Lattice-gas Poisson-Boltzmann approach for sterically asymmetric electrolytes

Abstract

We derive a modification of the Poisson-Boltzmann (PB) equation brought about by the finite and different sizes of mobile ions. The equation we obtain contains explicitly the size asymmetry of the electrolyte, enabling one to apply the PB approach to the cases where this effect may be of importance. We show that the modification we propose predicts the asymmetry of the double-layer capacitance. Our approach thus provides a transparent analytical framework for a previously proposed heuristic modification of the PB equation, which also predicts the same effect. In addition, a detailed exposition of the lattice-based calculation of the entropy, accounting for steric, spatial correlations, enables us to clearly pinpoint some of the drawbacks of such an approach, which are not entirely obvious in previous attempts to include the steric effects in the PB equation.