Thermodynamic properties of a polydisperse system.

We use the virial theorem to derive a closed analytic form of the Helmholtz free energy for a polydisperse system of sticky hard spheres (SHS) within the mean spherical model (MSM). To this end we calculate the free energy of the MSM for an N-component mixture of SHS via the virial route and apply to it-after imposing a Lorentz-Berthelot type rule on the interactions-the stochastic (i.e., polydisperse) limit. The resulting excess free energy of this polydisperse system is of the truncatable moment free energy format. We also discuss the compressibility and the energy routes.

Pair distribution functions of a binary Yukawa mixture and their asymptotic behavior.

Based on an analytic solution of the mean spherical model for a binary hard sphere Yukawa mixture, we have examined the pair distribution functions g(ij)(r), focusing, in particular, on two aspects: (i) We present two complementary methods to compute the g(ij)(r) accurately and efficiently over the entire r range. (ii) The poles of the Laplace transforms of the pair distribution functions in the left half of the complex plane close to the origin determine the universal asymptotic behavior of the g(ij)(r). Although the meaning of the role of the subsequent poles-which typically are arranged in two branches-is not yet completely clear, there are strong indications that the distribution pattern of the poles is related to the thermodynamic state of the system.

Analytic example of a free energy functional

We use the ideas of Percus for the construction of classical density functionals for two model interactions: simple hard spheres and adhesive hard spheres (AHSs). The required input, the properties of the uniform fluid, is taken from the analytic mean spherical solution for these two systems. For hard spheres we derive-via a bilinear decomposition of the direct correlation functions-a set of basis functions, which is the same as the one presented by Rosenfeld in his fundamental measure theory framework. For AHSs additional basis functions have to be considered to ensure the bilinear decomposition of the direct correlation functions; we present an expression for the free energy functional for the one-component case.