Electrochemical impedance of multistep mechanisms: a general theory

A general theory is presented for the electrochemical impedance of multistep mechanisms, consisting of reactions with electrons, diffusing species and adsorbed species. The complexity of the impedance spectra is dependent on three parameters that can be found by inspection of the mechanism: I, the number of independent reaction steps (i.e. steps having linearly independent stoichiometries), I-sol, the number of independent reactions that can be constructed from the soluble species, and X, which is zero or one, depending on the possible types of electron-transfer reactions that can be constructed from the species. The faradaic admittance, Y-f, is a rational polynomial in (i omega)(1/2) with 4I - 2I(sol) - X- 1 nonzero coefficients. There can be no more than 4I - 2I(sol) - X- 2 bends on a log magnitude versus log omega plot (Bode plot) of Y-f or 4I - 2I(sol) - X bends on a Bode plot of the total impedance (i.e. faradaic, double-layer and solution impedances together). The corresponding phase plot shows transitions between levels at the places where the log magnitude plot shows bends. The type of low frequency behavior (Warburg or capacitive) is dependent only on X. Simpler estimates result when all species are diffusing. A method is given for writing Y-f as a ratio of two I x I determinants, using chemical reactions as a mnemonic device. (C) 1998 Elsevier Science S.A. All rights reserved.