Percolation theory and the conductivity of random close packed mixtures of hard spheres

The conductivity of random close packed mixtures of conducting and insulating spheres has been measured. The composition dependence and the critical percolation density are similar to what has been observed in crystalline systems.     

Mixtures of hard spherocylinders and hard spheres

Monte Carlo simulations have been performed for equimolar mixtures of hard prolate spherocylinders of length: breadth ratio 2:1 and hard spheres, in the fluid region. Two systems have been studied. In the first the breadth of the spherocylinder was equal to the hard sphere diameter, and in the second system both components were of equal molecular volume.

The compressibility factor, PV/NkT, has been obtained for both mixtures at four reduced densities (packing fractions) from 0·20 to 0·45. The results have been compared with the predictions of several analytical equations appropriate to mixtures of hard convex molecules, and an equation due to Pavlicek et al. was found to be very accurate. The results have been used to calculate the excess volumes of mixing at constant pressure, in an attempt to establish the relative importance of the effects of differences in molecular volume and shape on the thermodynamic properties.

The structural properties of the mixtures have also been investigated by calculating pair distribution functions for the three types of pair interactions present in these mixtures.     

Kinetic theory of hard spheres

Kinetic equations for the hard-sphere system are derived by diagrammatic techniques. A linear equation is obtained for the one-particle-one particle equilibrium time correlation function and a nonlinear equation for the one-particle distribution function in nonequilibrium. Both equations are nonlocal, noninstantaneous, and extremely complicated. They are valid for general density, since statistical correlations are taken into account systematically. This method derives several known and new results from a unified point of view. Simple approximations lead to the Boltzmann equation for low densities and to a modified form of the Enskog equation for higher densities.     

Dissipative dynamics for hard spheres

The dynamics for a system of hard spheres with dissipative collisions is described at the levels of statistical mechanics, kinetic theory, and simulation. The Liouville operator(s) and associated binary scattering operators are defined as the generators for time evolution in phase space. The BBGKY hierarchy for reduced distribution functions is given, and an approximate kinetic equation is obtained that extends the revised Enskog theory to dissipative dynamics. A Monte Carlo simulation method to solve this equation is described, extending the Bird method to the dense, dissipative hard-sphere system. A practical kinetic model for theoretical analysis of this equation also is proposed. As an illustration of these results, the kinetic theory and the Monte Carlo simulations are applied to the homogeneous cooling state of rapid granular flow.     

Equilibrium fluid-solid coexistence of hard spheres

We present a tethered Monte Carlo simulation of the crystallization of hard spheres. Our method boosts the traditional umbrella sampling to the point of making practical the study of constrained Gibbs' free energies depending on several crystalline order parameters. We obtain high-accuracy estimates of the fluid-crystal coexistence pressure for up to 2916 particles (enough to accommodate fluid-solid interfaces). We are able to extrapolate to infinite volume the coexistence pressure [p(co)=11.5727(10)k(B)T/σ(3)] and the interfacial free energy [γ({100})=0.636(11)k(B)T/σ(2)].     

Shear viscosity for inelastic hard spheres

The hydrodynamic equations of the Enskog theory for inelastic hard spheres is considered as a model for rapid flow granular fluids at finite densities. A detailed analysis of the shear viscosity of the granular fluid has been done using homogenous cooling state (HCS) and uniform shear flow (USF) models. It is found that shear viscosity is sensitive to the coefficient of restitution α and pair correlation function at contact. The collisional part of the Newtonian shear viscosity is found to be dominant than its kinetic part.     

Equilibrium phase behavior of polydisperse hard spheres

We calculate the phase behavior of hard spheres with size polydispersity, using accurate free energies for the fluid and solid phases. Cloud and shadow curves are found exactly by the moment free energy method, but we also compute the complete phase diagram, taking full account of fractionation. In contrast to earlier, simplified treatments we find no point of equal concentration between fluid and solid or reentrant melting at higher densities. Rather, the fluid cloud curve continues to the largest polydispersity that we study (14%); from the equilibrium phase behavior a terminal polydispersity can thus be defined only for the solid, where we find it to be around 7%. At sufficiently large polydispersity, fractionation into several solid phases can occur, consistent with previous approximate calculations; we find, in addition, that coexistence of several solids with a fluid phase is also possible.     

