Accurate theory of the hard sphere fluid

Abstract

The spare volume V_s of an assembly of N spheres of diameter σ in a volume V is defined as the average over configurations of the volume which is not within σ of a sphere centre. V_s/V is the probability that another sphere can be placed at a random point in the assembly and it is the inverse of the thermodynamic activity. V_s is estimated by a method which involves only a linearity assumption and a parameter whose value is taken as 1. The equation of state which results is more accurate than any previous theoretical predictions and appears to represent recent computer simulation data better than the various numerical equations, including the Carnahan–Starling equation. The same assumptions yield an equally accurate equation of state for the hard disc fluid.