Electrolytes at charged interfaces: Pair integral equation approximations for model 2–2 electrolytes

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Abstract
The structure and thermodynamics for model 2–2 electrolytes at a charged interface have been determined by the so-called “pair” approximation of integral equation theory. In addition to Coulombic interactions, the potential models for the ion–ion and ion–wall interactions employ “soft” continuous potentials rather than “hard”-sphere or “hard”-wall potentials. The solvent is modeled as a structureless dielectric continuum at 25 °C. The structure is calculated using the inhomogeneous Ornstein–Zernike relation, together with the hypernetted chain closure and two choices for the functional relationship between the singlet and pair correlation functions. Both the interfacial density profile and the inhomogeneous pair correlation functions are calculated. Some thermodynamic properties of these systems are also evaluated. The results of the pair approximation are compared with the so-called “singlet” approximation, selected computer simulation results, Gouy–Chapman–Stern predictions, and experimental data. While qualitative agreement is generally found between the two levels of integral equation approximation, measurable quantitative improvements exist for both structural and thermodynamic predictions in the pair approximation.