Phase transitions in models for adsorption on electrodes: Further examination of the polarization catastrophe

Abstract

A statistical thermodynamic analysis of phase transitions at charged interfaces is presented. It is shown that the lattice models for adsorption on electrodes predict phase transitions with respect to both charge density σ M and potential E. However, it is proved that the transition properties with respect to σ M are an artifact, which is due to the continuity of the various thermodynamic functions inside the unstable region, when these functions are calculated from the canonical ensemble. For the same reason, the transition properties, calculated via the canonical ensemble, are characterized by the appearance of S-shaped curves when an extensive or a specific quantity is plotted against an intensive one. The transition loops in the plots of σ M vs. E always have portions of negative slope and therefore the differential capacity inevitably has negative values. These negative values are eliminated only when the equilibrium properties of the model are calculated from generalized ensembles, which use the potential as the independent electrical variable. In this case, all the S-shaped curves are replaced by curves with abrupt vertical steps, in agreement with experiment. Moreover, the differential capacitance vs. potential curves form characteristic pits wih properties which are also in qualitative agreement with experiment.