Impedance of multistep mechanisms: equivalent circuits at equilibrium

The form of the electrochemical impedance of multistep mechanisms at the equilibrium potential is investigated for mechanisms constructed from (i) adsorbed species obeying the Langmuir isotherm, static species (soluble species with fast mass transport) and electrons or (ii) diffusing species, static species and electrons. Except for some esoteric cases, the number of bends in a Bode plot and the number of circuit elements in the equivalent circuit is a maximum at equilibrium. These numbers depend only on the number of independent reactions and on whether or not a chemical reaction can be constructed from static species and electrons. The equivalent circuits at equilibrium are shown to be RC circuits for case (i), and resistance-Warburg circuits for case (ii). Inductive behaviour is not possible at the equilibrium potential.