct nonequilibrium protocols. We demonstrate that equilibrium fluid and nonequilibrium jammed states can have the same density, showing that the jamming transition cannot be the end point of the fluid branch. PMID:27341260
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.
Shells of charge: a density functional theory for charged hard spheres
NASA Astrophysics Data System (ADS)
Roth, Roland; Gillespie, Dirk
2016-06-01
A functional for the electrostatic excess free-energy for charged, hard sphere fluids is proposed. The functional is derived from two complementary, but equivalent, interpretations of the mean spherical approximation (MSA). The first combines fundamental measure theory (FMT) from hard-core interactions with the idea that MSA can be interpreted in terms of the interaction spherical shells of charge. This formulation gives the free-energy density as a function of weighted densities. When all the ions have the same size, the functional adopts an FMT-like form. The second in effect ‘functionalizes’ the derivation of MSA; that is, it generalizes the MSA as a functional-based version of MSA (fMSA). This formulation defines the free-energy density as a function of a position-dependent MSA screening parameter and the weighted densities of the FMT approach. This FMT/fMSA functional is shown to give accurate density profiles, as compared to Monte Carlo simulations, under a wide range of ion concentrations, size asymmetries, and valences.
Shells of charge: a density functional theory for charged hard spheres.
Roth, Roland; Gillespie, Dirk
2016-06-22
A functional for the electrostatic excess free-energy for charged, hard sphere fluids is proposed. The functional is derived from two complementary, but equivalent, interpretations of the mean spherical approximation (MSA). The first combines fundamental measure theory (FMT) from hard-core interactions with the idea that MSA can be interpreted in terms of the interaction spherical shells of charge. This formulation gives the free-energy density as a function of weighted densities. When all the ions have the same size, the functional adopts an FMT-like form. The second in effect 'functionalizes' the derivation of MSA; that is, it generalizes the MSA as a functional-based version of MSA (fMSA). This formulation defines the free-energy density as a function of a position-dependent MSA screening parameter and the weighted densities of the FMT approach. This FMT/fMSA functional is shown to give accurate density profiles, as compared to Monte Carlo simulations, under a wide range of ion concentrations, size asymmetries, and valences. PMID:27116385
Communication: Dynamical density functional theory for dense suspensions of colloidal hard spheres
NASA Astrophysics Data System (ADS)
Stopper, Daniel; Roth, Roland; Hansen-Goos, Hendrik
2015-11-01
We study structural relaxation of colloidal hard spheres undergoing Brownian motion using dynamical density functional theory. Contrary to the partial linearization route [D. Stopper et al., Phys. Rev. E 92, 022151 (2015)] which amounts to using different free energy functionals for the self and distinct part of the van Hove function G(r, t), we put forward a unified description employing a single functional for both components. To this end, interactions within the self part are removed via the zero-dimensional limit of the functional with a quenched self component. In addition, we make use of a theoretical result for the long-time mobility in hard-sphere suspensions, which we adapt to the inhomogeneous fluid. Our results for G(r, t) are in excellent agreement with numerical simulations even in the dense liquid phase. In particular, our theory accurately yields the crossover from free diffusion at short times to the slower long-time diffusion in a crowded environment.
Free Energy Calculations of Crystalline Hard Sphere Complexes Using Density Functional Theory
Gunawardana, K. G.S.H.; Song, Xueyu
2014-12-22
Recently developed fundamental measure density functional theory (FMT) is used to study binary hard sphere (HS) complexes in crystalline phases. By comparing the excess free energy, pressure and phase diagram, we show that the fundamental measure functional yields good agreements to the available simulation results of AB, AB_{2} and AB_{13} crystals. Additionally, we use this functional to study the HS models of five binary crystals, Cu_{5}Zr(C15_{b}), Cu_{51}Zr_{14}(β), Cu_{10}Zr_{7}(φ), CuZr(B2) and CuZr_{2} (C11_{b}), which are observed in the Cu-Zr system. The FMT functional gives well behaved minimum for most of the hard sphere crystal complexes in the two dimensional Gaussian space, namely a crystalline phase. However, the current version of FMT functional (white Bear) fails to give a stable minimum for the structure Cu_{10}Zr_{7}(φ). We argue that the observed solid phases for the HS models of the Cu-Zr system are true thermodynamic stable phases and can be used as a reference system in perturbation calculations.
Free Energy Calculations of Crystalline Hard Sphere Complexes Using Density Functional Theory
Gunawardana, K. G.S.H.; Song, Xueyu
2014-12-22
Recently developed fundamental measure density functional theory (FMT) is used to study binary hard sphere (HS) complexes in crystalline phases. By comparing the excess free energy, pressure and phase diagram, we show that the fundamental measure functional yields good agreements to the available simulation results of AB, AB2 and AB13 crystals. Additionally, we use this functional to study the HS models of five binary crystals, Cu5Zr(C15b), Cu51Zr14(β), Cu10Zr7(φ), CuZr(B2) and CuZr2 (C11b), which are observed in the Cu-Zr system. The FMT functional gives well behaved minimum for most of the hard sphere crystal complexes in the two dimensional Gaussian space,more » namely a crystalline phase. However, the current version of FMT functional (white Bear) fails to give a stable minimum for the structure Cu10Zr7(φ). We argue that the observed solid phases for the HS models of the Cu-Zr system are true thermodynamic stable phases and can be used as a reference system in perturbation calculations.« less
How to Extend the Bridge Density Functional Approximation to the Confined Non-hard Sphere Fluid
NASA Astrophysics Data System (ADS)
Zhou, Shi-qi
2006-08-01
A theoretical method was proposed to extend a bridge density functional approximation (BDFA) for the non-uniform hard sphere fluid to the non-uniform Lennard-Jones (LJ) fluid. The DFT approach for LJ fluid is simple, quantitatively accurate in a wide range of coexistence phase and external field parameters. Especially, the DFT approach only needs a second order direct correlation function (DCF) of the coexistence bulk fluid as input, and is therefore applicable to the subcritical temperature region. The present theoretical method can be regarded as a non-uniform counterpart of the thermodynamic perturbation theory, in which it is not at the level of the free energy but at the level of the second order DCF.
Hard sphere packings within cylinders.
Fu, Lin; Steinhardt, William; Zhao, Hao; Socolar, Joshua E S; Charbonneau, Patrick
2016-02-23
Arrangements of identical hard spheres confined to a cylinder with hard walls have been used to model experimental systems, such as fullerenes in nanotubes and colloidal wire assembly. Finding the densest configurations, called close packings, of hard spheres of diameter σ in a cylinder of diameter D is a purely geometric problem that grows increasingly complex as D/σ increases, and little is thus known about the regime for D > 2.873σ. In this work, we extend the identification of close packings up to D = 4.00σ by adapting Torquato-Jiao's adaptive-shrinking-cell formulation and sequential-linear-programming (SLP) technique. We identify 17 new structures, almost all of them chiral. Beyond D ≈ 2.85σ, most of the structures consist of an outer shell and an inner core that compete for being close packed. In some cases, the shell adopts its own maximum density configuration, and the stacking of core spheres within it is quasiperiodic. In other cases, an interplay between the two components is observed, which may result in simple periodic structures. In yet other cases, the very distinction between the core and shell vanishes, resulting in more exotic packing geometries, including some that are three-dimensional extensions of structures obtained from packing hard disks in a circle. PMID:26843132
NASA Astrophysics Data System (ADS)
Stopper, Daniel; Marolt, Kevin; Roth, Roland; Hansen-Goos, Hendrik
2015-08-01
We study the dynamics of colloidal suspensions of hard spheres that are subject to Brownian motion in the overdamped limit. We obtain the time evolution of the self- and distinct parts of the van Hove function by means of dynamical density functional theory. The free-energy model for the hard-sphere fluid that we use is the very accurate White Bear II version of Rosenfeld's fundamental measure theory. However, in order to remove interactions within the self-part of the van Hove function, a nontrivial modification has to be applied to the free-energy functional. We compare our theoretical results with data that we obtain from dynamical Monte Carlo simulations, and we find that the latter are well described by our approach even for colloid packing fractions as large as 40%.
Stopper, Daniel; Marolt, Kevin; Roth, Roland; Hansen-Goos, Hendrik
2015-08-01
We study the dynamics of colloidal suspensions of hard spheres that are subject to Brownian motion in the overdamped limit. We obtain the time evolution of the self- and distinct parts of the van Hove function by means of dynamical density functional theory. The free-energy model for the hard-sphere fluid that we use is the very accurate White Bear II version of Rosenfeld's fundamental measure theory. However, in order to remove interactions within the self-part of the van Hove function, a nontrivial modification has to be applied to the free-energy functional. We compare our theoretical results with data that we obtain from dynamical Monte Carlo simulations, and we find that the latter are well described by our approach even for colloid packing fractions as large as 40%. PMID:26382387
Odriozola, Gerardo; Berthier, Ludovic
2011-02-01
We use replica exchange Monte Carlo simulations to measure the equilibrium equation of state of the disordered fluid state for a binary hard sphere mixture up to very large densities where standard Monte Carlo simulations do not easily reach thermal equilibrium. For the moderate system sizes we use (up to N = 100), we find no sign of a pressure discontinuity near the location of dynamic glass singularities extrapolated using either algebraic or simple exponential divergences, suggesting they do not correspond to genuine thermodynamic glass transitions. Several scenarios are proposed for the fate of the fluid state in the thermodynamic limit. PMID:21303135
Segregation of Fluidized Binary Hard-Sphere Systems Under Gravity
NASA Astrophysics Data System (ADS)
Kim, Soon-Chul
We have derived an analytic expression for the contact value of the local density of binary hard-sphere systems under gravity. We have obtained the crossover conditions for the Brazil-nut type segregation of binary hard-sphere mixtures and binary hard-sphere chain mixtures from the segregation criterion, where the segregation occurs when the density (or the pressure) of the small spheres at the bottom is higher than that of the large spheres, or vice versa. For the binary hard-sphere chain mixtures, the crossover condition for the segregation depends on the number of monomers composed of hard-sphere chains as well as the mass and the diameter of each species. The fundamental-measure theories (FMTs) and local density approximation (LDA) are employed to examine the crossover condition for the segregation of the gravity-induced hard-sphere mixtures. The calculated results show that the LDA does not explain the density oscillation near the bottom, whereas the modified fundamental-measure theory (MFMT) compares with molecular dynamics simulations.
Demixing in binary mixtures of apolar and dipolar hard spheres
NASA Astrophysics Data System (ADS)
Almarza, N. G.; Lomba, E.; Martín, C.; Gallardo, A.
2008-12-01
We study the demixing transition of mixtures of equal size hard spheres and dipolar hard spheres using computer simulation and integral equation theories. Calculations are carried out at constant pressure, and it is found that there is a strong correlation between the total density and the composition. The critical temperature and the critical total density are found to increase with pressure. The critical mole fraction of the dipolar component on the contrary decreases as pressure is augmented. These qualitative trends are reproduced by the theoretical approaches that on the other hand overestimate by far the value of the critical temperature. Interestingly, the critical parameters for the liquid-vapor equilibrium extrapolated from the mixture results in the limit of vanishing neutral hard sphere concentration agree rather well with recent estimates based on the extrapolation of charged hard dumbbell phase equilibria when dumbbell elongation shrinks to zero [G. Ganzenmüller and P. J. Camp, J. Chem. Phys. 126, 191104 (2007)].
Computational polymer physics: Hard-sphere chain in solvent systems
NASA Astrophysics Data System (ADS)
Gautam, Avinash; Gavazzi, Daniel; Taylor, Mark
2009-10-01
In this work we present results for chain conformation in two simple chain-in-solvent systems constructed from hard-sphere monomers of diameter D. The first system consists of a flexible chain of fused hard spheres (i.e., bond length L=D) in a monomeric hard-sphere solvent. The second system consists of a flexible tangent hard-sphere chain (L=D) in a dimeric hard-sphere solvent with L=D. These systems are studied using Monte Carlo simulations which employ both single-site crankshaft and multi-site pivot moves to sample the configuration space of the chain. We report chain structure, in terms of site-site probability functions, as a function of solvent density. In all cases, increasing solvent density leads to an overall compression of the chain. At high solvent density the chain conformation is closely coupled to the local solvent structure and we speculate that incommensurate structures may lead to interesting conformational transitions.
Geometrical characterization of hard-sphere systems.
Richard, P; Oger, L; Troadec, J P; Gervois, A
1999-10-01
By using molecular dynamics simulations on a large number of hard spheres and the Voronoï tessellation we characterize hard-sphere systems geometrically at any packing fraction eta along the different branches of the phase diagram. Crystallization of disordered packings occurs only for a small range of packing fraction. For the other packing fractions the system behaves as either a fluid (stable or metastable) or a glass. We have studied the evolution of the statistics of the Voronoï tessellation during crystallization and characterized the apparition of order by an order parameter (Q(6)) built from spherical harmonics. PMID:11970312
Sesé, Luis M; Bailey, Lorna E
2007-04-28
The structural features of the quantum hard-sphere system in the region of the fluid-face-centered-cubic-solid transition, for reduced number densities 0.45
Glass transition of dense fluids of hard and compressible spheres.
Berthier, Ludovic; Witten, Thomas A
2009-08-01
We use computer simulations to study the glass transition of dense fluids made of polydisperse repulsive spheres. For hard particles, we vary the volume fraction, phi , and use compressible particles to explore finite temperatures, T>0 . In the hard sphere limit, our dynamic data show evidence of an avoided mode-coupling singularity near phi(MCT) is approximately 0.592; they are consistent with a divergence of equilibrium relaxation times occurring at phi(0) is approximately 0.635, but they leave open the existence of a finite temperature singularity for compressible spheres at volume fraction phi>phi(0). Using direct measurements and a scaling procedure, we estimate the equilibrium equation of state for the hard sphere metastable fluid up to phi(0), where pressure remains finite, suggesting that phi(0) corresponds to an ideal glass transition. We use nonequilibrium protocols to explore glassy states above phi(0) and establish the existence of multiple equations of state for the unequilibrated glass of hard spheres, all diverging at different densities in the range phi in [0.642, 0.664]. Glassiness thus results in the existence of a continuum of densities where jamming transitions can occur. PMID:19792128
Thermodynamic properties of non-conformal soft-sphere fluids with effective hard-sphere diameters.
Rodríguez-López, Tonalli; del Río, Fernando
2012-01-28
In this work we study a set of soft-sphere systems characterised by a well-defined variation of their softness. These systems represent an extension of the repulsive Lennard-Jones potential widely used in statistical mechanics of fluids. This type of soft spheres is of interest because they represent quite accurately the effective intermolecular repulsion in fluid substances and also because they exhibit interesting properties. The thermodynamics of the soft-sphere fluids is obtained via an effective hard-sphere diameter approach that leads to a compact and accurate equation of state. The virial coefficients of soft spheres are shown to follow quite simple relationships that are incorporated into the equation of state. The approach followed exhibits the rescaling of the density that produces a unique equation for all systems and temperatures. The scaling is carried through to the level of the structure of the fluids. PMID:22158949
Prediction of binary hard-sphere crystal structures.
Filion, Laura; Dijkstra, Marjolein
2009-04-01
We present a method based on a combination of a genetic algorithm and Monte Carlo simulations to predict close-packed crystal structures in hard-core systems. We employ this method to predict the binary crystal structures in a mixture of large and small hard spheres with various stoichiometries and diameter ratios between 0.4 and 0.84. In addition to known binary hard-sphere crystal structures similar to NaCl and AlB2, we predict additional crystal structures with the symmetry of CrB, gammaCuTi, alphaIrV, HgBr2, AuTe2, Ag2Se, and various structures for which an atomic analog was not found. In order to determine the crystal structures at infinite pressures, we calculate the maximum packing density as a function of size ratio for the crystal structures predicted by our GA using a simulated annealing approach. PMID:19518387
Aging dynamics of colloidal hard sphere glasses.
Martinez, V A; Bryant, G; van Megen, W
2010-09-21
We report the results of dynamic light scattering measurements of the coherent intermediate scattering function (ISF) of glasses of colloidal hard spheres for several volume fractions and a range of scattering vectors around the primary peak of the static structure factor. The ISF shows a clear crossover from an initial fast decay to a slower nonstationary decay. Aging is quantified in several different ways. However, regardless of the method chosen, the perfect "aged" glass is approached in a power law fashion. In particular the coupling between the fast and slow decays, as measured by the degree of stretching of the ISF at the crossover, also decreases algebraically with waiting time. The nonstationarity of this coupling implies that even the fastest detectable processes are themselves nonstationary. PMID:20866156
Dynamics of heterogeneous hard spheres in a file
NASA Astrophysics Data System (ADS)
Flomenbom, Ophir
2010-09-01
Normal dynamics in a quasi-one-dimensional channel of length L (→∞) of N hard spheres are analyzed. The spheres are heterogeneous: each has a diffusion coefficient D that is drawn from a probability density function (PDF), W˜D-γ for small D , where 0≤γ<1 . The initial spheres’ density ρ is nonuniform and scales with the distance (from the origin) l as ρ˜l-α , 0≤α≤1 . An approximation for the N -particle PDF for this problem is derived. From this solution, scaling law analysis and numerical simulations, we show here that the mean square displacement for a particle in such a system obeys ⟨r2⟩˜t(1-γ)/(2c-γ) , where c=1/(1+α) . The PDF of the tagged particle is Gaussian in position. Generalizations of these results are considered.
NASA Astrophysics Data System (ADS)
Oyarzún, Bernardo; van Westen, Thijs; Vlugt, Thijs J. H.
2013-05-01
The liquid crystal phase behavior of linear and partially flexible hard-sphere chain fluids and the solubility of hard spheres in hard-sphere chain fluids are studied by constant pressure Monte Carlo simulations. An extensive study on the phase behavior of linear fluids with a length of 7, 8, 9, 10, 11, 12, 13, 14, 15, and 20 beads is carried out. The phase behavior of partially flexible fluids with a total length of 8, 10, 14, and 15 beads and with different lengths for the linear part is also determined. A precise description of the reduced pressure and of the packing fraction change at the isotropic-nematic coexistence was achieved by performing long simulation runs. For linear fluids, a maximum in the isotropic to nematic packing fraction change is observed for a chain length of 15 beads. The infinite dilution solubility of hard spheres in linear and partially flexible hard-sphere chain fluids is calculated by the Widom test-particle insertion method. To identify the effect of chain connectivity and molecular anisotropy on free volume, solubility is expressed relative to that of hard spheres in a hard sphere fluid at same packing fraction as relative Henry's law constants. A linear relationship between relative Henry's law constants and packing fraction is observed for all linear fluids. Furthermore, this linearity is independent of liquid crystal ordering and seems to be independent of chain length for linear chains of 10 beads and longer. The same linear relationship was observed for the solubility of hard spheres in nematic forming partially flexible fluids for packing fractions up to a value slightly higher than the nematic packing fraction at the isotropic-nematic coexistence. At higher packing fractions, the small flexibility of these fluids seems to improve solubility in comparison with the linear fluids.
Non-hard sphere thermodynamic perturbation theory
NASA Astrophysics Data System (ADS)
Zhou, Shiqi
2011-08-01
A non-hard sphere (HS) perturbation scheme, recently advanced by the present author, is elaborated for several technical matters, which are key mathematical details for implementation of the non-HS perturbation scheme in a coupling parameter expansion (CPE) thermodynamic perturbation framework. NVT-Monte Carlo simulation is carried out for a generalized Lennard-Jones (LJ) 2n-n potential to obtain routine thermodynamic quantities such as excess internal energy, pressure, excess chemical potential, excess Helmholtz free energy, and excess constant volume heat capacity. Then, these new simulation data, and available simulation data in literatures about a hard core attractive Yukawa fluid and a Sutherland fluid, are used to test the non-HS CPE 3rd-order thermodynamic perturbation theory (TPT) and give a comparison between the non-HS CPE 3rd-order TPT and other theoretical approaches. It is indicated that the non-HS CPE 3rd-order TPT is superior to other traditional TPT such as van der Waals/HS (vdW/HS), perturbation theory 2 (PT2)/HS, and vdW/Yukawa (vdW/Y) theory or analytical equation of state such as mean spherical approximation (MSA)-equation of state and is at least comparable to several currently the most accurate Ornstein-Zernike integral equation theories. It is discovered that three technical issues, i.e., opening up new bridge function approximation for the reference potential, choosing proper reference potential, and/or using proper thermodynamic route for calculation of fex - ref, chiefly decide the quality of the non-HS CPE TPT. Considering that the non-HS perturbation scheme applies for a wide variety of model fluids, and its implementation in the CPE thermodynamic perturbation framework is amenable to high-order truncation, the non-HS CPE 3rd-order or higher order TPT will be more promising once the above-mentioned three technological advances are established.
Dynamics of hard sphere colloidal dispersions
NASA Technical Reports Server (NTRS)
Zhu, J. X.; Chaikin, Paul M.; Phan, S.-E.; Russel, W. B.
1994-01-01
Our objective is to perform on homogeneous, fully equilibrated dispersions the full set of experiments characterizing the transition from fluid to solid and the properties of the crystalline and glassy solid. These include measurements quantifying the nucleation and growth of crystallites, the structure of the initial fluid and the fully crystalline solid, and Brownian motion of particles within the crystal, and the elasticity of the crystal and the glass. Experiments are being built and tested for ideal microgravity environment. Here we describe the ground based effort, which exploits a fluidized bed to create a homogeneous, steady dispersion for the studies. The differences between the microgravity environment and the fluidized bed is gauged by the Peclet number Pe, which measures the rate of convection/sedimentation relative to Brownian motion. We have designed our experiment to accomplish three types of measurements on hard sphere suspensions in a fluidized bed: the static scattering intensity as a function of angle to determine the structure factor, the temporal autocorrelation function at all scattering angles to probe the dynamics, and the amplitude of the response to an oscillatory forcing to deduce the low frequency viscoelasticity. Thus the scattering instrument and the colloidal dispersion were chosen such as that the important features of each physical property lie within the detectable range for each measurement.
Dendritic Growth of Hard-Sphere Crystals. Experiment 34
NASA Technical Reports Server (NTRS)
Russel, W. B.; Chaikin, P. M.; Zhu, Ji-Xiang; Meyer, W. V.; Rogers, R.
1998-01-01
Recent observations of the disorder-order transition for colloidal hard spheres under microgravity revealed dendritic crystallites roughly 1-2 mm in size for samples in the coexistence region of the phase diagram. Order-of-magnitude estimates rationalize the absence of large or dendritic crystals under normal gravity and their stability to annealing in microgravity. A linear stability analysis of the Ackerson and Schaetzel model for crystallization of hard spheres establishes the domain of instability for diffusion-limited growth at small supersaturations. The relationship between hard-sphere and molecular crystal growth is established and exploited to relate the predicted linear instability to the well-developed dendrites observed.
Scaled particle theory for hard sphere pairs. I. Mathematical structure.
Stillinger, Frank H; Debenedetti, Pablo G; Chatterjee, Swaroop
2006-11-28
We develop an extension of the original Reiss-Frisch-Lebowitz scaled particle theory that can serve as a predictive method for the hard sphere pair correlation function g(r). The reversible cavity creation work is analyzed both for a single spherical cavity of arbitrary size, as well as for a pair of identical such spherical cavities with variable center-to-center separation. These quantities lead directly to a prediction of g(r). Smooth connection conditions have been identified between the small-cavity situation where the work can be exactly and completely expressed in terms of g(r), and the large-cavity regime where macroscopic properties become relevant. Closure conditions emerge which produce a nonlinear integral equation that must be satisfied by the pair correlation function. This integral equation has a structure which straightforwardly generates a solution that is a power series in density. The results of this series replicate the exact second and third virial coefficients for the hard sphere system via the contact value of the pair correlation function. The predicted fourth virial coefficient is approximately 0.6% lower than the known exact value. Detailed numerical analysis of the nonlinear integral equation has been deferred to the subsequent paper. PMID:17144712
Scaled particle theory for hard sphere pairs. I. Mathematical structure
NASA Astrophysics Data System (ADS)
Stillinger, Frank H.; Debenedetti, Pablo G.; Chatterjee, Swaroop
2006-11-01
We develop an extension of the original Reiss-Frisch-Lebowitz scaled particle theory that can serve as a predictive method for the hard sphere pair correlation function g(r ). The reversible cavity creation work is analyzed both for a single spherical cavity of arbitrary size, as well as for a pair of identical such spherical cavities with variable center-to-center separation. These quantities lead directly to a prediction of g(r ). Smooth connection conditions have been identified between the small-cavity situation where the work can be exactly and completely expressed in terms of g(r ), and the large-cavity regime where macroscopic properties become relevant. Closure conditions emerge which produce a nonlinear integral equation that must be satisfied by the pair correlation function. This integral equation has a structure which straightforwardly generates a solution that is a power series in density. The results of this series replicate the exact second and third virial coefficients for the hard sphere system via the contact value of the pair correlation function. The predicted fourth virial coefficient is approximately 0.6% lower than the known exact value. Detailed numerical analysis of the nonlinear integral equation has been deferred to the subsequent paper.
Inhomogeneous quasistationary state of dense fluids of inelastic hard spheres.
Fouxon, Itzhak
2014-05-01
We study closed dense collections of freely cooling hard spheres that collide inelastically with constant coefficient of normal restitution. We find inhomogeneous states (ISs) where the density profile is spatially nonuniform but constant in time. The states are exact solutions of nonlinear partial differential equations that describe the coupled distributions of density and temperature valid when inelastic losses of energy per collision are small. The derivation is performed without modeling the equations' coefficients that are unknown in the dense limit (such as the equation of state) using only their scaling form specific for hard spheres. Thus the IS is the exact state of this dense many-body system. It captures a fundamental property of inelastic collections of particles: the possibility of preserving nonuniform temperature via the interplay of inelastic cooling and heat conduction that generalizes previous results. We perform numerical simulations to demonstrate that arbitrary initial state evolves to the IS in the limit of long times where the container has the geometry of the channel. The evolution is like a gas-liquid transition. The liquid condenses in a vanishing part of the total volume but takes most of the mass of the system. However, the gaseous phase, which mass grows only logarithmically with the system size, is relevant because its fast particles carry most of the energy of the system. Remarkably, the system self-organizes to dissipate no energy: The inelastic decay of energy is a power law [1+t/t(c)](-2), where t(c) diverges in the thermodynamic limit. This is reinforced by observing that for supercritical systems the IS coincide in most of the space with the steady states of granular systems heated at one of the walls. We discuss the relation of our results to the recently proposed finite-time singularity in other container's geometries. PMID:25353790
Freezing, melting and the glass transition in a suspension of hard spheres
NASA Astrophysics Data System (ADS)
van Megen, W.
2002-08-01
When a suspension of hard spheres traverses the freezing volume fraction we find discontinuous changes in the character of the tagged particle density. In particular, the velocity auto-correlation function develops a negative algebraic decay and the fluctuations become subject to interruption. From these, and the exponent of the algebraic growth of the non-Gaussian parameter, the difference in mode of relaxation of the density fluctuations between the stable and metastable colloidal fluids can be quantified. A diagrammatic scheme is proposed that reconciles the dynamics of phase transitions observed in hard-sphere colloids.
Local order variations in confined hard-sphere fluids
NASA Astrophysics Data System (ADS)
Nygârd, Kim; Sarman, Sten; Kjellander, Roland
2013-10-01
Pair distributions of fluids confined between two surfaces at close distance are of fundamental importance for a variety of physical, chemical, and biological phenomena, such as interactions between macromolecules in solution, surface forces, and diffusion in narrow pores. However, in contrast to bulk fluids, properties of inhomogeneous fluids are seldom studied at the pair-distribution level. Motivated by recent experimental advances in determining anisotropic structure factors of confined fluids, we analyze theoretically the underlying anisotropic pair distributions of the archetypical hard-sphere fluid confined between two parallel hard surfaces using first-principles statistical mechanics of inhomogeneous fluids. For this purpose, we introduce an experimentally accessible ensemble-averaged local density correlation function and study its behavior as a function of confining slit width. Upon increasing the distance between the confining surfaces, we observe an alternating sequence of strongly anisotropic versus more isotropic local order. The latter is due to packing frustration of the spherical particles. This observation highlights the importance of studying inhomogeneous fluids at the pair-distribution level.
Depletion effects in smectic phases of hard-rod-hard-sphere mixtures.
Martínez-Ratón, Y; Cinacchi, G; Velasco, E; Mederos, L
2006-10-01
It is known that when hard spheres are added to a pure system of hard rods the stability of the smectic phase may be greatly enhanced, and that this effect can be rationalised in terms of depletion forces. In the present paper we first study the effect of orientational order on depletion forces in this particular binary system, comparing our results with those obtained adopting the usual approximation of considering the rods parallel and their orientations frozen. We consider mixtures with rods of different aspect ratios and spheres of different diameters, and we treat them within Onsager theory. Our results indicate that depletion effects, and consequently smectic stability, decrease significantly as a result of orientational disorder in the smectic phase when compared with corresponding data based on the frozen-orientation approximation. These results are discussed in terms of the tau parameter, which has been proposed as a convenient measure of depletion strength. We present closed expressions for tau, and show that it is intimately connected with the depletion potential. We then analyse the effect of particle geometry by comparing results pertaining to systems of parallel rods of different shapes (spherocylinders, cylinders and parallelepipeds). We finally provide results based on the Zwanzig approximation of a fundamental-measure density-functional theory applied to mixtures of parallelepipeds and cubes of different sizes. In this case, we show that the tau parameter exhibits a linear asymptotic behaviour in the limit of large values of the hard-rod aspect ratio, in conformity with Onsager theory, as well as in the limit of large values of the ratio of rod breadth to cube side length, d, in contrast to Onsager approximation, which predicts tau approximately d (3). Based on both this result and the Percus-Yevick approximation for the direct correlation function for a hard-sphere binary mixture in the same limit of infinite asymmetry, we speculate that, for
Solano-Altamirano, J M; Goldman, Saul
2015-12-01
We determined the total system elastic Helmholtz free energy, under the constraints of constant temperature and volume, for systems comprised of one or more perfectly bonded hard spherical inclusions (i.e. "hard spheres") embedded in a finite spherical elastic solid. Dirichlet boundary conditions were applied both at the surface(s) of the hard spheres, and at the outer surface of the elastic solid. The boundary conditions at the surface of the spheres were used to describe the rigid displacements of the spheres, relative to their initial location(s) in the unstressed initial state. These displacements, together with the initial positions, provided the final shape of the strained elastic solid. The boundary conditions at the outer surface of the elastic medium were used to ensure constancy of the system volume. We determined the strain and stress tensors numerically, using a method that combines the Neuber-Papkovich spherical harmonic decomposition, the Schwartz alternating method, and Least-squares for determining the spherical harmonic expansion coefficients. The total system elastic Helmholtz free energy was determined by numerically integrating the elastic Helmholtz free energy density over the volume of the elastic solid, either by a quadrature, or a Monte Carlo method, or both. Depending on the initial position of the hard sphere(s) (or equivalently, the shape of the un-deformed stress-free elastic solid), and the displacements, either stationary or non-stationary Helmholtz free energy minima were found. The non-stationary minima, which involved the hard spheres nearly in contact with one another, corresponded to lower Helmholtz free energies, than did the stationary minima, for which the hard spheres were further away from one another. PMID:26701708
Physics of Hard Spheres Experiment: Significant and Quantitative Findings Made
NASA Technical Reports Server (NTRS)
Doherty, Michael P.
