The statistical mechanics of systems with steep intermolecular potentials

Abstract

The classical configurational free-energy of a system of molecules with steep intermolecular potentials is obtained from that of a system of hard spheres by an expansion in powers of n -1, where n is a measure of the steepness of the potential. It is shown that the free energy can be obtained explicitly and exactly to the order of n -1. Higher terms have non-thermodynamic coefficients. The first-order term yields an excellent equation of state for gases at high temperatures and densities. It can also be used to calculate the course of the melting line of monatomic close-packed solids at high pressures in terms of the parameters of the repulsive potential. It is shown, subject only to the neglect of terms of the order of n -2, that there is no solid-fluid critical point for molecules with continuous but steep repulsive potentials.