Mean spherical approximation for the Yukawa fluid radial distribution function

Abstract

Waisman has obtained the direct correlation function (DCF) for the Yukawa fluid using the mean spherical approximation (MSA). Although his result has been used to obtain the thermodynamic functions of this fluid, the resultant radial distribution function (RDF) has not been calculated. In this study, the RDF is calculated by obtaining the Laplace transforms of the DCF and RDF of this fluid by analytic integration. These Laplace transforms are then converted to Fourier transforms that can be inverted numerically. Results are reported for a value of the decay parameter (z = 1.8) that mimics a Lennard-Jones (LJ) 12–6 fluid and for z = 5, which has been used in perturbation theory. For the cases studied, the RDF at contact is greater for the Yukawa fluid than for the hard-sphere fluid and increases monotonically with decreasing temperature. At low densities, the difference between the hard-sphere and LJ-like Yukawa RDFs is appreciable. However, at high densities this difference is much smaller. The dependence on temperature is stronger for z = 5 than for z = 1.8. A comparison of the MSA results with simulation results is made. The agreement of the MSA results with simulation is good except near contact where the MSA contact value always lies below the MC result.