Structural and Thermodynamic Properties of Electrolyte Solutions in Hard-Sphere Confinement:  Predictions of the Replica Integral Equation Theory

Abstract

The structural and thermodynamic properties of the primitive model for 1−1, 2−1, 3−1, and 4−1 electrolyte solutions in a disordered hard sphere matrix environment mimicking a microporous adsorbent were studied. The size of the matrix species and the matrix density were chosen as in the model of silica xerogel proposed by Kaminsky and Monson. The majority of the results of our study follows from the application of the replica Ornstein−Zernike (ROZ) integral equations complemented by the hypernetted-chain (HNC) closure. Theoretical predictions were tested versus Monte Carlo computer simulation results for one of the most difficult cases studied here, i.e., for a charge and size asymmetric 3−1 electrolyte, with the parameters mimicking LaCl3 solution. Steric effects due to matrix confinement are seen to influence substantially the equilibrium properties of the annealed electrolyte. In particular, our results show the development of a net attraction between the like-charged ions at small separations, not present in the absence of matrix. The pair distribution functions and thermodynamic properties of 3−1 electrolytes confined by the matrix were compared with data for pure electrolyte and with the results for a mixture of 3−1 electrolyte with a fully mobile neutral component. The excess chemical potential for adsorbed electrolyte in a dense uncharged matrix is close to that of the fully annealed mixture of the electrolyte and matrix species under the same conditions. We attribute this result to a large difference in size between the matrix and electrolyte particles, i.e., to low mobility of matrix particles versus the ions in the mixture. The comparison between Monte Carlo results and the replica integral equation theory for a 3−1 model electrolyte indicates the theory is successful: the ROZ/HNC approach provides reasonably accurate predictions for structural and thermodynamic properties.

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

“…The correlation functions h ij 11 and c ij 11 are divided into connected and blocking parts. [18][19][20][21][22][23][24] The connected parts correspond to correlations between particles belonging to the same replica, whereas the blocking parts, h ij 12 and c ij 12 , contain correlations between particles belonging to different replicas.…”

“…16 The model studied here differs from those presented before. [18][19][20][21][22][23][24][25] We assume again that the distribution of "frozen" charges corresponds to an equilibrium distribution of ions in an electrolyte solution with dielectric constant and temperature T 0 . However, in contrast to the previous studies, we assume that only anions are "frozen" (quenched) and the cations are allowed to equilibrate.…”

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

“…At first glance, it does not seem possible to work out analytically the integral on the right hand side of the second equality of equation (54). However, it is worthwhile noting that the effect of…”

A stepwise approximation for modeling of the wall–fluid potential of a mesoscopic pore

“…In general, based on the preassumed wall-fluid potential, the adsorption isotherms can easily be calculated using density functional theory (DFT) [2][3][4][5][6][7][8][9][10][11], molecular dynamics (MD), and Monte Carlo [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] (MC) simulations. If the wall-fluid potentials are given, using DFT or molecular simulations, it is possible to explore the effects of system variables on the adsorption behavior in a systematic manner.…”