J. A. Barker

Liquid argon: Monte carlo and molecular dynamics calculations

Thermodynamic properties of liquid argon are calculated by Monte Carlo and molecular dynamics techniques, using accurate pair-potential functions determined from the properties of solid and gaseous argon, together with the Axilrod-Teller three-body interaction. Satisfactory techniques for evaluating three-body contributions to thermodynamic properties without excessive requirements of computer time are described. Quantum corrections are included. Agreement with experiment is excellent: the best pair and triplet potentials give an excellent description of the properties of solid, gaseous and liquid argon.

Soft‐Sphere Equation of State

The pressure and entropy for soft‐sphere particles interacting with an inverse twelfth‐power potential are determined using the Monte Carlo method. The solid‐phase entropy is calculated in two ways: by integrating the single‐occupancy equation of state from the low density limit to solid densities, and by using solid‐phase Monte Carlo pressures to evaluate the anharmonic corrections to the lattice‐dynamics high‐density limit. The two methods agree, and the entropy is used to locate the melting transition. The computed results are compared with the predictions of the virial series, lattice dynamics, perturbation theories, and cell models. For the fluid phase, perturbation theory is very accurate up to two‐thirds of the freezing density. For the solid phase, a correlated cell model predicts pressures very close to the Monte Carlo results.

A quantum‐statistical Monte Carlo method; path integrals with boundary conditions

A new Monte Carlo method for problems in quantum‐statistical mechanics is described. The method is based on the use of iterated short‐time Green’s functions, for which ’’image’’ approximations are used. It is similar to the use of Feynman or Wiener path integrals but with a modification to take account of hard‐core boundary conditions. It is applied to two one‐dimensional test problems: that of a single particle in a hard‐walled box and that of two hard particles in a hard‐walled box. For these test problems, the results are in excellent agreement with exact quantum‐mechanical results both at high temperatures (near the classical limit) and at very low temperatures such that essentially only the ground state is occupied. Generalizations to three‐dimensional systems, to many‐body systems, and to more realistic potentials are discussed briefly.

Surface structure and surface tension: Perturbation theory and Monte Carlo calculation

A Monte Carlo computation of the surface structure and surface tension of a liquid with molecules interacting according to the Lennard‐Jones 12–6 potential is described. The computation demonstrates the presence of a well‐developed layer structure at the surface extending to a depth of about eight molecular layers. The calculated surface tension agrees well with that predicted by Toxvaerds extension of the Barker‐Henderson perturbation theory to nonuniform fluids. The latter theory also predicts well the averaged behavior of the surface density profile (though not the development of the layered structure). This theory is used with accurate pair and triplet potentials to calculate values of the surface tension of liquid argon that agree quantitatively with experiment over a wide range of temperatures.

Fifth Virial Coefficients

A numerical method for evaluating fifth virial coefficients for spherical pairwise‐additive potentials is described. Results are given for the case of the Lennard‐Jones 12–6 potential.

Phase diagram of the two-dimensional Lennard-Jones system; Evidence for first-order transitions

There has recently been extensive interest in the nature of the melting/freezing transition for a two-dimensional system of molecules interacting with Lennard-Jones 6:12 potentials, which is a prototype for physisorbed systems. We have therefore made a detailed study of the thermodynamics of the phase diagram for this system. We first made calculations using liquid-state perturbation theory for the fluid state and a self-consistent cell theory for the solid state to determine thermodynamic functions; these results led to ordinary first-order phase transitions between solid/fluid and liquid/gas phases, in agreement with the constant-pressure Monte Carlo results of Abraham. We refined the calculations by using constant-pressure and constant-density Monte Carlo results to improve the accuracy of the calculated free energies, and we determined the two-phase equilibria by making direct Monte Carlo calculations for two-phase systems. The results are internally consistent and lead to a phase diagram qualitatively similar to the three-dimensional Lennard-Jones system.

Improved potentials for Ne + Ar, Ne + Kr, and Ne + Xe

Improved interatomic potentials for Ne‐rare gas pairs have been obtained by fitting a multiparameter potential to low energy differential cross sections, second virial coefficients, and diffusion coefficients. All asymmetric Ne‐rare gas potentials have narrower attractive wells than those of the symmetric rare gas pairs. The values of rm and e for Ne+Ar, Ne+Kr, and Ne+Xe are 3.43 A, 71.9°K; 3.58 A, 74.5°K; and 3.75 A, 75.0°K, respectively.

A new Monte Carlo method for calculating surface tension

A new Monte Carlo method for calculating the surface tension of a liquid is described. The method is based on a direct evaluation of the free energy required to create a surface, unlike earlier Monte Carlo calculations which evaluated the surface stress. It is applied to the 6:12 fluid in conditions close to the triple point for argon. The calculated surface tension agrees within statistical uncertainty with previous Monte Carlo estimates, but the statistical uncertainty of the present method is much lower. Agreement with experimental data for argon is not good, as should be expected; estimates of the effects of using a correct pair potential and particularly of including three‐body interactions indicate that they would lead to good agreement.

Perturbation Theory and the Radial Distribution Function of the Square‐Well Fluid

Perturbation theory is used to derive the first‐order term of the inverse temperature expansion of the radial distribution function (RDF) for a fluid whose molecules have a hard core. Exact and approximate expressions, based on the local compressibility approximation, the superposition approximation (SA), and the Percus‐Yevick theory (PY) are derived. Numerical results are examined in the case of the square‐well potential with wellwidth 0.50. The RDF resulting from the exact and SA expression yield good results for the equation of state down to reduced temperatures below β e=1.

On the structure of a free surface of a Lennard‐Jones liquid: A Monte Carlo calculation

We report a Monte Carlo simulation of the Lennard−Jones liquid−vapor free surface at 84°K and conclude that, contrary to other recent numerical experiments, there exists no layer structure in the liquid region neighboring the free surface.