Isotropic fluid phases of dipolar hard spheres

Monte Carlo simulations are used to calculate the equation of state and free energy of dipolar hard sphere fluids at low temperatures and densities. Evidence for the existence of isotropic-fluid-isotropic-fluid phase transitions is presented and discussed. Condensation in the dipolar hard sphere fluid is unusual in that it is not accompanied by large energy or entropy changes. An explanation of this behavior is put forward.     

Reentrant surface melting of colloidal hard spheres

Concentrated suspensions of model colloidal hard spheres at a wall were studied in real space by means of time-resolved fluorescence confocal scanning microscopy. Both structure and dynamics of these systems differ dramatically from their bulk analogs (i.e., far away from a wall). In particular, systems that are a glass in the bulk show significant hexagonal order at a wall. Upon increasing the volume fraction of the colloids, a reentrant melting transition involving a hexatic structure is observed. The last observation points to two-dimensional behavior of matter at walls.     

Brownian dynamics simulation of polydisperse hard spheres

Standard algorithms used for the numerical integration of the Langevin equation require that interactions should slowly vary during the integration time-step. This in not the case for hard-body systems, where there is no clear-cut between the correlation time of the noise and the time-scale of the interactions. Starting with a short time approximation of the Smoluchowski equation, we introduce an algorithm for the simulation of the over-damped Brownian dynamics of polydisperse hard-spheres in absence of hydrodynamic interactions and briefly discuss the extension to the case of external drifts.     

Stationary state of thermostated inelastic hard spheres

We consider a fluid composed of inelastic hard spheres moving in a thermostat modelled by a hard sphere gas. The losses of energy due to inelastic collisions are balanced by the energy transfer via elastic collisions from the thermostat particles. The resulting stationary state is analysed within the Boltzmann kinetic theory. A numerical iterative method permits to study the nature of deviations from the Gaussian state. Some analytic results are obtained for a one-dimensional system.     

Orientational structure of dipolar hard spheres near a hard neutral wall

Spherical boundaries are used in a Monte Carlo simulation to calculate the angular structure of dipolar hard spheres near a neutral hard wall.     

Time evolution for infinitely many hard spheres

We construct the time evolution for infinitely many particles in F(x) = { *20c + ￥ 0 *20c |x| < a |x| \geqq a \Phi (x) = \left\{ {\begin{array}{*{20}c} { + \infty } \\ 0 \\ \end{array} } \right. \begin{array}{*{20}c} {|x|< a} \\ {|x| \geqq a} \\ \end{array}     

Optical properties of a suspension of hard spheres

The optical properties of suspensions are studied in a wide range of concentrations. An expression for the polarization operator is obtained taking into account the contributions of two-and three-particle correlations. The extinction length l and the transport length l* are calculated in terms of a model of hard spheres. A detailed comparison of the results of calculations with experimental data is performed. In calculations, the structure factor is determined in the Percus-Yevick approximation, while the form factor is taken into account in the Rayleigh-Gans approximation and in terms of the Mie theory. It is shown that taking into account the contribution of three-particle correlations improves the agreement of the theory with experiment. It is found that, in the range of high suspension concentrations, the optical parameters are more sensitive to the choice of the model for the structure factor than for the form factor.     

Phase transition in gas of hard core spheres

We present a new method of analyzing the gas of hard core spheres. We investigate analytic properties of the thermodynamic function over the circle of convergence of the cluster expansion and describe the way in which phase transition occurs.     

Dense packing of binary and polydisperse hard spheres

The packing of binary and polydisperse unimodal and bimodal ensembles of hard spheres in the limit of high pressure is studied using a sequential addition algorithm. Upon fixing the number of particles, and their size distribution, the average (maximum) packing fraction is determined for systems of up to 20 000 particles. The structures obtained correspond to amorphous states close to the dense random close packing density. Binary distributions obtained are denser than the equivalent monodisperse distribution and agree with the theoretical prediction for an infinite size ratio limit. Unimodal normal and lognormal polydisperse distributions obtained compare favourably with available simulation and experimental data. Results for bimodal lognormal distributions are presented. In all cases it is seen how an increase in polydispersity increases the packing fraction of the system. The results can be employed to gain insight into optimal formulations for dense emulsions.