Electrolyte Exclusion from Charged Adsorbent:  Replica Ornstein−Zernike Theory and Simulations

Abstract

Structural and thermodynamic properties of the restrictive primitive model +1:-1 electrolyte solution adsorbed in a disordered charged media were studied by means of the Grand Canonical Monte Carlo simulation and the replica Ornstein-Zernike theory. Disordered media (adsorbent, matrix) was represented by a distribution of negatively charged hard spheres frozen in a particular equilibrium distribution. The annealed counterions and co-ions were assumed to be distributed within the nanoporous adsorbent in thermodynamic equilibrium with an external reservoir of the same electrolyte. In accordance with the primitive model of electrolyte solutions, the solvent was treated as a dielectric continuum. The simulations were performed for a set of model parameters, varying the net charge of the matrix (i.e., concentrations of matrix ions) and of annealed electrolyte, in addition to the dielectric constant of the invading solution. The concentration of adsorbed electrolyte was found to be lower than the corresponding concentration of the equilibrium bulk solution. This electrolyte "exclusion" depends strongly on the dielectric constant of the invading solution, as also on concentrations of all components. The most important parameter is the net charge of the matrix. Interestingly, the electrolyte rejection decreases with increasing Bjerrum length for the range of parameters studied here. The latter finding can be ascribed to strong inter-ionic correlation in cases where the Bjerumm length is high enough. To a minor extent, the adsorption also depends on the spacial distribution of fixed charges in adsorbent material. The replica Ornstein-Zernike theory was modified to cater for this model and tested against the computer simulations. For the range of parameters explored in this work, the agreement between the two methods is very good. These calculations were also compared with the results of the classical Donnan theory for electrolyte exclusion.

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 annealed electrolyte ions were then distributed within the matrix and the system was studied by the grand canonical Monte Carlo (GCMC) method. The methodology of the method is well established and extensively described in several previous papers and therefore is not repeated here [6,23,24,27,28]. The details of the simulations are: the number of matrix particles was 1000 and the average number of a fluid cation species distributed within the matrix varied from 50 to 400.…”

Modelling the ion-exchange equilibrium in nanoporous materials

“…The porous material (matrix) is pictured as a set of charged obstacles. Distribution of the obstacles is obtained by a certain recipe (see, for example, [9,11]). Inhomogeneity that causes the field in which mobile ions are distributed is given on a molecular level.…”

“…The model was recently studied by the grand canonical Monte Carlo method [11,40] as well as the Brownian Dynamics approach [10]. The simulations indicate that the ROZ theory in the hypernetted-chain approximation, adapted to this model in [11], yields very good agreement with computer simulations.…”

A computational study of electrolyte adsorption in a simple model for intercalated clays

“…Our system is related to those that have been used to model electrolyte adsorption in charged matrices, [18][19][20] with the exception that in our case one of the matrix constituents acts as a template and is removed after quenching. Our system is related to those that have been used to model electrolyte adsorption in charged matrices, [18][19][20] with the exception that in our case one of the matrix constituents acts as a template and is removed after quenching.…”