Voigt circuit representation model for the diffusion-convection impedance of uniformly accessible rotating disk electrode

Abstract

Abstract The Voigt circuit results from n serially connected RC parallel elements. The Voigt circuit with infinitely many elements is an exact representation model for the diffusion-convection impedance of uniformly accessible rotating disk electrode (RDE). Starting from the Sturm-Liouville problem associated to the initial and boundary value problem for diffusion-convection near RDE, the resistances Rk, capacitances Ck and time constants (τk = RkCk) of the Voigt circuit, at least for its leading RC elements (k = 1, 2, 3), can be approximated accurately as a function of the angular velocity of RDE and the Schmidt number for redox species reacting at the electrode surface. When synthetic impedance data, generated from the initial and boundary value problem, are fitted to the Voigt circuit impedance at an increasing number of RC elements, the estimates of the first (largest) resistance and time constant converge rapidly towards their asymptotic formulations, R1 and τ1, respectively, unlike the estimates of the other Voigt circuit parameters for k = 2, 3, etc. The resistance R1 and the time constant τ1 should give access respectively to the diffusion-convection resistance of RDE and to the Schmidt number for the species involved in the electrochemical reaction with fast electron transfer kinetics and low double-layer charging effect. Possible deviations from the theoretical predictions caused by slow electrochemical kinetics, double-layer charging and possible time-drift of the electrochemical system at low frequency are briefly discussed.