The origin of the polarization catastrophe: the improper choice of the independent electrical variable

Abstract

It is shown that in molecular models of the solvent structure in the inner layer which idealize the interface as a two-dimensional layer, the charge density and the potential drop across the monolayer are not equivalent variables. The charge density may mask phenomena of a phase transition. On the contrary, the potential drop is free of this shortcoming and therefore it should be preferred as an independent variable. The use of this variable in itself does not lead to the elimination of the polarization catastrophe. However, it reveals that this unrealistic situation occurs only during a phase transition. It is shown that the infinitely high values of the inner-layer capacitance are consistent with thermodynamics and that they may be used as a strict criterion for a phase transition to occur. The negative capacities are associated with the transition loops appearing when the equilibrium properties of a model are calculated from an approximate canonical ensemble partition function. If the equilibrium properties are calculated from the grand ensemble partition function, the negative values are eliminated, whereas all the other properties remain intact.