A simple equilibrium statistical mechanical theory of dense hard sphere fluid mixtures

Abstract

The equilibrium statistical mechanical theory of Andrews for a hard core fluid is reformulated generally from simple, rigorous probability theory and is shown to apply to multicomponent systems. A simple expression is rigorously derived for the third virial coefficient of a mixture of nonadditive hard spheres. In the cases of additive potentials or binary systems, the expression is a great simplification of the previously known result. The exact theory of mixtures of not necessarily additive one-dimensional hard lines is developed simply for uniform mixing. Expressions for the reciprocal of the activity and the pressure in mixtures of additive hard spheres are determined approximately by similar methods. Calculations for binary mixtures with diameter ratios of 1.1 to 1, 1.667 to 1, and 3 to 1 are compared with computer experiments. The theory is significantly better than either the equation of state obtained from the Percus–Yevick equation or from the scaled particle theory. Indeed, it is about as accurate as the best empirical equation of Mansoori, Carnahan, Starling, and Leland. The physical origin of the decrease in pressure with diameter ratio at constant volume is discussed. Equations are listed, permitting calculation of various excess functions and excess functions of mixing for hard spheres.