Free-energy model for the inhomogeneous hard-sphere fluid inDdimensions: Structure factors for the hard-disk (D=2) mixtures in simple explicit form

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 yields explicit analytic predictions for the direct correlations of the uniform fluid in three dimensions, which are in overall good agreement with extensive Monte Carlo simulation results for the pair and triplet functions. In the present paper, general features of the model are further explicated, with special emphasis on those features enabling a straightforward application to the inhomogeneous hard-disk fluid mixture. In particular, an analytic theory for the structure factors of the hard-disk mixture is derived. The present results should be useful as reference for the statistical-thermodynamic analysis of two-dimensional systems.