Density-dependent interactions and thermodynamic consistency in integral equation theories

C.F Tejero,E Lomba

doi:10.1080/00268970902776765

C.F Tejero, E Lomba

Open Access

https://doi.org/10.1080/00268970902776765

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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.

Highlights

Density-dependent potentials are ubiquitous in the field of liquid state and soft matter physics
Such is the case of colloidal dispersions [1], in which the most widespread interaction model is described by the theory of Derjaguin–Landau–Verwey–Overbeek (DLVO) [2,3]
The aim of this paper is to present a reformulation of the integral equation approaches that, from an operational standpoint, make possible the definition of consistent virial pressures and fluctuation theorem compressibilities for density-dependent interactions

Summary

Introduction

Density-dependent potentials are ubiquitous in the field of liquid state and soft matter physics. In [15], it was stressed the approximate character of the coarse-graining procedures This implies that depending on the nature of the original problem that is being reduced to a system of ‘effective particles’ interacting via pairwise additive potentials and the route followed to perform the reduction, one will get different expressions for the same quantity. The aim of this paper is to present a reformulation of the integral equation approaches that, from an operational standpoint, make possible the definition of consistent virial pressures and fluctuation theorem compressibilities for density-dependent interactions These quantities should be fully consistent whenever an exact closure relation to the Ornstein–Zernike equation were available.

Effective interactions and consistent integral equations

A consistent approach

Effects on the virial pressure and the isothermal compressibility

A case study: the DLVO potential