2000-01-01
Direct examination of atomic interactions is difficult. One powerful approach to visualizing atomic interactions is to study near-index-matched colloidal dispersions of microscopic plastic spheres, which can be probed by visible light. Such spheres interact through hydrodynamic and Brownian forces, but they feel no direct force before an infinite repulsion at contact. Through the microgravity flight of the Physics of Hard Spheres Experiment (PHaSE), researchers have sought a more complete understanding of the entropically driven disorder-order transition in hard-sphere colloidal dispersions. The experiment was conceived by Professors Paul M. Chaikin and William B. Russel of Princeton University. Microgravity was required because, on Earth, index-matched colloidal dispersions often cannot be density matched, resulting in significant settling over the crystallization period. This settling makes them a poor model of the equilibrium atomic system, where the effect of gravity is truly negligible. For this purpose, a customized light-scattering instrument was designed, built, and flown by the NASA Glenn Research Center at Lewis Field on the space shuttle (shuttle missions STS 83 and STS 94). This instrument performed both static and dynamic light scattering, with sample oscillation for determining rheological properties. Scattered light from a 532- nm laser was recorded either by a 10-bit charge-coupled discharge (CCD) camera from a concentric screen covering angles of 0 to 60 or by sensitive avalanche photodiode detectors, which convert the photons into binary data from which two correlators compute autocorrelation functions. The sample cell was driven by a direct-current servomotor to allow sinusoidal oscillation for the measurement of rheological properties. Significant microgravity research findings include the observation of beautiful dendritic crystals, the crystallization of a "glassy phase" sample in microgravity that did not crystallize for over 1 year in 1g
Rowlinson’s concept of an effective hard sphere diameter
Henderson, Douglas
2010-01-01
Attention is drawn to John Rowlinson’s idea that the repulsive portion of the intermolecular interaction may be replaced by a temperature-dependent hard sphere diameter. It is this approximation that made the development of perturbation theory possible for realistic fluids whose intermolecular interactions have a steep, but finite, repulsion at short separations. PMID:20953320
Probing the evolution and morphology of hard carbon spheres
Pol, Vilas G.; Wen, Jianguo; Lau, Kah Chun; Callear, Samantha; Bowron, Daniel T.; Lin, Chi-Kai; Deshmukh, Sanket A.; Sankaranarayanan, Subramanian; Curtiss, Larry A.; David, William; Miller, Dean J.; Thackeray, Michael M.
2014-03-01
Monodispersed hard carbon spheres can be synthesized quickly and reproducibly by autogenic reactions of hydrocarbon precursors, notably polyethylene (including plastic waste), at high temperature and pressure. The carbon microparticles formed by this reaction have a unique spherical architecture, with a dominant internal nanometer layered motif, and they exhibit diamond-like hardness and electrochemical properties similar to graphite. In the present study, in-situ monitoring by X-ray diffraction along with electron microscopy, Raman spectroscopy, neutron pair-distribution function analysis, and computational modeling has been used to elucidate the morphology and evolution of the carbon spheres that form from the autogenic reaction of polyethylene at high temperature and pressure. A mechanism is proposed on how polyethylene evolves from a linear chain-based material to a layered carbon motif. Heating the spheres to 2400-2800 °C under inert conditions increases their graphitic character, particularly at the surface, which enhances their electrochemical and tribological properties.
Transport properties of highly asymmetric hard-sphere mixtures.
Bannerman, Marcus N; Lue, Leo
2009-04-28
The static and dynamic properties of binary mixtures of hard spheres with a diameter ratio of sigma(B)/sigma(A)=0.1 and a mass ratio of m(B)/m(A)=0.001 are investigated using event driven molecular dynamics. The contact values of the pair correlation functions are found to compare favorably with recently proposed theoretical expressions. The transport coefficients of the mixture, determined from simulation, are compared to the predictions of the revised Enskog theory using both a third-order Sonine expansion and direct simulation Monte Carlo. Overall, the Enskog theory provides a fairly good description of the simulation data, with the exception of systems at the smallest mole fraction of larger spheres (x(A)=0.01) examined. A "fines effect" was observed at higher packing fractions, where adding smaller spheres to a system of large spheres decreases the viscosity of the mixture; this effect is not captured by the Enskog theory. PMID:19405594
Transport properties of highly asymmetric hard-sphere mixtures
NASA Astrophysics Data System (ADS)
Bannerman, Marcus N.; Lue, Leo
2009-04-01
The static and dynamic properties of binary mixtures of hard spheres with a diameter ratio of σB/σA=0.1 and a mass ratio of mB/mA=0.001 are investigated using event driven molecular dynamics. The contact values of the pair correlation functions are found to compare favorably with recently proposed theoretical expressions. The transport coefficients of the mixture, determined from simulation, are compared to the predictions of the revised Enskog theory using both a third-order Sonine expansion and direct simulation Monte Carlo. Overall, the Enskog theory provides a fairly good description of the simulation data, with the exception of systems at the smallest mole fraction of larger spheres (xA=0.01) examined. A "fines effect" was observed at higher packing fractions, where adding smaller spheres to a system of large spheres decreases the viscosity of the mixture; this effect is not captured by the Enskog theory.
Clustering and gelation of hard spheres induced by the Pickering effect.
Fortini, Andrea
2012-04-01
A mixture of hard-sphere particles and model emulsion droplets is studied with a Brownian dynamics simulation. We find that the addition of nonwetting emulsion droplets to a suspension of pure hard spheres can lead to both gas-liquid and fluid-solid phase separations. Furthermore, we find a stable fluid of hard-sphere clusters. The stability is due to the saturation of the attraction that occurs when the surface of the droplets is completely covered with colloidal particles. At larger emulsion droplet densities a percolation transition is observed. The resulting networks of colloidal particles show dynamical and mechanical properties typical of a colloidal gel. The results of the model are in good qualitative agreement with recent experimental findings [E. Koos and N. Willenbacher, Science 331, 897 (2011)] in a mixture of colloidal particles and two immiscible fluids. PMID:22680411
Topological lifetimes of polydisperse colloidal hard spheres at a wall
NASA Astrophysics Data System (ADS)
Dullens, Roel P. A.; Kegel, Willem K.
2005-01-01
Confocal scanning laser microscopy was used to study the behavior of dense suspensions of model colloidal hard spheres at a single wall. Due to the slight polydispersity, our system shows a reentrant melting transition at high densities involving a hexatic structure [R. P. A. Dullens and W. K. Kegel, Phys. Rev. Lett 92, 195702 (2004)]. The reentrant melting transition is accompanied by an increase in the mean-squared displacement. The correlation between structure and dynamics was quantitatively analyzed on a single-particle level. In particular, the topological lifetime, being the average time that a particle spends having the same coordination number, is determined for all coordination numbers and as a function of volume fraction. The defective (non-sixfold-coordinated) particles exhibit shorter lifetimes than sixfold-coordinated particles, indicating that the mobility of the system is larger at or close to defective particles. The lifetime itself is a strong function of volume fraction. In particular, the global behavior of the mean-squared displacement is proportional to the hopping frequency (the inverse of the lifetime), showing that particles changing their coordination number contribute most to the local mobility.
Velocity and energy distributions in microcanonical ensembles of hard spheres.
Scalas, Enrico; Gabriel, Adrian T; Martin, Edgar; Germano, Guido
2015-08-01
In a microcanonical ensemble (constant NVE, hard reflecting walls) and in a molecular dynamics ensemble (constant NVEPG, periodic boundary conditions) with a number N of smooth elastic hard spheres in a d-dimensional volume V having a total energy E, a total momentum P, and an overall center of mass position G, the individual velocity components, velocity moduli, and energies have transformed beta distributions with different arguments and shape parameters depending on d, N, E, the boundary conditions, and possible symmetries in the initial conditions. This can be shown marginalizing the joint distribution of individual energies, which is a symmetric Dirichlet distribution. In the thermodynamic limit the beta distributions converge to gamma distributions with different arguments and shape or scale parameters, corresponding respectively to the Gaussian, i.e., Maxwell-Boltzmann, Maxwell, and Boltzmann or Boltzmann-Gibbs distribution. These analytical results agree with molecular dynamics and Monte Carlo simulations with different numbers of hard disks or spheres and hard reflecting walls or periodic boundary conditions. The agreement is perfect with our Monte Carlo algorithm, which acts only on velocities independently of positions with the collision versor sampled uniformly on a unit half sphere in d dimensions, while slight deviations appear with our molecular dynamics simulations for the smallest values of N. PMID:26382376
Velocity and energy distributions in microcanonical ensembles of hard spheres
NASA Astrophysics Data System (ADS)
Scalas, Enrico; Gabriel, Adrian T.; Martin, Edgar; Germano, Guido
2015-08-01
In a microcanonical ensemble (constant N V E , hard reflecting walls) and in a molecular dynamics ensemble (constant N V E PG , periodic boundary conditions) with a number N of smooth elastic hard spheres in a d -dimensional volume V having a total energy E , a total momentum P , and an overall center of mass position G , the individual velocity components, velocity moduli, and energies have transformed beta distributions with different arguments and shape parameters depending on d , N , E , the boundary conditions, and possible symmetries in the initial conditions. This can be shown marginalizing the joint distribution of individual energies, which is a symmetric Dirichlet distribution. In the thermodynamic limit the beta distributions converge to gamma distributions with different arguments and shape or scale parameters, corresponding respectively to the Gaussian, i.e., Maxwell-Boltzmann, Maxwell, and Boltzmann or Boltzmann-Gibbs distribution. These analytical results agree with molecular dynamics and Monte Carlo simulations with different numbers of hard disks or spheres and hard reflecting walls or periodic boundary conditions. The agreement is perfect with our Monte Carlo algorithm, which acts only on velocities independently of positions with the collision versor sampled uniformly on a unit half sphere in d dimensions, while slight deviations appear with our molecular dynamics simulations for the smallest values of N .
Replica exchange Monte Carlo applied to hard spheres.
Odriozola, Gerardo
2009-10-14
In this work a replica exchange Monte Carlo scheme which considers an extended isobaric-isothermal ensemble with respect to pressure is applied to study hard spheres (HSs). The idea behind the proposal is expanding volume instead of increasing temperature to let crowded systems characterized by dominant repulsive interactions to unblock, and so, to produce sampling from disjoint configurations. The method produces, in a single parallel run, the complete HS equation of state. Thus, the first order fluid-solid transition is captured. The obtained results well agree with previous calculations. This approach seems particularly useful to treat purely entropy-driven systems such as hard body and nonadditive hard mixtures, where temperature plays a trivial role. PMID:19831433
Self-consistent phonon theory of the crystallization and elasticity of attractive hard spheres.
Shin, Homin; Schweizer, Kenneth S
2013-02-28
We propose an Einstein-solid, self-consistent phonon theory for the crystal phase of hard spheres that interact via short-range attractions. The approach is first tested against the known behavior of hard spheres, and then applied to homogeneous particles that interact via short-range square well attractions and the Baxter adhesive hard sphere model. Given the crystal symmetry, packing fraction, and strength and range of attractive interactions, an effective harmonic potential experienced by a particle confined to its Wigner-Seitz cell and corresponding mean square vibrational amplitude are self-consistently calculated. The crystal free energy is then computed and, using separate information about the fluid phase free energy, phase diagrams constructed, including a first-order solid-solid phase transition and its associated critical point. The simple theory qualitatively captures all the many distinctive features of the phase diagram (critical and triple point, crystal-fluid re-entrancy, low-density coexistence curve) as a function of attraction range, and overall is in good semi-quantitative agreement with simulation. Knowledge of the particle localization length allows the crystal shear modulus to be estimated based on elementary ideas. Excellent predictions are obtained for the hard sphere crystal. Expanded and condensed face-centered cubic crystals are found to have qualitatively different elastic responses to varying attraction strength or temperature. As temperature increases, the expanded entropic solid stiffens, while the energy-controlled, fully-bonded dense solid softens. PMID:23464163
Monte Carlo methods: Application to hydrogen gas and hard spheres
NASA Astrophysics Data System (ADS)
Dewing, Mark Douglas
2001-08-01
Quantum Monte Carlo (QMC) methods are among the most accurate for computing ground state properties of quantum systems. The two major types of QMC we use are Variational Monte Carlo (VMC), which evaluates integrals arising from the variational principle, and Diffusion Monte Carlo (DMC), which stochastically projects to the ground state from a trial wave function. These methods are applied to a system of boson hard spheres to get exact, infinite system size results for the ground state at several densities. The kinds of problems that can be simulated with Monte Carlo methods are expanded through the development of new algorithms for combining a QMC simulation with a classical Monte Carlo simulation, which we call Coupled Electronic-Ionic Monte Carlo (CEIMC). The new CEIMC method is applied to a system of molecular hydrogen at temperatures ranging from 2800K to 4500K and densities from 0.25 to 0.46 g/cm3. VMC requires optimizing a parameterized wave function to find the minimum energy. We examine several techniques for optimizing VMC wave functions, focusing on the ability to optimize parameters appearing in the Slater determinant. Classical Monte Carlo simulations use an empirical interatomic potential to compute equilibrium properties of various states of matter. The CEIMC method replaces the empirical potential with a QMC calculation of the electronic energy. This is similar in spirit to the Car-Parrinello technique, which uses Density Functional Theory for the electrons and molecular dynamics for the nuclei. The challenges in constructing an efficient CEIMC simulation center mostly around the noisy results generated from the QMC computations of the electronic energy. We introduce two complementary techniques, one for tolerating the noise and the other for reducing it. The penalty method modifies the Metropolis acceptance ratio to tolerate noise without introducing a bias in the simulation of the nuclei. For reducing the noise, we introduce the two-sided energy
Using compressibility factor as a predictor of confined hard-sphere fluid dynamics.
Mittal, Jeetain
2009-10-22
We study the correlations between the diffusivity (or viscosity) and the compressibility factor of bulk hard-sphere fluid as predicted by the ultralocal limit of the barrier hopping theory. Our specific aim is to determine if these correlations observed in the bulk equilibrium hard-sphere fluid can be used to predict the self-diffusivity of fluid confined between a slit-pore or a rectangular channel. In this work, we consider a single-component and a binary mixture of hard spheres. To represent confining walls, we use purely reflecting hard walls and interacting square-well walls. Our results clearly show that the correspondence between the diffusivity and the compressibility factor can be used along with the knowledge of the confined fluid's compressibility factor to predict its diffusivity with quantitative accuracy. Our analysis also suggests that a simple measure, the average fluid density, can be an accurate predictor of confined fluid diffusivity for very tight confinements ( approximately 2-3 particle diameters wide) at low to intermediate density conditions. Together, these results provide further support for the idea that one can use robust connections between thermodynamic and dynamic quantities to predict dynamics of confined fluids from their thermodynamics. PMID:19702285
Using compressibility factor as a predictor of confined hard-sphere fluid dynamics
Mittal, Jeetain
2009-01-01
We study the correlations between the diffusivity (or viscosity) and the compressibility factor of bulk hard-sphere fluid as predicted by the ultralocal limit of the barrier hopping theory. Our specific aim is to determine if these correlations observed in the bulk equilibrium hard-sphere fluid can be used to predict the self-diffusivity of fluid confined between a slit-pore or a rectangular channel. In this work, we consider a single-component and a binary mixture of hard spheres. To represent confining walls, we use purely reflecting hard walls and interacting square-well walls. Our results clearly show that the correspondence between the diffusivity and the compressibility factor can be used along with the knowledge of the confined fluid's compressibility factor to predict its diffusivity with quantitative accuracy. Our analysis also suggests that a simple measure, the average fluid density, can be an accurate predictor of confined fluid diffusivity for very tight confinements (≈ 2-3 particle diameters wide) at low to intermediate density conditions. Together, these results provide further support for the idea that one can use robust connections between thermodynamic and dynamic quantities to predict dynamics of confined fluids from their thermodynamics. PMID:19702285
Simple liquids’ quasiuniversality and the hard-sphere paradigm
NASA Astrophysics Data System (ADS)
Dyre, Jeppe C.
2016-08-01
This topical review discusses the quasiuniversality of simple liquids’ structure and dynamics and two possible justifications of it. The traditional one is based on the van der Waals picture of liquids in which the hard-sphere system reflects the basic physics. An alternative explanation argues that all quasiuniversal liquids to a good approximation conform to the same equation of motion, referring to the exponentially repulsive pair-potential system as the basic reference system. The paper, which is aimed at non-experts, ends by listing a number of open problems in the field.
Simple liquids' quasiuniversality and the hard-sphere paradigm.
Dyre, Jeppe C
2016-08-17
This topical review discusses the quasiuniversality of simple liquids' structure and dynamics and two possible justifications of it. The traditional one is based on the van der Waals picture of liquids in which the hard-sphere system reflects the basic physics. An alternative explanation argues that all quasiuniversal liquids to a good approximation conform to the same equation of motion, referring to the exponentially repulsive pair-potential system as the basic reference system. The paper, which is aimed at non-experts, ends by listing a number of open problems in the field. PMID:27345623
New closed virial equation of state for hard-sphere fluids.
Tian, Jianxiang; Gui, Yuanxing; Mulero, Angel
2010-10-28
A new closed virial equation of state of hard-sphere fluids is proposed which reproduces the calculated or estimated values of the first 16 virial coefficients and at the same time gives very good accuracy when compared with computer simulation data for the compressibility factor over the entire fluid range, as well as having a pole at the correct closest packing density. PMID:20883000
Hoppe, Travis
2013-01-01
We compute the singular value decomposition of the radial distribution function for hard sphere, and square well solutions. We find that decomposes into a small set of basis vectors allowing for an extremely accurate representation at all interpolated densities and potential strengths. In addition, we find that the coefficient vectors describing the magnitude of each basis vector are well described by a low-order polynomial. We provide a program to calculate in this compact representation for the investigated parameter range. PMID:24143174
Thermodynamics of dipolar hard spheres with low-to-intermediate coupling constants.
Elfimova, Ekaterina A; Ivanov, Alexey O; Camp, Philip J
2012-08-01
The thermodynamic properties of the dipolar hard-sphere fluid are studied using theory and simulation. A new theory is derived using a convenient mathematical approximation for the Helmholtz free energy relative to that for the hard-sphere fluid. The approximation is designed to give the correct low-density virial expansion. New theoretical and numerical results for the fourth virial coefficient are given. Predictions of thermodynamic functions for dipolar coupling constants λ=1 and 2 show excellent agreement with simulation results, even at the highest value of the particle volume fraction φ. For higher values of λ, there are deviations at high volume fractions, but the correct low-density behavior is retained. The theory is compared critically against the established thermodynamic perturbation theory; it gives significant improvements at low densities and is more convenient in terms of the required numerics. Dipolar hard spheres provide a basic model for ferrofluids, and the theory is accurate for typical experimental parameters λ
Thermodynamic perturbation theory for fused hard-sphere and hard-disk chain fluids
Zhou, Y.; Hall, C.K.; Stell, G.
1995-08-15
We find that first-order thermodynamic perturbation theory (TPT1) which incorporates the reference monomer fluid used in the generalized Flory--{ital AB} (GF--{ital AB}) theory yields an equation of state for fused hard-sphere (FHS) chain fluids that has accuracy comparable to the GF--{ital AB} and GF--dimer--{ital AC} theories. The new TPT1 equation of state is significantly more accurate than other extensions of the TPT1 theory to FHS chain fluids. The TPT1 is also extended to two-dimensional fused hard-disk chain fluids. For the fused hard-disk dimer fluid, the extended TPT1 equation of state is found to be more accurate than the Boublik hard-disk dimer equation of state. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
Compact Collision Kernels for Hard Sphere and Coulomb Cross Sections; Fokker-Planck Coefficients
Chang Yongbin; Shizgal, Bernie D.
2008-12-31
A compact collision kernel is derived for both hard sphere and Coulomb cross sections. The difference between hard sphere interaction and Coulomb interaction is characterized by a parameter {eta}. With this compact collision kernel, the calculation of Fokker-Planck coefficients can be done for both the Coulomb and hard sphere interactions. The results for arbitrary order Fokker-Planck coefficients are greatly simplified. An alternate form for the Coulomb logarithm is derived with concern to the temperature relaxation in a binary plasma.
Astillero, Antonio; Santos, Andrés
2005-09-01
In the preceding paper, we have conjectured that the main transport properties of a dilute gas of inelastic hard spheres (IHSs) can be satisfactorily captured by an equivalent gas of elastic hard spheres (EHSs), provided that the latter are under the action of an effective drag force and their collision rate is reduced by a factor (1+alpha)/2 (where alpha is the constant coefficient of normal restitution). In this paper we test the above expectation in a paradigmatic nonequilibrium state, namely, the simple or uniform shear flow, by performing Monte Carlo computer simulations of the Boltzmann equation for both classes of dissipative gases with a dissipation range 0.5 < or = alpha < or = 0.95 and two values of the imposed shear rate a. It is observed that the evolution toward the steady state proceeds in two stages: a short kinetic stage (strongly dependent on the initial preparation of the system) followed by a slower hydrodynamic regime that becomes increasingly less dependent on the initial state. Once conveniently scaled, the intrinsic quantities in the hydrodynamic regime depend on time, at a given value of alpha, only through the reduced shear rate a*(t) is proportional to a/square root(T(t)), until a steady state, independent of the imposed shear rate and of the initial preparation, is reached. The distortion of the steady-state velocity distribution from the local equilibrium state is measured by the shear stress, the normal stress differences, the cooling rate, the fourth and sixth cumulants, and the shape of the distribution itself. In particular, the simulation results seem to be consistent with an exponential overpopulation of the high-velocity tail. These properties are common to both the IHS and EHS systems. In addition, the EHS results are in general hardly distinguishable from the IHS ones if alpha approximately > 0.7, so that the distinct signature of the IHS gas (higher anisotropy and overpopulation) only manifests itself at relatively high
NASA Astrophysics Data System (ADS)
Hanifpour, M.; Francois, N.; Robins, V.; Kingston, A.; Vaez Allaei, S. M.; Saadatfar, M.
2015-06-01
Here we present an experimental and numerical investigation on the grain-scale geometrical and mechanical properties of partially crystallized structures made of macroscopic frictional grains. Crystallization is inevitable in arrangements of monosized hard spheres with packing densities exceeding Bernal's limiting density ϕBernal≈0.64 . We study packings of monosized hard spheres whose density spans over a wide range (0.59 <ϕ <0.72 ) . These experiments harness x-ray computed tomography, three-dimensional image analysis, and numerical simulations to access precisely the geometry and the 3D structure of internal forces within the sphere packings. We show that clear geometrical transitions coincide with modifications of the mechanical backbone of the packing both at the grain and global scale. Notably, two transitions are identified at ϕBernal≈0.64 and ϕc≈0.68 . These results provide insights on how geometrical and mechanical features at the grain scale conspire to yield partially crystallized structures that are mechanically stable.
Hanifpour, M; Francois, N; Robins, V; Kingston, A; Allaei, S M Vaez; Saadatfar, M
2015-06-01
Here we present an experimental and numerical investigation on the grain-scale geometrical and mechanical properties of partially crystallized structures made of macroscopic frictional grains. Crystallization is inevitable in arrangements of monosized hard spheres with packing densities exceeding Bernal's limiting density ϕ(Bernal)≈0.64. We study packings of monosized hard spheres whose density spans over a wide range (0.59<ϕ<0.72). These experiments harness x-ray computed tomography, three-dimensional image analysis, and numerical simulations to access precisely the geometry and the 3D structure of internal forces within the sphere packings. We show that clear geometrical transitions coincide with modifications of the mechanical backbone of the packing both at the grain and global scale. Notably, two transitions are identified at ϕ(Bernal)≈0.64 and ϕ(c)≈0.68. These results provide insights on how geometrical and mechanical features at the grain scale conspire to yield partially crystallized structures that are mechanically stable. PMID:26172700
Detecting Phase Boundaries in Hard-Sphere Suspensions
NASA Technical Reports Server (NTRS)
McDowell, Mark; Rogers, Richard B.; Gray, Elizabeth
2009-01-01
A special image-data-processing technique has been developed for use in experiments that involve observation, via optical microscopes equipped with electronic cameras, of moving boundaries between the colloidal-solid and colloidal-liquid phases of colloidal suspensions of monodisperse hard spheres. During an experiment, it is necessary to adjust the position of a microscope to keep the phase boundary within view. A boundary typically moves at a speed of the order of microns per hour. Because an experiment can last days or even weeks, it is impractical to require human intervention to keep the phase boundary in view. The present image-data-processing technique yields results within a computation time short enough to enable generation of automated-microscope-positioning commands to track the moving phase boundary
Simple effective rule to estimate the jamming packing fraction of polydisperse hard spheres.
Santos, Andrés; Yuste, Santos B; López de Haro, Mariano; Odriozola, Gerardo; Ogarko, Vitaliy
2014-04-01
A recent proposal in which the equation of state of a polydisperse hard-sphere mixture is mapped onto that of the one-component fluid is extrapolated beyond the freezing point to estimate the jamming packing fraction ϕJ of the polydisperse system as a simple function of M1M3/M22, where Mk is the kth moment of the size distribution. An analysis of experimental and simulation data of ϕJ for a large number of different mixtures shows a remarkable general agreement with the theoretical estimate. To give extra support to the procedure, simulation data for seventeen mixtures in the high-density region are used to infer the equation of state of the pure hard-sphere system in the metastable region. An excellent collapse of the inferred curves up to the glass transition and a significant narrowing of the different out-of-equilibrium glass branches all the way to jamming are observed. Thus, the present approach provides an extremely simple criterion to unify in a common framework and to give coherence to data coming from very different polydisperse hard-sphere mixtures. PMID:24827171
NASA Astrophysics Data System (ADS)
Henderson, D.; Plischke, M.
1987-04-01
Starting from well-known relations for the derivatives of the radial distribution functions of a mixture of fluids, and allowing the diameter of one particle to become exceedingly large, three sum rules for a fluid with density inhomogeneities are obtained. None of these sum rules are new. However, the relation between the Lovett-Mou-Buff-Wertheim and the Born-Green hierarchy of equations seems not well known. The accuracy of a recent parametrization of the pair correlation of hard spheres near a hard wall and of the solutions of the Percus-Yevick and hypernetted-chain equation for this same function are examined by determination of how well these functions satisfy these sum rules and the accuracy of their surface tension, calculated from the sum rule of Triezenberg and Zwanzig. Generally speaking, the Percus-Yevick theory gives the best results and the hypernetted-chain approximation gives the worst results with the parametrization being intermediate.
Hard-sphere kinetic models for inert and reactive mixtures.
Polewczak, Jacek
2016-10-19
I consider stochastic variants of a simple reacting sphere (SRS) kinetic model (Xystris and Dahler 1978 J. Chem. Phys. 68 387-401, Qin and Dahler 1995 J. Chem. Phys. 103 725-50, Dahler and Qin 2003 J. Chem. Phys. 118 8396-404) for dense reacting mixtures. In contrast to the line-of-center models of chemical reactive models, in the SRS kinetic model, the microscopic reversibility (detailed balance) can be easily shown to be satisfied, and thus all mathematical aspects of the model can be fully justified. In the SRS model, the molecules behave as if they were single mass points with two internal states. Collisions may alter the internal states of the molecules, and this occurs when the kinetic energy associated with the reactive motion exceeds the activation energy. Reactive and non-reactive collision events are considered to be hard sphere-like. I consider a four component mixture A, B, A (*), B (*), in which the chemical reactions are of the type [Formula: see text], with A (*) and B (*) being distinct species from A and B. This work extends the joined works with George Stell to the kinetic models of dense inert and reactive mixtures. The idea of introducing smearing-type effect in the collisional process results in a new class of stochastic kinetic models for both inert and reactive mixtures. In this paper the important new mathematical properties of such systems of kinetic equations are proven. The new results for stochastic revised Enskog system for inert mixtures are also provided. PMID:27545341
Simple and accurate theory for strong shock waves in a dense hard-sphere fluid.
Montanero, J M; López de Haro, M; Santos, A; Garzó, V
1999-12-01
Following an earlier work by Holian et al. [Phys. Rev. E 47, R24 (1993)] for a dilute gas, we present a theory for strong shock waves in a hard-sphere fluid described by the Enskog equation. The idea is to use the Navier-Stokes hydrodynamic equations but taking the temperature in the direction of shock propagation rather than the actual temperature in the computation of the transport coefficients. In general, for finite densities, this theory agrees much better with Monte Carlo simulations than the Navier-Stokes and (linear) Burnett theories, in contrast to the well-known superiority of the Burnett theory for dilute gases. PMID:11970718
Jamming transition and inherent structures of hard spheres and disks.
Ozawa, Misaki; Kuroiwa, Takeshi; Ikeda, Atsushi; Miyazaki, Kunimasa
2012-11-16
Recent studies show that volume fractions φ(J) at the jamming transition of frictionless hard spheres and disks are not uniquely determined but exist over a continuous range. Motivated by this observation, we numerically investigate the dependence of φ(J) on the initial configurations of the parent fluid equilibrated at a volume fraction φ(eq), before compressing to generate a jammed packing. We find that φ(J) remains constant when φ(eq) is small but sharply increases as φ(eq) exceeds the dynamic transition point which the mode-coupling theory predicts. We carefully analyze configurational properties of both jammed packings and parent fluids and find that, while all jammed packings remain isostatic, the increase of φ(J) is accompanied with subtle but distinct changes of local orders, a static length scale, and an exponent of the finite-size scaling. These results are consistent with the scenario of the random first-order transition theory of the glass transition. PMID:23215507
NASA Astrophysics Data System (ADS)
Wang, Lin; An, Xizhong; Wang, Defeng; Qian, Quan
2016-01-01
Quantitative characterization on the topological and metrical properties of radical subunits (polyhedra) for two new ternary hard sphere crystals was studied. These two ideal crystalline structures are numerically constructed by filling small and medium spheres into interstices (corresponding to regular tetrahedral and octahedral pores) of perfect face centered cubic (FCC) and hexagonal close packed (HCP) crystals formed by the packing of large spheres. Topological properties such as face number, edge number, vertex number of each radical polyhedron (RP), edge number of each RP face and metrical properties such as volume, surface area, total perimeter and pore volume of each RP, area and perimeter of each RP face were analyzed and compared. The results show that even though the overall packing densities for FCC and HCP ternary crystals are the same, different characteristics of radical polyhedra for corresponding spheres in these two crystals can be identified. That is, in the former structure RPs are more symmetric than those in the latter; the orientations of corresponding RP in the latter are twice as many as that in the former. Moreover, RP topological and metrical properties in the HCP ternary crystal are much more complicated than those in the FCC ternary crystal. These differences imply the structure and property differences of these two ternary crystals. Analyses of RPs provide intensive understanding of pores in the structure.
Klatt, Michael A; Torquato, Salvatore
2016-08-01
In the first paper of this series, we introduced Voronoi correlation functions to characterize the structure of maximally random jammed (MRJ) sphere packings across length scales. In the present paper, we determine a variety of different correlation functions that arise in rigorous expressions for the effective physical properties of MRJ sphere packings and compare them to the corresponding statistical descriptors for overlapping spheres and equilibrium hard-sphere systems. Such structural descriptors arise in rigorous bounds and formulas for effective transport properties, diffusion and reactions constants, elastic moduli, and electromagnetic characteristics. First, we calculate the two-point, surface-void, and surface-surface correlation functions, for which we derive explicit analytical formulas for finite hard-sphere packings. We show analytically how the contact Dirac delta function contribution to the pair correlation function g_{2}(r) for MRJ packings translates into distinct functional behaviors of these two-point correlation functions that do not arise in the other two models examined here. Then we show how the spectral density distinguishes the MRJ packings from the other disordered systems in that the spectral density vanishes in the limit of infinite wavelengths; i.e., these packings are hyperuniform, which means that density fluctuations on large length scales are anomalously suppressed. Moreover, for all model systems, we study and compute exclusion probabilities and pore size distributions, as well as local density fluctuations. We conjecture that for general disordered hard-sphere packings, a central limit theorem holds for the number of points within an spherical observation window. Our analysis links problems of interest in material science, chemistry, physics, and mathematics. In the third paper of this series, we will evaluate bounds and estimates of a host of different physical properties of the MRJ sphere packings that are based on the
NASA Astrophysics Data System (ADS)
Wu, Liang; Malijevský, Alexandr; Jackson, George; Müller, Erich A.; Avendaño, Carlos
2015-07-01
We study the structure and fluid-phase behaviour of binary mixtures of hard spheres (HSs) and hard spherocylinders (HSCs) in isotropic and nematic states using the NPnAT ensemble Monte Carlo (MC) approach in which the normal component of the pressure tensor is fixed in a system confined between two hard walls. The method allows one to estimate the location of the isotropic-nematic phase transition and to observe the asymmetry in the composition between the coexisting phases, with the expected enhancement of the HSC concentration in the nematic phase. This is in stark contrast with the previously reported MC simulations where a conventional isotropic NPT ensemble was used. We further compare the simulation results with the theoretical predictions of two analytic theories that extend the original Parsons-Lee theory using the one-fluid and the many-fluid approximations [Malijevský et al., J. Chem. Phys. 129, 144504 (2008)]. In the one-fluid version of the theory, the properties of the mixture are related to an effective one-component HS system, while in the many-fluid theory, the components of the mixtures are represented as separate effective HS particles. The comparison reveals that both the one- and the many-fluid approaches provide a reasonably accurate quantitative description of the mixture including the predictions of the isotropic-nematic phase boundary and degree of orientational order of the HSC-HS mixture.
PREPARATION OF HIGH-DENSITY THORIUM OXIDE SPHERES
McNees, R.A. Jr.; Taylor, A.J.
