Equations of state for hard spheres. A review of accuracy and applications

Abstract

Twenty two different analytical expressions for the compressibility factor of the hard sphere system have been collected and reviewed in order to perform two applications: Firstly, the accuracy of these expressions in reproducing six available computer simulation data sets for the hard sphere system, some of which are very recent, is tested. It is shown that there is not a direct relation between the simplicity or complexity of their analytical form and their accuracy. Secondly, the expressions, together with the Verlet–Weis formula for the temperature dependence of the molecular diameter, have been used to reproduce our molecular dynamics results for the pressure of the Lennard-Jones reference system proposed in the Weeks–Chandler–Andersen theory. We conclude that the approximation of using hard sphere equations of state together with the Verlet–Weis formula is very accurate at temperatures and densities near the Lennard-Jones critical point. At densities close to the triple point or to the liquid curve in the liquid–vapour equilibrium, the coincidence is adequate (deviations around 3%) only if the appropriate hard sphere equation of state is used.