Evaluation of structural integrals in the perturbation of hard sphere mixture properties by intermolecular attraction in mixtures

Abstract

This paper discusses the evaluation of the structural integrals which weight the contribution of various attraction pair potentials to mixture properties. These integrals are generated when pairwise attraction in a mixture is considered to be a first order perturbation on a mixture of nonattracting hard spheres. For pure components these integrals have the form ∫^∞ ₀ y ^2-n g ^HS(y, ϱd ³) dy, where g ^HS is the pair distribution function for pure hard spheres of diameter d and y is the ratio r/d. This paper shows that the corresponding integral for the first order perturbation contribution of an i-j pair in a mixture can be evaluated to within about 3 per cent of its computer simulation value by means of an approximation given by ∫^∞ ₀ y ^2-n g ^HS(y, ϱ<d ³>) dy. In this approximation, the <d ³> term is a composition dependent average of the diameters of all constituents of the mixture, g ^HS is the pair distribution function for pure hard spheres with the pair interaction diameter d_ij , and y is the ratio r/d^ij . The form of the composition dependence of <d ³> is determined by a solution of the Ornstein-Zernike equation for a pair in a mixture of hard spheres.