1963-12-31
A method of preparing high-density thorium oxide spheres for use in pellet beds in nuclear reactors is presented. Sinterable thorium oxide is first converted to free-flowing granules by means such as compression into a compact and comminution of the compact. The granules are then compressed into cubes having a density of 5.0 to 5.3 grams per cubic centimeter. The cubes are tumbled to form spheres by attrition, and the spheres are then fired at 1250 to 1350 deg C. The fired spheres are then polished and fired at a temperature above 1650 deg C to obtain high density. Spherical pellets produced by this method are highly resistant to mechanical attrition hy water. (AEC)
Transport coefficients of a granular gas of inelastic rough hard spheres
NASA Astrophysics Data System (ADS)
Kremer, Gilberto M.; Santos, Andrés; Garzó, Vicente
2014-08-01
The Boltzmann equation for inelastic and rough hard spheres is considered as a model of a dilute granular gas. In this model, the collisions are characterized by constant coefficients of normal and tangential restitution, and hence the translational and rotational degrees of freedom are coupled. A normal solution to the Boltzmann equation is obtained by means of the Chapman-Enskog method for states near the homogeneous cooling state. The analysis is carried out to first order in the spatial gradients of the number density, the flow velocity, and the granular temperature. The constitutive equations for the momentum and heat fluxes and for the cooling rate are derived, and the associated transport coefficients are expressed in terms of the solutions of linear integral equations. For practical purposes, a first Sonine approximation is used to obtain explicit expressions of the transport coefficients as nonlinear functions of both coefficients of restitution and the moment of inertia. Known results for purely smooth inelastic spheres and perfectly elastic and rough spheres are recovered in the appropriate limits.
Solubilities of Solutes in Ionic Liquids from a SimplePerturbed-Hard-Sphere Theory
Qin, Yuan; Prausnitz, John M.
2005-09-20
In recent years, several publications have provided solubilities of ordinary gases and liquids in ionic liquids. This work reports an initial attempt to correlate the experimental data using a perturbed-hard-sphere theory; the perturbation is based on well-known molecular physics when the solution is considered as a dielectric continuum. For this correlation, the most important input parameters are hard-sphere diameters of the solute and of the cation and anion that constitute the ionic liquid. In addition, the correlation uses the solvent density and the solute's polarizability and dipole and quadrupole moments, if any. Dispersion-energy parameters are obtained from global correlation of solubility data. Results are given for twenty solutes in several ionic liquids at normal temperatures; in addition, some results are given for gases in two molten salts at very high temperatures. Because the theory used here is much simplified, and because experimental uncertainties (especially for gaseous solutes) are often large, the accuracy of the correlation presented here is not high; in general, predicted solubilities (Henry's constants) agree with experiment to within roughly {+-} 70%. As more reliable experimental data become available, modifications in the characterizing parameters are likely to improve accuracy. Nevertheless, even in its present form, the correlation may be useful for solvent screening in engineering design.
Paricaud, P.
2015-07-28
A simple modification of the Boublík-Mansoori-Carnahan-Starling-Leland equation of state is proposed for an application to the metastable disordered region. The new model has a positive pole at the jamming limit and can accurately describe the molecular simulation data of pure hard in the stable fluid region and along the metastable branch. The new model has also been applied to binary mixtures hard spheres, and an excellent description of the fluid and metastable branches can be obtained by adjusting the jamming packing fraction. The new model for hard sphere mixtures can be used as the repulsive term of equations of state for real fluids. In this case, the modified equations of state give very similar predictions of thermodynamic properties as the original models, and one can remove the multiple liquid density roots observed for some versions of the Statistical Associating Fluid Theory (SAFT) at low temperature without any modification of the dispersion term.
Phase behavior of binary hard-sphere mixtures from perturbation theory.
Velasco, E; Navascués, G; Mederos, L
1999-09-01
Using a first-order perturbation theory, we have studied the phase diagram of a binary mixture of hard spheres for different values of the size ratio. Recent models for the two-body depletion potential between large spheres are used to take into account the role of the small spheres. The theory predicts a complex phase diagram including a fluid-solid transition at high packing fraction of small spheres, metastability of fluid-fluid demixing, an isostructural solid-solid transition at high packing fraction of the large spheres for sufficiently small values of the size ratio q of the spheres, and the tendency to sticky-sphere behavior in the limit q-->0. The agreement with recent simulation results is quite good. We also show that this phenomenology was already implicit in the pioneering work of Asakura and Oosawa. PMID:11970123
Stochastic Hard-Sphere Dynamics for Hydrodynamics of Non-Ideal Fluids
Donev, A; Alder, B J; Garcia, A L
2008-02-26
A novel stochastic fluid model is proposed with a nonideal structure factor consistent with compressibility, and adjustable transport coefficients. This stochastic hard-sphere dynamics (SHSD) algorithm is a modification of the direct simulation Monte Carlo algorithm and has several computational advantages over event-driven hard-sphere molecular dynamics. Surprisingly, SHSD results in an equation of state and a pair correlation function identical to that of a deterministic Hamiltonian system of penetrable spheres interacting with linear core pair potentials. The fluctuating hydrodynamic behavior of the SHSD fluid is verified for the Brownian motion of a nanoparticle suspended in a compressible solvent.
Costa, L.A.; Zhou, Y.; Hall, C.K.; Carra, S.
1995-04-15
We report Monte Carlo simulation results for the bulk pressure of fused-hard-sphere (FHS) chain fluids with bond-length-to-bead-diameter ratios {approx} 0.4 at chain lengths {ital n}=4, 8 and 16. We also report density profiles for FHS chain fluids at a hard wall. The results for the compressibility factor are compared to results from extensions of the Generalized Flory (GF) and Generalized Flory Dimer (GFD) theories proposed by Yethiraj {ital et} {ital al}. and by us. Our new GF theory, GF-AB, significantly improves the prediction of the bulk pressure of fused-hard-sphere chains over the GFD theories proposed by Yethiraj {ital et} {ital al}. and by us although the GFD theories give slightly better low-density results. The GFD-A theory, the GFD-B theory and the new theories (GF-AB, GFD-AB, and GFD-AC) satisfy the exact zero-bonding-length limit. All theories considered recover the GF or GFD theories at the tangent hard-sphere chain limit.
Variational Monte Carlo study of soliton excitations in hard-sphere Bose gases
NASA Astrophysics Data System (ADS)
Rota, R.; Giorgini, S.
2015-10-01
By using a full many-body approach, we calculate the excitation energy, the effective mass, and the density profile of soliton states in a three-dimensional Bose gas of hard spheres at zero temperature. The many-body wave function used to describe the soliton contains a one-body term, derived from the solution of the Gross-Pitaevskii equation, and a two-body Jastrow term, which accounts for the repulsive correlations between atoms. We optimize the parameters in the many-body wave function via a variational Monte Carlo procedure, calculating the grand-canonical energy and the canonical momentum of the system in a moving reference frame where the soliton is stationary. As the density of the gas is increased, significant deviations from the mean-field predictions are found for the excitation energy and the density profile of both dark and gray solitons. In particular, the soliton effective mass m* and the mass m Δ N of missing particles in the region of the density depression are smaller than the result from the Gross-Pitaevskii equation, their ratio, however, being well reproduced by this theory up to large values of the gas parameter. We also calculate the profile of the condensate density around the soliton notch, finding good agreement with the prediction of the local-density approximation.
Jamming II: Edwards’ statistical mechanics of random packings of hard spheres
NASA Astrophysics Data System (ADS)
Wang, Ping; Song, Chaoming; Jin, Yuliang; Makse, Hernán A.
2011-02-01
The problem of finding the most efficient way to pack spheres has an illustrious history, dating back to the crystalline arrays conjectured by Kepler and the random geometries explored by Bernal in the 1960s. This problem finds applications spanning from the mathematician’s pencil, the processing of granular materials, the jamming and glass transitions, all the way to fruit packing in every grocery. There are presently numerous experiments showing that the loosest way to pack spheres gives a density of ∼55% (named random loose packing, RLP) while filling all the loose voids results in a maximum density of ∼63%-64% (named random close packing, RCP). While those values seem robustly true, to this date there is no well-accepted physical explanation or theoretical prediction for them. Here we develop a common framework for understanding the random packings of monodisperse hard spheres whose limits can be interpreted as the experimentally observed RLP and RCP. The reason for these limits arises from a statistical picture of jammed states in which the RCP can be interpreted as the ground state of the ensemble of jammed matter with zero compactivity, while the RLP arises in the infinite compactivity limit. We combine an extended statistical mechanics approach ‘a la Edwards’ (where the role traditionally played by the energy and temperature in thermal systems is substituted by the volume and compactivity) with a constraint on mechanical stability imposed by the isostatic condition. We show how such approaches can bring results that can be compared to experiments and allow for an exploitation of the statistical mechanics framework. The key result is the use of a relation between the local Voronoi volumes of the constituent grains (denoted the volume function) and the number of neighbors in contact that permits us to simply combine the two approaches to develop a theory of volume fluctuations in jammed matter. Ultimately, our results lead to a phase diagram that
Hard-sphere fluid adsorbed in an annular wedge: The depletion force of hard-body colloidal physics
NASA Astrophysics Data System (ADS)
Herring, A. R.; Henderson, J. R.
2007-01-01
Many important issues of colloidal physics can be expressed in the context of inhomogeneous fluid phenomena. When two large colloids approach one another in solvent, they interact at least partly by the response of the solvent to finding itself adsorbed in the annular wedge formed between the two colloids. At shortest range, this fluid mediated interaction is known as the depletion force/interaction because solvent is squeezed out of the wedge when the colloids approach closer than the diameter of a solvent molecule. An equivalent situation arises when a single colloid approaches a substrate/wall. Accurate treatment of this interaction is essential for any theory developed to model the phase diagrams of homogeneous and inhomogeneous colloidal systems. The aim of our paper is a test of whether or not we possess sufficient knowledge of statistical mechanics that can be trusted when applied to systems of large size asymmetry and the depletion force in particular. When the colloid particles are much larger than a solvent diameter, the depletion force is dominated by the effective two-body interaction experienced by a pair of solvated colloids. This low concentration limit of the depletion force has therefore received considerable attention. One route, which can be rigorously based on statistical mechanical sum rules, leads to an analytic result for the depletion force when evaluated by a key theoretical tool of colloidal science known as the Derjaguin approximation. A rival approach has been based on the assumption that modern density functional theories (DFT) can be trusted for systems of large size asymmetry. Unfortunately, these two theoretical predictions differ qualitatively for hard sphere models, as soon as the solvent density is higher than about 2/3 that at freezing. Recent theoretical attempts to understand this dramatic disagreement have led to the proposal that the Derjaguin and DFT routes represent opposite limiting behavior, for very large size asymmetry
A Thermodynamically-Consistent Non-Ideal Stochastic Hard-Sphere Fluid
Donev, A; Alder, B J; Garcia, A L
2009-08-03
A grid-free variant of the Direct Simulation Monte Carlo (DSMC) method is proposed, named the Isotropic DSMC (I-DSMC) method, that is suitable for simulating collision-dominated dense fluid flows. The I-DSMC algorithm eliminates all grid artifacts from the traditional DSMC algorithm and is Galilean invariant and microscopically isotropic. The stochastic collision rules in I-DSMC are modified to introduce a non-ideal structure factor that gives consistent compressibility, as first proposed in [Phys. Rev. Lett. 101:075902 (2008)]. The resulting Stochastic Hard Sphere Dynamics (SHSD) fluid is empirically shown to be thermodynamically identical to a deterministic Hamiltonian system of penetrable spheres interacting with a linear core pair potential, well-described by the hypernetted chain (HNC) approximation. We develop a kinetic theory for the SHSD fluid to obtain estimates for the transport coefficients that are in excellent agreement with particle simulations over a wide range of densities and collision rates. The fluctuating hydrodynamic behavior of the SHSD fluid is verified by comparing its dynamic structure factor against theory based on the Landau-Lifshitz Navier-Stokes equations. We also study the Brownian motion of a nano-particle suspended in an SHSD fluid and find a long-time power-law tail in its velocity autocorrelation function consistent with hydrodynamic theory and molecular dynamics calculations.
Relaxation rates in the Maxwellian collision model and its variable hard sphere surrogate
NASA Astrophysics Data System (ADS)
Rubinstein, Robert
2015-08-01
The variable hard sphere and related models have proven to be accurate and computationally convenient replacements for the inverse power law model of classical kinetic theory in direct simulation Monte Carlo calculations. We attempt to provide theoretical support for this remarkable success by comparing the relaxation rates in the linearized Boltzmann equation for the Maxwellian collision model with those of its variable hard sphere surrogate. The comparison demonstrates that the linearized collision operator with variable hard sphere interactions can accurately approximate the linearized collision operator with Maxwellian inverse power law interactions under well-defined and broadly applicable conditions. Extensions of the analysis to the general inverse power law model and to more realistic intermolecular potentials are briefly discussed.
Stochastic interactions of two Brownian hard spheres in the presence of depletants
Karzar-Jeddi, Mehdi; Fan, Tai-Hsi; Tuinier, Remco; Taniguchi, Takashi
2014-06-07
A quantitative analysis is presented for the stochastic interactions of a pair of Brownian hard spheres in non-adsorbing polymer solutions. The hard spheres are hypothetically trapped by optical tweezers and allowed for random motion near the trapped positions. The investigation focuses on the long-time correlated Brownian motion. The mobility tensor altered by the polymer depletion effect is computed by the boundary integral method, and the corresponding random displacement is determined by the fluctuation-dissipation theorem. From our computations it follows that the presence of depletion layers around the hard spheres has a significant effect on the hydrodynamic interactions and particle dynamics as compared to pure solvent and uniform polymer solution cases. The probability distribution functions of random walks of the two interacting hard spheres that are trapped clearly shift due to the polymer depletion effect. The results show that the reduction of the viscosity in the depletion layers around the spheres and the entropic force due to the overlapping of depletion zones have a significant influence on the correlated Brownian interactions.
Chaudhari, Mangesh I.; Holleran, Sinead A.; Ashbaugh, Henry S.; Pratt, Lawrence R.
2013-01-01
The osmotic second virial coefficients, B2, for atomic-sized hard spheres in water are attractive (B2 < 0) and become more attractive with increasing temperature (ΔB2/ΔT < 0) in the temperature range 300 K ≤ T ≤ 360 K. Thus, these hydrophobic interactions are attractive and endothermic at moderate temperatures. Hydrophobic interactions between atomic-sized hard spheres in water are more attractive than predicted by the available statistical mechanical theory. These results constitute an initial step toward detailed molecular theory of additional intermolecular interaction features, specifically, attractive interactions associated with hydrophobic solutes. PMID:24297918
Equilibrium distribution of hard-sphere systems and revised Enskog theory
NASA Astrophysics Data System (ADS)
van Beijeren, H.
1983-10-01
A revised Enskog theory (RET) is shown to lead to a correct equilibrium distribution in hard-sphere systems in a stationary external potential, while the standard Enskog theory (SET) does not. Attention is given to the s-component hard-sphere mixture with constant external potential acting on particles of a particular species. The different definition of the pair correlation function at a contact point of two different species used in RET is demonstrated to be consistent with equilibrium statistical mechanics, whereas the definition chosen for the contact point in SET is not.
Note: equation of state and the freezing point in the hard-sphere model.
Robles, Miguel; López de Haro, Mariano; Santos, Andrés
2014-04-01
The merits of different analytical equations of state for the hard-sphere system with respect to the recently computed high-accuracy value of the freezing-point packing fraction are assessed. It is found that the Carnahan-Starling-Kolafa and the branch-point approximant equations of state yield the best performance. PMID:24712819
Brandani, V.; Prausnitz, J. M.
1982-01-01
This paper is the second of three describing a two-fluid theory of binary liquid mixtures. The general theory presented in the preceding paper is used to derive a model for calculating thermodynamic properties of hard-sphere mixtures. Calculations indicate that desirable boundary conditions are satisfied. PMID:16593220
NASA Astrophysics Data System (ADS)
Ogarko, Vitaliy; Luding, Stefan
2013-03-01
Polydisperse hard sphere mixtures have equilibrium properties which essentially depend on the number density and a reduced number K of moments of the size distribution function. Such systems are equivalent to other systems with different size distributions if the K moments are matched. In particular, a small number s of components, such that 2 s - 1 = K is sufficient to mimic systems with continuous size distributions. For most of the fluid phase K = 3 moments (s = 2 components) are enough to define an equivalent system, while in the glassy states one needs K = 5 moments (s = 3 components) to achieve good agreement between the polydisperse and its maximally-equivalent tridisperse system. With K = 5 matched moments they are also close in number- and volume-fractions of rattlers. Finally, also the jamming density of maximally-equivalent jammed packings is very close, where the tiny differences can be explained by the distribution of rattlers. This research is supported by the Dutch Technology Foundation STW, which is the applied science division of NWO, and the Technology Programme of the Ministry of Economic Affairs, project Nr. STW-MUST 10120.
Radial distribution function for hard spheres in fractal dimensions: A heuristic approximation
NASA Astrophysics Data System (ADS)
Santos, Andrés; de Haro, Mariano López
2016-06-01
Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension d (1 ≤d ≤3 ) are developed as heuristic interpolations from the knowledge of the exact and Percus-Yevick results for the hard-rod and hard-sphere fluids, respectively. In order to assess their value, such approximate results are compared with those of recent Monte Carlo simulations and numerical solutions of the Percus-Yevick equation for a fractal dimension [M. Heinen et al., Phys. Rev. Lett. 115, 097801 (2015), 10.1103/PhysRevLett.115.097801], a good agreement being observed.
Hard sphere-like glass transition in eye lens α-crystallin solutions
Savin, Gabriela; Bucciarelli, Saskia; Dorsaz, Nicolas; Thurston, George M.; Stradner, Anna; Schurtenberger, Peter
2014-01-01
We study the equilibrium liquid structure and dynamics of dilute and concentrated bovine eye lens α-crystallin solutions, using small-angle X-ray scattering, static and dynamic light scattering, viscometry, molecular dynamics simulations, and mode-coupling theory. We find that a polydisperse Percus–Yevick hard-sphere liquid-structure model accurately reproduces both static light scattering data and small-angle X-ray scattering liquid structure data from α-crystallin solutions over an extended range of protein concentrations up to 290 mg/mL or 49% vol fraction and up to ca. 330 mg/mL for static light scattering. The measured dynamic light scattering and viscosity properties are also consistent with those of hard-sphere colloids and show power laws characteristic of an approach toward a glass transition at α-crystallin volume fractions near 58%. Dynamic light scattering at a volume fraction beyond the glass transition indicates formation of an arrested state. We further perform event-driven molecular dynamics simulations of polydisperse hard-sphere systems and use mode-coupling theory to compare the measured dynamic power laws with those of hard-sphere models. The static and dynamic data, simulations, and analysis show that aqueous eye lens α-crystallin solutions exhibit a glass transition at high concentrations that is similar to those found in hard-sphere colloidal systems. The α-crystallin glass transition could have implications for the molecular basis of presbyopia and the kinetics of molecular change during cataractogenesis. PMID:25385638
Hynninen, Antti-Pekka; Dijkstra, Marjolein
2005-04-01
Phase diagrams of hard and soft spheres with a fixed dipole moment are determined by calculating the Helmholtz free energy using simulations. The pair potential is given by a dipole-dipole interaction plus a hard-core and a repulsive Yukawa potential for soft spheres. Our system models colloids in an external electric or magnetic field, with hard spheres corresponding to uncharged and soft spheres to charged colloids. The phase diagram of dipolar hard spheres shows fluid, face-centered-cubic (fcc), hexagonal-close-packed (hcp), and body-centered-tetragonal (bct) phases. The phase diagram of dipolar soft spheres exhibits, in addition to the above mentioned phases, a body-centered-orthorhombic (bco) phase, and it agrees well with the experimental phase diagram [Nature (London) 421, 513 (2003)]. Our results show that bulk hcp, bct, and bco crystals can be realized experimentally by applying an external field. PMID:15904046
NASA Astrophysics Data System (ADS)
Reiss, Howard; Manzanares, José A.
2016-09-01
Using several theoretical toolsldots (i) the nucleation theorem, (ii) an equivalent cavity, (iii) the reversible work of adding a cavity to an open hard sphere system, and (iv) the theory of "stability"... the authors estimated the density at which the hard sphere freezing transition occurs. No direct involvement of the equilibrium solid phase is involved. The reduced density \\uppi a^3ρ _f/6 (where a is the hard sphere diameter and ρ _f is the actual density at which freezing occurs) is found to be 0.4937 while the value obtained by computer simulation is 0.494. The agreement is good, but the new method still contains some approximation. However, the approximation is based on the idea that at a density just below ρ _f the fluid adopts a distorted structure resembling the solid, but different enough so that long-range order vanishes. Initial loss of stability may not be involved in every fluid-solid transition, but it may be an early step in the hard sphere and related systems.
NASA Astrophysics Data System (ADS)
Virrueta, A.; Gaines, J.; O'Hern, C. S.; Regan, L.
2015-03-01
Current research in the O'Hern and Regan laboratories focuses on the development of hard-sphere models with stereochemical constraints for protein structure prediction as an alternative to molecular dynamics methods that utilize knowledge-based corrections in their force-fields. Beginning with simple hydrophobic dipeptides like valine, leucine, and isoleucine, we have shown that our model is able to reproduce the side-chain dihedral angle distributions derived from sets of high-resolution protein crystal structures. However, methionine remains an exception - our model yields a chi-3 side-chain dihedral angle distribution that is relatively uniform from 60 to 300 degrees, while the observed distribution displays peaks at 60, 180, and 300 degrees. Our goal is to resolve this discrepancy by considering clashes with neighboring residues, and averaging the reduced distribution of allowable methionine structures taken from a set of crystallized proteins. We will also re-evaluate the electron density maps from which these protein structures are derived to ensure that the methionines and their local environments are correctly modeled. This work will ultimately serve as a tool for computing side-chain entropy and protein stability. A. V. is supported by an NSF Graduate Research Fellowship and a Ford Foundation Fellowship. J. G. is supported by NIH training Grant NIH-5T15LM007056-28.
Mendoza, Carlos I; Santamaría-Holek, I
2009-01-28
We propose a simple and general model accounting for the dependence of the viscosity of a hard sphere suspension at arbitrary volume fractions. The model constitutes a continuum-medium description based on a recursive-differential method where correlations between the spheres are introduced through an effective volume fraction. In contrast to other differential methods, the introduction of the effective volume fraction as the integration variable implicitly considers interactions between the spheres of the same recursive stage. The final expression for the viscosity scales with this effective volume fraction, which allows constructing a master curve that contains all the experimental situations considered. The agreement of our expression for the viscosity with experiments at low- and high-shear rates and in the high-frequency limit is remarkable for all volume fractions. PMID:19191410
Thorneywork, Alice L; Roth, Roland; Aarts, Dirk G A L; Dullens, Roel P A
2014-04-28
Two-dimensional hard disks are a fundamentally important many-body model system in classical statistical mechanics. Despite their significance, a comprehensive experimental data set for two-dimensional single component and binary hard disks is lacking. Here, we present a direct comparison between the full set of radial distribution functions and the contact values of a two-dimensional binary colloidal hard sphere model system and those calculated using fundamental measure theory. We find excellent quantitative agreement between our experimental data and theoretical predictions for both single component and binary hard disk systems. Our results provide a unique and fully quantitative mapping between experiments and theory, which is crucial in establishing the fundamental link between structure and dynamics in simple liquids and glass forming systems. PMID:24784245
Physics of Hard Spheres Experiment (PhaSE) or "Making Jello in Space"
NASA Technical Reports Server (NTRS)
Ling, Jerri S.; Doherty, Michael P.
1998-01-01
The Physics of Hard Spheres Experiment (PHaSE) is a highly successful experiment that flew aboard two shuttle missions to study the transitions involved in the formation of jellolike colloidal crystals in a microgravity environment. A colloidal suspension, or colloid, consists of fine particles, often having complex interactions, suspended in a liquid. Paint, ink, and milk are examples of colloids found in everyday life. In low Earth orbit, the effective force of gravity is thousands of times less than at the Earth's surface. This provides researchers a way to conduct experiments that cannot be adequately performed in an Earth-gravity environment. In microgravity, colloidal particles freely interact without the complications of settling that occur in normal gravity on Earth. If the particle interactions within these colloidal suspensions could be predicted and accurately modeled, they could provide the key to understanding fundamental problems in condensed matter physics and could help make possible the development of wonderful new "designer" materials. Industries that make semiconductors, electro-optics, ceramics, and composites are just a few that may benefit from this knowledge. Atomic interactions determine the physical properties (e.g., weight, color, and hardness) of ordinary matter. PHaSE uses colloidal suspensions of microscopic solid plastic spheres to model the behavior of atomic interactions. When uniformly sized hard spheres suspended in a fluid reach a certain concentration (volume fraction), the particle-fluid mixture changes from a disordered fluid state, in which the spheres are randomly organized, to an ordered "crystalline" state, in which they are structured periodically. The thermal energy of the spheres causes them to form ordered arrays, analogous to crystals. Seven of the eight PHaSE samples ranged in volume fraction from 0.483 to 0.624 to cover the range of interest, while one sample, having a concentration of 0.019, was included for
Newman, Hugh D; Yethiraj, Anand
2015-01-01
In this work, we use structure and dynamics in sedimentation equilibrium, in the presence of gravity, to examine, via confocal microscopy, a Brownian colloidal system in the presence of an external electric field. The zero field equation of state (EOS) is hard sphere without any re-scaling of particle size, and the hydrodynamic corrections to the long-time self-diffusion coefficient are quantitatively consistent with the expected value for hard spheres. Care is taken to ensure that both the dimensionless gravitational energy, which is equivalent to a Peclet number Peg, and dipolar strength Λ are of order unity. In the presence of an external electric field, anisotropic chain-chain clusters form; this cluster formation manifests itself with the appearance of a plateau in the diffusion coefficient when the dimensionless dipolar strength Λ ~ 1. The structure and dynamics of this chain-chain cluster state is examined for a monodisperse system for two particle sizes. PMID:26323363
The Dynamics of Disorder-Order Transition in Hard Sphere Colloidal Dispersions
NASA Technical Reports Server (NTRS)
Chaikin, Paul M.; Zhu, Jixiang; Cheng, Zhengdong; Phan, See-Eng; Russel, William B.; Lant, Christian T.; Doherty, Michael P.; Meyer, William V.; Rogers, Richard; Cannell, D. S.; Ottewill, R. H.
1998-01-01
The Physics of Hard Spheres Experiment (PHaSE) seeks a complete understanding of the entropically driven disorder-order transition in hard sphere colloidal dispersions. The light scattering instrument designed for flight collects Bragg and low angle light scattering in the forward direction via a CCD camera and performs conventional static and dynamic light scattering at 10-160 deg. through fiber optic cables. Here we report on the kinetics of nucleation and growth extracted from time-resolved Bragg images and measurements of the elastic modulus of crystalline phases obtained by monitoring resonant responses to sinusoidal forcing through dynamic light scattering. Preliminary analysis of the former indicates a significant difference from measurements on the ground, while the latter confirms nicely laboratory experiments with the same instrument and predictions from computer simulations.
The structural origin of the hard-sphere glass transition in granular packing
Xia, Chengjie; Li, Jindong; Cao, Yixin; Kou, Binquan; Xiao, Xianghui; Fezzaa, Kamel; Xiao, Tiqiao; Wang, Yujie
2015-09-28
Glass transition is accompanied by a rapid growth of the structural relaxation time and a concomitant decrease of configurational entropy. It remains unclear whether the transition has a thermodynamic origin, and whether the dynamic arrest is associated with the growth of a certain static order. Using granular packing as a model hard-sphere glass, we show the glass transition as a thermodynamic phase transition with a ‘hidden’ polytetrahedral order. This polytetrahedral order is spatially correlated with the slow dynamics. It is geometrically frustrated and has a peculiar fractal dimension. Additionally, as the packing fraction increases, its growth follows an entropy-driven nucleationmore » process, similar to that of the random first-order transition theory. In conclusion, our study essentially identifies a long-sought-after structural glass order in hard-sphere glasses.« less
The structural origin of the hard-sphere glass transition in granular packing
Xia, Chengjie; Li, Jindong; Cao, Yixin; Kou, Binquan; Xiao, Xianghui; Fezzaa, Kamel; Xiao, Tiqiao; Wang, Yujie
2015-09-28
Glass transition is accompanied by a rapid growth of the structural relaxation time and a concomitant decrease of configurational entropy. It remains unclear whether the transition has a thermodynamic origin, and whether the dynamic arrest is associated with the growth of a certain static order. Using granular packing as a model hard-sphere glass, we show the glass transition as a thermodynamic phase transition with a ‘hidden’ polytetrahedral order. This polytetrahedral order is spatially correlated with the slow dynamics. It is geometrically frustrated and has a peculiar fractal dimension. Additionally, as the packing fraction increases, its growth follows an entropy-driven nucleation process, similar to that of the random first-order transition theory. In conclusion, our study essentially identifies a long-sought-after structural glass order in hard-sphere glasses.
The structural origin of the hard-sphere glass transition in granular packing
Xia, Chengjie; Li, Jindong; Cao, Yixin; Kou, Binquan; Xiao, Xianghui; Fezzaa, Kamel; Xiao, Tiqiao; Wang, Yujie
2015-01-01
Glass transition is accompanied by a rapid growth of the structural relaxation time and a concomitant decrease of configurational entropy. It remains unclear whether the transition has a thermodynamic origin, and whether the dynamic arrest is associated with the growth of a certain static order. Using granular packing as a model hard-sphere glass, we show the glass transition as a thermodynamic phase transition with a ‘hidden' polytetrahedral order. This polytetrahedral order is spatially correlated with the slow dynamics. It is geometrically frustrated and has a peculiar fractal dimension. Additionally, as the packing fraction increases, its growth follows an entropy-driven nucleation process, similar to that of the random first-order transition theory. Our study essentially identifies a long-sought-after structural glass order in hard-sphere glasses. PMID:26412008
Regularized 13 moment equations for hard sphere molecules: Linear bulk equations
NASA Astrophysics Data System (ADS)
Struchtrup, Henning; Torrilhon, Manuel
2013-05-01
The regularized 13 moment equations of rarefied gas dynamics are derived for a monatomic hard sphere gas in the linear regime. The equations are based on an extended Grad-type moment system, which is systematically reduced by means of the Order of Magnitude Method [H. Struchtrup, "Stable transport equations for rarefied gases at high orders in the Knudsen number," Phys. Fluids 16(11), 3921-3934 (2004)], 10.1063/1.1782751. Chapman-Enskog expansion of the final equations yields the linear Burnett and super-Burnett equations. While the Burnett coefficients agree with literature values, this seems to be the first time that super-Burnett coefficients are computed for a hard sphere gas. As a first test of the equations the dispersion and damping of sound waves is considered.
Newman, Hugh D.; Yethiraj, Anand
2015-01-01
In this work, we use structure and dynamics in sedimentation equilibrium, in the presence of gravity, to examine, via confocal microscopy, a Brownian colloidal system in the presence of an external electric field. The zero field equation of state (EOS) is hard sphere without any re-scaling of particle size, and the hydrodynamic corrections to the long-time self-diffusion coefficient are quantitatively consistent with the expected value for hard spheres. Care is taken to ensure that both the dimensionless gravitational energy, which is equivalent to a Peclet number Peg, and dipolar strength Λ are of order unity. In the presence of an external electric field, anisotropic chain-chain clusters form; this cluster formation manifests itself with the appearance of a plateau in the diffusion coefficient when the dimensionless dipolar strength Λ ~ 1. The structure and dynamics of this chain-chain cluster state is examined for a monodisperse system for two particle sizes. PMID:26323363
López de Haro, Mariano; Tejero, Carlos F; Santos, Andrés
2013-04-28
The problem of demixing in a binary fluid mixture of highly asymmetric additive hard spheres is revisited. A comparison is presented between the results derived previously using truncated virial expansions for three finite size ratios with those that one obtains with the same approach in the extreme case in which one of the components consists of point particles. Since this latter system is known not to exhibit fluid-fluid segregation, the similarity observed for the behavior of the critical constants arising in the truncated series in all instances, while not being conclusive, may cast serious doubts as to the actual existence of a demixing fluid-fluid transition in disparate-sized binary additive hard-sphere mixtures. PMID:23635104
The structural origin of the hard-sphere glass transition in granular packing
NASA Astrophysics Data System (ADS)
Xia, Chengjie; Li, Jindong; Cao, Yixin; Kou, Binquan; Xiao, Xianghui; Fezzaa, Kamel; Xiao, Tiqiao; Wang, Yujie
2015-09-01
Glass transition is accompanied by a rapid growth of the structural relaxation time and a concomitant decrease of configurational entropy. It remains unclear whether the transition has a thermodynamic origin, and whether the dynamic arrest is associated with the growth of a certain static order. Using granular packing as a model hard-sphere glass, we show the glass transition as a thermodynamic phase transition with a `hidden' polytetrahedral order. This polytetrahedral order is spatially correlated with the slow dynamics. It is geometrically frustrated and has a peculiar fractal dimension. Additionally, as the packing fraction increases, its growth follows an entropy-driven nucleation process, similar to that of the random first-order transition theory. Our study essentially identifies a long-sought-after structural glass order in hard-sphere glasses.
