The Diffusional (Warburg) Impedance at a Sinusoidal Shape Electrode

Abstract

The surface average, diffusional impedance at a sinusoidal shape electrode is calculated using a perturbation solution to the transient‐diffusion equation for the concentration field, with the perturbation parameter being the amplitude‐to‐length ratio of the sinusoid, A. Terms in the perturbation expansion up to and including A4 are included in the solution, and the error in is determined to be less than 2% for A less than 0.15. It is shown that at low and high frequency (ω) is proportional to , the standard planar electrode dependency, but with a different proportionality coefficient in each limit. At intermediate frequencies, deviation from this ideal is predicted with the occurrence of an amplitude‐dependent maximum in the phase lag. The local diffusional impedance at high frequency is spatially uniform, whereas at low frequency it is the most nonuniform, even though , which is the area weighted average, is identical to a planar electrode in this limit. It is noted that, more generally, the diffusional impedance at an electrode at which the surface profile may be expressed as a Fourier series will also show a proportionality to the square root of frequency in the low and high asymptotic limit.