Voigt circuit representation model for electrochemical impedances under finite-length diffusion conditions

Abstract

Abstract The Voigt circuit, which is the serial association of a number of RC parallel elements, should provide an adequate description of the finite-length diffusion impedance Zd, as conjectured and numerically experimented in previous electrochemical works. In this article, it is proved that the Voigt circuit, with infinitely many RC elements, is an exact representation model for Zd. Next, a generalization is proposed to establish the appropriate Voigt circuit for the electrode impedance, taking into account the electron transfer reaction kinetics and the double-layer charging process at the electrode/electrolyte interface. Theoretical derivation of the Voigt circuit parameters in terms of the kinetic and mass transport parameters of the electrochemical system makes it possible to discuss the dependence of the largest time constant of the circuit on the rate constant of the electrochemical reaction, the diffusion parameters of redox species, the double-layer capacitance at the interface, and the steady-state potential imposed for EIS calculation or measurement. The theoretical predictions in this article are used in an attempt to analyze some experimental results from the electrochemical literature.