The structural origin of the hard-sphere glass transition in granular packing.
Xia, Chengjie; Li, Jindong; Cao, Yixin; Kou, Binquan; Xiao, Xianghui; Fezzaa, Kamel; Xiao, Tiqiao; Wang, Yujie
2015-01-01
Glass transition is accompanied by a rapid growth of the structural relaxation time and a concomitant decrease of configurational entropy. It remains unclear whether the transition has a thermodynamic origin, and whether the dynamic arrest is associated with the growth of a certain static order. Using granular packing as a model hard-sphere glass, we show the glass transition as a thermodynamic phase transition with a 'hidden' polytetrahedral order. This polytetrahedral order is spatially correlated with the slow dynamics. It is geometrically frustrated and has a peculiar fractal dimension. Additionally, as the packing fraction increases, its growth follows an entropy-driven nucleation process, similar to that of the random first-order transition theory. Our study essentially identifies a long-sought-after structural glass order in hard-sphere glasses. PMID:26412008
Parallelized event chain algorithm for dense hard sphere and polymer systems
Kampmann, Tobias A. Boltz, Horst-Holger; Kierfeld, Jan
2015-01-15
We combine parallelization and cluster Monte Carlo for hard sphere systems and present a parallelized event chain algorithm for the hard disk system in two dimensions. For parallelization we use a spatial partitioning approach into simulation cells. We find that it is crucial for correctness to ensure detailed balance on the level of Monte Carlo sweeps by drawing the starting sphere of event chains within each simulation cell with replacement. We analyze the performance gains for the parallelized event chain and find a criterion for an optimal degree of parallelization. Because of the cluster nature of event chain moves massive parallelization will not be optimal. Finally, we discuss first applications of the event chain algorithm to dense polymer systems, i.e., bundle-forming solutions of attractive semiflexible polymers.
Radial distribution function of penetrable sphere fluids to the second order in density
NASA Astrophysics Data System (ADS)
Santos, Andrés; Malijevský, Alexandr
2007-02-01
The simplest bounded potential is that of penetrable spheres, which takes a positive finite value γ if the two spheres are overlapped, being zero otherwise. In this paper we derive the cavity function to second order in density and the fourth virial coefficient as functions of T*≡kBT/γ (where kB is the Boltzmann constant and T is the temperature) for penetrable sphere fluids. The expressions are exact, except for the function represented by an elementary diagram inside the core, which is approximated by a polynomial form in excellent agreement with accurate results obtained by Monte Carlo integration. Comparison with the hypernetted-chain (HNC) and Percus-Yevick (PY) theories shows that the latter is better than the former for T*≲1 only. However, even at zero temperature (hard sphere limit), the PY solution is not accurate inside the overlapping region, where no practical cancellation of the neglected diagrams takes place. The exact fourth virial coefficient is positive for T*≲0.73 , reaches a minimum negative value at T*≈1.1 , and then goes to zero from below as 1/T*4 for high temperatures. These features are captured qualitatively, but not quantitatively, by the HNC and PY predictions. In addition, in both theories the compressibility route is the best one for T*≲0.7 , while the virial route is preferable if T*≳0.7 .
Tracking three-phase coexistences in binary mixtures of hard plates and spheres
NASA Astrophysics Data System (ADS)
Aliabadi, Roohollah; Moradi, Mahmood; Varga, Szabolcs
2016-02-01
The stability of demixing phase transition in binary mixtures of hard plates (with thickness L and diameter D) and hard spheres (with diameter σ) is studied by means of Parsons-Lee theory. The isotropic-isotropic demixing, which is found in mixtures of large spheres and small plates, is very likely to be pre-empted by crystallization. In contrast, the nematic-nematic demixing, which is obtained in mixtures of large plates and small spheres, can be stabilized at low diameter ratios (σ/D) and aspect ratios (L/D). At intermediate values of σ/D, where the sizes of the components are similar, neither the isotropic-isotropic nor the nematic-nematic demixing can be stabilized, but a very strong fractionation takes place between a plate rich nematic and a sphere rich isotropic phases. Our results show that the excluded volume interactions are capable alone to explain the experimental observation of the nematic-nematic demixing, but they fail in the description of isotropic-isotropic one [M. Chen et al., Soft Matter 11, 5775 (2015)].
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.
NASA Astrophysics Data System (ADS)
Urrutia, Ignacio
2014-12-01
This work is devoted to analyze the relation between the thermodynamic properties of a confined fluid and the shape of its confining vessel. Recently, new insights in this topic were found through the study of cluster integrals for inhomogeneous fluids that revealed the dependence on the vessel shape of the low density behavior of the system. Here, the statistical mechanics and thermodynamics of fluids confined in wedges or by edges is revisited, focusing on their cluster integrals. In particular, the well known hard sphere fluid, which was not studied in this framework so far, is analyzed under confinement and its thermodynamic properties are analytically studied up to order two in the density. Furthermore, the analysis is extended to the confinement produced by a corrugated wall. These results rely on the obtained analytic expression for the second cluster integral of the confined hard sphere system as a function of the opening dihedral angle 0 < β < 2π. It enables a unified approach to both wedges and edges.
Urrutia, Ignacio
2014-12-28
This work is devoted to analyze the relation between the thermodynamic properties of a confined fluid and the shape of its confining vessel. Recently, new insights in this topic were found through the study of cluster integrals for inhomogeneous fluids that revealed the dependence on the vessel shape of the low density behavior of the system. Here, the statistical mechanics and thermodynamics of fluids confined in wedges or by edges is revisited, focusing on their cluster integrals. In particular, the well known hard sphere fluid, which was not studied in this framework so far, is analyzed under confinement and its thermodynamic properties are analytically studied up to order two in the density. Furthermore, the analysis is extended to the confinement produced by a corrugated wall. These results rely on the obtained analytic expression for the second cluster integral of the confined hard sphere system as a function of the opening dihedral angle 0 < β < 2π. It enables a unified approach to both wedges and edges.
Urrutia, Ignacio
2014-12-28
This work is devoted to analyze the relation between the thermodynamic properties of a confined fluid and the shape of its confining vessel. Recently, new insights in this topic were found through the study of cluster integrals for inhomogeneous fluids that revealed the dependence on the vessel shape of the low density behavior of the system. Here, the statistical mechanics and thermodynamics of fluids confined in wedges or by edges is revisited, focusing on their cluster integrals. In particular, the well known hard sphere fluid, which was not studied in this framework so far, is analyzed under confinement and its thermodynamic properties are analytically studied up to order two in the density. Furthermore, the analysis is extended to the confinement produced by a corrugated wall. These results rely on the obtained analytic expression for the second cluster integral of the confined hard sphere system as a function of the opening dihedral angle 0 < β < 2π. It enables a unified approach to both wedges and edges. PMID:25554179
Scaled Particle Theory for Multicomponent Hard Sphere Fluids Confined in Random Porous Media.
Chen, W; Zhao, S L; Holovko, M; Chen, X S; Dong, W
2016-06-23
The formulation of scaled particle theory (SPT) is presented for a quite general model of fluids confined in a random porous media, i.e., a multicomponent hard sphere (HS) fluid in a multicomponent hard sphere or a multicomponent overlapping hard sphere (OHS) matrix. The analytical expressions for pressure, Helmholtz free energy, and chemical potential are derived. The thermodynamic consistency of the proposed theory is established. Moreover, we show that there is an isomorphism between the SPT for a multicomponent system and that for a one-component system. Results from grand canonical ensemble Monte Carlo simulations are also presented for a binary HS mixture in a one-component HS or a one-component OHS matrix. The accuracy of various variants derived from the basic SPT formulation is appraised against the simulation results. Scaled particle theory, initially formulated for a bulk HS fluid, has not only provided an analytical tool for calculating thermodynamic properties of HS fluid but also helped to gain very useful insight for elaborating other theoretical approaches such as the fundamental measure theory (FMT). We expect that the general SPT for multicomponent systems developed in this work can contribute to the study of confined fluids in a similar way. PMID:27294670
NASA Astrophysics Data System (ADS)
Parisi, Giorgio
In a hard spheres systems particles cannot overlap. Increasing the density we reach a point where most of the particles are blocked and the density cannot be increased any more: this is the jamming point. The jamming point separates the phase, where all the constraint can be satisfied, from an unsatifiable phase, where spheres do have to overlap. A scaling theory of the behavior around the jamming critical point has been formulated and a few critical exponents have been introduced. The exponents are apparently super-universal, as far as they do seem to be independent from the space dimensions. The mean field version of the model (i.e. the infinite dimensions limit) has been solved analytically using broken replica symmetry techniques and the computed critical exponents have been found in a remarkable agreement with three-dimensional and two-dimensional numerical results and experiments. The theory predicts in hard spheres (in glasses) a new transition (the Gardener transition) from the replica symmetric phase to the replica broken phase at high density (at low temperature), in agreement with simulations on hard sphere systems. I will briefly discuss the possible consequences of this new picture on the very low temperature behavior of glasses in the quantum regime.
Radial distribution function for hard spheres in fractal dimensions: A heuristic approximation.
Santos, Andrés; de Haro, Mariano López
2016-06-01
Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension d (1≤d≤3) are developed as heuristic interpolations from the knowledge of the exact and Percus-Yevick results for the hard-rod and hard-sphere fluids, respectively. In order to assess their value, such approximate results are compared with those of recent Monte Carlo simulations and numerical solutions of the Percus-Yevick equation for a fractal dimension [M. Heinen et al., Phys. Rev. Lett. 115, 097801 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.097801], a good agreement being observed. PMID:27415227
Equations of state of freely jointed hard-sphere chain fluids: Theory
Stell, G.; Lin, C.; Kalyuzhnyi, Y.V.
1999-03-01
Using the analytical solution of a multidensity integral equation solved in our previous papers [J. Chem. Phys. {bold 108}, 6513, 6525 (1998)], we derive two compressibility and two virial equations of state (EOS) for freely jointed hard-sphere chain fluids on the basis of the approximations defined by the polymer Percus{endash}Yevick (PPY) closure and of the PPY ideal-chain closure for the integral equations. We also extend a version of first-order thermodynamic perturbation theory to polymers, using a dimer fluid as the reference system, to treat mixtures of heteronuclear chain fluids and polymer solutions; the structural information of the dimer fluid is obtained from the PPY ideal-chain approximation in the complete-association limit. The attractive forces between monomers of chain molecules are treated using simple perturbation theory. We find that the compressibility EOS derived on the basis of the PPY approximation subject to the chain-connectivity condition reduces to the compressibility EOS based upon the PPY ideal-chain approximation in the complete-association limit, which is also equivalent to the EOS derived by Chiew [Mol. Phys. {bold 70}, 129 (1990)] and to the EOS derived by Kalyuzhnyi and Cummings [J. Chem. Phys. {bold 105}, 2011 (1996)]. On the other hand, the virial EOS derived on the basis of the PPY ideal-chain approximation coincides with Attard{close_quote}s virial EOS [J. Chem. Phys. {bold 102}, 5411 (1995)] only in the zero-density limit. The advantages in numerical implementation of the EOS presented in this work are also discussed, but a full quantitative assessment of our results and a detailed numerical comparison among them are made in a companion paper, as is comparison with available simulation results. {copyright} {ital 1999 American Institute of Physics.}
The Physics of Hard Spheres Experiment on MSL-1: Required Measurements and Instrument Performance
NASA Technical Reports Server (NTRS)
Doherty, Michael P.; Lant, Christian T.; Ling, Jerri S.
1998-01-01
The Physics of HArd Spheres Experiment (PHaSE), one of NASA Lewis Research Center's first major light scattering experiments for microgravity research on complex fluids, flew on board the Space Shuttle's Microgravity Science Laboratory (MSL-1) in 1997. Using colloidal systems of various concentrations of micron-sized plastic spheres in a refractive index-matching fluid as test samples, illuminated by laser light during and after crystallization, investigations were conducted to measure the nucleation and growth rate of colloidal crystals as well as the structure, rheology, and dynamics of the equilibrium crystal. Together, these measurements support an enhanced understanding of the nature of the liquid-to-solid transition. Achievement of the science objectives required an accurate experimental determination of eight fundamental properties for the hard sphere colloidal samples. The instrument design met almost all of the original measurement requirements, but with compromise on the number of samples on which data were taken. The instrument performs 2-D Bragg and low angle scattering from 0.4 deg. to 60 deg., dynamic and single-channel static scattering from 10 deg. to 170 deg., rheology using fiber optics, and white light imaging of the sample. As a result, PHaSE provided a timely microgravity demonstration of critical light scattering measurement techniques and hardware concepts, while generating data already showing promise of interesting new scientific findings in the field of condensed matter physics.
Long-range weight functions in fundamental measure theory of the non-uniform hard-sphere fluid.
Hansen-Goos, Hendrik
2016-06-22
We introduce long-range weight functions to the framework of fundamental measure theory (FMT) of the non-uniform, single-component hard-sphere fluid. While the range of the usual weight functions is equal to the hard-sphere radius R, the modified weight functions have range 3R. Based on the augmented FMT, we calculate the radial distribution function g(r) up to second order in the density within Percus' test particle theory. Consistency of the compressibility and virial routes on this level allows us to determine the free parameter γ of the theory. As a side result, we obtain a value for the fourth virial coefficient B 4 which deviates by only 0.01% from the exact result. The augmented FMT is tested for the dense fluid by comparing results for g(r) calculated via the test particle route to existing results from molecular dynamics simulations. The agreement at large distances (r > 6R) is significantly improved when the FMT with long-range weight functions is used. In order to improve agreement close to contact (r = 2R) we construct a free energy which is based on the accurate Carnahan-Starling equation of state, rather than the Percus-Yevick compressibility equation underlying standard FMT. PMID:27115721
Jiang, Hao; Adidharma, Hertanto
2014-11-07
The thermodynamic modeling of flexible charged hard-sphere chains representing polyampholyte or polyelectrolyte molecules in solution is considered. The excess Helmholtz energy and osmotic coefficients of solutions containing short polyampholyte and the osmotic coefficients of solutions containing short polyelectrolytes are determined by performing canonical and isobaric-isothermal Monte Carlo simulations. A new equation of state based on the thermodynamic perturbation theory is also proposed for flexible charged hard-sphere chains. For the modeling of such chains, the use of solely the structure information of monomer fluid for calculating the chain contribution is found to be insufficient and more detailed structure information must therefore be considered. Two approaches, i.e., the dimer and dimer-monomer approaches, are explored to obtain the contribution of the chain formation to the Helmholtz energy. By comparing with the simulation results, the equation of state with either the dimer or dimer-monomer approach accurately predicts the excess Helmholtz energy and osmotic coefficients of polyampholyte and polyelectrolyte solutions except at very low density. It also well captures the effect of temperature on the thermodynamic properties of these solutions.
Mirigian, Stephen; Schweizer, Kenneth
2014-01-01
We generalize the force-level nonlinear Langevin equation theory of single particle hopping to include collective effects associated with long range elastic distortion of the liquid. The activated alpha relaxation event is of a mixed spatial character, involving two distinct, but inter-related, local and collective barriers. There are no divergences at volume fractions below jamming or temperatures above zero Kelvin. The ideas are first developed and implemented analytically and numerically in the context of hard sphere fluids. In an intermediate volume fraction crossover regime, the local cage process is dominant in a manner consistent with an apparent Arrhenius behavior. The super-Arrhenius collective barrier is more strongly dependent on volume fraction, dominates the highly viscous regime, and is well described by a nonsingular law below jamming. The increase of the collective barrier is determined by the amplitude of thermal density fluctuations, dynamic shear modulus or transient localization length, and a growing microscopic jump length. Alpha relaxation time calculations are in good agreement with recent experiments and simulations on dense fluids and suspensions of hard spheres. Comparisons of the theory with elastic models and entropy crisis ideas are explored. The present work provides a foundation for constructing a quasi-universal, fit-parameter-free theory for relaxation in thermal molecular liquids over 14 orders of magnitude in time.
NASA Astrophysics Data System (ADS)
Mirigian, Stephen; Schweizer, Kenneth S.
2014-05-01
We generalize the force-level nonlinear Langevin equation theory of single particle hopping to include collective effects associated with long range elastic distortion of the liquid. The activated alpha relaxation event is of a mixed spatial character, involving two distinct, but inter-related, local and collective barriers. There are no divergences at volume fractions below jamming or temperatures above zero Kelvin. The ideas are first developed and implemented analytically and numerically in the context of hard sphere fluids. In an intermediate volume fraction crossover regime, the local cage process is dominant in a manner consistent with an apparent Arrhenius behavior. The super-Arrhenius collective barrier is more strongly dependent on volume fraction, dominates the highly viscous regime, and is well described by a nonsingular law below jamming. The increase of the collective barrier is determined by the amplitude of thermal density fluctuations, dynamic shear modulus or transient localization length, and a growing microscopic jump length. Alpha relaxation time calculations are in good agreement with recent experiments and simulations on dense fluids and suspensions of hard spheres. Comparisons of the theory with elastic models and entropy crisis ideas are explored. The present work provides a foundation for constructing a quasi-universal, fit-parameter-free theory for relaxation in thermal molecular liquids over 14 orders of magnitude in time.
Long-range weight functions in fundamental measure theory of the non-uniform hard-sphere fluid
NASA Astrophysics Data System (ADS)
Hansen-Goos, Hendrik
2016-06-01
We introduce long-range weight functions to the framework of fundamental measure theory (FMT) of the non-uniform, single-component hard-sphere fluid. While the range of the usual weight functions is equal to the hard-sphere radius R, the modified weight functions have range 3R. Based on the augmented FMT, we calculate the radial distribution function g(r) up to second order in the density within Percus’ test particle theory. Consistency of the compressibility and virial routes on this level allows us to determine the free parameter γ of the theory. As a side result, we obtain a value for the fourth virial coefficient B 4 which deviates by only 0.01% from the exact result. The augmented FMT is tested for the dense fluid by comparing results for g(r) calculated via the test particle route to existing results from molecular dynamics simulations. The agreement at large distances (r > 6R) is significantly improved when the FMT with long-range weight functions is used. In order to improve agreement close to contact (r = 2R) we construct a free energy which is based on the accurate Carnahan–Starling equation of state, rather than the Percus–Yevick compressibility equation underlying standard FMT.
An Automatic Phase-Change Detection Technique for Colloidal Hard Sphere Suspensions
NASA Technical Reports Server (NTRS)
McDowell, Mark; Gray, Elizabeth; Rogers, Richard B.
2005-01-01
Colloidal suspensions of monodisperse spheres are used as physical models of thermodynamic phase transitions and as precursors to photonic band gap materials. However, current image analysis techniques are not able to distinguish between densely packed phases within conventional microscope images, which are mainly characterized by degrees of randomness or order with similar grayscale value properties. Current techniques for identifying the phase boundaries involve manually identifying the phase transitions, which is very tedious and time consuming. We have developed an intelligent machine vision technique that automatically identifies colloidal phase boundaries. The algorithm utilizes intelligent image processing techniques that accurately identify and track phase changes vertically or horizontally for a sequence of colloidal hard sphere suspension images. This technique is readily adaptable to any imaging application where regions of interest are distinguished from the background by differing patterns of motion over time.
Edison, John R; Dasgupta, Tonnishtha; Dijkstra, Marjolein
2016-08-01
We study the phase behaviour of a binary mixture of colloidal hard spheres and freely jointed chains of beads using Monte Carlo simulations. Recently Panagiotopoulos and co-workers predicted [Nat. Commun. 5, 4472 (2014)] that the hexagonal close packed (HCP) structure of hard spheres can be stabilized in such a mixture due to the interplay between polymer and the void structure in the crystal phase. Their predictions were based on estimates of the free-energy penalty for adding a single hard polymer chain in the HCP and the competing face centered cubic (FCC) phase. Here we calculate the phase diagram using free-energy calculations of the full binary mixture and find a broad fluid-solid coexistence region and a metastable gas-liquid coexistence region. For the colloid-monomer size ratio considered in this work, we find that the HCP phase is only stable in a small window at relatively high polymer reservoir packing fractions, where the coexisting HCP phase is nearly close packed. Additionally we investigate the structure and dynamic behaviour of these mixtures. PMID:27497577
NASA Astrophysics Data System (ADS)
Edison, John R.; Dasgupta, Tonnishtha; Dijkstra, Marjolein
2016-08-01
We study the phase behaviour of a binary mixture of colloidal hard spheres and freely jointed chains of beads using Monte Carlo simulations. Recently Panagiotopoulos and co-workers predicted [Nat. Commun. 5, 4472 (2014)] that the hexagonal close packed (HCP) structure of hard spheres can be stabilized in such a mixture due to the interplay between polymer and the void structure in the crystal phase. Their predictions were based on estimates of the free-energy penalty for adding a single hard polymer chain in the HCP and the competing face centered cubic (FCC) phase. Here we calculate the phase diagram using free-energy calculations of the full binary mixture and find a broad fluid-solid coexistence region and a metastable gas-liquid coexistence region. For the colloid-monomer size ratio considered in this work, we find that the HCP phase is only stable in a small window at relatively high polymer reservoir packing fractions, where the coexisting HCP phase is nearly close packed. Additionally we investigate the structure and dynamic behaviour of these mixtures.
Yan, Zhenyu; Buldyrev, Sergey V; Giovambattista, Nicolas; Debenedetti, Pablo G; Stanley, H Eugene
2006-05-01
We investigate the equation of state, diffusion coefficient, and structural order of a family of spherically symmetric potentials consisting of a hard core and a linear repulsive ramp. This generic potential has two characteristic length scales: the hard and soft core diameters. The family of potentials is generated by varying their ratio, lambda. We find negative thermal expansion (thermodynamic anomaly) and an increase of the diffusion coefficient upon isothermal compression (dynamic anomaly) for 0< or =lambda<6/7. As in water, the regions where these anomalies occur are nested domes in the (T, p) or (T, P) planes , with the thermodynamic anomaly dome contained entirely within the dynamic anomaly dome. We calculate translational and orientational order parameters (t and Q6), and project equilibrium state points onto the (t, Q6) plane, or order map. The order map evolves from waterlike behavior to hard-sphere-like behavior upon varying lambda between 4/7 and 6/7. Thus, we traverse the range of liquid behavior encompassed by hard spheres (lanbda=1) and waterlike (lambda approximately 4/7) with a family of tunable spherically symmetric potentials by simply varying the ratio of hard to soft-core diameters. Although dynamic and thermodynamic anomalies occur almost across the entire range 0< or=lambda< or=1, waterlike structural anomalies (i.e., decrease in both t and Q6 upon compression and strictly correlated T and Q6 in the anomalous region) occur only around lambda=4/7. Waterlike anomalies in structure, dynamics and thermodynamics arise solely due to the existence of two length scales, with their ratio lambda being the single control parameter, orientation-dependent interactions being absent by design. PMID:16802925
The role of bond tangency and bond gap in hard sphere crystallization of chains.
Karayiannis, Nikos Ch; Foteinopoulou, Katerina; Laso, Manuel
2015-03-01
We report results from Monte Carlo simulations on dense packings of linear, freely-jointed chains of hard spheres of uniform size. In contrast to our past studies where bonded spheres along the chain backbone were tangent, in the present work a finite tolerance in the bond is allowed. Bond lengths are allowed to fluctuate in the interval [σ, σ + dl], where σ is the sphere diameter. We find that bond tolerance affects the phase behaviour of hard-sphere chains, especially in the close vicinity of the melting transition. First, a critical dl(crit) exists marking the threshold for crystallization, whose value decreases with increasing volume fraction. Second, bond gaps enhance the onset of phase transition by accelerating crystal nucleation and growth. Finally, bond tolerance has an effect on crystal morphologies: in the tangent limit the majority of structures correspond to stack-faulted random hexagonal close packing (rhcp). However, as bond tolerance increases a wealth of diverse structures can be observed: from single fcc (or hcp) crystallites to random hcp/fcc stackings with multiple directions. By extending the simulations over trillions of MC steps (10(12)) we are able to observe crystal-crystal transitions and perfection even for entangled polymer chains in accordance to the Ostwald's rule of stages in crystal polymorphism. Through simple geometric arguments we explain how the presence of rigid or flexible constraints affects crystallization in general atomic and particulate systems. Based on the present results, it can be concluded that proper tuning of bond gaps and of the connectivity network can be a controlling factor for the phase behaviour of model, polymer-based colloidal and granular systems. PMID:25594158
Glass-transition properties of Yukawa potentials: from charged point particles to hard spheres.
Yazdi, Anoosheh; Ivlev, Alexei; Khrapak, Sergey; Thomas, Hubertus; Morfill, Gregor E; Löwen, Hartmut; Wysocki, Adam; Sperl, Matthias
2014-06-01
The glass transition is investigated in three dimensions for single and double Yukawa potentials for the full range of control parameters. For vanishing screening parameter, the limit of the one-component plasma is obtained; for large screening parameters and high coupling strengths, the glass-transition properties cross over to the hard-sphere system. Between the two limits, the entire transition diagram can be described by analytical functions. Unlike other potentials, the glass-transition and melting lines for Yukawa potentials are found to follow shifted but otherwise identical curves in control-parameter space. PMID:25019902
NASA Astrophysics Data System (ADS)
Gámez, Francisco; Acemel, Rafael D.; Cuetos, Alejandro
2013-10-01
Parsons-Lee approach is formulated for the isotropic-nematic transition in a binary mixture of oblate hard spherocylinders and hard spheres. Results for the phase coexistence and for the equation of state in both phases for fluids with different relative size and composition ranges are presented. The predicted behaviour is in agreement with Monte Carlo simulations in a qualitative fashion. The study serves to provide a rational view of how to control key aspects of the behaviour of these binary nematogenic colloidal systems. This behaviour can be tuned with an appropriate choice of the relative size and molar fractions of the depleting particles. In general, the mixture of discotic and spherical particles is stable against demixing up to very high packing fractions. We explore in detail the narrow geometrical range where demixing is predicted to be possible in the isotropic phase. The influence of molecular crowding effects on the stability of the mixture when spherical molecules are added to a system of discotic colloids is also studied.
NASA Astrophysics Data System (ADS)
Michailidou, V. N.; Swan, J. W.; Brady, J. F.; Petekidis, G.
2013-10-01
Evanescent wave dynamic light scattering and Stokesian dynamics simulations were employed to study the dynamics of hard-sphere colloidal particles near a hard wall in concentrated suspensions. The evanescent wave averaged short-time diffusion coefficients were determined from experimental correlation functions over a range of scattering wave vectors and penetration depths. Stokesian dynamics simulations performed for similar conditions allow a direct comparison of both the short-time self- and collective diffusivity. As seen earlier [V. N. Michailidou, G. Petekidis, J. W. Swan, and J. F. Brady, Phys. Rev. Lett. 102, 068302 (2009)] while the near wall dynamics in the dilute regime slow down compared to the free bulk diffusion, the reduction is negligible at higher volume fractions due to an interplay between the particle-wall and particle-particle hydrodynamic interactions. Here, we provide a comprehensive comparison between experiments and simulations and discuss the interplay of particle-wall and particle-particle hydrodynamics in the self- and cooperative dynamics determined at different scattering wave vectors and penetration depths.
Hard-sphere behavior in the dynamics of all mono-atomic liquids at the de Gennes minimum
NASA Astrophysics Data System (ADS)
Montfrooij, Wouter
2016-08-01
We show that the position of the de Gennes minimum in scattering spectra, where the dynamics of liquids shows down, is given by a hard-sphere expression for a range of mono-atomic liquids that crystallize in a close packed structure. This expression relates the position of the minimum to the number density of the liquid, without any adjustable or unknown parameters. We argue that this implies that a liquid can be viewed as a close packed structure of the cages that represent the confinement of atoms by their neighbors. We further show that some metals deviate from this expression, namely those metals that crystallize in a structure that is not close packed. Our expression should prove very useful in identifying what liquids to study in inelastic scattering experiments given that deviations from normal fluid behavior can already be predicted based on the peak position of the static structure factor.
Physics of Hard Sphere Experiment: Scattering, Rheology and Microscopy Study of Colloidal Particles
NASA Technical Reports Server (NTRS)
Cheng, Z.-D.; Zhu, J.; Phan, S.-E.; Russel, W. B.; Chaikin, P. M.; Meyer, W. V.
2002-01-01
The Physics of Hard Sphere Experiment has two incarnations: the first as a scattering and rheology experiment on STS-83 and STS-94 and the second as a microscopy experiment to be performed in the future on LMM on the space station. Here we describe some of the quantitative and qualitative results from previous flights on the dynamics of crystallization in microgravity and especially the observed interaction of growing crystallites in the coexistance regime. To clarify rheological measurements we also present ground based experiments on the low shear rate viscosity and diffusion coefficient of several hard sphere experiments at high volume fraction. We also show how these experiments will be performed with confocal microscopy and laser tweezers in our lab and as preparation for the phAse II experiments on LMM. One of the main aims of the microscopy study will be the control of colloidal samples using an array of applied fields with an eye toward colloidal architectures. Temperature gradients, electric field gradients, laser tweezers and a variety of switchable imposed surface patterns are used toward this control.
NASA Astrophysics Data System (ADS)
Gazzillo, Domenico; Giacometti, Achille; Fantoni, Riccardo; Sollich, Peter
2006-11-01
We investigate the dependence of the stickiness parameters tij=1/(12τij) —where the τij are the conventional Baxter parameters—on the solute diameters σi and σj in multicomponent sticky hard sphere (SHS) models for fluid mixtures of mesoscopic neutral particles. A variety of simple but realistic interaction potentials, utilized in the literature to model short-ranged attractions present in real solutions of colloids or reverse micelles, is reviewed. We consider: (i) van der Waals attractions, (ii) hard-sphere-depletion forces, (iii) polymer-coated colloids, and (iv) solvation effects (in particular hydrophobic bonding and attractions between reverse micelles of water-in-oil microemulsions). We map each of these potentials onto an equivalent SHS model by requiring the equality of the second virial coefficients. The main finding is that, for most of the potentials considered, the size-dependence of tij(T,σi,σj) can be approximated by essentially the same expression, i.e., a simple polynomial in the variable σiσj/σij2 , with coefficients depending on the temperature T , or—for depletion interactions—on the packing fraction η0 of the depletant particles.
Sedov, I A; Magsumov, T I
2015-07-16
Thermodynamic solvation properties of mixtures of water with tetrahydrofuran at 298 K are studied. The Gibbs free energies and enthalpies of solvation of n-octane and toluene are determined experimentally. For molecular dynamics simulations of the binary solvent, we have modified a TraPPE-UA model for tetrahydrofuran and combined it with the SPC/E potential for water. The excess thermodynamic functions of neon, xenon, and hard spheres with two different radii are calculated using the particle insertion method. Simulated and real systems share the same characteristic trends for the thermodynamic functions. A maximum is present on dependencies of the enthalpy of solvation from the composition of solvent at 70-90 mol % water, making it higher than in both of the cosolvents. It is caused by a high enthalpy of cavity formation in the mixtures rich with water due to solvent reorganization around the cavity, which is shown by calculation of the enthalpy of solvation of hard spheres. Addition of relatively small amounts of tetrahydrofuran to water effectively suppresses the hydrophobic effect, leading to a quick increase of both the entropy and enthalpy of cavity formation and solvation of low polar molecules. PMID:26115405
NASA Astrophysics Data System (ADS)
Filion, L.; Ni, R.; Frenkel, D.; Dijkstra, M.
