Treatment of Ion-Size Asymmetry in Lattice-Gas Models for Electrical Double Layer

A discreet consideration of the ubiquitous ion-size asymmetry is essential for an accurate description of the electrical double layer. The diversity of approaches in the literature to treat this effect just signifies that a deep and coherent understanding is yet to come. To fill this gap, this article compares six lattice-gas models in terms of the physical significance, the lattice configuration number, the dimensionless excess chemical potential, and the differential capacitance (C). In this process, three subtle issues in the lattice-gas approach are discussed: the sequence effect (namely, the effect of the sequence in which ions are placed into the lattice), the flexibility of extension to multicomponent systems, and the effect of the reference size of the lattice unit. It is found that these six treatments, though greatly differing in the configuration number, can be classified into two categories in terms of C, that the more detailed treatments show an artificial sequence-dependent effect and have less flexibility when extended to multicomponent systems, and that the C versus electrode potential curve is invariant with respect to the reference size of the lattice unit.