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

摘要

We study the properties of symmetric binary mixtures of hard spheres with positive nonadditive diametersRij, namely twohyphen;component systems withR11=R22=RandR12R, at equimolar concentration. The functional form of the direct correlation functionscij(r) is investigated, within the Percusndash;Yevick approximation, by using Hiroike and Fukuirsquo;s version of the Ornsteinndash;Zernike integral equation for multicomponent fluids. It is shown that, by introducing simple polynomial expressions for the cross termC12(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 Percusndash;Yevick integral equation and a very good agreement is found. Finally, calculations based on a simple firsthyphen;order perturbation method, which gives a slight extension of analytic expressions derived from the Barkerndash;Henderson perturbation theory, are reported and discussed.