Succession of stacking disorder in hard-sphere crystal under gravity by Monte Carlo simulation

We have performed Monte Carlo simulations of hard spheres under gravity. Vertical boundaries are hard walls, which are well separated with each other. On the other hand, the periodic boundary condition is imposed in the horizontal direction. While we previously reported enhancement of crystallinity as well as crystallization due to gravity, we present here the results that demonstrate the succession of a defect. In case that the crystal formed at the bottom of the system includes kinds of stacking disorders for the (0 0 1) growth, twin band structure develops as mediated by a stacking disorder succeeded in the crystal formed in the fluid region which lies on the bottom crystal. In case that the stacking structure along horizontal direction changes from the (1 1 1) stacking to the (0 0 1) stacking, twin band structure in the (0 0 1) stacking region develops as succeeded in the crystal transformed. The twin band structure also becomes large with its upward growth.     

First-principle proof of the modified collision boundary conditions for the hard-sphere system

A fundamental issue lying at the foundation of classical statistical mechanics is the determination of the collision boundary conditions that characterize the dynamical evolution of multi-particle probability density functions (PDF) and are applicable to systems of hard-spheres undergoing multiple elastic collisions. In this paper it is proved that, when the deterministic N-body PDF is included in the class of admissible solutions of the Liouville equation, the customary form of collision boundary conditions adopted in previous literature becomes physically inconsistent and must actually be replaced by suitably modified collision boundary conditions.     

Mean-field cage theory for the random close packed state of a metastable hard-sphere glass

In 2005, we developed a mean-field cage theory for the freezing of a stable hard-sphere fluid using the character of a stable hard-sphere fluid, some observations and the mean-configuration approximation [X.Z. Wang, J. Chem. Phys. 122 (2005) 044515]. It was found that near the freezing point, a thermal fluctuation of a cage causes the hard sphere in this cage to exchange positions with one of its nearest neighbors. In this paper, we extend the theory to the random close packed state of a metastable hard-sphere glass. It is found that near the random close packing point, a thermal fluctuation of a cage sets three of the hard spheres in this cage and its nearest cages into the local circulatory motion, resulting in indirect position exchanges among these three hard spheres. We obtain an analytical formula for the random close packing density. The predicted values are in good agreement with the experimental and simulation results for spatial dimensions d=2–7$d=2\text{–}7$.     

The GMSA for a hard-sphere fluid revisited: evaluation of the Henderson-Blum approximation[*

The Generalized Mean Spherical Approximation for a hard-sphere fluid developed by Waisman [E. Waisman, Mol. Phys. 25, 45 (1973)] over forty years ago is revisited. The relatively recent [C. F. Tejero and M. López de Haro, Mol. Phys. 105, 2999 (2007)] completely analytical results for the direct correlation function of such approximation are used to assess the simplification introduced by Henderson and Blum [D. Henderson and L. Blum, Mol. Phys. 32, 1627 (1976)]. The conclusion is reached that such simplification is a rather valuable compromise between simplicity and accuracy.     

A new theory for polymer/solvent mixtures based on hard-sphere limit

Based on hard-sphere limit of binary mixtures with different molecular size of components a theory has been developed for calculating activities of solvents in polymer/solvent mixtures. The theory considers various chain configurations for polymer molecules, varying from extended chain to the coiled chain. According to this theory the activity of solvent can be calculated from molecular weights (MWs) and densities as the only input data. The only adjustable parameter in the calculations, is the hard-sphere diameter of polymer, which provides useful criteria for the judgement on the chain configuration of polymer.The activity calculations have been performed for seven binary mixtures of polymer/solvent and compared with experimental data at various temperatures and for a varying range of MWs of polymers.The solvents in the mixtures were both of polar and nonpolar natures. The activity calculations for the same systems were performed by the well-known Flory-Huggins theory. Comparing the results of calculations with those of Flory-Huggins theory indicates that, the proposed theory is able to predict the activities of the solvent with good accuracy.The radius of gyration, excluded volume and interaction parameter for polymer chain have been calculated using the parameter obtained in the new theory. The calculated interaction parameter in the new theory, is interpreted in terms of attraction, repulsion and interchange energy of polymer and solvent in the mixture.     

Binary nonadditive hard-sphere mixtures at high dimension

At high spatial dimension, a suitably scaled classical system of interacting particles truncates at second virial terms. A binary mixture of nonadditive hard spheres with sufficiently repulsive interaction between unlike particles decomposes at sufficiently high density into two coexisting phases. The region around the critical density behaves classically.     

Large energy behavior of the velocity distribution for the hard-sphere gas

The initial-value problem for the Boltzmann-Lorentz equation for hard spheres at zero temperature is shown to be ill defined, the general solution depending on an arbitrary function. The uniqueness of the solution can be obtained by imposing the conservation of the number of particles (Carleman's type of condition does not suffice). The linearized Boltzmann equation for hard spheres is then analyzed, as it occurs in Enskog's method for calculating transport coefficients. It is demonstrated that in the case of viscosity and diffusion it is necessary to add supplementary conditions to obtain the uniqueness of the solution. The nonuniform character of Enskog's expansion and violation of positivity in the large velocity region are exhibited.     

On predicting self-diffusion coefficients in fluids

A modification of an existing correlative equation for self-diffusion coefficients is presented. A free-volume theory for liquids has been corrected to reproduce diffusivities of hard-sphere and Lennard–Jones fluids from low-density limit to melting points, and has been applied to correlate a wide database of non-polar, polar, quantic and hydrogen-bonding substances, although it is unable to fit helium, water and hydrogen fluoride. The adjustable parameters are generalized with available fluid properties, and the three resulting predictive formulas present lower deviations than other correlative equations used in a predictive way for non-quantic and non-associated fluids.     

Analytical representation of the density derivative of the Percus–Yevick hard-sphere radial distribution function

ABSTRACT

Explicit analytical expressions are presented for the density derivative, ?g_HS(R; ρ)/?ρ, of the Percus–Yevick approximation to the hard-sphere radial distribution function for R ≤ 6σ, where σ is the hard-sphere diameter and ρ = (N/V)σ³ is the reduced density, where N is the number of particles and V is the volume. A FORTRAN program is provided for the implementation of these for R ≤ 6σ, which includes code for the calculation of g_HS(R; ρ) itself over this range. We also present and incorporate within the program code convenient analytical expressions for the numerical extrapolation of both quantities past R = 6σ. Our expressions are numerically tested against exact results.     

Alternative ensemble averages in molecular dynamics simulation of hard spheres

ABSTRACT

We consider application to the hard sphere (HS) model of the mapped-averaging framework for generating alternative ensemble averages for thermodynamic properties. Specifically, we develop and examine new formulas for the pressure, the singlet and pair densities, and the cavity-correlation function inside the HS core; the pressure formula in particular is constructed such that it gives an ensemble average that exactly corrects the second-order virial equation of state. The force plays a central role in mapped-averaging expressions, and we write them in a way that accounts for the impulsive, event-driven nature of the HS dynamics. Comparison between results obtained conventionally versus mapped averaging finds that the latter has some advantage at low density, while both perform equally well (in terms of uncertainties for a given amount of sampling) at higher densities.