Translational and rotational diffusion in liquids. I. Translational single-particle correlation functions

Abstract

This is the first of two articles which together present a theory for translational and orientational single-particle correlation functions in molecular liquids. The theory is based on the assumption that the single-particle motion in a liquid is determined primarily by the harsh repulsive parts of the intermolecular forces. It is shown that the dynamics due to the repulsive forces can be related to the particle motion in a model rough hard sphere fluid. The dynamics of the model hard sphere system is studied within the context of a binary collision expansion. An approximate formula is derived for the translational self-correlation function of the rough hard sphere fluid. The formula is computationally convenient. Arguments are given which indicate that the formula is accurate. In particular, it is shown that the single-particle distribution function obtained from the approximation is positive; the function is well behaved in the hydrodynamic limit, the approximation becomes exact at low densities; the first three time derivatives of the distribution function at t = 0 are exact for all densities; and the velocity autocorrelation function obtained from the distribution function is the Enskog result when the hard spheres are perfectly smooth. A quantitative criterion is proposed to determine the rough hard sphere model which is most closely related to a real liquid.