On the van der Waals Theory of the Vapor-Liquid Equilibrium. IV. The Pair Correlation Function and Equation of State for Long-Range Forces

Abstract

A fluid where the pair interaction potential between the particles consists of a hard core and a weak attraction of long range is considered. The pair correlation function and the equation of state in the one-phase region are calculated by a perturbation method with the ratio of the volume of the hard core to the interaction volume as perturbation parameter. The technique used is to expand the well-known density expansion in this perturbation parameter, and finally resum to all orders in the density. To lowest order, the equation of state is of the van der Waals type, and the asymptotic behavior of the pair correlation function near the critical point is that described by the Ornstein-Zernike theory. Higher approximations to these results are given.