Electrolytes confined to a plane in the Debye-Hückel theory

An electroneutral system of charged hard three-dimensional spheres confined to a two-dimensional plane is studied in the linearized Poisson-Boltzmann approximation. This system can be considered a model for ions on a membrane or ions adsorbed at an electrode. The extreme coupling limits are studied and the Onsager condition for infinite coupling, TΔS/ΔE → 0, is shown to be satisfied.