Liquid-vapour coexistence and correlations in the interface

Abstract

From the derivative of the statistical mechanical definition of the number density (the first Yvon equation), we derive an infinite set of sum rules that must be satisfied by the density profile and the pair correlation function of a liquid-vapour system with pairwise central interactions. For a particular class of approximate pair correlation functions, the sum rules reduce to equations linking the pressure and temperature with the densities of the two bulk phases. Good agreement with experimental data is obtained.