This paper is an investigation into the distribution of mobile ionic species (such as $Na^{+}$, $K^{+}$, $Ca^{++}$ and $Cl^{-}$) adjacent to the membrane walls of a model neuron. The geometry of the model neuron is that of the slab surrounded by electrolyte system considered by Carnie and Chan, (Molecular Physics 51 (1984) 1047), 1984. The formulation of the electrostatic potentials is via the BBGKY hierarchy for the molecular distribution functions in the civilised model of an electrolyte and is similar to that of Outhwaite's derivation for the primitive model, (J. Chem. Soc. Faraday Trans. II. 74 (1978) 1214). Though, the usual assumption of bulk electroneutrality is replaced by the macroscopic electroneutrality condition with the inclusion of surface charges. This has particular relevance to the modelling of the electrolyte for a neuron. The results obtained for the pair correlation functions exhibit a shielding both in the normal and transverse directions. This is contrasted with the algebraic form in both directions for the one plate system of Carnie and Chan.

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