Comment on: Fluid distributions in two-phase random media: Arbitrary matrices

Abstract

It is pointed out that the Ornstein–Zernike equations recently used by Madden in treating quenched-annealed mixtures are approximate. The exact equations are given and briefly discussed.

The Screening Potentials of Ion-Dipole System Adsorbed in Ion-Dipolar Disordered Matrices

“…In this way Given and Stell [1][2] recently proposed a set of coupled integral equations, the so-called replica Ornstein-Zernike (ROZ) equations, relating the total pair correlation functions h αβ (r) of fluid-matrix mixture to the corresponding direct For this time the application of ROZ equations was restricted the description of simple fluids in random and quenched matrices [3][4][5][6].Only recently a study of associating fluids [6][7] and ionic fluids [8][9] in porous media using ROZ equations was initiated. In particular, in [8] the ROZ equations were applied for the investigation of the screening potentials for the proposed in [10] model of ionic fluids adsorbed in an electroneutral totally disordered matrix of ion.…”

Effects of porous confinement on the structural properties of the Gaussian core model

“…This averaging can conveniently be effectuated using the replica trick [33]. Starting from the Ornstein-Zernike equations of an equilibrated (s + 1) component system, which consists of the matrix and s non-interacting copies (replicas) of the fluid, one arrives, after taking the limit s → 0, at the replica Ornstein-Zernike equations [29,30] …”

“…A successful theoretical approach to describe the structural and thermodynamic properties of QA systems was pioneered by Madden and Glandt [29] and later by Given and Stell [30]. The properties of the annealed component that equilibrates in the presence of a matrix are calculated in a double averaging procedure: first, over the degrees of freedom of the fluid particles for a given matrix configuration, and, second, over all possible matrix configurations.…”

“…formalism [29,30], a framework that is known to be highly successful in describing the structural and thermodynamic properties of fluids confined in disordered porous structures. The first part of the investigation is dedicated to the influence of the structure of the matrix on the structural properties of the fluid, identifying thereby fingerprints of the matrix-matrix correlations in the fluid-fluid structure factor.…”

Application of Replica Ornstein-Zernike equations in studies of the adsorption of electrolyte mixtures in disordered matrices of charged particles

“…In the last decades, new class of theories appeared in which the disordered porous materials filled with fluid are treated as partly quenched systems in which some of the degrees of freedom are quenched and others are annealed. The systems differ from regular mixtures; the statistical-mechanical average which is needed to obtain the free energy describing the confined fluid, becomes a double ensemble average [10][11][12][13][14][15][16][17]. The thermodynamic and structural properties of these systems can be calculated using the computer simulations and/or the replica integral equation theories.…”