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 th e matrix species and the matrix density were chosen as in the model of sili ca 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. T heoretical predictions were tested versus Monte Carlo computer simulation r esults 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 s olution. Steric effects due to matrix confinement are seen to influence sub stantially the equilibrium properties of the annealed electrolyte. In parti cular, our results show the development of a net attraction between the lik e-charged ions at small separations, not present in the absence of matrix. The pair distribution functions and thermodynamic properties of 3-1 electro lytes confined by the matrix were compared with data for pure electrolyte a nd with the results for a mixture of 3-1 electrolyte with a fully mobile ne utral 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 electrolyt e particles, i.e., to low mobility of matrix particles versus the ions in t he mixture. The comparison between Monte Carlo results and the replica inte gral equation theory for a 3-1 model electrolyte indicates the theory is su ccessful: the ROZ/HNC approach provides reasonably accurate predictions for structural and thermodynamic properties.