John M. Kincaid

Radial distribution function of a hard-sphere solid

New Monte Carlo estimates of the radial distribution function of a hardsphere solid are given, along with a simple analytic approximation for that function. The approximation is useful over a wider range of densities than that developed earlier by one of us.

Isostructural phase transitions due to core collapse. II. A three‐dimensional model with a solid–solid critical point

We give a theoretical treatment of isostructural phase transitions that result from partial collapse of the repulsive core of the interparticle pair potential. We use an approximation procedure that is tailored to the high‐density regime in which an isostructural solid–solid transition is found for a potential that is the sum of a hard‐sphere term and a repulsive shoulder term. A study is made of the transition and its critical point as a function of the potential parameters. We also give an extension of our theory to mixtures, as well as to the shouldered hard‐sphere potential to which a long‐range attractive tail is added.

Isostructural phase transitions due to core collapse. I. A one‐dimensional model

This is the first of a two part study of a statistical mechanical system that exhibits an isostructural phase transition at high density and pressure. Here, in Paper I, we consider a one‐dimensional fluid; in Paper II we go on to treat the same system in three dimensions, using the approximation methods developed and tested here for one of the systems studied exactly by Stell and Hemmer [J. Chem. Phys. 56, 4274 (1972)]. Our pair potential φ (r) consists of a hard core of diameter d plus a shoulder of constant positive magnitude V0 for d<r<d (1+λ), to which a weak long‐range attraction term is added. We study the results of first‐order perturbation theory in V0, as well as in f0=exp(−βV0)−1, β= (kT)−1, and find that used jointly they yield remarkably accurate results that promise to be similarly accurate in three dimensions, where an exact theory is lacking. In particular, we note that first‐order perturbation theory in V0 becomes rigorously exact in one‐dimension for fixed β as the density ρ approaches cl...

Nonequilibrium molecular dynamics calculation of the thermal diffusion factor

Abstract A nonequilibrium molecular dynamics method that allows direct calculation of the thermal diffusion factor, α, is presented. Using boundary conditions to establish a temperature gradient between two opposing faces of a cubic volume, a steady state is achieved in which the temperature and composition fields are spatially nonuniform. The thermal diffusion factor is obtained from observations of the temperature, composition and their gradients. We report calculations of α for a binary (isotopic) mixture of particles that interact with a (12-6) Lennard-Jones potential that is modified so that the interparticle force tends smoothly to zero at a finite range; supercritical systems of 108,256,500, and 1372 particles at a moderate fluid density are examined in which the particle mass ratios are 2, 5, and 10. We find that the dependence of α on the mass ratio (at fixed density, composition, and temperature) is similar to that observed in the Enskog theory for hard spheres.

Thermal diffusion factors for the Lennard-Jones/spline system

A steady-state, molecular-dynamics method is used to calculate the thermal diffusion factor α for binary isotopic mixtures at a single, supercritical temperature. The variation of α with density, c...

Isostructural phase transitions due to core collapse. III. A model for solid mixtures

Our earlier development of a statistical mechanical theory of isostructural phase transitions due to core collapse [J. Chem. Phys. 65, 2161, 2172 (1976)] is extended to the treatment of solid mixtures exhibiting isostructural transitions. Since mixtures in which two solid phases coexist are typically in states of mechanical but not material equilibrium, we consider the theory for states of mechanical equilibrium only, as well as the theory for coexisting phases in true stable thermodynamic equilibrium. Using an extremely simple Hamiltonian model we find good qualitative agreement between the results of a first‐order perturbation theory and the recent experimental results for Ce1−xThx mixtures. In particular, the theory accounts for the experimentally observed decrease in critical temperature with increasing x and for the dependence of the observed resistivity–temperature isobars upon x.

A thermodynamic perturbation theory for multicomponent and polydisperse mixtures

We describe a general perturbation method that can be used to solve the equilibrium and critical‐point conditions for model systems described by an analytic Helmholtz free energy. The general technique is developed within the framework of continuous or polydisperse systems; it may be applied to systems with discrete components, as well as to systems described by a continuous distribution of components. The expansion is based on the assumption that the microscopic parameters characterizing the system may be expressed as those of a reference system plus a series of ‘‘small’’ corrections. Explicit formulas for the first‐ and second‐order solutions to the equilibrium and critical‐point conditions are given. The low‐order perturbation solutions will be useful when the phase boundaries of the system are close to those of the reference system.

A test of the modified Enskog theory for self-diffusion

The method of molecular dynamics has been used to calculate the self-diffusion coefficient for a system of particles whose pairwise additive interactions are governed by the Lennard-Jones/spline potential, a finite ranged modification of the Lennard-Jones potential. The coefficient of self-diffusion D has been calculated for the states nσ3 = 0·05, 0·1, 0·2, 0·3, 0·4, and 0·5, with k B T/e = 2·0 (n is the number density, T the temperature, k B Boltzmanns constant, and σ and e are the length and energy parameters of the Lennard-Jones potential). The non-equilibrium molecular dynamics calculations were made for systems having N particles, with N = 256, 500, and 1372. D was obtained by extrapolating the finite N results to the N = ∞ limit. To evaluate the modified Enskog theory (MET) we calculated the second and third virial coefficients and D 0, the dilute gas value of D, by numerical quadrature. The thermal pressure T(δp/δT) n , which plays a central role in the MET, was calculated using molecular dynamics...

Phase equilibrium in a special class of polydisperse fluid models

For a special class of polydisperse fluid models we have developed methods for obtaining (numerically) exact solutions to the equilibrium conditions. The models considered are special in the sense that the functional dependence of thermodynamic properties on the mole–fraction distribution density F(I) and microscopic parameter functions is restricted. For example, the pressure may depend only on a single moment of F(I). For our special class of models, we show how the dew/bubble conditions can be given a simple two‐dimensional geometric representation, and the dew/bubble conditions are reduced to solving two equations in two unknowns. The solution of the full equilibrium conditions can be obtained by an iterative procedure given the solutions of the dew/bubble equations. Three specific models, based on the van der Waals and Soave–Redlich–Kwong equations of state, are examined in detail. We also show how to implement these new solution techniques when the mixture contains a finite number of chemical species.

Deviations from hydrodynamics on the nanoscale

This study has examined the decay of an instantaneously imposed heat pulse on an equilibrium model of a dense fluid. The spatial extent of the initial pulse is quite small, of the order of 100 cubic nanometres; the amount of energy added to the system is only 5% of the total system kinetic energy. This small pulse decays quite rapidly, within several picoseconds, but the decay proceeds more slowly than predicted by the hydrodynamic equations. During the first picosecond of the decay, the kinetic energy is not equipartitioned, and a rapid process of energy transfer from kinetic energy to potential energy via interparticle interactions takes place. A new transport theory is developed that includes the ‘pre-hydrodynamic’ stage of evolution of non-equilibrium systems. Formally exact expressions for the local density, velocity, and kinetic energy (temperature) fields are developed in terms of Greens functions that depend on dynamic quantities, such as the mean-square displacement, averaged over the ensemble of initial states. No partial differential equations are involved.