Replica Ornstein Zernike Research Articles

A hard sphere fluid in equilibrium with microporous membranes. Inhomogeneous replica Ornstein—Zernike equations and grand canonical Monte Carlo simulations

An inhomogeneous system is studied consisting of a hard sphere fluid and a microporous slitlike membrane. The structure of the membrane is generated by filling a slit by randomly centred spheres and by subsequent quench. The membrane is set at the centre of a slit-like pore with hard impenetrable walls. The pore is wide enough for there to be a ‘bulk’ state of a fluid between the pore wall and the membrane boundary. We investigate the equilibrium between a fluid and a single membrane, and also between a fluid and two separated membranes. This model is studied using the inhomogeneous replica Ornstein—Zernike equations with the Born—Green—Yvon equation and the inhomogeneous Percus—Yevick closure and by Monte Carlo simulations. The density profile outside and inside the membrane are calculated and their dependence on the density of membrane species, on the chemical potential of the fluid, and on the distance between two membranes are discussed. A comparison of the simulation data with theoretical predictions shows that the proposed theory successfully describes the fluid structure in the investigated systems. There is a decreasing density to the centre of the microporous membrane body and layers of fluid species are formed between two separated random matrix membranes.

Ion–ion correlations in electrolyte solutions adsorbed in disordered electroneutral charged matrices from replica Ornstein–Zernike equations

The replica Ornstein–Zernike (ROZ) equations, supplemented by the hypernetted chain and mean spherical closures, were solved for an ionic fluid adsorbed in a disordered charged matrix. To obtain the numerical solution of the ROZ equations we performed renormalization of the initial equations. Both the matrix and adsorbed fluid were modeled as charged hard spheres in a dielectric continuum, i.e., in the so-called restricted primitive model. As a result, the pair distribution functions between fluid ions and for fluid-matrix correlations were obtained. Structural properties were studied as a function of the matrix density, the concentration of adsorbed electrolyte and for different prequenching conditions. The isothermal compressibility, excess internal energy, and the chemical potential were calculated and discussed with respect to of the model parameters. Comparison with the Monte Carlo computer simulations of Bratko and Chakraborty [J. Chem. Phys. 104, 7700 (1996)] indicates that the theory yields qualitatively correct results for the model system.

Adsorption of a hard-sphere fluid in a slitlike pore with molecularly rough walls

We have investigated adsorption of a hard-sphere fluid in a slitlike pore with composite walls that permit penetration of fluid particles into the wall body for a given depth. Each of the walls is prepared by quenching of a layer of an ideal gas on a hard wall substrate. Our interest is in the adsorption isotherms and in partitioning of the fluid between random microporous layers of a given thickness and an empty space between these layers. The inhomogeneous replica Ornstein–Zernike equations and the Percus–Yevick approximation in conjunction with the Born–Green–Yvon equation for the density profile are used to study the system. The theoretical predictions are compared with the grand canonical ensemble Monte Carlo simulations. The adsorption isotherms and in-plane correlation functions are evaluated and compared with the reference system. We have shown that the presence of random matrix layers deposited on the pore walls significantly influences the structure of the confined fluid. The adsorption isotherms reflect decreasing penetrability of the fluid into a pore with microporous walls. In-plane correlations for two particles located at a rough wall are stronger than the correlations at a hard wall.

Capillary condensation of Lennard-Jones fluid in a slitlike pore filled with quenched disordered matrix

We have studied a capillary condensation of a Lennard-Jones fluid in a slitlike pore filled with a quenched disordered hard-sphere matrix using the Born–Green–Yvon (BGY) equation with the Fisher–Methfessel (FM) approximation. The solution of the replica Ornstein–Zernike (ROZ) equation in the Percus–Yevick (PY) approximation for a fluid in a homogeneous matrix is used as an input. The adsorption isotherms exhibit hysteresis loops for matrix-free and highly microporous matrix-filled slitlike pores.

Replica Ornstein-Zernike equations and the structure of a simple fluid mixture in disordered porous media: application to a composite monomolecular adlayer

A two-dimensional (2D) model for a simple fluid mixture, consisting of spherical particles with different diameters that is adsorbed on a disordered porous medium, i.e., in a plane claiming hard discs in a frozen configuration, is studied by means of replica Ornstein–Zernike equations. The hypernetted chain and Percus–Yevick approximations are used. The structural and thermodynamic properties of the composite monomolecular adlayer are addressed, and the density and composition of the monolayer and their dependence on the presence of a disordered quenched 2D matrix in the plane of absorption at a fixed chemical potential is examined. It is shown that porous 2D media exhibit the effect of selectivity. The concentration of the smaller particles is larger on the porous media compared with the bulk phase. The model and methodology can be extended to study phase transitions in 2D partly quenched systems.

