Accuracy of the mean activity coefficient expression (Hansen-Vieillefosse-Belloni equation), valid within the hypernetted chain (HNC) approximation, was tested in a wide concentration range against new Monte Carlo (MC) data for +1:−1 and +2:−2 primitive model electrolytes. The expression has an advantage that the excess chemical potential can be obtained directly, without invoking the time consuming Gibbs-Duhem calculation. We found the HNC results for the mean activity coefficient to be in good agreement with the machine calculations performed for the same model. In addition, the thermodynamic consistency of the HNC approximation was tested. The mean activity coefficients, calculated via the Gibbs-Duhem equation, seem to follow the MC data slightly better than the Hansen-Vieillefosse-Belloni expression. For completeness of the calculation, the HNC excess internal energies and osmotic coefficients are also presented. These results are compared with the calculations based on other theories commonly used to describe electrolyte solutions, such as the mean spherical approximation, Pitzer's extension of the Debye-Hückel theory, and the Debye-Hückel limiting law.

The Replica Ornstein-Zernike (ROZ) equations were used to study the adsorption of ions from electrolyte mixtures. The adsorbent was represented as a quenched primitive model +1:−1 size symmetric electrolyte, while the mobile particles were ions differing in charge and/or size. The ROZ equations in hypernetted-chain (HNC) approximation were tested against new Monte Carlo results in the grand canonical ensemble; good agreement between the two methods was obtained. The ROZ/HNC theory was then used to study the exclusion coefficients as a function of size and/or charge asymmetry of the annealed ions.

We compared the results of the Madden-Glandt (MG) integral equation approximation for partly-quenched systems with the commonly accepted formalism of Given and Stell (GS). The system studied was a ½ ½ restricted primitive model (RPM) electrolyte confined in a quenched ½ ½ RPM matrix. A renormalization scheme was proposed for a set of MG replica Ornstein-Zernike equations. Long-ranged direct and total correlation functions, describing the interactions between the annealed electrolyte species within the same replicas and between the annealed and matrix particles, appeared to be the same for MG and GS approach. Both versions of the theory give very similar results for the structure and thermodynamics of an annealed subsystem. Differences between excess internal energy, excess chemical potential, and isothermal compressibility become pronounced only at high concentrations of matrix particles.