We model ion solvation in water. We use the MB model of water, a simple two-dimensional statistical mechanical model in which waters are represented as Lennard-Jones disks having Gaussian hydrogen-bonding arms. We introduce a charge dipole into MB waters. We perform (NPT) Monte Carlo simulations to explore how water molecules are organized around ions and around nonpolar solutes in salt solutions. The model gives good qualitative agreement with experiments, including Jones-Dole viscosity B coefficients, Samoilov and Hirata ion hydration activation energies, ion solvation thermodynamics, and Setschenow coefficients for Hofmeister series ions, which describe the salt concentration dependence of the solubilities of hydrophobic solutes. The two main ideas captured here are (1) that charge densities govern the interactions of ions with water, and (2) that a balance of forces determines water structure: electrostatics (water's dipole interacting with ions) and hydrogen bonding (water interacting with neighboring waters). Small ions (kosmotropes) have high charge densities so they cause strong electrostatic ordering of nearby waters, breaking hydrogen bonds. In contrast, large ions (chaotropes) have low charge densities, and surrounding water molecules are largely hydrogen bonded.

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.

In this paper, we present results of computer simulations for a primitive model of asymmetric electrolyte solutions containing macroions, counterions and in a few cases, also co-ions. The results show that the valency of counterions plays an important role in shaping the net interaction between the macroions. For solutions with monovalent counterions, the macroions are distributed at larger distances, and in solutions with divalent counterions, the macroions come closer to each other and share a layer of counterions, whereas, in solutions with trivalent counterions, the macroions form clusters. These clusters dissolve upon dilution or addition of a simple electrolyte. These findings suggest a mechanism whereby the nonuniform distribution of macroions observed experimentally in charged systems may occur.

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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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We present a theoretical study of the quenched−annealed system consisting of an annealed +1:  −1 electrolyte and a disordered quenched matrix modeled as a charge and size asymmetric +Z:  −1 electrolyte, with Z = 4 or 10. The annealed electrolyte is in thermodynamic equilibrium with an external reservoir of electrolyte at concentration c b such that the chemical potentials of the confined and external electrolytes are equal. Both the matrix and the adsorbed electrolyte are modeled as charged hard spheres in a dielectric continuum. The replica Ornstein−Zernike (ROZ) equations, supplemented by the hypernetted chain (HNC) approximation, are solved for this system. The effects of charge and size asymmetry of the matrix ions, their concentration, the prequenched conditions on the pair distribution functions, and the thermodynamic properties of the annealed electrolyte are investigated. The concentration of adsorbed electrolyte c 1 is calculated as a function of the concentration of external electrolyte c b . For low concentration of external electrolyte, the average concentrations of electrolyte inside the matrix c 1 is higher than c b . On the contrary, for higher values of c b , the electrolyte is desorbed from the matrix, c 1 < c b . The theoretical results are supplemented by data from a grand canonical Monte Carlo computer simulation. It is shown that the ROZ/HNC theory yields results which are generally in good agreement with the simulations.