Replica Ornstein-Zernike equations and the structure of a simple fluid mixture in disordered porous media: application to a composite monomolecular adlayer

A two-dimensional (2D) model for a simple fluid mixture, consisting of spherical particles with different diameters that is adsorbed on a disordered porous medium, i.e., in a plane claiming hard discs in a frozen configuration, is studied by means of replica Ornstein–Zernike equations. The hypernetted chain and Percus–Yevick approximations are used. The structural and thermodynamic properties of the composite monomolecular adlayer are addressed, and the density and composition of the monolayer and their dependence on the presence of a disordered quenched 2D matrix in the plane of absorption at a fixed chemical potential is examined. It is shown that porous 2D media exhibit the effect of selectivity. The concentration of the smaller particles is larger on the porous media compared with the bulk phase. The model and methodology can be extended to study phase transitions in 2D partly quenched systems.

The structure and adsorption of the four bonding sites model for associating fluids in disordered porous media from replica Ornstein–Zernike integral equation theory

A model for a network-forming associating fluid in which each of the particles have four sites available for bonding is considered. The model possesses liquid–gas transition in the absence of attractive long-range nonassociative interactions. We have studied the adsorption of the fluid in a disordered porous media that corresponds to an equilibrium configuration of hard spheres. The associative replica Ornstein–Zernike (ROZ) equations are solved with the Percus–Yevick (PY) and hypernetted chain (HNC) closures and with the ideal network approximation. The pair distribution functions and the structure factors have been obtained. The adsorption isotherms have been calculated using a system of hard spheres adsorbed in a hard-sphere matrix as a reference. The associative contribution to the chemical potential follows from Wertheim’s thermodynamic perturbation theory, however, with monomer fraction from the solution of the ROZ equations. The liquid–vapor coexistence curve has been evaluated. We have observed shrinking of the coexistence envelope with increasing matrix density. The critical temperature and the critical density are sensitive to the density of adsorbent. Both decrease with increasing matrix density.

Replica Ornstein−Zernike Equations and Simulations of the Structure of a Simple Fluid in Disordered Porous Media. Application to Monomolecular Adsorption

A two-dimensional (2D) model for a simple fluid adsorbed in a disordered porous medium is investigated by means of the replica Ornstein−Zernike (ROZ) equations with the hypernetted chain (HNC) and ...

Screening of ion–ion correlations in electrolyte solutions adsorbed in electroneutral disordered matrices of charged particles: Application of replica Ornstein–Zernike equations

The replica Ornstein–Zernike (ROZ) equations for an ionic fluid adsorbed in an electroneutral, disordered matrix of ions were applied to a model where both ionic subsystems were presented as point charges interacting only via Coulomb forces. The effects of fluid (electrolyte) and matrix concentration on the screening of the ion–ion interactions in the fluid phase were investigated. The effects of the prequenching conditions were also examined. It was shown that augmenting the matrix concentration promotes attraction between equally charged ions and repulsion between ions of opposite sign. This peculiar behavior, observed first in the simulation study of Bratko and Chakraborty [J. Chem. Phys. 104, 7700 (1996)], follows straightforwardly from the ROZ equations. Moreover, we generalized the expression for the disorder averaged ion–ion potential for an arbitrary fluid concentration and prequenching conditions. In addition to these results, which are consistent with computer studies, we present some new results that have not been observed in simulations. For example, alternating ionic ordering, generated by the influence of the charged matrix was observed. This contribution can be considered as a first step toward a study of primitive model electrolytes adsorbed in disordered matrices of hard-sphere ions. The solution of this problem will be presented elsewhere.

Adsorption of a Hard Sphere Fluid in a Disordered Polymerized Matrix: Application of the Replica Ornstein–Zernike Equations

A model of hard spheres adsorbed in disordered porous media is studied using the associative replica Ornstein–Zernike (ROZ) equations. Extending previous studies of adsorption in a hard sphere matrices, we investigate a polymerized matrix. We consider an associating fluid of hard spheres with two intracore attractive sites per particle; consequently chains consisting of overlapping hard spheres can be formed due to the chemical association. This is the generalization of the model with sites on the surface of Wertheim that has been studied in the bulk by Chang and Sandler. The matrix structure is obtained in the polymer Percus–Yevick approximation. We solve the ROZ equations in the associative hypernetted chain approximation. The pair distribution functions, the fluid compressibility, the equation of state and chemical potential of the adsorbed fluid are obtained and discussed. It is shown that the adsorption of a hard sphere fluid in a matrix at given density, but consisting of longer chains of overlapping hard spheres, is higher than the adsorption of this fluid in a hard sphere matrix.

