Symmetric mixtures of hard spheres with positively nonadditive diameters: An approximate analytic solution of the Percus–Yevick integral equation

Abstract

We study the properties of symmetric binary mixtures of hard spheres with positive nonadditive diameters Rij, namely two-component systems with R11=R22=R and R12>R, at equimolar concentration. The functional form of the direct correlation functions cij(r) is investigated, within the Percus–Yevick approximation, by using Hiroike and Fukui’s version of the Ornstein–Zernike integral equation for multicomponent fluids. It is shown that, by introducing simple polynomial expressions for the cross term C12(r)=rc12(r), the problem of finding an approximate analytic solution of the abovementioned integral equations can be reduced to an algebraic one, i.e., to solving a closed set of a few nonlinear algebraic equations for some unknown parameters. Results corresponding to three different approximations are presented for the radial distribution functions at contact, the virial pressure and the so called bulk modulus. Comparison is made with our exact numerical solutions of the Percus–Yevick integral equation and a very good agreement is found. Finally, calculations based on a simple first-order perturbation method, which gives a slight extension of analytic expressions derived from the Barker–Henderson perturbation theory, are reported and discussed.