Ion-cell model for electric double layers composed of rigid ions

The ion-cell model for electric double layers is proposed, at which a cation and an anion are included in the cell volume equivalent to the bulk concentration without extra condensation by an electric field. It is different from the Gouy–Chapman theory at the point of avoiding the condensation. The differential capacitance was evaluated by analyzing the model with statistical mechanics. The model assumes that the rigid, spherical ions of 1:1 electrolyte are not adsorbed chemically on the electrode, that they are subjected to both ion–ion interactions and the external electric field, and that they keep thermal equilibrium by moving in the direction normal to the electrode. Partition functions of the anion and the cation were obtained from the electrostatic energy for these forces on the basis of the canonical ensemble. The average location of these ions and the differential capacitance were evaluated as a function of both ionic concentrations and the electrode potential. The potential variation of the capacitance showed two humps over a constant value, whereas the Gouy–Chapman theory predicts a sharp minimum at a potential of zero charge. The capacitance was nearly proportional to 1/3 powers of the concentration. A typical capacitance value was ca. 65 μF cm−2 for 1 mol dm−3 salt solution. The model is suitable for high concentration of salts. This model does not need to incorporate the inner layer capacitance.

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► Electric double layers are modeled with rigid ions at different locations.
► The model includes no mean-field theory.
► Differential capacitance vs. potential curves have two humps.
► Capacitance was proportional to the one-third of ion concentration.