Simulation and approximate formulae for the radial distribution functions of highly asymmetric hard sphere mixtures

Abstract

The Henderson and Chan (HC) formulae for the contact values of the radial distribution functions (RDFs) of a highly asymmetric hard sphere mixture are reconsidered in light of a recent formula of Roth, Evans and Dietrich for the RDF of a pair of exceedingly large spheres at zero concentration in a solvent of small hard spheres. Two modifications of the HC formulae using this result give a large sphere–large sphere contact value that is considerably smaller than that of the original formulation. These new HC results are compared with the molecular dynamics simulations of Lue and Woodcock, for a diameter ratio of 1:10, supplemented by a few new results that are reported here. The new HC formulae are in much better agreement with the MD results than is the popular Boublik–Mansoori–Carnahan–Starling–Leland formula. Also, some simulation results for the RDFs as functions of separation are reported.