2011-04-01
In this paper we examine the phase behavior of the Weeks-Chandler-Andersen (WCA) potential with βɛ = 40. Crystal nucleation in this model system was recently studied by Kawasaki and Tanaka [Proc. Natl. Acad. Sci. U.S.A. 107, 14036 (2010)], 10.1021/pr100656u, who argued that the computed nucleation rates agree well with experiment, a finding that contradicted earlier simulation results. Here we report an extensive numerical study of crystallization in the WCA model, using three totally different techniques (Brownian dynamics, umbrella sampling, and forward flux sampling). We find that all simulations yield essentially the same nucleation rates. However, these rates differ significantly from the values reported by Kawasaki and Tanaka and hence we argue that the huge discrepancy in nucleation rates between simulation and experiment persists. When we map the WCA model onto a hard-sphere system, we find good agreement between the present simulation results and those that had been obtained for hard spheres [L. Filion, M. Hermes, R. Ni, and M. Dijkstra, J. Chem. Phys. 133, 244115 (2010), 10.1063/1.3506838; S. Auer and D. Frenkel, Nature 409, 1020 (2001), 10.1038/35059035].
NASA Astrophysics Data System (ADS)
Hopkins, Paul; Fortini, Andrea; Archer, Andrew J.; Schmidt, Matthias
2010-12-01
We describe a test particle approach based on dynamical density functional theory (DDFT) for studying the correlated time evolution of the particles that constitute a fluid. Our theory provides a means of calculating the van Hove distribution function by treating its self and distinct parts as the two components of a binary fluid mixture, with the "self " component having only one particle, the "distinct" component consisting of all the other particles, and using DDFT to calculate the time evolution of the density profiles for the two components. We apply this approach to a bulk fluid of Brownian hard spheres and compare to results for the van Hove function and the intermediate scattering function from Brownian dynamics computer simulations. We find good agreement at low and intermediate densities using the very simple Ramakrishnan-Yussouff [Phys. Rev. B 19, 2775 (1979)] approximation for the excess free energy functional. Since the DDFT is based on the equilibrium Helmholtz free energy functional, we can probe a free energy landscape that underlies the dynamics. Within the mean-field approximation we find that as the particle density increases, this landscape develops a minimum, while an exact treatment of a model confined situation shows that for an ergodic fluid this landscape should be monotonic. We discuss possible implications for slow, glassy, and arrested dynamics at high densities.
Hopkins, Paul; Fortini, Andrea; Archer, Andrew J; Schmidt, Matthias
2010-12-14
We describe a test particle approach based on dynamical density functional theory (DDFT) for studying the correlated time evolution of the particles that constitute a fluid. Our theory provides a means of calculating the van Hove distribution function by treating its self and distinct parts as the two components of a binary fluid mixture, with the "self " component having only one particle, the "distinct" component consisting of all the other particles, and using DDFT to calculate the time evolution of the density profiles for the two components. We apply this approach to a bulk fluid of Brownian hard spheres and compare to results for the van Hove function and the intermediate scattering function from Brownian dynamics computer simulations. We find good agreement at low and intermediate densities using the very simple Ramakrishnan-Yussouff [Phys. Rev. B 19, 2775 (1979)] approximation for the excess free energy functional. Since the DDFT is based on the equilibrium Helmholtz free energy functional, we can probe a free energy landscape that underlies the dynamics. Within the mean-field approximation we find that as the particle density increases, this landscape develops a minimum, while an exact treatment of a model confined situation shows that for an ergodic fluid this landscape should be monotonic. We discuss possible implications for slow, glassy, and arrested dynamics at high densities. PMID:21171689
NASA Astrophysics Data System (ADS)
de las Heras, Daniel; Varga, Szabolcs; Vesely, Franz J.
2011-06-01
We present the phase diagram of a system of mesogenic top-shaped molecules based on the Parsons-Lee density functional theory and Monte Carlo simulation. The molecules are modeled as a hard spherocylinder with a hard sphere embedded in its center. The stability of five different phases is studied, namely, isotropic, nematic, smectic A, smectic C, and columnar phases. The positionally ordered phases are investigated only for the case of parallel alignment. It is found that the central spherical unit destabilizes the nematic with respect to the isotropic phase, while increasing the length of the cylinder has the opposite effect. Also, the central hard sphere has a strong destabilizing effect on the smectic A phase, due the inefficient packing of the molecules into layers. For large hard sphere units the smectic A phase is completely replaced by a smectic C structure. The columnar phase is first stabilized with increasing diameter of the central unit, but for very large hard sphere units it becomes less stable again. The density functional results are in good agreement with the simulations.
Rovibrationally Inelastic Atom-Molecule Collision Cross Sections from a Hard Sphere Model
NASA Astrophysics Data System (ADS)
Lashner, Jacob; Stewart, Brian
2016-05-01
Hard-shell models have long been used to elucidate the principal features of molecular energy transfer and exchange reaction in the A + BC system. Nevertheless, no three-dimensional hard-shell calculation of inelastic collision cross sections has been reported. This work aims to fill that void. A particular motivation comes from our experimental results, which show the importance of equatorial impacts in the vibrational excitation process. Working with the simple hard-sphere model, we incorporated secondary impacts, defined as those in which A strikes C after striking B. Such collisions are important in systems such as Li2 - X, in which vibrational energy transfer occurs principally through side impacts. We discuss the complexity this adds to the model and present fully three-dimensional cross sections for rovibrational excitation of an initially stationary molecule in the homonuclear A + B2 system, examining the cross section as a function of the masses and radii of the atoms. We show how the features in the cross section evolve as these parameters are varied and calculate the contribution of secondary (near-equatorial) impacts to the dynamics. We compare with recent measurements in our laboratory and with the results of quasiclassical trajectories.
Nonclassical Nucleation in a Solid-Solid Transition of Confined Hard Spheres
NASA Astrophysics Data System (ADS)
Qi, Weikai; Peng, Yi; Han, Yilong; Bowles, Richard K.; Dijkstra, Marjolein
2015-10-01
A solid-solid phase transition of colloidal hard spheres confined between two planar hard walls is studied using a combination of molecular dynamics and Monte Carlo simulation. The transition from a solid consisting of five crystalline layers with square symmetry (5 □ ) to a solid consisting of four layers with triangular symmetry (4 △ ) is shown to occur through a nonclassical nucleation mechanism that involves the initial formation of a precritical liquid cluster, within which the cluster of the stable 4 △ phase grows. Free-energy calculations show that the transition occurs in one step, crossing a single free-energy barrier, and that the critical nucleus consists of a small 4 △ solid cluster wetted by a metastable liquid. In addition, the liquid cluster and the solid cluster are shown to grow at the planar hard walls. We also find that the critical nucleus size increases with supersaturation, which is at odds with classical nucleation theory. The △-solid-like cluster is shown to contain both face-centered-cubic and hexagonal-close-packed ordered particles.
Correlation between dynamical and structural heterogeneities in colloidal hard-sphere suspensions
NASA Astrophysics Data System (ADS)
Golde, Sebastian; Palberg, Thomas; Schöpe, Hans Joachim
2016-07-01
Dynamical and structural heterogeneities have long been thought to play a key role in a unified picture of solidification in view of the two competitive processes of crystallization and vitrification. Here, we study these heterogeneities by means of a combination of dynamic and static light-scattering techniques applied to the simplest model system exhibiting crystallization and vitrification: the colloidal hard-sphere system. Our method enables us to quantify and correlate the temporal evolution of the amount of ordered clusters (precursors) and the amount of slow particles. Our analysis shows that their temporal evolutions are closely related and that there is an intimate link between structural and dynamic heterogeneities, crystal nucleation and the non-crystallization transition.
Creep and aging of hard-sphere glasses under constant stress
NASA Astrophysics Data System (ADS)
Ballesta, P.; Petekidis, G.
2016-04-01
We investigate the aging behavior of glassy suspensions of nearly hard-sphere colloids submitted to a constant shear stress. For low stresses, below the yield stress, the system is subject to creep motion. As the sample ages, the shear rate exhibits a power-law decrease with time with exponents that depend on the sample age. We use a combination of rheological experiments with time-resolved photon correlation spectroscopy to investigate the time evolution of the sample dynamics under shear on various time and length scales. Long-time light-scattering experiments reveal the occurrence of microscopic rearrangement events that are linked with the macroscopic strain deformation of the sample. Dynamic time sweep experiments indicate that while the internal microscopic dynamics slow down continuously with waiting time, the storage and loss moduli are almost constant after a fast, weak decrease, resembling the behavior of quenched systems with partially frozen-in stresses.
Hlushak, Stepan
2015-09-28
An analytical expression for the Laplace transform of the radial distribution function of a mixture of hard-sphere chains of arbitrary segment size and chain length is used to rigorously formulate the first-order Barker-Henderson perturbation theory for the contribution of the segment-segment dispersive interactions into thermodynamics of the Lennard-Jones chain mixtures. Based on this approximation, a simple variant of the statistical associating fluid theory is proposed and used to predict properties of several mixtures of chains of different lengths and segment sizes. The theory treats the dispersive interactions more rigorously than the conventional theories and provides means for more accurate description of dispersive interactions in the mixtures of highly asymmetric components.
Equation of state of sticky-hard-sphere fluids in the chemical-potential route.
Rohrmann, René D; Santos, Andrés
2014-04-01
The coupling-parameter method, whereby an extra particle is progressively coupled to the rest of the particles, is applied to the sticky-hard-sphere fluid to obtain its equation of state in the so-called chemical-potential route (μ route). As a consistency test, the results for one-dimensional sticky particles are shown to be exact. Results corresponding to the three-dimensional case (Baxter's model) are derived within the Percus-Yevick approximation by using different prescriptions for the dependence of the interaction potential of the extra particle on the coupling parameter. The critical point and the coexistence curve of the gas-liquid phase transition are obtained in the μ route and compared with predictions from other thermodynamics routes and from computer simulations. The results show that the μ route yields a general better description than the virial, energy, compressibility, and zero-separation routes. PMID:24827207
Apparent wall slip in non-Brownian hard-sphere suspensions.
Korhonen, Marko; Mohtaschemi, Mikael; Puisto, Antti; Illa, Xavier; Alava, Mikko J
2015-05-01
We analyze apparent wall slip, the reduction of particle concentration near the wall, in hard-sphere suspensions at concentrations well below the jamming limit utilizing a continuum level diffusion model. The approach extends a constitutive equation proposed earlier with two additional potentials describing the effects of gravitation and wall-particle repulsion. We find that although both mechanisms are shear independent by nature, due to the shear-rate-dependent counter-balancing particle migration fluxes, the resulting net effect is non-linearly shear dependent, causing larger slip at small shear rates. In effect, this shows up in the classically measured flow curves as a mild shear thickening regime at the transition from small to intermediate shear rates. PMID:25998170
Direct measurement of the free energy of aging hard sphere colloidal glasses.
Zargar, Rojman; Nienhuis, Bernard; Schall, Peter; Bonn, Daniel
2013-06-21
The nature of the glass transition is one of the most important unsolved problems in condensed matter physics. The difference between glasses and liquids is believed to be caused by very large free energy barriers for particle rearrangements; however, so far it has not been possible to confirm this experimentally. We provide the first quantitative determination of the free energy for an aging hard sphere colloidal glass. The determination of the free energy allows for a number of new insights in the glass transition, notably the quantification of the strong spatial and temporal heterogeneity in the free energy. A study of the local minima of the free energy reveals that the observed variations are directly related to the rearrangements of the particles. Our main finding is that the probability of particle rearrangements shows a power law dependence on the free energy changes associated with the rearrangements similar to the Gutenberg-Richter law in seismology. PMID:23829762
Upper bound on the Edwards entropy in frictional monodisperse hard-sphere packings.
Baranau, Vasili; Zhao, Song-Chuan; Scheel, Mario; Tallarek, Ulrich; Schröter, Matthias
2016-05-01
We extend the Widom particle insertion method [B. Widom, J. Chem. Phys., 1963, 39, 2808-2812] to determine an upper bound sub on the Edwards entropy in frictional hard-sphere packings. sub corresponds to the logarithm of the number of mechanically stable configurations for a given volume fraction and boundary conditions. To accomplish this, we extend the method for estimating the particle insertion probability through the pore-size distribution in frictionless packings [V. Baranau, et al., Soft Matter, 2013, 9, 3361-3372] to the case of frictional particles. We use computer-generated and experimentally obtained three-dimensional sphere packings with volume fractions φ in the range 0.551-0.65. We find that sub has a maximum in the vicinity of the Random Loose Packing Limit φRLP = 0.55 and decreases then monotonically with increasing φ to reach a minimum at φ = 0.65. Further on, sub does not distinguish between real mechanical stability and packings in close proximity to mechanical stable configurations. The probability to find a given number of contacts for a particle inserted in a large enough pore does not depend on φ, but it decreases strongly with the contact number. PMID:27020114
Fluids density functional theory studies of supramolecular polymers at a hard surface
NASA Astrophysics Data System (ADS)
McGarrity, E. S.; Thijssen, J. M.; Besseling, N. A. M.
2010-08-01
We have applied a fluids density functional theory based on that of Yu and Wu [J. Chem. Phys. 116, 7094 (2002)] to treat reversible supramolecular polymers near a hard surface. This approach combines a hard-sphere fluids density functional theory with the first-order thermodynamic perturbation theory of Wertheim. The supramolecular polymers are represented in the theory by hard-spheres with two associating sites. We explore the effects of the bonding scheme, monomer concentration, and association energy upon the equilibrium chain sizes and the depletion lengths. This study is performed on simple systems containing two-site monomers and binary mixtures of two-site monomers combined with end stopper monomers which have only a single association site. Our model has correct behavior in the dilute and overlap regimes and the bulk results can be easily connected to simpler random-flight models. We find that there is a nonmonotonic behavior of the depletion length of the polymers as a function of concentration and that this depletion length can be controlled through the concentration of end stoppers. These results are applicable to the study of colloidal dispersions in supramolecular polymer solutions.
Thorneywork, Alice L; Rozas, Roberto E; Dullens, Roel P A; Horbach, Jürgen
2015-12-31
We compare experimental results from a quasi-two-dimensional colloidal hard sphere fluid to a Monte Carlo simulation of hard disks with small particle displacements. The experimental short-time self-diffusion coefficient D(S) scaled by the diffusion coefficient at infinite dilution, D(0), strongly depends on the area fraction, pointing to significant hydrodynamic interactions at short times in the experiment, which are absent in the simulation. In contrast, the area fraction dependence of the experimental long-time self-diffusion coefficient D(L)/D(0) is in quantitative agreement with D(L)/D(0) obtained from the simulation. This indicates that the reduction in the particle mobility at short times due to hydrodynamic interactions does not lead to a proportional reduction in the long-time self-diffusion coefficient. Furthermore, the quantitative agreement between experiment and simulation at long times indicates that hydrodynamic interactions effectively do not affect the dependence of D(L)/D(0) on the area fraction. In light of this, we discuss the link between structure and long-time self-diffusion in terms of a configurational excess entropy and do not find a simple exponential relation between these quantities for all fluid area fractions. PMID:26765032
NASA Astrophysics Data System (ADS)
Thorneywork, Alice L.; Rozas, Roberto E.; Dullens, Roel P. A.; Horbach, Jürgen
2015-12-01
We compare experimental results from a quasi-two-dimensional colloidal hard sphere fluid to a Monte Carlo simulation of hard disks with small particle displacements. The experimental short-time self-diffusion coefficient DS scaled by the diffusion coefficient at infinite dilution, D0, strongly depends on the area fraction, pointing to significant hydrodynamic interactions at short times in the experiment, which are absent in the simulation. In contrast, the area fraction dependence of the experimental long-time self-diffusion coefficient DL/D0 is in quantitative agreement with DL/D0 obtained from the simulation. This indicates that the reduction in the particle mobility at short times due to hydrodynamic interactions does not lead to a proportional reduction in the long-time self-diffusion coefficient. Furthermore, the quantitative agreement between experiment and simulation at long times indicates that hydrodynamic interactions effectively do not affect the dependence of DL/D0 on the area fraction. In light of this, we discuss the link between structure and long-time self-diffusion in terms of a configurational excess entropy and do not find a simple exponential relation between these quantities for all fluid area fractions.
Tensorial density functional theory for non-spherical hard-body fluids.
Hansen-Goos, Hendrik; Mecke, Klaus
2010-09-15
In a recent publication (Hansen-Goos and Mecke 2009 Phys. Rev. Lett. 102 018302) we constructed a free energy functional for the inhomogeneous hard-body fluid, which reduces to Rosenfeld's fundamental measure theory (Rosenfeld 1989 Phys. Rev. Lett. 63 980) when applied to hard spheres. The new functional is able to yield the isotropic-nematic transition for the hard-spherocylinder fluid in contrast to Rosenfeld's fundamental measure theory for non-spherical particles (Rosenfeld 1994 Phys. Rev. E 50 R3318). The description of inhomogeneous isotropic fluids is also improved when compared with data from Monte Carlo simulations for hard spherocylinders in contact with a planar hard wall. However, the new functional for the inhomogeneous fluid in general does not comply with the exact second order virial expansion. We introduced the ζ correction in order to minimize the deviation from Onsager's exact result in the isotropic bulk fluid. In this article we give a detailed account of the construction of the new functional. An extension of the ζ correction makes the latter better suited for non-isotropic particle distributions. The extended ζ correction is shown to improve the description of the isotropic-nematic bulk phase diagram while it has little effect on the results for the isotropic but inhomogeneous hard-spherocylinder fluid. We argue that the gain from using higher order tensorial weighted densities in the theory is likely to be inferior to the associated increase in complexity. PMID:21386523
Härtel, A; Löwen, H
2010-03-17
The recently developed fundamental measure density functional theory (Hansen-Goos and Mecke 2009 Phys. Rev. Lett. 102 018302) for an inhomogeneous anisotropic hard body fluid is used as a basic ingredient in treating the Brownian dynamics of hard spherocylinders. After discussing the relevance of a free parameter in the fundamental measure density functional for the isotropic-nematic transition in equilibrium, we discuss the equilibrium phase behaviour of hard spherocylinders in a static external potential which couples only to the orientations. For external potentials favouring rod orientations along the poles of the unit sphere, there is a well-known paranematic-nematic transition which ceases to exist above a threshold of the strength V(0) of the external potential. However, when orientations along the equator are more favoured, in the plane of the potential energy V(0) and density, there is a phase transition from paranematic to nematic for any strength, which becomes second order above a critical threshold of V(0). The full equilibrium phase diagram in the V(0)-density plane is computed for a fixed rod aspect ratio of 5. For the equatorial cases, strength V(0) is then oscillating in time and dynamical density functional theory is used to compute the evolution of the orientational distribution. A subtle resonance for increasing oscillation frequencies is detected if the oscillating V(0) crosses the paranematic-nematic phase transition. PMID:21389446
NASA Astrophysics Data System (ADS)
McBride, Carl; Vega, Carlos
2002-12-01
A study of a rigid fully flexible fused hard sphere model [C. McBride, C. Vega, and L. G. MacDowell, Phys. Rev. E 64, 011703 (2001)] is extended to the smectic and solid branches of the phase diagram. Computer simulations have been performed for a completely rigid model composed of 15 fused hard spheres (15+0), a model of 15 fused hard spheres of which 2 monomers at one end of the model form a flexible tail (13+2), and a model consisting of 15 fused hard spheres with 5 monomers forming a flexible tail (10+5). For the 15+0 model the phase sequence isotropic-nematic-smectic A-columnar is found on compression, and the sequence solid-smectic A-nematic-isotropic on expansion. For the 13+2 model the phase sequence isotropic-nematic-smectic C is found on compression, and the sequence solid-smectic A-nematic-isotropic on expansion. For the 10+5 model the phase sequence isotropic-glass is found on compression. The expansion runs displayed the phase sequence solid-smectic A-isotropic. The introduction of flexibility was seen to stabilize the smectic A phase at the expense of the nematic phase.
ERIC Educational Resources Information Center
Duer, W. C.; And Others
1977-01-01
Discusses comparisons of packing densities derived from known molar volume data of liquids and solutions. Suggests further studies for using assemblies of spheres as models for simple liquids and solutions. (MLH)
NASA Astrophysics Data System (ADS)
Qiao, Yu; Liu, Xuejiao; Chen, Minxin; Lu, Benzhuo
2016-04-01
The hard sphere repulsion among ions can be considered in the Poisson-Nernst-Planck (PNP) equations by combining the fundamental measure theory (FMT). To reduce the nonlocal computational complexity in 3D simulation of biological systems, a local approximation of FMT is derived, which forms a local hard sphere PNP (LHSPNP) model. In the derivation, the excess chemical potential from hard sphere repulsion is obtained with the FMT and has six integration components. For the integrands and weighted densities in each component, Taylor expansions are performed and the lowest order approximations are taken, which result in the final local hard sphere (LHS) excess chemical potential with four components. By plugging the LHS excess chemical potential into the ionic flux expression in the Nernst-Planck equation, the three dimensional LHSPNP is obtained. It is interestingly found that the essential part of free energy term of the previous size modified model (Borukhov et al. in Phys Rev Lett 79:435-438, 1997; Kilic et al. in Phys Rev E 75:021502, 2007; Lu and Zhou in Biophys J 100:2475-2485, 2011; Liu and Eisenberg in J Chem Phys 141:22D532, 2014) has a very similar form to one term of the LHS model, but LHSPNP has more additional terms accounting for size effects. Equation of state for one component homogeneous fluid is studied for the local hard sphere approximation of FMT and is proved to be exact for the first two virial coefficients, while the previous size modified model only presents the first virial coefficient accurately. To investigate the effects of LHS model and the competitions among different counterion species, numerical experiments are performed for the traditional PNP model, the LHSPNP model, the previous size modified PNP (SMPNP) model and the Monte Carlo simulation. It's observed that in steady state the LHSPNP results are quite different from the PNP results, but are close to the SMPNP results under a wide range of boundary conditions. Besides, in both
NASA Astrophysics Data System (ADS)
Lechman, Jeremy; Pierce, Flint
2012-02-01
Diffusive transport is a ubiquitous process that is typically understood in terms of a classical random walk of non-interacting particles. Here we present the results for a model of hard-sphere colloids in a Newtonian incompressible solvent at various volume fractions below the ordering transition (˜50%). We numerically simulate the colloidal systems via Fast Lubrication Dynamics -- a Brownian Dynamics approach with corrected mean-field hydrodynamic interactions. Colloid-colloid interactions are also included so that we effectively solve a system of interacting Langevin equations. The results of the simulations are analyzed in terms of the diffusion coefficient as a function of time with the early and late time diffusion coefficients comparing well with experimental results. An interpretation of the full time dependent behavior of the diffusion coefficient and mean-squared displacement is given in terms of a continuous time random walk. Therefore, the deterministic, continuum diffusion equation which arises from the discrete, interacting random walkers is presented. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Low-shear Viscosity and Diffusion of Hard-sphere Dispersion at High Concentration
NASA Astrophysics Data System (ADS)
Cheng, Zhengdong; Chaikin, P. M.; Phan, See-Eng; Zhu, Jixiang; Russel, W. B.
1997-03-01
We are interested in the rheology of hard-sphere dispersion at high concentration, especially the asymptotic behavior near the glass transition, which is the ideal place to test various theories.(J.F. Brady, J. Chem. phys. 99(1993)567) (M. Tokuyama and I. Oppenheim, Phys. Rev. E. 50(1994)R16) The dispersion studied is silica in Ethylene glycol/Glycerol/NaCl. Low-shear viscosity is measured by a Zimm viscometer. The data are consistent with recent PMMA measurement at low concentration(P.N. Segreet. al.), Phys. Rev. Lett. 75(1995)958; 76(1996)585 (See-eng Phan et. al.), Phys. rev. E., to be published., and at high concentration (metastable state) are better described by the Doolittle equation as in earlier experiments (L. Marshall, C.F. Zukoski IV, J. Phys. Chem. 94(1990)1164) (L.V. Woodcock, C.A. Angell, Phys. Rev. Lett. 47(1981)1129)). No theory yet gives a complete interpretion of the data. Dynamic light scattering (ensemble averaged) is used to measure self diffusion.
Disappearance of a Stacking Fault in Hard-Sphere Crystals under Gravity
NASA Astrophysics Data System (ADS)
Mori, A.; Suzuki, Y.; Matsuo, S.
In the first part of this paper, a review is given on the mechanismfor the disappearance of an intrinsic stacking fault in a hard-sphere (HS) crystal under gravity, which we recently discovered by Monte Carlo (MC) simulations [A. Mori et al., J. Chem. Phys. 124 (2006), 17450; Mol. Phys. 105 (2007), 1377]. We have observed, in the case of fcc (001) stacking, that the intrinsic stacking fault running along an oblique direction shrunk through the gliding of a Shockley partial dislocation at the lower end of the stacking fault. In order to address the shortcomings and approximations of previous simulations, such as the use of periodic ] boundary condition (PBC) and the fact that the fcc (001) stacking had been realized by the stress from the small PBC box, we present an elastic strain energy calculation for an infinite system and a MC simulation result for HSs in a pyramidal pit under gravity. In particular, the geometry of the latter has already been tested experi mentally [S. Matsuo et al., Appl. Phys. Lett. 82 (2003), 4283]. The advantage of using a pyramidal pit as a template as well as the feasibility of the mechanism we describe is demonstrated.
Cavity averages for hard spheres in the presence of polydispersity and incomplete data.
Schindler, Michael; Maggs, A C
2015-09-01
We develop a cavity-based method which allows to extract thermodynamic properties from position information in hard-sphere/disk systems. So far, there are available-volume and free-volume methods. We add a third one, which we call available volume after take-out, and which is shown to be mathematically equivalent to the others. In applications, where data sets are finite, all three methods show limitations, and they do this in different parameter ranges. We illustrate the principal equivalence and the limitations on data from molecular dynamics: In particular, we test robustness against missing data. We have in mind experimental limitations where there is a small polydispersity, say 4% in the particle radii, but individual radii cannot be determined. We observe that, depending on the used method, the errors in such a situation are easily 100% for the pressure and 10kT for the chemical potentials. Our work is meant as guideline to the experimentalists for choosing the right one of the three methods, in order to keep the outcome of experimental data analysis meaningful. PMID:26359237
Crystal nucleation in the hard-sphere system revisited: a critical test of theoretical approaches.
Tóth, Gyula I; Gránásy, László
2009-04-16
The hard-sphere system is the best known fluid that crystallizes: the solid-liquid interfacial free energy, the equations of state, and the height of the nucleation barrier are known accurately, offering a unique possibility for a quantitative validation of nucleation theories. A recent significant downward revision of the interfacial free energy from approximately 0.61kT/sigma(2) to (0.56 +/- 0.02)kT/sigma(2) [Davidchack, R.; Morris, J. R.; Laird, B. B. J. Chem. Phys. 2006, 125, 094710] necessitates a re-evaluation of theoretical approaches to crystal nucleation. This has been carried out for the droplet model of the classical nucleation theory (CNT), the self-consistent classical theory (SCCT), a phenomenological diffuse interface theory (DIT), and single- and two-field variants of the phase field theory that rely on either the usual double-well and interpolation functions (PFT/S1 and PFT/S2, respectively) or on a Ginzburg-Landau expanded free energy that reflects the crystal symmetries (PFT/GL1 and PFT/GL2). We find that the PFT/GL1, PFT/GL2, and DIT models predict fairly accurately the height of the nucleation barrier known from Monte Carlo simulations in the volume fraction range of 0.52 < varphi < 0.54, whereas the CNT, SCCT, PFT/S1, and PFT/S2 models underestimate it significantly. PMID:19320450
NASA Astrophysics Data System (ADS)
Elfimova, Ekaterina A.; Karavaeva, Tatyana E.; Ivanov, Alexey O.
2014-12-01
A method for calculation of the free energy of dipolar hard spheres under the presence of an applied magnetic field is presented. The method is based on the virial expansion in terms of density as well as the dipolar coupling constant λ, and it uses diagram technique. The formulas and the diagrams, needed to calculate the second B2 and third B3 virial coefficients, are derived up to the order of ˜λ3, and compared to the zero-field case. The formula for B2 is the same as in the zero-field case; the formula for B3, however, is different in an applied field, and a derivation is presented. This is a surprising result which is not emphasized in standard texts, but which has been noticed before in the virial expansion for flexible molecules (Caracciolo et al., 2006; Caracciolo et al., 2008). To verify the correctness of the obtained formulas, B2 and B3 were calculated within the accuracy of λ2, which were applied to initial magnetic susceptibility. The obtained expression fully coincides with the well-known theories (Morozov and Lebedev, 1990; Huke and Lücke, 2000; Ivanov and Kuznetsova, 2001), which used different methods to calculate the initial magnetic susceptibility.
Liu, Yi; Bławzdziewicz, Jerzy; Cichocki, Bogdan; Dhont, Jan K G; Lisicki, Maciej; Wajnryb, Eligiusz; Young, Y-N; Lang, Peter R
2015-10-01
In this article we report on a study of the near-wall dynamics of suspended colloidal hard spheres over a broad range of volume fractions. We present a thorough comparison of experimental data with predictions based on a virial approximation and simulation results. We find that the virial approach describes the experimental data reasonably well up to a volume fraction of ϕ≈ 0.25 which provides us with a fast and non-costly tool for the analysis and prediction of evanescent wave DLS data. Based on this we propose a new method to assess the near-wall self-diffusion at elevated density. Here, we qualitatively confirm earlier results [Michailidou, et al., Phys. Rev. Lett., 2009, 102, 068302], which indicate that many-particle hydrodynamic interactions are diminished by the presence of the wall at increasing volume fractions as compared to bulk dynamics. Beyond this finding we show that this diminishment is different for the particle motion normal and parallel to the wall. PMID:26264420
Combined temperature and density series for fluid-phase properties. I. Square-well spheres
Elliott, J. Richard; Schultz, Andrew J.; Kofke, David A.
2015-09-21
Cluster integrals are evaluated for the coefficients of the combined temperature- and density-expansion of pressure: Z = 1 + B{sub 2}(β) η + B{sub 3}(β) η{sup 2} + B{sub 4}(β) η{sup 3} + ⋯, where Z is the compressibility factor, η is the packing fraction, and the B{sub i}(β) coefficients are expanded as a power series in reciprocal temperature, β, about β = 0. The methodology is demonstrated for square-well spheres with λ = [1.2-2.0], where λ is the well diameter relative to the hard core. For this model, the B{sub i} coefficients can be expressed in closed form as a function of β, and we develop appropriate expressions for i = 2-6; these expressions facilitate derivation of the coefficients of the β series. Expanding the B{sub i} coefficients in β provides a correspondence between the power series in density (typically called the virial series) and the power series in β (typically called thermodynamic perturbation theory, TPT). The coefficients of the β series result in expressions for the Helmholtz energy that can be compared to recent computations of TPT coefficients to fourth order in β. These comparisons show good agreement at first order in β, suggesting that the virial series converges for this term. Discrepancies for higher-order terms suggest that convergence of the density series depends on the order in β. With selection of an appropriate approximant, the treatment of Helmholtz energy that is second order in β appears to be stable and convergent at least to the critical density, but higher-order coefficients are needed to determine how far this behavior extends into the liquid.
Combined temperature and density series for fluid-phase properties. I. Square-well spheres.
Elliott, J Richard; Schultz, Andrew J; Kofke, David A
2015-09-21
Cluster integrals are evaluated for the coefficients of the combined temperature- and density-expansion of pressure: Z = 1 + B2(β) η + B3(β) η(2) + B4(β) η(3) + ⋯, where Z is the compressibility factor, η is the packing fraction, and the B(i)(β) coefficients are expanded as a power series in reciprocal temperature, β, about β = 0. The methodology is demonstrated for square-well spheres with λ = [1.2-2.0], where λ is the well diameter relative to the hard core. For this model, the B(i) coefficients can be expressed in closed form as a function of β, and we develop appropriate expressions for i = 2-6; these expressions facilitate derivation of the coefficients of the β series. Expanding the B(i) coefficients in β provides a correspondence between the power series in density (typically called the virial series) and the power series in β (typically called thermodynamic perturbation theory, TPT). The coefficients of the β series result in expressions for the Helmholtz energy that can be compared to recent computations of TPT coefficients to fourth order in β. These comparisons show good agreement at first order in β, suggesting that the virial series converges for this term. Discrepancies for higher-order terms suggest that convergence of the density series depends on the order in β. With selection of an appropriate approximant, the treatment of Helmholtz energy that is second order in β appears to be stable and convergent at least to the critical density, but higher-order coefficients are needed to determine how far this behavior extends into the liquid. PMID:26395690
Combined temperature and density series for fluid-phase properties. I. Square-well spheres
NASA Astrophysics Data System (ADS)
Elliott, J. Richard; Schultz, Andrew J.; Kofke, David A.
