Extensive molecular-dynamics simulations of Lennard-Jones and soft-sphere fluids were performed. The Lennard-Jones state points agreed well with the predictions of an equation of state for this fluid. Self-diffusion coefficients obtained from the Lennard-Jones mean-square displacements at equilibrium were fitted to a simple analytic expression, involving temperature and density, which had a density and temperature range of wider applicability than that of Levesque and Verlet. The corresponding shear viscosities in the limit of zero shear rate were obtained using a non-equilibrium molecular dynamics technique, which involved orthogonal longitudinal distortions (eliminating pure expansion or compression terms). The Lennard-Jones shear rigidity moduli were fitted to better than 1% by a simple analytic expression. A similar relationship for the shear viscosities was less satisfactory but this merely reflects the greater uncertainty in this collective transport property. The Stokes-Einstein relationship using slip boundary conditions gave an effective 'flow unit' diameter which decreased from several molecular diameters to one as the density increased. This suggested that the motion between a molecule and those in its first coordination shell was more cooperative at moderate densities resulting in greater coupling between molecular trajectories. Support for this comes from the direct evaluation of the friction coefficient by non-equilibrium molecular dynamics, pair radial and pair fluctuation correlation functions. The Verlet algorithm was used in these calculations. The more accurate Toxvaerd algorithm was shown not to improve noticeably the accuracy of the systematic component of single (and hence possibly collective) particle motion, as measured by velocity and force autocorrelation functions.

Self-Diffusion and Shear Viscosity of Simple Fluids. a Molecular-Dynamics Study. Heyes, D.M.: Journal of the Chemical Society, Faraday Transactions 2, 1983, 79[12], 1741-58