A test particle approach to the zero separation theorems of molecular distribution functions

Abstract

It is shown that the potential distribution of a strong test particle leads to the zero separation values of the cavity distribution functions yab(0) in a mixture. This relation furnishes a direct means of computing by Monte Carlo simulations the coincidence values of the cavity function ln yab(0) and the potential distribution 〈exp[−βΨa−βΨb]〉. Test particle simulations have been carried out for mixtures of Lennard-Jones molecules differing considerably in size [(σab/σbb)3 =0.25, 0.5, 0.75, 1.00, 1.25, 1.50, 1.75, and 2.00] and in strength of interaction (εab/εbb =0.5, 1.0, 1.5, and 2.0). Alternative Monte Carlo methods are employed to check the statistics. In order to predict the behavior of the potential distribution, a distribution function theory, the reference hypernetted chain (RHNC) equation, is solved based on the universality of the bridge functions. Hard sphere mixtures are taken as reference fluids. The criteria recently proposed by Rosenfeld and Blum are used to select the equivalent hard sphere diameters. Close agreement with MC results is attained for most of the states considered. This provides further evidence that the RHNC equation is a reliable theory for mixtures of simple fluids.