Structural and thermodynamic properties of electrolyte solutions in hard-sphere confinement: Predictions of the replica integral equation theory

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.