An investigation of Faradaic admittance for electrode processes involving n state variables besides electrode potential

Both the general Faradaic admittance equation and the stability condition of steady state for Faradaic electrode processes involving n state variables besides electrode potential are derived from the linear approximation around a steady state when the diffusion effect is ignored. Moreover, the Faradaic admittance equations that n less than or equal to 3 are examined by Kramers-Kronig transforms. Only under the stability conditions can the transform of their real and imaginary parts obey the Kramers-Kronig relations, indicating that the conditions required by stability for these equations must also be satisfied in Kramers-Kronig transforms, and testifying that these equations are true mathematic models describing changes of the Faradaic admittance with frequency. These results can be extended to the electrode processes containing more than three state variables in addition to the electrode potential. In addition, a general equivalent circuit to analyze common electrochemical impedance spectroscopy has been established in this paper. The use of the equivalent circuit, together with the mathematic model of Faradaic admittance, exhibits the advantage in analysis of impedance parameters of complicated alternating current impedance spectra.