A linearized potential equation for the interfacial region in an unsymmetrical electrolyte

Abstract

The fluctuation potential at an ion in a diffuse interfacial region is investigated, the ion being considered as a dielectric sphere with a point-charge at the centre and a concentric exclusion sphere within which other ion centres cannot penetrate. The fluctuation contribution to the potential of mean force proves to be the sum of a cavity term, due to displacement of mean diffuse region charge by the ionic volume, and a term due to the point charge at the ionic centre, the latter containing the most important image effect. A linearized mean potential equation for a general electrolyte type is derived. The effect on the fluctuation terms of the deviation of ionic concentrations from bulk values, resulting in a local Debye-Hückel constant different from its bulk value, and the excluded volume effect are incorporated. For a symmetrical electrolyte all terms except those due to the mean and cavity potentials cancel in the linearized equation. This is not true for an unsymmetrical electrolyte where the deviation from bulk values of local ionic concentrations has a strong effect in the particular case of a point-ion model. However, at small concentrations of 2-1 electrolyte with a non-zero exclusion radius, results are found that are considerably closer to those of the elementary theory, with the local Debye-Hückel constant given the bulk value. In suitable circumstances results close to the classical theory are obtained. At larger electrolyte concentrations ‘instability’ occurs and the mean potential oscillates instead of exponentially decreasing. Instability conditions for unsymmetrical electrolytes are formulated, numerical results being obtained for the 2-1 case and compared with results derived from Outhwaite's work for symmetrical electrolytes.