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

Twenty two different analytical expressions for the compressibility factor of the hard sphere system have been collected and reviewed in order to perf orm two applications : Firstly, the accuracy of these expressions in reprod ucing six available computer simulation data sets for the hard sphere syste m, 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 Verle t-Weis formula for the temperature dependence of the molecular diameter, ha ve been used to reproduce our molecular dynamics results for the pressure o f the Lennard-Jones reference system proposed in the Weeks-Chandler-Anderse n theory. We conclude that the approximation of using hard sphere equations of state together with the Verlet-Weis formula is very accurate at tempera tures and densities near the Lennard-Jones critical point. At densities clo se to the triple point or to the liquid curve in the liquid-vapour equilibr ium, the coincidence is adequate (deviations around 3%) only if the appropr iate hard sphere equation of state is used.