Free-energy model for the inhomogeneous hard-sphere fluid: ‘‘Closure’’ relation between generating functionals for ‘‘direct’’ and ‘‘cavity’’ distribution functions

Abstract

A free-energy model for the inhomogeneous hard sphere fluid mixture was derived recently [Phys. Rev. Lett. 63, 980 (1989)] which is based on the fundamental geometric measures of the particles. It features convolution forms for the direct correlation functions as obtained by functional differentiation from the free energy. General features of the model are further explicated in this paper. In particular, fused-spheres overlap forms for the cavity distribution functions are obtained by recursive application of the model to the free energy of composite particles. It is shown how the scaled-particle theory provides an explicit ‘‘closure’’ relation between these two alternative description of the correlations.