The impedance spectroscopy response for a reversible electrode reaction based on diffusion limited chronoamperometry at an inlaid disk electrode

• Derivation of a useful link between the PSCA and EIS responses for E reaction.
• Application to an inlaid (micro)disk electrode under reversible conditions.
• Accurate computation of the impedance of (micro)disk electrode at equilibrium.
• Derivation of approximate formulae for this impedance.
• Fitting of this impedance using a representation model (modified Voigt circuit).

First, a simple relationship is derived between the diffusion-controlled current transient resulting from application of a large potential step (PSCA method) and the diffusion impedance (EIS method) calculated at the equilibrium potential of a uniformly accessible electrode when a one-step redox reaction takes place at the electrode surface. The derivation is valid under one-dimensional (1D) diffusion conditions in the electrolyte, assuming in addition the same diffusion coefficient for both redox species involved in the electrochemical reaction. The theoretical relationship also applies to 2D diffusion from/towards an inlaid (micro)disk electrode provided the electron transfer reaction displays reversible kinetics at the electrode surface. Accurate values for the diffusion impedance at the equilibrium potential of (micro)disk electrode are obtained starting from the explicit formulation of the diffusion-controlled current transient in the article by L.K. Bieniasz, Electrochim. Acta 199 (2016) 1–11. These values can be used as benchmark data for checking the accuracy of numerical methods, e.g. finite element methods, employed for solving the initial boundary value problem under consideration. Finally, approximation formulae are derived for the diffusion impedance either in closed form or using a representation model together with a complex nonlinear least squares procedure.