Stability and electrochemical impedance of mechanisms with a single adsorbed species

The stability, impedances, all possible equivalent circuits, and criteria for inductive behavior are investigated for mechanisms with a single adsorbed species obeying Langmuir kinetics (mass-action kinetics). An eigenvalue analysis shows that these mechanisms are stable when (i) there is a reaction taking free sites to adsorbed species and a reaction taking adsorbed species to free sites and (ii) any autocatalytic reactions proceed in the backwards (autoinhibitory) direction. Stability is maintained even when autocatalytic reaction steps proceed in the forward direction, provided that the ratio of the forward rate to the backward rate does not exceed a critical value. The concept of e-stability is introduced and it is shown that these mechanisms have impedances that are realizable as an equivalent circuit when they are stable and e-stable. Inductive behavior can occur only if the mechanism has an electron-transfer step that is oxidizing in the direction of adsorption and an electron-transfer step that is reducing in the direction of adsorption. A simple quantitative condition for inductive behavior is derived. The example of the hydrogen evolution reaction (her) is used to illustrate the ideas.