Numerical computation of the Faradaic impedance of inlaid microdisk electrodes using a finite element method with anisotropic mesh adaptation

The Faradaic impedance of a microdisk electrode inlaid in an insulating surface is revisited by numerical computation using a finite element method (FEM) with anisotropic mesh adaptation. New features of the numerical results, as compared to previous works, are analyzed. A first attractive feature is that the diffusion impedance relative to a microdisk electrode, evaluated at the equilibrium potential of the electrode, depends both on electron-transfer and mass-transport kinetics, in contrast with the usual behaviour of uniformly accessible electrodes. Next, the domain of validity of the Fleishmann and Pons semi-analytical formulation of diffusion impedance is determined. Finally, the characteristic of impedance graphs, which are the diffusion resistance, the characteristic frequency at the apex of the Nyquist diagram and the imaginary part of the diffusion impedance at this apex, are studied as functions of a dimensionless parameter that compares the standard rate constant of electron transfer to the microelectrode diffusion constant. Closed form approximations are proposed for all quantities in order to help the analysis of experimental data.