Replica Ornstein-Zernike theory for chemically associating fluids with directional forces in disordered porous media: Smith-Nezbeda model in a hard sphere matrix

The associative replica Ornstein-Zernike equations, supplemented by the associative hypernetted chain approximation are used to describe the Smith-Nezbeda model for an associating fluid adsorbed in a disordered hard sphere matrix. These equations have been developed by combining the replica Ornstein-Zernike equations with the Wertheim theory of association in fluids. The pair distribution functions and fraction of unbonded species are calculated. Also investigated is the influence of the association on the equation of state and the chemical potential of the absorbed fluid.

Replica Ornstein—Zernike theory for chemically associating fluids with directional forces in disordered porous media: Smith—Nezbeda model in a hard sphere matrix

Replica Ornstein—Zernike theory for chemically associating fluids with directional forces in disordered porous media: Smith—Nezbeda model in a hard sphere matrix

Associative replica Ornstein–Zernike equations and the structure of chemically reacting fluids in porous media

A model for a chemically associating fluid, adsorbed in a disordered porous media, is proposed. The formation of the associates occurs through the directional bonding between the fluid particles. For simplicity, we restrict our attention to the dimerization of particles. In the absence of association, this model reduces to that of Kaminsky and Monson (KM) for the adsorption of methane in a xerosilica gel. This model is studied by means of the replica Ornstein–Zernike ROZ equations, with the hypernetted chain approximation, extended for associating fluids. It follows from a comparison with the computer simulation data that this theory yields a very good description of the structural properties of the KM model. The influence of the fluid density, the matrix packing fraction, and the association energy on the dimerization in the disordered matrix is studied. The fluid compressibility for the KM model and for the dimerizing fluid in a disordered matrix is obtained via the compressibility equation.

Ornstein-Zernike equations and simulation results for hard-sphere fluids adsorbed in porous media.

In this paper we solve the replica Ornstein-Zernike (ROZ) equations in the hypernetted-chain (HNC), Percus-Yevick (PY), and reference Percus-Yevick (RPY) approximations for partly quenched systems. The ROZ equations, which apply to the general class of partly quenched systems, are here applied to a class of models for porous media. These models involve two species of particles: an annealed or equilibrated species, which is used to model the fluid phase, and a quenched or frozen species, whose excluded-volume interactions constitute the matrix in which the fluid is adsorbed. We study two models for the quenched species of particles: a hard-sphere matrix, for which the fluid-fluid, matrix-matrix, and matrix-fluid sphere diameters ${\mathrm{\ensuremath{\sigma}}}_{11}$, ${\mathrm{\ensuremath{\sigma}}}_{00}$, and ${\mathrm{\ensuremath{\sigma}}}_{01}$ are additive, and a matrix of randomly overlapping particles (which still interact with the fluid particle as hard spheres) that gives a ``random'' matrix with interconnected pore structure. For the random-matrix case we study a ratio ${\mathrm{\ensuremath{\sigma}}}_{01}$/${\mathrm{\ensuremath{\sigma}}}_{11}$ of 2.5, which is a demanding one for the theories. The HNC and RPY results represent significant improvements over the PY result when compared with the Monte Carlo simulations we have generated for this study, with the HNC result yielding the best results overall among those studied. A phenomenological percolating-fluid approximation is also found to be of comparable accuracy to the HNC results over a significant range of matrix and fluid densities. In the hard-sphere matrix case, the RPY is the best of the theories that we have considered.

A Realistic Model for a Spin Glass

AbstractWe develop exact integral equations satisfied by the spin-spin correlation functions of a realistic spin glass model. This is done by considering the magnetic particles in a spin glass to be bound states of hard sphere ‘atoms’ and classical ‘spins’, the former of which are quenched in position, while the latter are allowed to equilibrate. We develop the replica Ornstein-Zernike (ROZ) equations, which are satisfied by the correlation functions of such a partly quenched mixture. We prove that two widely used OZ closures, the Percus-Yevick approximation and mean-spherical approximation are indifferent to quenched disorder, i.e., they give tihe same results for quenched and for fully annealed systems. We extend the ROZ equations to apply to the spin glass by using the proper interaction-site formalism. Preliminary numerical results are discussed.