The replica Ornstein-Zernike ͑ROZ͒ equations, supplemented by the hypernetted chain and mean spherical closures, were solved for an ionic fluid adsorbed in a disordered charged matrix. To obtain the numerical solution of the ROZ equations we performed renormalization of the initial equations. Both the matrix and adsorbed fluid were modeled as charged hard spheres in a dielectric continuum, i.e., in the so-called restricted primitive model. As a result, the pair distribution functions between fluid ions and for fluid-matrix correlations were obtained. Structural properties were studied as a function of the matrix density, the concentration of adsorbed electrolyte and for different prequenching conditions. The isothermal compressibility, excess internal energy, and the chemical potential were calculated and discussed with respect to of the model parameters. Comparison with the Monte Carlo computer simulations of Bratko and Chakraborty ͓J. Chem. Phys. 104, 7700 ͑1996͔͒ indicates that the theory yields qualitatively correct results for the model system.

The replica Ornstein–Zernike (ROZ) equations for an ionic fluid adsorbed in an electroneutral, disordered matrix of ions were applied to a model where both ionic subsystems were presented as point charges interacting only via Coulomb forces. The effects of fluid (electrolyte) and matrix concentration on the screening of the ion–ion interactions in the fluid phase were investigated. The effects of the prequenching conditions were also examined. It was shown that augmenting the matrix concentration promotes attraction between equally charged ions and repulsion between ions of opposite sign. This peculiar behavior, observed first in the simulation study of Bratko and Chakraborty [J. Chem. Phys. 104, 7700 (1996)], follows straightforwardly from the ROZ equations. Moreover, we generalized the expression for the disorder averaged ion–ion potential for an arbitrary fluid concentration and prequenching conditions. In addition to these results, which are consistent with computer studies, we present some new results that have not been observed in simulations. For example, alternating ionic ordering, generated by the influence of the charged matrix was observed. This contribution can be considered as a first step toward a study of primitive model electrolytes adsorbed in disordered matrices of hard-sphere ions. The solution of this problem will be presented elsewhere.

We present a density functional theory of nonuniform ionic fluids. This theory is based on the application of the electrostatic contribution to the free energy functional arising from mean spherical approximation for a bulk restricted primitive model and from the energy route bulk equation of state. In order to employ this functional we define a reference fluid and additional averaged densities, according to the approach introduced by Gillespie, Nonner and Eisenberg [J. Phys.: Condens. Matter 14, 12129 (2002)]. In the case of bulk systems the proposed theory reduces to the mean spherical approximation equation of state, arising from the energy route and thus it predicts the first-order phase transition. We use this theory to investigate the effects of confinement on the liquid-vapor equilibria. Two cases are considered, namely an electrolyte confined to the pore with uncharged walls and with charged walls. The dependence of the capillary evaporation diagrams on the pore width and on the electrostatic potential is determined.

A number of interaction potential models for liquid water are scrutinized from the point of view of their compatibility with results of neutron diffraction experiments on pure heavy water. For the quantitative assessment a protocol developed recently [L. Pusztai et al., Chem. Phys. Lett. 457, 96 (2008)] using the reverse Monte Carlo method has been applied. The approach combines the experimental total scattering structure factor (tssf) and partial radial distribution functions (prdfs) from molecular dynamics simulations in a single structural model (particle configuration). Goodness-of-fit values to the three (O-O, O-H, and H-H) simulated prdfs and to the experimental tssf provided an unbiased measure characterizing the level of consistency between various interaction potentials and diffraction experiments. Out of the sets of prdfs investigated here, corresponding to SPCE, BJH, ST2, POL3, TIP4P, TIP4P-2005, TTMF3, and ENCS interaction potentials, the ones from the TIP4P-2005 potential proved to be the most consistent with the experimental neutron-weighted tssf of heavy water. More importantly, it is shown that none of the above interaction potentials are seriously inconsistent with the measured structure factor at ambient conditions.

A detailed study of the microscopic structure of an electrolyte solution, cesium chloride (CsCl) in water, is presented. For revealing the influence of salt concentration on the structure, CsCl solutions at concentrations of 1.5, 7.5, and 15 mol % are investigated. For each concentration, we combine total scattering structure factors from neutron and X-ray diffraction and 10 partial radial distribution functions from molecular dynamics simulations in one single structural model, generated by reverse Monte Carlo modeling. This combination of computer modeling methods is capable of (a) showing the extent to which simulation results are consistent with experimental diffraction data and (b) tracking down distribution functions in computer simulation that are the least comfortable with diffraction data. For the present solutions, we show that the level of consistency between simulations that use simple pair potentials and experimental structure factors is nearly quantitative. Remaining inconsistencies seem to be caused by water-water distribution functions. Changing the pair potentials of water-water interactions from SPC/E to TIP4P-2005 has not had any effect in this respect. As a final result, we obtained particle configurations from reverse Monte Carlo modeling that were in quantitative agreement with both diffraction data and most of the molecular dynamics (MD) simulated partial radial distribution functions (prdf's). From the particle coordinates, the distribution of the number of first neighbors, as well as angular correlation functions, were calculated. The average number of water molecules around cations decreases from about 8 to about 6.5 as concentration increases from 1.5 to 15 mol %, whereas the same quantity for the anions changes from about 7 to about 5. It was also found that the average angle of Cl...H-O particle arrangements, characteristic of anion-water hydrogen bonds, is closer to 180 degrees than that found for O...H-O arrangements (water-water hydrogen bonds). The present combination of experimental and computer simulation methods appears to be promising for the study of other electrolyte solutions.

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.

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A theoretical study of a quenched−annealed system where both components were modeled as charge symmetric +1:−1 primitive model electrolytes is presented. The adsorbed model electrolyte, mimicking lithium chloride solution, was assumed to be in thermodynamic equilibrium with an external reservoir of the same electrolyte. This partly quenched system was studied by applying the replica Ornstein−Zernike (ROZ) integral equation in the hypernetted chain (HNC) approximation and the grand canonical Monte Carlo technique. The effects of the concentration of matrix ions, pre-quenching conditions, and the electrolyte and solvent conditions on the adsorption of electrolyte were examined. The results indicate that the mean activity coefficient of the adsorbed electrolyte may differ substantially from the value of the corresponding quantity in the equilibrium bulk solution. The concentration of the annealed electrolyte in the matrix can be higher (sorption) or lower (rejection) than the corresponding equilibrium bulk concentration, depending on conditions of matrix preparation and on the temperature of adsorption. An important observation of this study is that the ROZ/HNC approximation can be solved for very high couplings, i.e., we can obtain valid results in the region of parameters where the regular OZ/HNC, applied to the equivalent bulk electrolyte solution, fails to converge. The agreement between the computer simulations and ROZ/HNC results for the adsorption isotherms is good.