Structure and thermodynamics of the primitive model electrolyte in a charged matrix: The evaluation of the Madden-Glandt approximation

Luksic Luksic

doi:10.5488/cmp.16.43803

Abstract

We compared the results of the Madden-Glandt (MG) integral equation approximation for partly-quenched systems with the commonly accepted formalism of Given and Stell (GS). The system studied was a +1:-1 restricted primitive model (RPM) electrolyte confined in a quenched +1:-1 RPM matrix. A renormalization scheme was proposed for a set of MG replica Ornstein-Zernike equations. Long-ranged direct and total correlation functions, describing the interactions between the annealed electrolyte species within the same replicas and between the annealed and matrix particles, appeared to be the same for MG and GS approach. Both versions of the theory give very similar results for the structure and thermodynamics of an annealed subsystem. Differences between excess internal energy, excess chemical potential, and isothermal compressibility become pronounced only at high concentrations of matrix particles.

Highlights

In the last decades, much attention has been paid to the properties of electrolyte solutions adsorbed in random matrices
To develop the integral equation theory for partly-quenched systems, Madden and Glandt [8, 9] split the total correlation functions, ́Ö μ, and direct correlation functions, ́Ö μ, into a “connected” part, representing the interactions between annealed particles within the same replica, and a “blocking” part, describing the interactions between the annealed particles mediated by the matrix particles
While the renormalization scheme for the Replica Ornstein-Zernike (ROZ) set of equations (1.2) is well established [1, 14], no such scheme for Madden-Glandt Ornsten-Zernike (MGOZ) equations (1.1) has been previously proposed

Summary

Introduction

Much attention has been paid to the properties of electrolyte solutions adsorbed in random matrices (for review see reference [1]) These systems can be considered as partly-quenched, meaning that some degrees of freedom are quenched and others are annealed [1]. To develop the integral equation theory for partly-quenched systems, Madden and Glandt [8, 9] split the total correlation functions, ́Ö μ, and direct correlation functions, ́Ö μ, into a “connected” part, representing the interactions between annealed particles within the same replica, and a “blocking” part (here denoted by index 12), describing the interactions between the annealed particles mediated by the matrix particles. They set a blocking part of the direct correlation function to zero

Methods

Results

Conclusion