2015-09-01
Cluster integrals are evaluated for the coefficients of the combined temperature- and density-expansion of pressure: Z = 1 + B2(β) η + B3(β) η2 + B4(β) η3 + ⋯, where Z is the compressibility factor, η is the packing fraction, and the Bi(β) coefficients are expanded as a power series in reciprocal temperature, β, about β = 0. The methodology is demonstrated for square-well spheres with λ = [1.2-2.0], where λ is the well diameter relative to the hard core. For this model, the Bi coefficients can be expressed in closed form as a function of β, and we develop appropriate expressions for i = 2-6; these expressions facilitate derivation of the coefficients of the β series. Expanding the Bi coefficients in β provides a correspondence between the power series in density (typically called the virial series) and the power series in β (typically called thermodynamic perturbation theory, TPT). The coefficients of the β series result in expressions for the Helmholtz energy that can be compared to recent computations of TPT coefficients to fourth order in β. These comparisons show good agreement at first order in β, suggesting that the virial series converges for this term. Discrepancies for higher-order terms suggest that convergence of the density series depends on the order in β. With selection of an appropriate approximant, the treatment of Helmholtz energy that is second order in β appears to be stable and convergent at least to the critical density, but higher-order coefficients are needed to determine how far this behavior extends into the liquid.
Kalyuzhnyi, Y.V. |; Lin, C.; Stell, G.
1998-04-01
We continue here our series of studies in which integral-equation theory is developed and used for the monomer-monomer correlation functions in a fluid of multicomponent freely jointed hard-sphere polymers. In this study our approach is based on Wertheim{close_quote}s polymer Percus{endash}Yevick (PPY) theory supplemented by the ideal-chain approximation; it can be regarded as a simplified version of Wertheim{close_quote}s four-density PPY approximation for associating fluids considered in the complete-association limit. The numerical procedure of this simplified theory is much easier than that of the original Wertheim{close_quote}s four-density PPY approximation, but the degree of accuracy is reduced. The theory can also be regarded as an extension of the PPY theory for the homonuclear polymer system proposed by Chang and Sandler [J. Chem. Phys. {bold 102}, 437 (1995)]. Their work is based upon a description of a system of hard-sphere monomers that associate into a polydisperse system of chains of prescribed mean length. Our theory instead directly describes a multicomponent system of associating monomers that form monodisperse chains of prescribed length upon complete association. An analytical solution of the PPY ideal-chain approximation for the general case of a multicomponent mixture of heteronuclear hard-sphere linear chain molecules is given. Its use is illustrated by numerical results for two models of copolymer fluids, a symmetrical diblock copolymer system, and an alternating copolymer system. The comparison with Monte Carlo simulations is given to gauge the accuracy of the theory. We find for the molecules we study here that predictions of our theory for heteronuclear chain systems have the same degree of accuracy as Chang and Sandler{close_quote}s theory for homonuclear chain systems. {copyright} {ital 1998 American Institute of Physics.}
Hayashi, Tomohiko; Oshima, Hiraku; Harano, Yuichi; Kinoshita, Masahiro
2016-09-01
For neutral hard-sphere solutes, we compare the reduced density profile of water around a solute g(r), solvation free energy μ, energy U, and entropy S under the isochoric condition predicted by the two theories: dielectrically consistent reference interaction site model (DRISM) and angle-dependent integral equation (ADIE) theories. A molecular model for water pertinent to each theory is adopted. The hypernetted-chain (HNC) closure is employed in the ADIE theory, and the HNC and Kovalenko-Hirata (K-H) closures are tested in the DRISM theory. We also calculate g(r), U, S, and μ of the same solute in a hard-sphere solvent whose molecular diameter and number density are set at those of water, in which case the radial-symmetric integral equation (RSIE) theory is employed. The dependences of μ, U, and S on the excluded volume and solvent-accessible surface area are analyzed using the morphometric approach (MA). The results from the ADIE theory are in by far better agreement with those from computer simulations available for g(r), U, and μ. For the DRISM theory, g(r) in the vicinity of the solute is quite high and becomes progressively higher as the solute diameter d U increases. By contrast, for the ADIE theory, it is much lower and becomes further lower as d U increases. Due to unphysically positive U and significantly larger |S|, μ from the DRISM theory becomes too high. It is interesting that μ, U, and S from the K-H closure are worse than those from the HNC closure. Overall, the results from the DRISM theory with a molecular model for water are quite similar to those from the RSIE theory with the hard-sphere solvent. Based on the results of the MA analysis, we comparatively discuss the different theoretical methods for cases where they are applied to studies on the solvation of a protein. PMID:27366886
NASA Astrophysics Data System (ADS)
Hayashi, Tomohiko; Oshima, Hiraku; Harano, Yuichi; Kinoshita, Masahiro
2016-09-01
For neutral hard-sphere solutes, we compare the reduced density profile of water around a solute g(r), solvation free energy μ, energy U, and entropy S under the isochoric condition predicted by the two theories: dielectrically consistent reference interaction site model (DRISM) and angle-dependent integral equation (ADIE) theories. A molecular model for water pertinent to each theory is adopted. The hypernetted-chain (HNC) closure is employed in the ADIE theory, and the HNC and Kovalenko–Hirata (K–H) closures are tested in the DRISM theory. We also calculate g(r), U, S, and μ of the same solute in a hard-sphere solvent whose molecular diameter and number density are set at those of water, in which case the radial-symmetric integral equation (RSIE) theory is employed. The dependences of μ, U, and S on the excluded volume and solvent-accessible surface area are analyzed using the morphometric approach (MA). The results from the ADIE theory are in by far better agreement with those from computer simulations available for g(r), U, and μ. For the DRISM theory, g(r) in the vicinity of the solute is quite high and becomes progressively higher as the solute diameter d U increases. By contrast, for the ADIE theory, it is much lower and becomes further lower as d U increases. Due to unphysically positive U and significantly larger |S|, μ from the DRISM theory becomes too high. It is interesting that μ, U, and S from the K–H closure are worse than those from the HNC closure. Overall, the results from the DRISM theory with a molecular model for water are quite similar to those from the RSIE theory with the hard-sphere solvent. Based on the results of the MA analysis, we comparatively discuss the different theoretical methods for cases where they are applied to studies on the solvation of a protein.
NASA Astrophysics Data System (ADS)
Oshima, Hiraku; Kinoshita, Masahiro
2015-04-01
In earlier works, we showed that the entropic effect originating from the translational displacement of water molecules plays the pivotal role in protein folding and denaturation. The two different solvent models, hard-sphere solvent and model water, were employed in theoretical methods wherein the entropic effect was treated as an essential factor. However, there were similarities and differences in the results obtained from the two solvent models. In the present work, to unveil the physical origins of the similarities and differences, we simultaneously consider structural transition, cold denaturation, and pressure denaturation for the same protein by employing the two solvent models and considering three different thermodynamic states for each solvent model. The solvent-entropy change upon protein folding/unfolding is decomposed into the protein-solvent pair (PA) and many-body (MB) correlation components using the integral equation theories. Each component is further decomposed into the excluded-volume (EV) and solvent-accessible surface (SAS) terms by applying the morphometric approach. The four physically insightful constituents, (PA, EV), (PA, SAS), (MB, EV), and (MB, SAS), are thus obtained. Moreover, (MB, SAS) is discussed by dividing it into two factors. This all-inclusive investigation leads to the following results: (1) the protein-water many-body correlation always plays critical roles in a variety of folding/unfolding processes; (2) the hard-sphere solvent model fails when it does not correctly reproduce the protein-water many-body correlation; (3) the hard-sphere solvent model becomes problematic when the dependence of the many-body correlation on the solvent number density and temperature is essential: it is not quite suited to studies on cold and pressure denaturating of a protein; (4) when the temperature and solvent number density are limited to the ambient values, the hard-sphere solvent model is usually successful; and (5) even at the ambient
Oshima, Hiraku; Kinoshita, Masahiro
2015-04-14
In earlier works, we showed that the entropic effect originating from the translational displacement of water molecules plays the pivotal role in protein folding and denaturation. The two different solvent models, hard-sphere solvent and model water, were employed in theoretical methods wherein the entropic effect was treated as an essential factor. However, there were similarities and differences in the results obtained from the two solvent models. In the present work, to unveil the physical origins of the similarities and differences, we simultaneously consider structural transition, cold denaturation, and pressure denaturation for the same protein by employing the two solvent models and considering three different thermodynamic states for each solvent model. The solvent-entropy change upon protein folding/unfolding is decomposed into the protein-solvent pair (PA) and many-body (MB) correlation components using the integral equation theories. Each component is further decomposed into the excluded-volume (EV) and solvent-accessible surface (SAS) terms by applying the morphometric approach. The four physically insightful constituents, (PA, EV), (PA, SAS), (MB, EV), and (MB, SAS), are thus obtained. Moreover, (MB, SAS) is discussed by dividing it into two factors. This all-inclusive investigation leads to the following results: (1) the protein-water many-body correlation always plays critical roles in a variety of folding/unfolding processes; (2) the hard-sphere solvent model fails when it does not correctly reproduce the protein-water many-body correlation; (3) the hard-sphere solvent model becomes problematic when the dependence of the many-body correlation on the solvent number density and temperature is essential: it is not quite suited to studies on cold and pressure denaturating of a protein; (4) when the temperature and solvent number density are limited to the ambient values, the hard-sphere solvent model is usually successful; and (5) even at the ambient
Zhang, Kai; Smith, W Wendell; Wang, Minglei; Liu, Yanhui; Schroers, Jan; Shattuck, Mark D; O'Hern, Corey S
2014-09-01
We perform molecular dynamics simulations to compress binary hard spheres into jammed packings as a function of the compression rate R, size ratio α, and number fraction x(S) of small particles to determine the connection between the glass-forming ability (GFA) and packing efficiency in bulk metallic glasses (BMGs). We define the GFA by measuring the critical compression rate R(c), below which jammed hard-sphere packings begin to form "random crystal" structures with defects. We find that for systems with α≳0.8 that do not demix, R(c) decreases strongly with Δϕ(J), as R(c)∼exp(-1/Δϕ(J)(2)), where Δϕ(J) is the difference between the average packing fraction of the amorphous packings and random crystal structures at R(c). Systems with α≲0.8 partially demix, which promotes crystallization, but we still find a strong correlation between R(c) and Δϕ(J). We show that known metal-metal BMGs occur in the regions of the α and x(S) parameter space with the lowest values of R(c) for binary hard spheres. Our results emphasize that maximizing GFA in binary systems involves two competing effects: minimizing α to increase packing efficiency, while maximizing α to prevent demixing. PMID:25314450
Trokhymchuk; Orozco; Pizio; Vlachy
1998-11-15
The thermodynamics of a two-component fluid with a hard core interaction and screened Coulomb (Yukawa) interaction between particles, similar to the primitive model of an electrolyte solution, adsorbed in a disordered matrix of hard spheres, is studied by using replica Ornstein-Zernike integral equations and the mean spherical approximation (MSA). The gas-liquid transition is localized. The coexistence curve is investigated dependent on the range of interaction between fluid species, on matrix density, and on fluid-matrix attraction. We have observed shrinking of the coexistence envelope with increasing matrix density. The critical temperature of adsorbed mixture decreases with increasing matrix density. The critical density is less affected; however, it also decreases slightly. The critical temperature is sensitive to the fluid species-matrix attraction and depends nonmonotonously on their strength. For a given matrix microporosity, it increases slightly and then decreases with augmenting strength of fluid-matrix attraction. The critical density is less affected by this attraction. However, it decreases for the model with a sufficiently long-range tail of fluid-matrix attraction. Copyright 1998 Academic Press. PMID:9792783
Sedimentation and Crystallization of Hard-Sphere Colloidal Suspensions: Theory and Experiment
NASA Astrophysics Data System (ADS)
Davis, Kevin Eugene
Sedimentation and ultrafiltration are important processes for removing solids from suspensions. The Kynch theory describes the transient settling of non-colloidal particles forming an incompressible sediment by providing a solution to the convective conservation equation. This solution predicts the evolution of several different regions. Subsequent treatments have accounted for compressibility within the sediment. These modifications, nevertheless, rely entirely on Kynch theory for analytical description, differing only by the assumed boundary condition imposed by the sediment. We present a model of sedimentation for colloidal systems by including a diffusion term in the governing equation. In the regions above the sediment, this term acts as a small perturbation to the Kynch theory. Within the sediment, owing to the high volume fraction, diffusion is comparable to convection. Slow compression to the maximum volume fraction contrasts the incompressibility of the Kynch theory. Application of the method of matched asymptotic expansions to the conservation equation enables us to complete a description of the settling process, in particular, the volume fraction evolution within the sediment. This method is also applied to the related ultrafiltration process. Colloidal dispersions exhibit thermodynamic properties similar to molecular systems, including a hard-sphere disorder -to-order transition, i.e. freezing or crystallization, at particle volume fractions above 0.50. Throughout concentrated suspensions investigators have observed nucleation and growth of small ordered regions. Our dilute suspensions of organophilic silica in cyclohexane depend on settling to concentrate particles. In contrast to the above we observe ordered sediments produced by one-dimensional crystal growth. The slow sedimentation of small particles permits rearrangement into the iridescent ordered structure at the phase boundary. Suspensions with particle sizes of up to 0.34mum easily form fully
Density-functional theory of inhomogeneous systems of hard spherocylinders
Velasco; Mederos; Sullivan
2000-09-01
The smectic-A phase boundaries of a hard-spherocylinder fluid are calculated using a density-functional theory based on one proposed earlier by Somoza and Tarazona [Phys. Rev. A 41, 965 (1990)]. Our calculations do not employ the translation-rotation decoupling approximation used in previous density-functional theories. The calculated phase boundaries agree well with computer simulation results up to aspect ratios L/D approximately 5 and are in better agreement with the simulations than are previous theories. We generalize the model fluid by including long-range interactions with quadrupolar orientational symmetry, which are taken into account by mean-field approximation. For sufficiently large strength, these interactions produce a smectic-C phase, which undergoes either a continuous or weakly first-order transition to the smectic-A phase. The theory and numerical methods discussed here can be applied to the analysis of interfacial phenomena. PMID:11088887
Bending rigidity and higher-order curvature terms for the hard-sphere fluid near a curved wall.
Urrutia, Ignacio
2014-03-01
In this work I derive analytic expressions for the curvature-dependent fluid-substrate surface tension of a hard-sphere fluid on a hard curved wall. In the first step, the curvature thermodynamic properties are found as truncated power series in the activity in terms of the exactly known second- and third-order cluster integrals of the hard-sphere fluid near spherical and cylindrical walls. These results are then expressed as packing fraction power series and transformed to different reference regions, which is equivalent to considering different positions of the dividing surface. Based on the truncated series it is shown that the bending rigidity of the system is non-null and that higher-order terms in the curvature also exist. In the second step, approximate analytic expressions for the surface tension, the Tolman length, the bending rigidity, and the Gaussian rigidity as functions of the packing fraction are found by considering the known terms of the series expansion complemented with a simple fitting approach. It is found that the obtained formulas accurately describe the curvature thermodynamic properties of the system; further, they are more accurate than any previously published expressions. PMID:24730805
NASA Astrophysics Data System (ADS)
Wolf, Aaron S.; Asimow, Paul D.; Stevenson, David J.
2015-08-01
We develop a new model to understand and predict the behavior of oxide and silicate melts at extreme temperatures and pressures, including deep mantle conditions like those in the early Earth magma ocean. The Coordinated Hard Sphere Mixture (CHaSM) is based on an extension of the hard sphere mixture model, accounting for the range of coordination states available to each cation in the liquid. By utilizing approximate analytic expressions for the hard sphere model, this method is capable of predicting complex liquid structure and thermodynamics while remaining computationally efficient, requiring only minutes of calculation time on standard desktop computers. This modeling framework is applied to the MgO system, where model parameters are trained on a collection of crystal polymorphs, producing realistic predictions of coordination evolution and the equation of state of MgO melt over a wide range of pressures and temperatures. We find that the typical coordination number of the Mg cation evolves continuously upward from 5.25 at 0 GPa to 8.5 at 250 GPa. The results produced by CHaSM are evaluated by comparison with predictions from published first-principles molecular dynamics calculations, indicating that CHaSM is accurately capturing the dominant physics controlling the behavior of oxide melts at high pressure. Finally, we present a simple quantitative model to explain the universality of the increasing Grüneisen parameter trend for liquids, which directly reflects their progressive evolution toward more compact solid-like structures upon compression. This general behavior is opposite that of solid materials, and produces steep adiabatic thermal profiles for silicate melts, thus playing a crucial role in magma ocean evolution.
NASA Astrophysics Data System (ADS)
Zhou, Yaoqi; Stell, George
1988-12-01
An exact integral-equation formalism for a system of a binary hard-sphere mixture interacting with a spherical semipermeable vesicle (SPV) and plane semipermeable membrane (SPM) is derived by using the Ornstein-Zernike (OZ) equation with appropriate closures. The Percus-Yevick (PY) closure or the hypernetted chain (HNC) closure, in which the bulk correlation is obtained by the PY approximation, are considered as examples. We refer to these as the PY/PY and HNC/PY approximations, respectively. The mixture contains solvent particles, which are permeable to the membrane, and solute particles (``protein'' or ``polymer'' particles), which can not pass through the membrane. We develop an exact general formalism for this problem and as an illustration of its use give quantative results for solvent and solute particles modeled as hard spheres of different diameters. An analytical expression for the density ratio in the PY/PY and HNC/PY approximations between two sides of a plane SPM is obtained. Results obtained from these expressions agree very well with results obtained by equating chemical potentials in the region of interest. It turns out that the protein-membrane direct correlation function can be given by a simple analytic expression for the limit of a point solvent in the PY/PY approximation. The osmotic pressure and density profiles for the system containing an ideal spherical SPV or plane SPM in the PY/PY approximation are evaluated. Extension to the nonlocal density-functional closures previously introduced by Blum and Stell is discussed. Finally, we note that certain impenetrable-wall problems previously considered elsewhere can be regarded as semipermeable membrane problems treated via McMillan-Mayer formalism in the continuum-solvent approximation.
Hard-sphere dispersions: Small-wave-vector structure-factor measurements in a linear shear flow
NASA Astrophysics Data System (ADS)
Ackerson, Bruce J.; van der Werff, Jos; de Kruif, C. G.
1988-06-01
Small-scattering-wave-vector structure-factor measurements have been made for model hard-sphere suspensions undergoing a steady linear shear flow. The samples are comprised of sterically stabilized silica particles in cyclohexane and have been well characterized previously by rheological, light scattering, and neutron scattering measurements. These combined measurements provide a strict test of recent theories of microscopic order in suspensions undergoing shear and suggest a picture which unifies several intuitive notions about suspensions undergoing shear flow: distortion of the pair correlation function, clustering, layering, and nonequilibrium phase transitions.
NASA Astrophysics Data System (ADS)
Cai, Zhenning; Torrilhon, Manuel
2015-08-01
A sequence of approximate linear collision models for hard-sphere and inverse-power-law gases is introduced. These models are obtained by expanding the linearized Boltzmann collision operator into series, and a practical algorithm is proposed for evaluating the coefficients in the series. The sequence is proven to be convergent to the linearized Boltzmann operator, and it established a connection between the Shakhov model and the linearized collision model. The convergence is demonstrated by solving the spatially homogeneous Boltzmann equation. By observing the magnitudes of the coefficients, simpler models are developed through removing small entries in the coefficient matrices.
Malijevský, Alexandr; Jackson, George; Varga, Szabolcs
2008-10-14
The extension of Onsager's second-virial theory [L. Onsager, Ann. N.Y. Acad. Sci. 51, 627 (1949)] for the orientational ordering of hard rods to mixtures of nonspherical hard bodies with finite length-to-breadth ratios is examined using the decoupling approximations of Parsons [Phys. Rev. A 19, 1225 (1979)] and Lee [J. Chem. Phys. 86, 6567 (1987); 89, 7036 (1988)]. Invariably the extension of the Parsons-Lee (PL) theory to mixtures has in the past involved a van der Waals one-fluid treatment in which the properties of the mixture are approximated by those of a reference one-component hard-sphere fluid with an effective diameter which depends on the composition of the mixture and the molecular parameters of the various components; commonly this is achieved by equating the molecular volumes of the effective hard sphere and of the components in the mixture and is referred to as the PL theory of mixtures. It is well known that a one-fluid treatment is not the most appropriate for the description of the thermodynamic properties of isotropic fluids, and inadequacies are often rectified with a many-fluid (MF) theory. Here, we examine MF theories which are developed from the virial theorem and the virial expansion of the Helmholtz free energy of anisotropic fluid mixtures. The use of the decoupling approximation of the pair distribution function at the level of a multicomponent hard-sphere reference system leads to our MF Parsons (MFP) theory of anisotropic mixtures. Alternatively the mapping of the virial coefficients of the hard-body mixtures onto those of equivalent hard-sphere systems leads to our MF Lee (MFL) theory. The description of the isotropic-nematic phase behavior of binary mixtures of hard Gaussian overlap particles is used to assess the adequacy of the four different theories, namely, the original second-virial theory of Onsager, the usual PL one-fluid theory, and the MF theories based on the Lee (MFL) and Parsons (MFP) approaches. A comparison with the
Baranau, Vasili; Tallarek, Ulrich
2016-06-01
We estimate the excess chemical potential Δμ and excess entropy per particle Δs of computer-generated, monodisperse and polydisperse, frictionless hard-sphere fluids. For this purpose, we utilize the Widom particle insertion method, which for hard-sphere systems relates Δμ to the probability to successfully (without intersections) insert a particle into a system. This insertion probability is evaluated directly for each configuration of hard spheres by extrapolating to infinity the pore radii (nearest-surface) distribution and integrating its tail. The estimates of Δμ and Δs are compared to (and comply well with) predictions from the Boublík-Mansoori-Carnahan-Starling-Leland equation of state. For polydisperse spheres, we employ log-normal particle radii distributions with polydispersities δ = 0.1, 0.2, and 0.3. PMID:27276959
Disordered strictly jammed binary sphere packings attain an anomalously large range of densities
NASA Astrophysics Data System (ADS)
Hopkins, Adam B.; Stillinger, Frank H.; Torquato, Salvatore
2013-08-01
Previous attempts to simulate disordered binary sphere packings have been limited in producing mechanically stable, isostatic packings across a broad spectrum of packing fractions. Here we report that disordered strictly jammed binary packings (packings that remain mechanically stable under general shear deformations and compressions) can be produced with an anomalously large range of average packing fractions 0.634≤ϕ≤0.829 for small to large sphere radius ratios α restricted to α≥0.100. Surprisingly, this range of average packing fractions is obtained for packings containing a subset of spheres (called the backbone) that are exactly strictly jammed, exactly isostatic, and also generated from random initial conditions. Additionally, the average packing fractions of these packings at certain α and small sphere relative number concentrations x approach those of the corresponding densest known ordered packings. These findings suggest for entropic reasons that these high-density disordered packings should be good glass formers and that they may be easy to prepare experimentally. We also identify an unusual feature of the packing fraction of jammed backbones (packings with rattlers excluded). The backbone packing fraction is about 0.624 over the majority of the α-x plane, even when large numbers of small spheres are present in the backbone. Over the (relatively small) area of the α-x plane where the backbone is not roughly constant, we find that backbone packing fractions range from about 0.606 to 0.829, with the volume of rattler spheres comprising between 1.6% and 26.9% of total sphere volume. To generate isostatic strictly jammed packings, we use an implementation of the Torquato-Jiao sequential linear programming algorithm [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.82.061302 82, 061302 (2010)], which is an efficient producer of inherent structures (mechanically stable configurations at the local maxima in the density landscape). The identification and
Mills, P; Snabre, P
2009-11-01
We consider the steady shear flow of a homogeneous and dense assembly of hard spheres suspended in a Newtonian viscous fluid. In a first part, a mean-field approach based on geometric arguments is used to determine the viscous dissipation in a dense isotropic suspension of smooth hard spheres and the hydrodynamic contribution to the suspension viscosity. In a second part, we consider the coexistence of transient solid clusters coupled to regions with free flowing particles near the jamming transition. The fraction of particles in transient clusters is derived through the Landau-Ginzburg concepts for first-order phase transition with an order parameter corresponding to the proportion of "solid" contacts. A state equation for the fraction of particle-accessible volume is introduced to derive the average normal stresses and a constitutive law that relates the total shear stress to the shear rate. The analytical expression of the average normal stresses well accounts for numerical or experimental evaluation of the particle pressure and non-equilibrium osmotic pressure in a dense sheared suspension. Both the friction level between particles and the suspension dilatancy are shown to determine the singularity of the apparent shear viscosity and the flow stability near the jamming transition. The model further predicts a Newtonian behavior for a concentrated suspension of neutrally buoyant particles and no shear thinning behavior in relation with the shear liquefaction of transient solid clusters. PMID:19856003
NASA Astrophysics Data System (ADS)
Filion, L.; Hermes, M.; Ni, R.; Dijkstra, M.
2010-12-01
Over the last number of years several simulation methods have been introduced to study rare events such as nucleation. In this paper we examine the crystal nucleation rate of hard spheres using three such numerical techniques: molecular dynamics, forward flux sampling, and a Bennett-Chandler-type theory where the nucleation barrier is determined using umbrella sampling simulations. The resulting nucleation rates are compared with the experimental rates of Harland and van Megen [Phys. Rev. E 55, 3054 (1997)], Sinn et al. [Prog. Colloid Polym. Sci. 118, 266 (2001)], Schätzel and Ackerson [Phys. Rev. E 48, 3766 (1993)], and the predicted rates for monodisperse and 5% polydisperse hard spheres of Auer and Frenkel [Nature 409, 1020 (2001)]. When the rates are examined in units of the long-time diffusion coefficient, we find agreement between all the theoretically predicted nucleation rates, however, the experimental results display a markedly different behavior for low supersaturation. Additionally, we examined the precritical nuclei arising in the molecular dynamics, forward flux sampling, and umbrella sampling simulations. The structure of the nuclei appears independent of the simulation method, and in all cases, the nuclei contains on average significantly more face-centered-cubic ordered particles than hexagonal-close-packed ordered particles.
NASA Astrophysics Data System (ADS)
Zhou, Shiqi
2011-12-01
Thermodynamic and structural properties of liquids are of fundamental interest in physics, chemistry, and biology, and perturbation approach has been fundamental to liquid theoretical approaches since the dawn of modern statistical mechanics and remains so to this day. Although thermodynamic perturbation theory (TPT) is widely used in the chemical physics community, one of the most popular versions of the TPT, i.e. Zwanzig (Zwanzig, R. W. J. Chem. Phys. 1954, 22, 1420-1426) 1st-order high temperature series expansion (HTSE) TPT and its 2nd-order counterpart under a macroscopic compressibility approximation of Barker-Henderson (Barker, J. A.; Henderson, D. J. Chem. Phys. 1967, 47, 2856-2861), have some serious shortcomings: (i) the nth-order term of the HTSE is involved with reference fluid distribution functions of order up to 2n, and the higher-order terms hence progressively become more complicated and numerically inaccessible; (ii) the performance of the HTSE rapidly deteriorates and the calculated results become even qualitatively incorrect as the temperature of interest decreases. This account deals with the developments that we have made over the last five years or so to advance a coupling parameter series expansion (CPSE) and a non hard sphere (HS) perturbation strategy that has scored some of its greatest successes in overcoming the above-mentioned difficulties. In this account (i) we expatiate on implementation details of our schemes: how input information indispensable to high-order truncation of the CPSE in both the HS and non HS perturbation schemes is calculated by an Ornstein-Zernike integral equation theory; how high-order thermodynamic quantities, such as critical parameters and excess constant volume heat capacity, are extracted from the resulting excess Helmholtz free energy with irregular and inevitable numerical errors; how to select reference potential in the non HS perturbation scheme. (ii) We give a quantitative analysis on why convergence
NASA Astrophysics Data System (ADS)
Wolf, A. S.; Asimow, P. D.; Stevenson, D. J.
2015-12-01
Recent first-principles calculations (e.g. Stixrude, 2009; de Koker, 2013), shock-wave experiments (Mosenfelder, 2009), and diamond-anvil cell investigations (Sanloup, 2013) indicate that silicate melts undergo complex structural evolution at high pressure. The observed increase in cation-coordination (e.g. Karki, 2006; 2007) induces higher compressibilities and lower adiabatic thermal gradients in melts as compared with their solid counterparts. These properties are crucial for understanding the evolution of impact-generated magma oceans, which are dominated by the poorly understood behavior of silicates at mantle pressures and temperatures (e.g. Stixrude et al. 2009). Probing these conditions is difficult for both theory and experiment, especially given the large compositional space (MgO-SiO2-FeO-Al2O3-etc). We develop a new model to understand and predict the behavior of oxide and silicate melts at extreme P-T conditions (Wolf et al., 2015). The Coordinated Hard Sphere Mixture (CHaSM) extends the Hard Sphere mixture model, accounting for the range of coordination states for each cation in the liquid. Using approximate analytic expressions for the hard sphere model, this fast statistical method compliments classical and first-principles methods, providing accurate thermodynamic and structural property predictions for melts. This framework is applied to the MgO system, where model parameters are trained on a collection of crystal polymorphs, producing realistic predictions of coordination evolution and the equation of state of MgO melt over a wide P-T range. Typical Mg-coordination numbers are predicted to evolve continuously from 5.25 (0 GPa) to 8.5 (250 GPa), comparing favorably with first-principles Molecular Dynamics (MD) simulations. We begin extending the model to a simplified mantle chemistry using empirical potentials (generally accurate over moderate pressure ranges, <~30 GPa), yielding predictions rooted in statistical representations of melt structure
Dynamics of Disorder-Order Transitions in Hard Sphere Colloidal Dispersions in micro-g
NASA Technical Reports Server (NTRS)
Zhu, J. X.; Li, M.; Phan, S. E.; Russel, W. B.; Chaikin, Paul M.; Rogers, Rick; Meyers, W.
1996-01-01
We performed a series of experiments on 0.518 millimeter PMMA spheres suspended in an index matching mixture of decalin and tetralin the microgravity environment provided by the Shuttle Columbia on mission STS-73. The samples ranged in concentration from 0.49 to 0.62. volume fraction (phi) of spheres, which covers the range in which liquid, coexistence, solid and glass phases are expected from Earth bound experiments. Light scattering was used to probe the static structure, and the particle dynamics. Digital and 35 mm photos provided information on the morphology of the crystals. In general, the crystallites grew considerably larger (roughly an order of magnitude larger) than the same samples with identical treatment in 1 g. The dynamic light scattering shows the typical short time diffusion and long time caging effects found in 1 g. The surprises that were encountered in microgravity include the preponderance of random hexagonal close packed (RHCP) structures and the complete absence of the expected face centered cubic (FCC) structure, existence of large dendritic crystals floating in the coexistence samples (where liquid and solid phases coexist) and the rapid crystallization of samples which exist only in glass phase under the influence of one g. These results suggest that colloidal crystal growth is profoundly effected by gravity in yet unrecognized ways. We suspect that the RCHP structure is related to the nonequilibrium growth that is evident from the presence of dendrites. An analysis of the dendritic growth instabilities is presented within the framework of the Ackerson-Schatzel equation.
Uniform electron gases. III. Low-density gases on three-dimensional spheres
Agboola, Davids; Knol, Anneke L.; Gill, Peter M. W. Loos, Pierre-François
2015-08-28
By combining variational Monte Carlo (VMC) and complete-basis-set limit Hartree-Fock (HF) calculations, we have obtained near-exact correlation energies for low-density same-spin electrons on a three-dimensional sphere (3-sphere), i.e., the surface of a four-dimensional ball. In the VMC calculations, we compare the efficacies of two types of one-electron basis functions for these strongly correlated systems and analyze the energy convergence with respect to the quality of the Jastrow factor. The HF calculations employ spherical Gaussian functions (SGFs) which are the curved-space analogs of Cartesian Gaussian functions. At low densities, the electrons become relatively localized into Wigner crystals, and the natural SGF centers are found by solving the Thomson problem (i.e., the minimum-energy arrangement of n point charges) on the 3-sphere for various values of n. We have found 11 special values of n whose Thomson sites are equivalent. Three of these are the vertices of four-dimensional Platonic solids — the hyper-tetrahedron (n = 5), the hyper-octahedron (n = 8), and the 24-cell (n = 24) — and a fourth is a highly symmetric structure (n = 13) which has not previously been reported. By calculating the harmonic frequencies of the electrons around their equilibrium positions, we also find the first-order vibrational corrections to the Thomson energy.
