Free energy model for inhomogeneous fluid mixtures: Yukawa-charged hard spheres, general interactions, and plasmas

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. Along with an updated assessment of its accuracy, this model is first generalized for charged hard-sphere fluid mixtures, in which every particle carries a central Yukawa charge, and it is then extended to general fluid mixtures in external fields. The Yukawa-charged hard-sphere mixture provides a quite general reference system for many interesting physical systems including plasmas, molten salts, and colloidal dispersions, the screening parameter enabling to interpolate between the long range Coulomb forces and the short range hard cores. A special renormalization property of the Yukawa potential provides the means to derive the exact Onsager-type lower bound for the potential energy of the mixture, and its related asymptotic strong-coupling limit of the liquid pair correlation functions. These results are obtained analytically for the general homogeneous mixture with Yukawa interactions. They enable to extend the fundamental measure free energy model to inhomogeneous charged Yukawa mixtures, with the charge contributions given by a truncated second order expansion from the uniform (bulk) fluid limit. The resulting free energy model, which interpolates between the ideal-gas and ‘‘ideal-liquid’’ limits, then leads to a self-consistent method for calculating the density profiles for general fluid mixtures in external fields. This method is equivalent to an ansatz of ‘‘universality of the bridge functional.’’ The ‘‘bridge functional’’ consists of all the terms beyond the second order, in the expansion of the excess free energy functional around a reference uniform fluid. The self-consistency is imposed by applying the general method in the special case when the external potential is generated by a ‘‘test particle’’ at the origin of coordinates. In this limit, our general method for nonuniform fluids corresponds to an established and successful theory for the bulk uniform fluid pair structure, namely the thermodynamically consistent modified-hypernetted-chain theory, with the bridge functions now generated by an explicit and demonstratively accurate, ‘‘universal,’’ hard-sphere bridge functional. As a stringent test for the general model, the strongly coupled one-component plasma, in the bulk and near a hard wall, is considered in some detail.