Equilibrium Theory of Simple Liquids

Abstract

The perturbation theory of liquids developed recently by Weeks, Chandler, and Andersen (WCA) is examined in detail: Each assumption introduced by these authors is tested by comparison with "exact" computer results. It is shown that the basic assumptions of WCA are justified. An improved expression for the radial distribution function of the hard-sphere gas enables us to correct for some further inconsistent assumptions of the WCA theory. We then succeed in giving simple analytical expressions for the thermodynamic functions of the Lennard-Jones fluid shown to be quite good at high density. We show that the remainder of the perturbation series, which converges slowly at lower density, can be evaluated with the help of the Percus-Yevick equation. We therefore possess a unified theory of liquids which is especially simple at high density. Finally we reexpress the original WCA theory in an analytical form.