Uniform electron gases. III. Low-density gases on three-dimensional spheres
NASA Astrophysics Data System (ADS)
Agboola, Davids; Knol, Anneke L.; Gill, Peter M. W.; Loos, Pierre-François
2015-08-01
By combining variational Monte Carlo (VMC) and complete-basis-set limit Hartree-Fock (HF) calculations, we have obtained near-exact correlation energies for low-density same-spin electrons on a three-dimensional sphere (3-sphere), i.e., the surface of a four-dimensional ball. In the VMC calculations, we compare the efficacies of two types of one-electron basis functions for these strongly correlated systems and analyze the energy convergence with respect to the quality of the Jastrow factor. The HF calculations employ spherical Gaussian functions (SGFs) which are the curved-space analogs of Cartesian Gaussian functions. At low densities, the electrons become relatively localized into Wigner crystals, and the natural SGF centers are found by solving the Thomson problem (i.e., the minimum-energy arrangement of n point charges) on the 3-sphere for various values of n. We have found 11 special values of n whose Thomson sites are equivalent. Three of these are the vertices of four-dimensional Platonic solids — the hyper-tetrahedron (n = 5), the hyper-octahedron (n = 8), and the 24-cell (n = 24) — and a fourth is a highly symmetric structure (n = 13) which has not previously been reported. By calculating the harmonic frequencies of the electrons around their equilibrium positions, we also find the first-order vibrational corrections to the Thomson energy.
Finite-size effects in the microscopic structure of a hard-sphere fluid in a narrow cylindrical pore
NASA Astrophysics Data System (ADS)
Román, F. L.; White, J. A.; González, A.; Velasco, S.
2006-04-01
We examine the microscopic structure of a hard-sphere fluid confined to a small cylindrical pore by means of Monte Carlo simulation. In order to analyze finite-size effects, the simulations are carried out in the framework of different statistical mechanics ensembles. We find that the size effects are specially relevant in the canonical ensemble where noticeable differences are found with the results in the grand canonical ensemble (GCE) and the isothermal isobaric ensemble (IIE) which, in most situations, remain very close to the infinite system results. A customary series expansion in terms of fluctuations of either the number of particles (GCE) or the inverse volume (IIE) allows us to connect with the results of the canonical ensemble.
Nanopatterned ferroelectrics for ultrahigh density rad-hard nonvolatile memories.
Brennecka, Geoffrey L.; Stevens, Jeffrey; Scrymgeour, David; Gin, Aaron V.; Tuttle, Bruce Andrew
2010-09-01
Radiation hard nonvolatile random access memory (NVRAM) is a crucial component for DOE and DOD surveillance and defense applications. NVRAMs based upon ferroelectric materials (also known as FERAMs) are proven to work in radiation-rich environments and inherently require less power than many other NVRAM technologies. However, fabrication and integration challenges have led to state-of-the-art FERAMs still being fabricated using a 130nm process while competing phase-change memory (PRAM) has been demonstrated with a 20nm process. Use of block copolymer lithography is a promising approach to patterning at the sub-32nm scale, but is currently limited to self-assembly directly on Si or SiO{sub 2} layers. Successful integration of ferroelectrics with discrete and addressable features of {approx}15-20nm would represent a 100-fold improvement in areal memory density and would enable more highly integrated electronic devices required for systems advances. Towards this end, we have developed a technique that allows us to carry out block copolymer self-assembly directly on a huge variety of different materials and have investigated the fabrication, integration, and characterization of electroceramic materials - primarily focused on solution-derived ferroelectrics - with discrete features of {approx}20nm and below. Significant challenges remain before such techniques will be capable of fabricating fully integrated NVRAM devices, but the tools developed for this effort are already finding broader use. This report introduces the nanopatterned NVRAM device concept as a mechanism for motivating the subsequent studies, but the bulk of the document will focus on the platform and technology development.
Diffuse interface analysis of crystal nucleation in hard-sphere liquid
NASA Astrophysics Data System (ADS)
Gránásy, László; Pusztai, Tamás
2002-12-01
We show that the increase of the interface free energy with deviation from equilibrium seen in recent Monte Carlo simulations [S. Auer and D. Frenkel, Nature (London) 413, 711 (2001)] can be recovered if the molecular scale diffuseness of the crystal-liquid interface is considered. We compare two models, Gránásy's phenomenological diffuse interface theory, and a density functional theory that relies on the type of Ginzburg-Landau expansion for fcc nucleation, that Shih et al. introduced for bcc crystal. It is shown that, in the range of Monte Carlo simulations, the nucleation rate of the stable fcc phase is by several orders of magnitude higher than for the metastable bcc phase, seen to nucleate first in other fcc systems. The nucleation barrier that the diffuse interface theories predict for small deviations from equilibrium is in far better agreement with the simulations than the classical droplet model. The behavior expected at high densities is model dependent. Gránásy's phenomenological diffuse interface theory indicates a spinodal point close to glass transition, while a nonsingular behavior is predicted by the density functional theory with constant Ginzburg-Landau coefficients. Remarkably, a minimum of the nucleation barrier, similar to the one seen in polydisperse systems, occurs if the known density dependence of the Ginzburg-Landau coefficients is considered.
Funakoshi, Ken-ichi; Nozawa, Akifumi
2012-10-01
We describe a new method for the in situ measurement of the density of a liquid at high pressure and high temperature using the falling-sphere technique. Combining synchrotron radiation X-ray radiography with a large-volume press, the newly developed falling-sphere method enables the determination of the density of a liquid at high pressure and high temperature based on Stokes' flow law. We applied this method to liquid sulfur and successfully obtained the density at pressures up to 9 GPa. Our method could be used for the determination of the densities of other liquid materials at higher static pressures than are currently possible. PMID:23126783
Funakoshi, Ken-ichi; Nozawa, Akifumi
2012-10-15
We describe a new method for the in situ measurement of the density of a liquid at high pressure and high temperature using the falling-sphere technique. Combining synchrotron radiation X-ray radiography with a large-volume press, the newly developed falling-sphere method enables the determination of the density of a liquid at high pressure and high temperature based on Stokes' flow law. We applied this method to liquid sulfur and successfully obtained the density at pressures up to 9 GPa. Our method could be used for the determination of the densities of other liquid materials at higher static pressures than are currently possible.
Santos, Andres
2011-05-20
The Boltzmann collision operator for a dilute granular gas of inelastic rough hard spheres is much more intricate than its counterpart for inelastic smooth spheres. Now the one-body distribution function depends not only on the translational velocity v of the center of mass but also on the angular velocity {omega} of the particle. Moreover, the collision rules couple v and {omega}, involving not only the coefficient of normal restitution {alpha} but also the coefficient of tangential restitution {beta}. The aim of this paper is to propose an extension to inelastic rough particles of a Bhatnagar-Gross-Krook-like kinetic model previously proposed for inelastic smooth particles. The Boltzmann collision operator is replaced by the sum of three terms representing: (i) the relaxation to a two-temperature local equilibrium distribution, (ii) the action of a nonconservative drag force F proportional to v-u(u being the flow velocity), and (iii) the action of a nonconservative torque M equal to a linear combination of {omega} and {Omega}({Omega} being the mean angular velocity). The three coefficients in F and M are fixed to reproduce the Boltzmann collisional rates of change of {Omega} and of the two granular temperatures (translational and rotational). A simpler version of the model is also constructed in the form of two coupled kinetic equations for the translational and rotational velocity distributions. The kinetic model is applied to the simple shear flow steady state and the combined influence of {alpha} and {beta} on the shear and normal stresses and on the translational velocity distribution function is analyzed.
Equations of state of freely jointed hard-sphere chain fluids: Numerical results
Stell, G.; Lin, C.; Kalyuzhnyi, Y.V.
1999-03-01
We continue our series of studies in which the equations of state (EOS) are derived based on the product-reactant Ornstein{endash}Zernike approach (PROZA) and first-order thermodynamic perturbation theory (TPT1). These include two compressibility EOS, two virial EOS, and one TPT1 EOS (TPT1-D) that uses the structural information of the dimer fluid as input. In this study, we carry out the numerical implementation for these five EOS and compare their numerical results as well as those obtained from Attard{close_quote}s EOS and GF-D (generalized Flory-dimer) EOS with computer simulation results for the corresponding chain models over a wide range of densities and chain length. The comparison shows that our compressibility EOS, GF-D, and TPT1-D are in quantitative agreement with simulation results, and TPT1-D is the best among various EOS according to its average absolute deviation (AAD). On the basis of a comparison of limited data, our virial EOS appears to be superior to the predictions of Attard{close_quote}s approximate virial EOS and the approximate virial EOS derived by Schweizer and Curro in the context of the PRISM approach; all of them are only qualitatively accurate. The degree of accuracy predicted by our compressibility EOS is comparable to that of GF-D EOS, and both of them overestimate the compressibility factor at low densities and underestimate it at high densities. The compressibility factor of a polydisperse homonuclear chain system is also investigated in this work via our compressibility EOS; the numerical results are identical to those of a monodisperse system with the same chain length. {copyright} {ital 1999 American Institute of Physics.}
NASA Astrophysics Data System (ADS)
Zhou, Alice; O'Hern, Corey; Regan, Lynne
2013-03-01
We seek to dramatically improve computational protein design using minimal models that include only the dominant physical interactions. By modeling proteins with hard-sphere interactions and stereochemical constraints, we are able to explain the side-chain dihedral angle distributions for Leu, Ile, and other hydrophobic residues that are observed in protein crystal structures. We also consider inter-residue interactions on the distribution of side-chain dihedral angles for residues in the hydrophobic core of T4 lysozyme. We calculate the energetic and entropic contributions to the free energy differences between wildtype T4 lysozyme and several mutants involving Leu to Ala substitutions. We find a strong correlation between the entropy difference and the decrease in the melting temperature of the mutatants. These results emphasize that considering both entropy and enthalpy is crucial for obtaining a quantitative understanding of protein stability. NSF DMR-1006537 and PHY-1019147, the Raymond and Beverly Sackler Institute for Biological, Physical and Engineering Sciences, and Howard Hughes Medical Institute International Research Fellowship
NASA Technical Reports Server (NTRS)
Woo, Myeung-Jouh; Greber, Isaac
1995-01-01
Molecular dynamics simulation is used to study the piston driven shock wave at Mach 1.5, 3, and 10. A shock tube, whose shape is a circular cylinder, is filled with hard sphere molecules having a Maxwellian thermal velocity distribution and zero mean velocity. The piston moves and a shock wave is generated. All collisions are specular, including those between the molecules and the computational boundaries, so that the shock development is entirely causal, with no imposed statistics. The structure of the generated shock is examined in detail, and the wave speed; profiles of density, velocity, and temperature; and shock thickness are determined. The results are compared with published results of other methods, especially the direct simulation Monte-Carlo method. Property profiles are similar to those generated by direct simulation Monte-Carlo method. The shock wave thicknesses are smaller than the direct simulation Monte-Carlo results, but larger than those of the other methods. Simulation of a shock wave, which is one-dimensional, is a severe test of the molecular dynamics method, which is always three-dimensional. A major challenge of the thesis is to examine the capability of the molecular dynamics methods by choosing a difficult task.
NASA Astrophysics Data System (ADS)
van Westen, Thijs; Vlugt, Thijs J. H.; Gross, Joachim
2014-01-01
An analytical equation of state (EoS) is derived to describe the isotropic (I) and nematic (N) phase of linear- and partially flexible tangent hard-sphere chain fluids and their mixtures. The EoS is based on an extension of Onsager's second virial theory that was developed in our previous work [T. van Westen, B. Oyarzún, T. J. H. Vlugt, and J. Gross, J. Chem. Phys. 139, 034505 (2013)]. Higher virial coefficients are calculated using a Vega-Lago rescaling procedure, which is hereby generalized to mixtures. The EoS is used to study (1) the effect of length bidispersity on the I-N and N-N phase behavior of binary linear tangent hard-sphere chain fluid mixtures, (2) the effect of partial molecular flexibility on the binary phase diagram, and (3) the solubility of hard-sphere solutes in I- and N tangent hard-sphere chain fluids. By changing the length bidispersity, two types of phase diagrams were found. The first type is characterized by an I-N region at low pressure and a N-N demixed region at higher pressure that starts from an I-N-N triphase equilibrium. The second type does not show the I-N-N equilibrium. Instead, the N-N region starts from a lower critical point at a pressure above the I-N region. The results for the I-N region are in excellent agreement with the results from molecular simulations. It is shown that the N-N demixing is driven both by orientational and configurational/excluded volume entropy. By making the chains partially flexible, it is shown that the driving force resulting from the configurational entropy is reduced (due to a less anisotropic pair-excluded volume), resulting in a shift of the N-N demixed region to higher pressure. Compared to linear chains, no topological differences in the phase diagram were found. We show that the solubility of hard-sphere solutes decreases across the I-N phase transition. Furthermore, it is shown that by using a liquid crystal mixture as the solvent, the solubility difference can by maximized by tuning the
NASA Astrophysics Data System (ADS)
Haataja, Mikko; Gránásy, László; Löwen, Hartmut
2010-08-01
evolving microstructures in spatially extended system with atomic scale spatial resolution over diffusive time scales, DFT provides both its theoretical underpinning and (hopefully) the means to construct microscopically more quantitative density functionals for use in engineering materials. Outstanding issues within the PFC and DFT approaches, discussed next, will provide further opportunities for interactions between the PFC and DFT communities. 3. Important open issues and exciting avenues for further research In the following we summarize some of the exciting topics for future research, which were discussed during the CECAM workshop. They concern both fundamental problems and applications, all within the framework of DFT and PFC. Addressing these issues will provide a framework for future work in these two overlapping fields. (a) How to construct a reliable density functional (DF) for soft repulsions? Most of the recent developments in classical density functional theory were focussed on hard-sphere-like interactions in the framework of fundamental-measure-theory (FMT) [30-33]. While this approach can be extended to additive and nonadditive mixtures [34, 35] and to non-spherical hard objects [36, 37], it is much more difficult to include soft-core interactions, such as inverse-power-law pair-potentials. There have been attempts to include those, mainly using the Ramakrishnan-Yussouff [38] or the weighted-density [39-41] approximation, or other modifications (see e.g., [42, 43]), but the accuracy of these functionals are inferior to that of FMT for hard spheres. Clearly the FMT of Rosenfeld needs an extension for the hard-core Coulomb system. A complementary approach is to start from a density functional for hard orientable objects [36] and to integrate out the orientational degrees of freedom. This would lead to a softened effective repulsion between spherical objects. We mention finally that in the extreme limit of ultrasoft pair potentials, which are penetrable, the
NASA Technical Reports Server (NTRS)
Zhu, Ji-Xiang; Chaikin, P. M.; Li, Min; Russel, W. B.; Ottewill, R. H.; Rogers, R.; Meyer, W. V.
1998-01-01
Classical hard spheres have long served as a paradigm for our understanding of the structure of liquids, crystals, and glasses and the transitions between these phases. Ground-based experiments have demonstrated that suspensions of uniform polymer colloids are near-ideal physical realizations of hard spheres. However, gravity appears to play a significant and unexpected role in the formation and structure of these colloidal crystals. In the microgravity environment of the Space Shuttle, crystals grow purely via random stacking of hexagonal close-packed planes, lacking any of the face-centered cubic (FCC) component evident in crystals grown in 1 g beyond melting and allowed some time to settle. Gravity also masks 33-539 the natural growth instabilities of the hard sphere crystals which exhibit striking dendritic arms when grown in microgravity. Finally, high volume fraction "glass" samples which fail to crystallize after more than a year in 1 g begin nucleation after several days and fully crystallize in less than 2 weeks on the Space Shuttle.
Drude-type conductivity of charged sphere colloidal crystals: density and temperature dependence.
Medebach, Martin; Jordán, Raquel Chuliá; Reiber, Holger; Schöpe, Hans-Joachim; Biehl, Ralf; Evers, Martin; Hessinger, Dirk; Olah, Julianna; Palberg, Thomas; Schönberger, Ernest; Wette, Patrick
2005-09-01
We report on extensive measurements in the low-frequency limit of the ac conductivity of colloidal fluids and crystals formed from charged colloidal spheres suspended in de-ionized water. Temperature was varied in a range of 5 degrees C < Theta < 35 degrees C and the particle number density n between 0.2 and 25 microm(-3) for the larger, respectively, 2.75 and 210 microm(-3) for the smaller of two investigated species. At fixed Theta the conductivity increased linearly with increasing n without any significant change at the fluid-solid phase boundary. At fixed n it increased with increasing Theta and the increase was more pronounced for larger n. Lacking a rigorous electrohydrodynamic treatment for counterion-dominated systems we describe our data with a simple model relating to Drude's theory of metal conductivity. The key parameter is an effectively transported particle charge or valence Z(*). All temperature dependencies other than that of Z(*) were taken from literature. Within experimental resolution Z(*) was found to be independent of n irrespective of the suspension structure. Interestingly, Z(*) decreases with temperature in near quantitative agreement with numerical calculations. PMID:16178620
Hsu, Wei-Hung; Masim, Frances Camille P; Porta, Matteo; Nguyen, Mai Thanh; Yonezawa, Tetsu; Balčytis, Armandas; Wang, Xuewen; Rosa, Lorenzo; Juodkazis, Saulius; Hatanaka, Koji
2016-09-01
Femtosecond laser-induced hard X-ray generation in air from a 100-µm-thick solution film of distilled water or Au nano-sphere suspension was carried out by using a newly-developed automatic positioning system with 1-µm precision. By positioning the solution film for the highest X-ray intensity, the optimum position shifted upstream as the laser power increased due to breakdown. Optimized positioning allowed us to control X-ray intensity with high fidelity. X-ray generation from Au nano-sphere suspension and distilled water showed different power scaling. Linear and nonlinear absorption mechanism are analyzed together with numerical modeling of light delivery. PMID:27607607
Effect of gamma irradiation on high temperature hardness of low-density polyethylene
NASA Astrophysics Data System (ADS)
Chen, Pei-Yun; Yang, Fuqian; Lee, Sanboh
2015-11-01
Gamma irradiation can cause the change of microstructure and molecular structure of polymer, resulting in the change of mechanical properties of polymers. Using the hardness measurement, the effect of gamma irradiation on the high temperature hardness of low-density polyethylene (LDPE) was investigated. The gamma irradiation caused the increase in the melting point, the enthalpy of fusion, and the portion of crystallinity of LDPE. The Vickers hardness of the irradiated LDPE increases with increasing the irradiation dose, annealing temperature, and annealing time. The activation energy for the rate process controlling the reaction between defects linearly decreases with the irradiation dose. The process controlling the hardness evolution in LDPE is endothermic because LDPE is semi-crystalline.
NASA Astrophysics Data System (ADS)
Prasanth, P. S.; Kakkassery, Jose K.; Vijayakumar, R.
2012-04-01
A modified phenomenological model is constructed for the simulation of rarefied flows of polyatomic non-polar gas molecules by the direct simulation Monte Carlo (DSMC) method. This variable hard sphere-based model employs a constant rotational collision number, but all its collisions are inelastic in nature and at the same time the correct macroscopic relaxation rate is maintained. In equilibrium conditions, there is equi-partition of energy between the rotational and translational modes and it satisfies the principle of reciprocity or detailed balancing. The present model is applicable for moderate temperatures at which the molecules are in their vibrational ground state. For verification, the model is applied to the DSMC simulations of the translational and rotational energy distributions in nitrogen gas at equilibrium and the results are compared with their corresponding Maxwellian distributions. Next, the Couette flow, the temperature jump and the Rayleigh flow are simulated; the viscosity and thermal conductivity coefficients of nitrogen are numerically estimated and compared with experimentally measured values. The model is further applied to the simulation of the rotational relaxation of nitrogen through low- and high-Mach-number normal shock waves in a novel way. In all cases, the results are found to be in good agreement with theoretically expected and experimentally observed values. It is concluded that the inelastic collision of polyatomic molecules can be predicted well by employing the constructed variable hard sphere (VHS)-based collision model.
NASA Astrophysics Data System (ADS)
Virrueta, Alejandro; O'Hern, Corey; Regan, Lynne
Methionine (Met) is a versatile amino acid found frequently both in protein cores and at protein-protein interfaces. Thus, a complete description of the structure of Met is tantamount to a fundamental understanding of protein structure and design. In previous work, we showed that our hard-sphere dipeptide model is able to recapitulate the side chain dihedral angle distributions observed in high-resolution protein crystal structures for the 8 amino acids we have studied to date: Val, Thr, Ser, Leu, Ile, Cys, Tyr, and Phe. Using the same approach, we can predict the observed Met side chain dihedral angle distributions P (χ1) and P (χ2) , but not P (χ3) . In this manuscript, we investigate the possible origins of the discrepancy and identify the minimal additions to the hard-sphere dipeptide model necessary to quantitatively predict P (χ3) of Met. We find that applying a Lennard-Jones potential with weak attraction between hydrogen atoms is sufficient to achieve predictions that match the observed χ3 side chain dihedral angle probability distributions for Met, Nle, and Mse without negatively affecting our results for the 8 previously studied amino acids. A. V. is supported by an NSF Graduate Research Fellowship and a Ford Foundation Fellowship.
NASA Technical Reports Server (NTRS)
Lubken, F.-J.; Hillert, W.; Lehmacher, G.; Von Zahn, U.; Bittner, M.; Offermann, D.; Schmidlin, F. J.; Hauchecorne, A.; Mourier, M.; Czechowsky, P.
1994-01-01
During the course of the DYnamics Adapted Network for the Atmosphere (DYANA) campaign in early 1990, various techniques to measure densities and temperatures from the ground up to the lower thermosphere were employed. Some of these measurements were performed near simultaneously (maximum allowed time difference: 1 h) and at the same location, and therefore offered the unique chance of intercomparison of different techniques. In this study, we will report on intercomparisons of data from ground-based instruments (Rayleigh- and sodium-lidar), balloon-borne methods (datasondes and radiosondes) and rocket-borne techniques (falling spheres and ionization gauges). The main result is that there is good agreement between the various measurements when considering the error bars. Only occasionally did we notice small but systematic differences (e.g. for the datasondes above 65 km). The most extensive intercomparison was possible between the Rayleigh lidar and the falling sphere technique, both employed in Biscarrosse (44 deg N, 1 deg W). Concerning densities, excellent agreement was found below 63 km: the mean of the deviations is less than 1% and the root mean square (RMS) is approximately 3%. Systematic differences of the order of 5% were noticed around 67 km and above 80 km. The former can be accounted for by an instrumental effect of the falling sphere (Ma = 1 transition; Ma = Mach number), whereas the latter is tentatively explained by the presence of Mie scatterers in the upper mesosphere. Concerning temperatures, the agreement is excellent between 35 and 65 km: the mean of the deviations is less than +/- 3 K and the variability is +/- 5 K. The two systematic density differences mentioned above also affect the temperatures: between 65 and 80 km, the Rayleigh lidar temperatures are systematically lower than the falling sphere values by approximately 5 K.
Steel and titanium hollow sphere foams
Hurysz, K.M.; Clark, J.L.; Nagel, A.R.; Lee, K.J.; Cochran, J.K.; Sanders, T.H. Jr.; Hardwicke, C.U.
1998-12-31
Metal hollow sphere foams are fabricated by bonding millimeter sized metal alloy hollow spheres at points of contact. The spheres are formed as powder shells from slurries. For stainless steel spheres, the starting powder is a mixture of iron and chromium oxide. Thermal treatment in hydrogen reduces the oxides to Fe/Cr alloys with less than 2% porosity in sphere walls. The nominal composition is close to that of 405 stainless. Carburization in CO/CO{sub 2} atmosphere followed by heat treatment produces foams of either 410 or 420 type stainless steels depending on carbon content. Compressive stress-strain behavior was measured on point contact bonded stainless foams both before and after carburization. Hardness measurements on steel sphere walls were used to estimate the yield strength. Relative strengths of the foams were positioned between open and closed cell models. This was encouraging because bonding in the foams was less than optimum and the hollow sphere walls contained defects. As processing improves, strengths should increase. To produce titanium alloy spheres, the starting powder is titanium alloy hydride. Thermal treatment in an inert atmosphere decomposes the hydride and sinters the titanium powder in the sphere walls to greater than 96% relative density. Both titanium and Ti-6V-4V spheres and foams have been produced. Oxygen contents are a concern for titanium compositions and processing is being altered to reduce oxygen levels to increase ductility.
Howard, David M.; Kearfott, Kimberlee J.; Wilderman, Scott J.
2011-01-01
Abstract High computational requirements restrict the use of Monte Carlo algorithms for dose estimation in a clinical setting, despite the fact that they are considered more accurate than traditional methods. The goal of this study was to compare mean tumor absorbed dose estimates using the unit density sphere model incorporated in OLINDA with previously reported dose estimates from Monte Carlo simulations using the dose planning method (DPMMC) particle transport algorithm. The dataset (57 tumors, 19 lymphoma patients who underwent SPECT/CT imaging during I-131 radioimmunotherapy) included tumors of varying size, shape, and contrast. OLINDA calculations were first carried out using the baseline tumor volume and residence time from SPECT/CT imaging during 6 days post-tracer and 8 days post-therapy. Next, the OLINDA calculation was split over multiple time periods and summed to get the total dose, which accounted for the changes in tumor size. Results from the second calculation were compared with results determined by coupling SPECT/CT images with DPM Monte Carlo algorithms. Results from the OLINDA calculation accounting for changes in tumor size were almost always higher (median 22%, range −1%–68%) than the results from OLINDA using the baseline tumor volume because of tumor shrinkage. There was good agreement (median −5%, range −13%–2%) between the OLINDA results and the self-dose component from Monte Carlo calculations, indicating that tumor shape effects are a minor source of error when using the sphere model. However, because the sphere model ignores cross-irradiation, the OLINDA calculation significantly underestimated (median 14%, range 2%–31%) the total tumor absorbed dose compared with Monte Carlo. These results show that when the quantity of interest is the mean tumor absorbed dose, the unit density sphere model is a practical alternative to Monte Carlo for some applications. For applications requiring higher accuracy, computer-intensive Monte
Hardness of FeB{sub 4}: Density functional theory investigation
Zhang, Miao; Du, Yonghui; Gao, Lili; Lu, Mingchun; Lu, Cheng; Liu, Hanyu
2014-05-07
A recent experimental study reported the successful synthesis of an orthorhombic FeB{sub 4} with a high hardness of 62(5) GPa [H. Gou et al., Phys. Rev. Lett. 111, 157002 (2013)], which has reignited extensive interests on whether transition-metal borides compounds will become superhard materials. However, it is contradicted with some theoretical studies suggesting transition-metal boron compounds are unlikely to become superhard materials. Here, we examined structural and electronic properties of FeB{sub 4} using density functional theory. The electronic calculations show the good metallicity and covalent Fe–B bonding. Meanwhile, we extensively investigated stress-strain relations of FeB{sub 4} under various tensile and shear loading directions. The calculated weakest tensile and shear stresses are 40 GPa and 25 GPa, respectively. Further simulations (e.g., electron localization function and bond length along the weakest loading direction) on FeB{sub 4} show the weak Fe–B bonding is responsible for this low hardness. Moreover, these results are consistent with the value of Vickers hardness (11.7–32.3 GPa) by employing different empirical hardness models and below the superhardness threshold of 40 GPa. Our current results suggest FeB{sub 4} is a hard material and unlikely to become superhard (>40 GPa)
Effective densities of hard coals as a function of their genetic characteristics
Dobronravov, V.F.
1985-01-01
A quantitative analysis has been made of the change in the effective densities of hard coals as a function of the stage of metamorphism, petrographic composition, and degree of reduction. In the sintering and in the leaning components, this index changes along a curve with a minimum at the medium states of metamorphism. The influence of the petrographic composition is a maximum in the region of fat coals and is the range of 0.04-0.07 g/cm/sup 3/. The influence of the degree of reduction is small and decreases with a rise in rank. A formula is proposed for calculating the effective densities of hard coals from their genetic parameters.
The high density phase of the k-NN hard core lattice gas model
NASA Astrophysics Data System (ADS)
Nath, Trisha; Rajesh, R.
2016-07-01
The k-NN hard core lattice gas model on a square lattice, in which the first k next nearest neighbor sites of a particle are excluded from being occupied by another particle, is the lattice version of the hard disc model in two dimensional continuum. It has been conjectured that the lattice model, like its continuum counterpart, will show multiple entropy-driven transitions with increasing density if the high density phase has columnar or striped order. Here, we determine the nature of the phase at full packing for k up to 820 302 . We show that there are only eighteen values of k, all less than k = 4134, that show columnar order, while the others show solid-like sublattice order.
High-density ferroelectric recording using a hard disk drive-type data storage system
NASA Astrophysics Data System (ADS)
Aoki, Tomonori; Hiranaga, Yoshiomi; Cho, Yasuo
2016-05-01
Ferroelectric probe data storage has been proposed as a novel data storage method in which bits are recorded based on the polarization directions of individual domains. These bits are subsequently read by scanning nonlinear dielectric microscopy. The domain walls of typical ferroelectric materials are quite thin: often only several times the lattice constant, which is advantageous for high-density data storage. In this work, high-density read/write (R/W) demonstrations were conducted using a hard disk drive-type test system, and the writing of bit arrays with a recording density of 3.4 Tbit/in.2 was achieved. Additionally, a series of writing and reading operations was successfully demonstrated at a density of 1 Tbit/in.2. Favorable characteristics of ferroelectric recording media for use with the proposed method are discussed in the latter part of this paper.
NASA Technical Reports Server (NTRS)
Miller, C. G., III
1975-01-01
Measured shock shapes are presented for sphere and hemisphere models in helium, air, CF4, C2F6, and CO2 test gases, corresponding to normal-shock density ratios (primary factor governing shock detachment distance of blunt bodies at hypersonic speeds) from 4 to 19. These shock shapes were obtained in three facilities capable of generating the high density ratios experienced during planetary entry at hypersonic conditions; namely, the 6-inch expansion tube, with hypersonic CF4 tunnel, and pilot CF4 Mach 6 tunnel (with CF4 replaced by C2F6). Measured results are compared with several inviscid perfect-gas shock shape predictions, in which an effective ratio of specific heats is used as input, and with real-gas predictions which include effects of a laminar viscous layer and thermochemical nonequilibrium.
The column density distribution of hard X-ray radio galaxies
NASA Astrophysics Data System (ADS)
Panessa, F.; Bassani, L.; Landi, R.; Bazzano, A.; Dallacasa, D.; La Franca, F.; Malizia, A.; Venturi, T.; Ubertini, P.
2016-09-01
In order to investigate the role of absorption in active galactic nuclei (AGN) with jets, we have studied the column density distribution of a hard X-ray selected sample of radio galaxies, derived from the INTEGRAL/Imager on Board the Integral Satellite (IBIS) and Swift/The Burst Alert Telescope (BAT) AGN catalogues (˜7-10 per cent of the total AGN population). The 64 radio galaxies have a typical FR II radio morphology and are characterized by high 20-100 keV luminosities (from 1042 to 1046 erg s-1) and high Eddington ratios (log LBol/LEdd typically larger than ˜0.01). The observed fraction of absorbed AGN (NH > 1022 cm-2) is around 40 per cent among the total sample, and ˜75 per cent among type 2 AGN. The majority of obscured AGN are narrow-line objects, while unobscured AGN are broad-line objects, obeying to the zeroth-order predictions of unified models. A significant anti-correlation between the radio core dominance parameter and the X-ray column density is found. The observed fraction of Compton thick AGN is ˜2-3 per cent, in comparison with the 5-7 per cent found in radio-quiet hard X-ray selected AGN. We have estimated the absorption and Compton thick fractions in a hard X-ray sample containing both radio galaxies and non-radio galaxies and therefore affected by the same selection biases. No statistical significant difference was found in the absorption properties of radio galaxies and non-radio galaxies sample. In particular, the Compton thick objects are likely missing in both samples and the fraction of obscured radio galaxies appears to decrease with luminosity as observed in hard X-ray non-radio galaxies.
Encircling the dark: constraining dark energy via cosmic density in spheres
NASA Astrophysics Data System (ADS)
Codis, S.; Pichon, C.; Bernardeau, F.; Uhlemann, C.; Prunet, S.
