A simple expression for radial distribution functions of pure fluids and mixtures

Abstract

A simple expression for the radial distribution function (RDF) of pure fluids and mixtures is presented. It satisfies the limiting conditions of zero density and infinite distance imposed by statistical thermodynamics. The equation contains seven adjustable parameters; they have been fitted to extensive literature data of RDF’s for a Lennard-Jones fluid at different values of temperature and density. These in turn have been expressed as functions of reduced temperature and density, thus allowing a complete parametrization with respect to these variables using 21 parameters altogether with fairly good accuracy. The values of the reduced pressure and internal energy calculated by numerical integration of the completely parametrized equation compare fairly with literature molecular dynamics simulation results. The capability of the expression to fit to RDF’s of mixtures has been checked against some of the extensive RDF simulation data of binary mixtures of Lennard-Jones fluids with different diameters available in the literature. Data pertaining to different molar fractions as well as to different εAA/εBB ratios have been considered, and the agreement between calculated and simulation curves has resulted satisfactory. The proposed expression can be used to calculate by integration related quantities such as compressibility, internal energy, pressure and, using the Kirkwood–Buff theory, the chemical potentials and partial molar volumes of the components of mixtures for which RDF data are available.