Series representation of the equation of state for hard particle fluids

Abstract

In most perturbation theory or mean field studies of the structural and thermodynamic properties of fluids, the reference system is taken to be a fluid of hard core particles which reflect the correct shape and size of the constituent molecules. As an alternative to the several existing scaled particle and integral equation approaches, we propose in this paper a simple series representation of the thermodynamic functions: Our basic expansion parameter is y=?/(1−?), where ? is the dimensionless packing factor (i.e. hard core volume times the number density). The coefficient of yn is obtained directly from the first n virial coefficients, with generalization to multicomponent systems being straightforward. Truncated forms of this series representation of the pressure are evaluated for hard spheres, dumbells, spherocylinders, and hard sphere mixtures (including nonadditivity). These results are compared with available Monte Carlo and molecular dynamics calculations, Percus–Yevick theory, Padé approximants, various versions of scaled-particle theory and truncated forms of the virial series. It is concluded that a three-term truncation of the y expansion provides a relatively simple and accurate description of the thermodynamics of hard-core reference systems.