Density-dependent interactions and thermodynamic consistency in integral equation theories

Abstract

In this paper we present an alternative formulation of the well-known integral equation approximations designed to keep a consistent approach to the determination of thermodynamic properties in the case of density-dependent interactions. Obviously, residual inconsistencies inherent to the approximate character of the closure relations of the Ornstein–Zernike equation will not be corrected. In this connection, we will show how this approach is particularly successful when applied in conjunction with approximations in which the aforementioned inconsistencies are minimal, as is the case of the optimised Reference Hypernetted Chain equation. As a case study we will consider the Derjaguin–Landau–Verwey–Overbeek model of charged colloids which is one of the simplest realisations of density-dependent interactions.

Keywords:

• integral equations
• thermodynamic consistency
• density-dependent interactions
• effective potentials

Acknowledgements

E.L. and C.F.T. acknowledge support from the Dirección General de Universidades e Investigación de la Comunidad de Madrid under Grant S0505/ESP/0299, program MOSSNOHO-CM, and from the Dirección General de Investigación Científica y Técnica (Ministerio de Ciencia en Innovación) under grants no. MAT2007-65711-C04-04 (E.L) and FIS2008-03801/FIS (C.F.T.).