Equilibrium Properties of a Model Electrolyte Adsorbed in Quenched Disordered Charged Media:  the ROZ Theory and GCMC Simulations

Abstract

We present a theoretical study of the quenched−annealed system consisting of an annealed +1: −1 electrolyte and a disordered quenched matrix modeled as a charge and size asymmetric +Z: −1 electrolyte, with Z = 4 or 10. The annealed electrolyte is in thermodynamic equilibrium with an external reservoir of electrolyte at concentration c b such that the chemical potentials of the confined and external electrolytes are equal. Both the matrix and the adsorbed electrolyte are modeled as charged hard spheres in a dielectric continuum. The replica Ornstein−Zernike (ROZ) equations, supplemented by the hypernetted chain (HNC) approximation, are solved for this system. The effects of charge and size asymmetry of the matrix ions, their concentration, the prequenched conditions on the pair distribution functions, and the thermodynamic properties of the annealed electrolyte are investigated. The concentration of adsorbed electrolyte c 1 is calculated as a function of the concentration of external electrolyte c b . For low concentration of external electrolyte, the average concentrations of electrolyte inside the matrix c 1 is higher than c b . On the contrary, for higher values of c b , the electrolyte is desorbed from the matrix, c 1 < c b . The theoretical results are supplemented by data from a grand canonical Monte Carlo computer simulation. It is shown that the ROZ/HNC theory yields results which are generally in good agreement with the simulations.

Fluids confined in porous media: An ideal gas in different matrices

“…The result for the adsorbed fluid density as a function of the fluid chemical potential is also identical to that obtained for a HS matrix [see equation (55)]. The Helmholtz free energy is given by…”

A three dimensional integral equation approach for fluids under confinement: Argon in zeolites

“…(7) and (10) can now be solved iteratively. Finally, the adsorption isotherm from the ROZ-HNC can be evaluated computing the chemical potential in terms of the adsorbed fluid density, the former being given by [31][32][33] …”

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

“…The thermodynamic and structural properties of these systems can be calculated using the computer simulations and/or the replica integral equation theories. This work presents the continuation of our previous studies of partly quenched systems containing charges [18][19][20][21][22][23][24][25]. The quenched "phase" (we shall call it the matrix) is some frozen (quenched) equilibrium distribution of a symmetric model +1:−1 electrolyte.…”

“…The model used here was similar to the one described in several previous papers [19,21,22,24]. The system studied consisted of two subsystems: the first, here called the matrix, was composed of the quenched, and the second of the annealed ions.…”