2016-05-01
The recently published analytic probability density function for the mildly non-linear cosmic density field within spherical cells is used to build a simple but accurate maximum likelihood estimate for the redshift evolution of the variance of the density, which, as expected, is shown to have smaller relative error than the sample variance. This estimator provides a competitive probe for the equation of state of dark energy, reaching a few percent accuracy on wp and wa for a Euclid-like survey. The corresponding likelihood function can take into account the configuration of the cells via their relative separations. A code to compute one-cell density probability density functions for arbitrary initial power spectrum, top-hat smoothing and various spherical collapse dynamics is made available online so as to provide straightforward means of testing the effect of alternative dark energy models and initial power-spectra on the low-redshift matter distribution.
Encircling the dark: constraining dark energy via cosmic density in spheres
NASA Astrophysics Data System (ADS)
Codis, S.; Pichon, C.; Bernardeau, F.; Uhlemann, C.; Prunet, S.
2016-08-01
The recently published analytic probability density function for the mildly non-linear cosmic density field within spherical cells is used to build a simple but accurate maximum likelihood estimate for the redshift evolution of the variance of the density, which, as expected, is shown to have smaller relative error than the sample variance. This estimator provides a competitive probe for the equation of state of dark energy, reaching a few per cent accuracy on wp and wa for a Euclid-like survey. The corresponding likelihood function can take into account the configuration of the cells via their relative separations. A code to compute one-cell-density probability density functions for arbitrary initial power spectrum, top-hat smoothing and various spherical-collapse dynamics is made available online, so as to provide straightforward means of testing the effect of alternative dark energy models and initial power spectra on the low-redshift matter distribution.
Hu, Yougen; Zhao, Tao; Zhu, Pengli; Zhu, Yu; Liang, Xianwen; Sun, Rong; Wong, Ching-Ping
2016-09-01
Silver nanoparticles (AgNPs) were deposited onto the monodispersed carboxylic polystyrene (CPS) spheres by an improved in situ reduction method. The size and coverage density of the AgNPs on the surface of CPS spheres could be easily tailored by tuning the concentrations of carboxylic functional groups and silver precursor. The morphologies and structures of the resulting CPS/Ag hybrid particles were studied by scanning electron microscopy (SEM), transmission electron microscopy (TEM), X-ray diffraction (XRD), UV-Vis-NIR spectrometer and X-ray photoelectron spectroscopy (XPS), etc. The surface enhanced Raman scattering (SERS) performances of the resulting uniform CPS/Ag hybrid particles were investigated using 4-aminobenzenethiol (4-ABT) as the probe molecule. The optimized CPS/Ag hybrid particles show high enhancement factor (EF) of 2.71×10(7) , low limit of detection (LOD) of 10(-10) m and good reproducibility with relative standard deviation (RSD) of 9.64 %. The good SERS improvement properties demonstrate these hybrid particles could be employed as simple and effective substrates in the SERS spectroscopy. PMID:27511618
NASA Technical Reports Server (NTRS)
Nemeth, Noel
2013-01-01
Models that predict the failure probability of monolithic glass and ceramic components under multiaxial loading have been developed by authors such as Batdorf, Evans, and Matsuo. These "unit-sphere" failure models assume that the strength-controlling flaws are randomly oriented, noninteracting planar microcracks of specified geometry but of variable size. This report develops a formulation to describe the probability density distribution of the orientation of critical strength-controlling flaws that results from an applied load. This distribution is a function of the multiaxial stress state, the shear sensitivity of the flaws, the Weibull modulus, and the strength anisotropy. Examples are provided showing the predicted response on the unit sphere for various stress states for isotropic and transversely isotropic (anisotropic) materials--including the most probable orientation of critical flaws for offset uniaxial loads with strength anisotropy. The author anticipates that this information could be used to determine anisotropic stiffness degradation or anisotropic damage evolution for individual brittle (or quasi-brittle) composite material constituents within finite element or micromechanics-based software
Boss, Alan P.; Keiser, Sandra A.
2013-02-20
Magnetic fields are important contributors to the dynamics of collapsing molecular cloud cores, and can have a major effect on whether collapse results in a single protostar or fragmentation into a binary or multiple protostar system. New models are presented of the collapse of magnetic cloud cores using the adaptive mesh refinement code Enzo2.0. The code was used to calculate the ideal magnetohydrodynamics (MHD) of initially spherical, uniform density, and rotation clouds with density perturbations, i.e., the Boss and Bodenheimer standard isothermal test case for three-dimensional (3D) hydrodynamics codes. After first verifying that Enzo reproduces the binary fragmentation expected for the non-magnetic test case, a large set of models was computed with varied initial magnetic field strengths and directions with respect to the cloud core axis of rotation (parallel or perpendicular), density perturbation amplitudes, and equations of state. Three significantly different outcomes resulted: (1) contraction without sustained collapse, forming a denser cloud core; (2) collapse to form a single protostar with significant spiral arms; and (3) collapse and fragmentation into binary or multiple protostar systems, with multiple spiral arms. Comparisons are also made with previous MHD calculations of similar clouds with a barotropic equations of state. These results for the collapse of initially uniform density spheres illustrate the central importance of both magnetic field direction and field strength for determining the outcome of dynamic protostellar collapse.
Significance of gluon density at soft and hard processes at LHC
NASA Astrophysics Data System (ADS)
Grinyuk, A. A.; Lipatov, A. V.; Lykasov, G. I.
2015-11-01
We study the role of the non-perturbative input to the transverse momentum dependent (TMD) gluon density in hard processes at the LHC. We derive the TMD gluon distribution from the fit of the inclusive hadron spectra measured at low transverse momenta in pp collisions at the LHC and demonstrate that the best description of these spectra for larger hadron transverse momenta can be achieved by matching the derived TMD gluon distribution with the exact solution of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation obtained at small transverse momenta outside the saturation region. A special attention is put to the phenomenological applications of presented TMD parton densities to some LHC processes, which are sensitive to the quark and gluon content of a proton.
Density-functional study of the nematic-isotropic interface of hard spherocylinders.
Velasco, E; Mederos, L; Sullivan, D E
2002-08-01
The Somoza-Tarazona density-functional theory is applied to the isotropic-nematic interface of hard spherocylinders with length (L)-to-diameter (D) ratios in the range L/D=5-20. Properties such as the density and orientational order-parameter profiles and the variation of interfacial tension with bulk nematic tilt angle agree qualitatively with results of previous studies at larger values of L/D using both computer simulation and the Onsager second-virial approximation. The minimum interfacial tension is obtained at a tilt angle of 90 degrees. For values of L/D approximately 5, it is found that the Onsager approximation predicts a spurious minimum in the interfacial tension at small tilt angles. PMID:12241197
NASA Astrophysics Data System (ADS)
Haataja, Mikko; Gránásy, László; Löwen, Hartmut
2010-08-01
Herein we provide a brief summary of the background, events and results/outcome of the CECAM workshop 'Classical density functional theory methods in soft and hard matter held in Lausanne between October 21 and October 23 2009, which brought together two largely separately working communities, both of whom employ classical density functional techniques: the soft-matter community and the theoretical materials science community with interests in phase transformations and evolving microstructures in engineering materials. After outlining the motivation for the workshop, we first provide a brief overview of the articles submitted by the invited speakers for this special issue of Journal of Physics: Condensed Matter, followed by a collection of outstanding problems identified and discussed during the workshop. 1. Introduction Classical density functional theory (DFT) is a theoretical framework, which has been extensively employed in the past to study inhomogeneous complex fluids (CF) [1-4] and freezing transitions for simple fluids, amongst other things. Furthermore, classical DFT has been extended to include dynamics of the density field, thereby opening a new avenue to study phase transformation kinetics in colloidal systems via dynamical DFT (DDFT) [5]. While DDFT is highly accurate, the computations are numerically rather demanding, and cannot easily access the mesoscopic temporal and spatial scales where diffusional instabilities lead to complex solidification morphologies. Adaptation of more efficient numerical methods would extend the domain of DDFT towards this regime of particular interest to materials scientists. In recent years, DFT has re-emerged in the form of the so-called 'phase-field crystal' (PFC) method for solid-state systems [6, 7], and it has been successfully employed to study a broad variety of interesting materials phenomena in both atomic and colloidal systems, including elastic and plastic deformations, grain growth, thin film growth, solid
Expansion-free evolving spheres must have inhomogeneous energy density distributions
Herrera, L.; Le Denmat, G.; Santos, N. O.
2009-04-15
In a recent paper a systematic study on shearing expansion-free spherically symmetric distributions was presented. As a particular case of such systems, the Skripkin model was mentioned, which corresponds to a nondissipative perfect fluid with a constant energy density. Here we show that such a model is inconsistent with junction conditions. It is shown that in general for any nondissipative fluid distribution, the expansion-free condition requires the energy density to be inhomogeneous. As an example we consider the case of dust, which allows for a complete integration.
Size and Fiber Density Controlled Synthesis of Fibrous Nanosilica Spheres (KCC-1)
Bayal, Nisha; Singh, Baljeet; Singh, Rustam; Polshettiwar, Vivek
2016-01-01
We report a facile protocol for the synthesis of fibrous nano-silica (KCC-1) with controllable size and fiber density. In this work, we have shown that the particle size, fiber density, surface area and pore volume of KCC-1 can be effectively controlled and tuned by changing various reaction parameters, such as the concentrations of urea, CTAB, 1-pentanol, reaction time, temperature, solvent ratio, and even outside stirring time. For the first time, we were able to control the particle size ranging from as small as 170 nm to as large as 1120 nm. We were also able to control the fiber density from low to medium to very dense, which consequently allowed the tuning of the pore volume. We were able to achieve a pore volume of 2.18 cm3/g, which is the highest reported for such a fibrous material. Notably we were even able to increase the surface area up to 1244 m2/g, nearly double the previously reported surface area of KCC-1. Thus, one can now synthesize KCC-1 with various degrees of size, surface area, pore volume, and fiber density. PMID:27118152
Size and Fiber Density Controlled Synthesis of Fibrous Nanosilica Spheres (KCC-1)
NASA Astrophysics Data System (ADS)
Bayal, Nisha; Singh, Baljeet; Singh, Rustam; Polshettiwar, Vivek
2016-04-01
We report a facile protocol for the synthesis of fibrous nano-silica (KCC-1) with controllable size and fiber density. In this work, we have shown that the particle size, fiber density, surface area and pore volume of KCC-1 can be effectively controlled and tuned by changing various reaction parameters, such as the concentrations of urea, CTAB, 1-pentanol, reaction time, temperature, solvent ratio, and even outside stirring time. For the first time, we were able to control the particle size ranging from as small as 170 nm to as large as 1120 nm. We were also able to control the fiber density from low to medium to very dense, which consequently allowed the tuning of the pore volume. We were able to achieve a pore volume of 2.18 cm3/g, which is the highest reported for such a fibrous material. Notably we were even able to increase the surface area up to 1244 m2/g, nearly double the previously reported surface area of KCC-1. Thus, one can now synthesize KCC-1 with various degrees of size, surface area, pore volume, and fiber density.
NASA Astrophysics Data System (ADS)
van Westen, Thijs; Vlugt, Thijs J. H.; Gross, Joachim
2012-07-01
Onsager-like theories are commonly used to describe the phase behavior of nematic (only orientationally ordered) liquid crystals. A key ingredient in such theories is the orientation-dependent excluded volume of two molecules. Although for hard convex molecular models this is generally known in analytical form, for more realistic molecular models that incorporate intramolecular flexibility, one has to rely on approximations or on computationally expensive Monte Carlo techniques. In this work, we provide a general correlation for the excluded volume of tangent hard-sphere chains of arbitrary chain length and flexibility. The flexibility is introduced by means of the rod-coil model. The resulting correlation is of simple analytical form and accurately covers a wide range of pure component excluded volume data obtained from Monte Carlo simulations of two-chain molecules. The extension to mixtures follows naturally by applying simple combining rules for the parameters involved. The results for mixtures are also in good agreement with data from Monte Carlo simulations. We have expressed the excluded volume as a second order power series in sin (γ), where γ is the angle between the molecular axes. Such a representation is appealing since the solution of the Onsager Helmholtz energy functional usually involves an expansion of the excluded volume in Legendre coefficients. Both for pure components and mixtures, the correlation reduces to an exact expression in the limit of completely linear chains. The expression for mixtures, as derived in this work, is thereby an exact extension of the pure component result of Williamson and Jackson [Mol. Phys. 86, 819-836 (1995)], 10.1080/00268979500102391.
NASA Astrophysics Data System (ADS)
Hansen-Goos, Hendrik
2016-04-01
We derive an analytical equation of state for the hard-sphere fluid that is within 0.01% of computer simulations for the whole range of the stable fluid phase. In contrast, the commonly used Carnahan-Starling equation of state deviates by up to 0.3% from simulations. The derivation uses the functional form of the isothermal compressibility from the Percus-Yevick closure of the Ornstein-Zernike relation as a starting point. Two additional degrees of freedom are introduced, which are constrained by requiring the equation of state to (i) recover the exact fourth virial coefficient B4 and (ii) involve only integer coefficients on the level of the ideal gas, while providing best possible agreement with the numerical result for B5. Virial coefficients B6 to B10 obtained from the equation of state are within 0.5% of numerical computations, and coefficients B11 and B12 are within the error of numerical results. We conjecture that even higher virial coefficients are reliably predicted.
NASA Astrophysics Data System (ADS)
Virrueta, Alejandro; Zhou, Alice; O'Hern, Corey; Regan, Lynne
2014-03-01
Molecular dynamics methods have significantly advanced the understanding of protein folding and stability. However, current force-fields cannot accurately calculate and rank the stability of modified or de novo proteins. One possible reason is that current force-fields use knowledge-based corrections that improve dihedral angle sampling, but do not satisfy the stereochemical constraints for amino acids. I propose the use of simple hard-sphere models for amino acids with stereochemical constraints taken from high-resolution protein crystal structures. This model can enable a correct consideration of the entropy of side-chain rotations, and may be sufficient to predict the effects of single residue mutations in the hydrophobic cores of staphylococcal nuclease and T4 lysozyme on stability changes. I will computationally count the total number of allowed side-chain conformations Ω and calculate the associated entropy, S = kBln(Ω) , before and after each mutation. I will then rank the stability of the mutated cores based on my computed entropy changes, and compare my results with structural and thermodynamic data published by the Stites and Matthews groups. If successful, this project will provide a novel framework for the evaluation of entropic protein stabilities, and serve as a possible tool for computational protein design.
Hansen-Goos, Hendrik
2016-04-28
We derive an analytical equation of state for the hard-sphere fluid that is within 0.01% of computer simulations for the whole range of the stable fluid phase. In contrast, the commonly used Carnahan-Starling equation of state deviates by up to 0.3% from simulations. The derivation uses the functional form of the isothermal compressibility from the Percus-Yevick closure of the Ornstein-Zernike relation as a starting point. Two additional degrees of freedom are introduced, which are constrained by requiring the equation of state to (i) recover the exact fourth virial coefficient B4 and (ii) involve only integer coefficients on the level of the ideal gas, while providing best possible agreement with the numerical result for B5. Virial coefficients B6 to B10 obtained from the equation of state are within 0.5% of numerical computations, and coefficients B11 and B12 are within the error of numerical results. We conjecture that even higher virial coefficients are reliably predicted. PMID:27131556
Ferracane, J L; Ferracane, L L; Braga, R R
2003-07-15
Additives that provide stress relief may be incorporated into dental composites to reduce contraction stress (CS). This study attempted to test the hypothesis that conventional fillers could be replaced by high-density polyethylene (HDPE) spheres in hybrid and nanofill composites to reduce CS, but with minimal effect on mechanical properties. Nanofill and hybrid composites were made from a Bis-GMA/TEGDMA resin having either all silica nanofiller or 75 wt.% strontium glass + 5 wt.% silica and replacing some of the nanofiller or the glass with 0%, 5% (hybrid only), 10% or 20 wt.% HDPE. The surface of the HDPE was either left untreated or had a reactive gas surface treatment (RGST). Contraction stress (CS) was monitored for 10 min in a tensilometer (n = 5) after light curing for 60 s at 390 mW/cm(2). Other specimens (n = 5) were light cured 40 s from two sides in a light-curing unit and aged 1 d in water before testing fracture toughness (K(Ic)), flexure strength (FS), and modulus (E). Results were analyzed by ANOVA with Tukey's multiple comparison test at p < 0.05. There was no difference between composites with RGST and untreated HDPE except for FS-10% HDPE hybrid (RGST higher). An increased level of HDPE reduced contraction stress for both types of composites. Flexure strength, modulus (hybrid only), and fracture toughness were also reduced as the concentration of HDPE increased. SEM showed evidence for HDPE debonding and plastic deformation during fracture of the hybrid composites. In conclusion, the addition of HDPE spheres reduces contraction stress in composites, either through stress relief or a reduction in elastic modulus. PMID:12808590
Improved Contact X-Ray Microradiographic Method to Measure Mineral Density of Hard Dental Tissues.
Schmuck, B D; Carey, C M
2010-03-01
Contact X-ray microradiography is the current gold standard for measuring mineral densities of partially demineralized tooth specimens. The X-ray sensitive film specified in the last J Res NIST publication on the subject is no longer commercially available. OBJECTIVES: Develop a new microradiographic method by identifying a commercially available film with greater than 3000 lines per millimeter resolution, which is sensitive to X rays, and develop correct film processing for X-ray microradiographic application. METHODS: A holographic film was identified as a potential replacement film. Proper exposure was determined utilizing a thick nickel plate to create test-strips. Film development was bracketed around manufacturer suggestions. Film linearity was determined with aluminum step-wedges. Microradiographs of 100 µm thick tooth sections, before and after acidic challenges, were a final test for film. Magnified images were captured with a digital microscope camera with 0.305 micrometers per pixel resolution. RESULTS: The appropriate film exposure was 30 minutes at 80 kV(p) and 3 mA with a development time of 2 minutes. Step-wedge experiments show the system to be linear in terms of pixel intensities with respect to x-ray attenuation for normalized pixel intensity values that are 10% to 90% of full scale (r(2) = 0.997) which encompasses the full exposure region of tooth tissue. Enamel sections were analyzed and show distinctive differences between erosion and demineralization. The image capture device resolution of 0.305 micrometers per pixel limits the system resolution. CONCLUSION: Use of the identified holographic film when combined with the described processing modifications has resulted in an improved X-ray microradiographic method for the measurement of mineral density of dental hard tissues. The method described can be further improved by using a higher resolution digitization system. The method is appropriate for quantitatively measuring changes in mineral
THE FIRST HARD X-RAY POWER SPECTRAL DENSITY FUNCTIONS OF ACTIVE GALACTIC NUCLEUS
Shimizu, T. Taro; Mushotzky, Richard F.
2013-06-10
We present results of our power spectral density (PSD) analysis of 30 active galactic nuclei (AGNs) using the 58 month light curves from Swift's Burst Alert Telescope (BAT) in the 14-150 keV band. PSDs were fit using a Monte Carlo based algorithm to take into account windowing effects and measurement error. All but one source were found to be fit very well using an unbroken power law with a slope of {approx} - 1, consistent at low frequencies with previous studies in the 2-10 keV band, with no evidence of a break in the PSD. For five of the highest signal-to-noise ratio sources, we tested the energy dependence of the PSD and found no significant difference in the PSD at different energies. Unlike previous studies of X-ray variability in AGNs, we do not find any significant correlations between the hard X-ray variability and different properties of the AGN including luminosity and black hole mass. The lack of break frequencies and correlations seem to indicate that AGNs are similar to the high state of Galactic black holes.
Wang Jianfeng; Li Ran; Xu Tao; Li Yan; Liu Zengqian; Huang Lu; Hua Nengbin; Zhang Tao; Xiao Ruijuan; Li Gong; Li Yanchun
2011-10-10
An incompressible Co{sub 54}Ta{sub 11}B{sub 35} bulk metallic glass (BMG) was investigated using in situ high-pressure synchrotron diffraction and nanoindendation. The elastic constants were deduced from the experiments based on the isotropic model. The Vickers hardness was measured to be 17.1 GPa. The elastic moduli and hardness are the highest values known in BMGs. The theoretically calculated elastic properties by density-functional study were well consistent with experimental measurements. The analysis of charge density and bonding character indicates the covalent character of Co-B and B-B bonds, underlying the unusually high elastic modulus and hardness in this material.
Ates, C.; Moseley, Ch.; Ziegler, K.
2005-06-15
The characteristic oscillations of the density-density correlation function and the resulting structure factor are studied for a hard-core Bose gas in a one-dimensional lattice. Their wavelength diverges as the system undergoes a continuous transition from an incommensurate to a Mott insulating phase. The transition is associated with a unit static structure factor and a vanishing sound velocity. The qualitative picture is unchanged when a weak confining potential is applied to the system.
Sun, K.
2011-05-04
This slide show presents: space exploration applications; high energy density physics applications; UV LED and photodiode radiation hardness; UV LED and photodiode space qualification; UV LED AC charge management; and UV LED satellite payload instruments. A UV LED satellite will be launched 2nd half 2012.
Brambrink, E; Wei, H G; Barbrel, B; Audebert, P; Benuzzi-Mounaix, A; Boehly, T; Endo, T; Gregory, C D; Kimura, T; Kodama, R; Ozaki, N; Park, H-S; Koenig, M
2009-11-01
We present the application of short-pulse laser-driven hard x rays (>40 keV) for the direct density measurement of iron compressed by a laser-driven shock. By using an on-shot calibration of the spectral absorption, we are able to obtain line densities with 5%-10% precision, although the x-ray source is not monochromatic. We also discuss possibilities for increasing the precision, which would be an improvement for equation of state measurements. PMID:20365083
Large attractive depletion interactions in soft repulsive-sphere binary mixtures.
Cinacchi, Giorgio; Martínez-Ratón, Yuri; Mederos, Luis; Navascués, Guillermo; Tani, Alessandro; Velasco, Enrique
2007-12-01
We consider binary mixtures of soft repulsive spherical particles and calculate the depletion interaction between two big spheres mediated by the fluid of small spheres, using different theoretical and simulation methods. The validity of the theoretical approach, a virial expansion in terms of the density of the small spheres, is checked against simulation results. Attention is given to the approach toward the hard-sphere limit and to the effect of density and temperature on the strength of the depletion potential. Our results indicate, surprisingly, that even a modest degree of softness in the pair potential governing the direct interactions between the particles may lead to a significantly more attractive total effective potential for the big spheres than in the hard-sphere case. This might lead to significant differences in phase behavior, structure, and dynamics of a binary mixture of soft repulsive spheres. In particular, a perturbative scheme is applied to predict the phase diagram of an effective system of big spheres interacting via depletion forces for a size ratio of small and big spheres of 0.2; this diagram includes the usual fluid-solid transition but, in the soft-sphere case, the metastable fluid-fluid transition, which is probably absent in hard-sphere mixtures, is close to being stable with respect to direct fluid-solid coexistence. From these results, the interesting possibility arises that, for sufficiently soft repulsive particles, this phase transition could become stable. Possible implications for the phase behavior of real colloidal dispersions are discussed. PMID:18067358
Characterization of maximally random jammed sphere packings: Voronoi correlation functions.
Klatt, Michael A; Torquato, Salvatore
2014-11-01
We characterize the structure of maximally random jammed (MRJ) sphere packings by computing the Minkowski functionals (volume, surface area, and integrated mean curvature) of their associated Voronoi cells. The probability distribution functions of these functionals of Voronoi cells in MRJ sphere packings are qualitatively similar to those of an equilibrium hard-sphere liquid and partly even to the uncorrelated Poisson point process, implying that such local statistics are relatively structurally insensitive. This is not surprising because the Minkowski functionals of a single Voronoi cell incorporate only local information and are insensitive to global structural information. To improve upon this, we introduce descriptors that incorporate nonlocal information via the correlation functions of the Minkowski functionals of two cells at a given distance as well as certain cell-cell probability density functions. We evaluate these higher-order functions for our MRJ packings as well as equilibrium hard spheres and the Poisson point process. It is shown that these Minkowski correlation and density functions contain visibly more information than the corresponding standard pair-correlation functions. We find strong anticorrelations in the Voronoi volumes for the hyperuniform MRJ packings, consistent with previous findings for other pair correlations [A. Donev et al., Phys. Rev. Lett. 95, 090604 (2005)PRLTAO0031-900710.1103/PhysRevLett.95.090604], indicating that large-scale volume fluctuations are suppressed by accompanying large Voronoi cells with small cells, and vice versa. In contrast to the aforementioned local Voronoi statistics, the correlation functions of the Voronoi cells qualitatively distinguish the structure of MRJ sphere packings (prototypical glasses) from that of not only the Poisson point process but also the correlated equilibrium hard-sphere liquids. Moreover, while we did not find any perfect icosahedra (the locally densest possible structure in which a
NASA Astrophysics Data System (ADS)
Grinyuk, A. A.; Lipatov, A. V.; Lykasov, G. I.; Zotov, N. P.
2016-01-01
We study the role of the nonperturbative input to the transverse momentum dependent (TMD) gluon density in hard processes at the LHC. We derive the input TMD gluon distribution at a low scale μ02˜1 GeV2 from a fit of inclusive hadron spectra measured at low transverse momenta in p p collisions at the LHC and demonstrate that the best description of these spectra for larger hadron transverse momenta can be achieved by matching the derived TMD gluon distribution with the exact solution of the Balitsky-Fadin-Kuraev-Lipatov equation obtained at low x and small gluon transverse momenta outside the saturation region. Then, we extend the input TMD gluon density to higher μ2 numerically using the Catani-Ciafoloni-Fiorani-Marchesini gluon evolution equation. Special attention is paid to phenomenological applications of the obtained TMD gluon density to some LHC processes, which are sensitive to the gluon content of a proton.
Pinter, Balazs; Nagels, Nick; Herrebout, Wouter A; De Proft, Frank
2013-01-01
Halogen bonds between the trifluoromethyl halides CF(3)Cl, CF(3)Br and CF(3)I, and dimethyl ether, dimethyl sulfide, trimethylamine and trimethyl phosphine were investigated using Pearson's hard and soft acids and bases (HSAB) concept with conceptual DFT reactivity indices, the Ziegler-Rauk-type energy-decomposition analysis, the natural orbital for chemical valence (NOCV) framework and the non-covalent interaction (NCI) index. It is found that the relative importance of electrostatic and orbital (charge transfer) interactions varies as a function of both the donor and acceptor molecules. Hard and soft interactions were distinguished and characterised by atomic charges, electrophilicity and local softness indices. Dual-descriptor plots indicate an orbital σ hole on the halogen similar to the electrostatic σ hole manifested in the molecular electrostatic potential. The predicted high halogen-bond-acceptor affinity of N-heterocyclic carbenes was evidenced in the highest complexation energy for the hitherto unknown CF(3) I·NHC complex. The dominant NOCV orbital represents an electron-density deformation according to a n→σ*-type interaction. The characteristic signal found in the reduced density gradient versus electron-density diagram corresponds to the non-covalent interaction between contact atoms in the NCI plots, which is the manifestation of halogen bonding within the NCI theory. The unexpected C-X bond strengthening observed in several cases was rationalised within the molecular orbital framework. PMID:23169478
Sun, K. X.
2011-05-31
This presentation provides an overview of robust, radiation hard AlGaN optoelectronic devices and their applications in space exploration & high energy density physics. Particularly, deep UV LED and deep UV photodiodes are discussed with regard to their applications, radiation hardness and space qualification. AC charge management of UV LED satellite payload instruments, which were to be launched in late 2012, is covered.
Wang, George T.; Li, Qiming
2013-04-23
A method for growing low-dislocation-density material atop a layer of the material with an initially higher dislocation density using a monolayer of spheroidal particles to bend and redirect or directly block vertically propagating threading dislocations, thereby enabling growth and coalescence to form a very-low-dislocation-density surface of the material, and the structures made by this method.
NASA Technical Reports Server (NTRS)
Wang, Taylor G. (Inventor); Elleman, Daniel D. (Inventor); Lee, Mark C. (Inventor); Kendall, Jr., James M. (Inventor)
1986-01-01
The improved, heterogeneous catalysts are in the form of gas-impervious, hollow, thin-walled spheres (10) suitably formed of a shell (12) of metal such as aluminum having a cavity (14) containing a gas at a pressure greater than atmospheric pressure. The wall material may be, itself, catalytic or the catalyst can be coated onto the sphere as a layer (16), suitably platinum or iron, which may be further coated with a layer (18) of activator or promoter. The density of the spheres (30) can be uniformly controlled to a preselected value within .+-.10 percent of the density of the fluid reactant such that the spheres either remain suspended or slowly fall or rise through the liquid reactant.
Catalytic, hollow, refractory spheres
NASA Technical Reports Server (NTRS)
Wang, Taylor G. (Inventor); Elleman, Daniel D. (Inventor); Lee, Mark C. (Inventor); Kendall, Jr., James M. (Inventor)
1987-01-01
Improved, heterogeneous, refractory catalysts are in the form of gas-impervious, hollow, thin-walled spheres (10) suitable formed of a shell (12) of refractory such as alumina having a cavity (14) containing a gas at a pressure greater than atmospheric pressure. The wall material may be itself catalytic or a catalytically active material coated onto the sphere as a layer (16), suitably platinum or iron, which may be further coated with a layer (18) of activator or promoter. The density of the spheres (30) can be uniformly controlled to a preselected value within .+-.10 percent of the density of the fluid reactant such that the spheres either remain suspended or slowly fall or rise through the liquid reactant.
NASA Technical Reports Server (NTRS)
Wang, Taylor G. (Inventor); Elleman, Daniel D. (Inventor); Lee, Mark C. (Inventor); Kendall, Jr., James M. (Inventor)
1989-01-01
The improved, heterogeneous catalysts are in the form of gas-impervious, hollow, thin-walled spheres (10) suitably formed of a shell (12) of metal such as aluminum having a cavity (14) containing a gas at a pressure greater than atmospheric pressure. The wall material may be, itself, catalytic or the catalyst can be coated onto the sphere as a layer (16), suitably platinum or iron, which may be further coated with a layer (18) of activator or promoter. The density of the spheres (30) can be uniformly controlled to a preselected value within .+-.10 percent of the density of the fluid reactant such that the spheres either remain suspended or slowly fall or rise through the liquid reactant.
Colloidal rod-sphere mixtures: fluid-fluid interfaces and the Onsager limit.
Brader, Joseph M; Esztermann, Ansgar; Schmidt, Matthias
2002-09-01
Using a geometry-based density functional theory we investigate the free interface between demixed bulk fluid phases of a colloidal mixture of hard spheres and vanishingly thin needles. Results are presented for the spatial and orientational density distributions of the particles, as well as for the interface tension. Density profiles display oscillations on the sphere-rich side of the interface provided the sphere liquid phase is on the oscillatory side of the Fisher-Widom line in the bulk phase diagram. Needles tend to align parallel (perpendicular) to the interface on the needle-rich (sphere-rich) side displaying biaxial (uniaxial) order. Furthermore, we generalize the theory to the Onsager limit for interacting rods, and give explicit expressions for the functional in simple geometries. PMID:12366111
NASA Technical Reports Server (NTRS)
Huebner, W. F.; Keady, J. J.
1984-01-01
Energy-independent first-flight transport kernels are evaluated for a spherical region with an R(-2) density distribution. The uncollided angular-flux distribution is obtained and integrated for a source distribution that is proportional to the density to give the uncollided emitted particle flux and current density. These are useful for the calculation of mass, energy, and momentum carried away by fast particles born in the medium. The data are relevant to estimate escape from weakly bound atmospheres such as comet comae, dilute circumstellar envelopes, and some unconfined laboratory plasmas.
Band structures and charge densities of KCl, NaF, and LiF obtained by the intersecting-spheres model
NASA Astrophysics Data System (ADS)
Antoci, S.; Mihich, L.
1980-01-01
The self-consistent electronic structures of KCl, NaF, and LiF have been calculated by the intersecting-spheres model and the results were compared with band structures calculated by other methods using the approximation of the exchange potential adopted by us. While for KCl close agreement was found between the augmented-plane-wave non-muffin-tin results by De Cicco and the intersecting-spheres-model (ISM) band structure, in the case of LiF differences of even 2.5 eV were found between conduction bands calculated by the ISM and the corresponding levels determined by linear-combination-of-atomic-orbitals (LCAO) methods. This disagreement seems to be imputable to a lack of convergence occurring in the LCAO calculations. The Fourier components of the charge densities (scattering factors) were determined using the Kohn-Sham-Gáspár form of the exchange potential. The agreement of the calculated scattering factors with experiment is not much worse than that obtained by Hartree-Fock calculations.