Richard J. Bearman

Molecular dynamics simulation of the mutual and self diffusion coefficients in Lennard-Jones liquid mixtures

A molecular dynamics calculation has been attempted for the mutual diffusion coefficient in a Lennard-Jones liquid mixture utilizing about 200 000 timesteps and incorporating the contribution for the thermodynamic factor. The precision of the result is about 8 per cent, excluding errors arising from the N dependence of the coefficient. For the same mixture, a number of calculations have been made for the self diffusion coefficients D 1 and D 2 varying the total number of particles. A significant apparent N dependence is noted for D 1 and D 2 individually but the ration D 1/D 2 is constant.

Hard dumbells: Monte Carlo pressures and virial coefficients

The equation of state was determined by Monte Carlo simulation for 108 dumb-bells subject to periodic boundary conditions. The isotropic fluid-solid phase transition was observed. An orientational phase transition was not observed. Virial coefficients through B5 were calculated.

Mass dependence of the self diffusion coefficients in two equimolar binary liquid Lennard-Jones systems determined through molecular dynamics simulation

Careful molecular dynamics simulations have been made on the mass dependence of the self diffusion coefficients of two liquid Lennard-Jones systems corresponding, respectively, to equimolar solutions of ‘argon(1)-argon(2)’ and ‘argon(1)-krypton(2)’. In each case the mass m 1 of component 1 was held at 39·948 amu, and the mass m 2 of component 2 was varied over a wide range, holding constant the potential parameters, mole fractions, density and temperature. The linear contributions to the slopes of the curves in a log-log plot of the diffusion coefficients versus m 2/m 1 were found to be of the order of -0·25. This was justified heuristically and, in the ‘argon-argon’ case, on the basis of a perturbation theory developed by Ebbsjo and collaborators. The analogous linear contributions for the diffusion coefficient ratios D 1/D 2 in a log-log plot versus m 2/m 1, were found to be much weaker, 0·064 and 0·075, respectively.

Solution of the mean spherical model for dipolar mixtures

The mean spherical model is solved analytically for mixtures of dipolar fluids. The components are identified by different but additive molecular radii and different magnitudes of the dipole moment. The direct and indirect correlation functions are found to be functionally dependent on the corresponding hard-sphere functions calculated at certain adjusted densities. Equations for the parameters concerned in calculating such densities are given. The reduction to the equal radii case follows immediately from this analysis.

Scaled particle theory for mixtures of nonadditive hard disks or hard spheres: An alternative scaling

The scaled particle theory of nonadditive hard disks or spheres of Tenne and Bergman, studied numerically by us in two previous papers, has been modified by relaxing the requirement that the particle radius scaling respect the nonadditivity out to arbitrarily large radii. The resulting theory is much simpler to implement numerically, while the results are comparable to those of the previous theory. A comparison is made between the predictions of phase separation of the present theory and those of numerical simulations.

Equation of state of heteronuclear hard dumbbells

Abstract The equation of state of five heteronuclear dumbbells has been calculated by standard Monte Carlo techniques. Approximate theories are also used to calculate the equation of state and are compared to the “simulation” results.

The extension of simulation radial distribution functions to an arbitrary range by baxter's factorisation technique

Abstract Baxters transformation of the Ornstein—Zeraike equation is used to obtain the radial distribution function for the infinite Lennard-Jones potential from simulation results for the truncated potential. The method is more stable and efficient than Verlets treatment of the single component case. The method also has the advantage that is is easily extended to mixtures.

Molecular dynamics simulations of self-diffusion coefficients in binary isotopic Lennard-Jones solutions

Molecular dynamics simulations of self-diffusion coefficients in binary solutions of isotopes have been carried out for mole fractions 0·2, 0·5, and 0·8 at constant density and temperature, over a wide range of molecular mass ratios, with Lennard-Jones potential parameters corresponding to argon. A symmetry relation is demonstrated which provides results for two mass ratios from a single calculation. The data are fitted to empirical equations and extrapolated to infinite dilution to give tracer diffusion coefficients. It is found that the calculations are in agreement with experimental data on the diffusion of benzene isotopes in a variety of hydrocarbon solvents. The relationship of the results to perturbation theory is considered briefly, and a prediction is verified numerically. The paper concludes with a general discussion of the effects of the medium on the diffusion coefficient ratios.

Studies of a version of scaled particle theory for nonadditive hard disks. II. Fluid–fluid phase equilibria

The scaled particle theory of Tenne and Bergmann [J. Chem. Phys. 70, 1952 (1979)] studied in paper I [J. Chem. Phys. 88, 1235 (1988)] has been examined for fluid–fluid phase equilibria in binary solutions of equal size particles. For a large deviation from additivity, changes in curvature of the Gibbs free energy identify regions of complete miscibility, partial miscibility, and immiscibility. The compositions of coexisting phases are determined using the double tangent construction. The simplicity of the intermolecular potential leads to an inverse relationship between the pressure–mole fraction phase diagram at constant temperature and the temperature–mole fraction phase diagram at constant pressure. The binary solutions are found to possess a lower solution critical pressure at constant temperature and an upper solution critical temperature at constant pressure. The critical exponent β is found numerically to be classical as would be expected from a scaled particle theory. The phase equilibria reported...

Virial expansion for hard ellipsoids of revolution

The third, fourth, and fifth virial coefficients for four different ellipsoids of revolution have been calculated by a Monte Carlo method. The virial coefficients and the Pade representation of the virial series give agreement with scaled particle theory at moderate densities to within a few per cent.