On the theory of the generalized Gerischer impedance for an electrode with modeling roughness

•We investigate peculiarities of Gerischer impedance behavior of a rough electrode.•We derive expression for the roughness function and establish its limiting behavior.•Roughness influences parameters extracted from low-frequency region of impedance.•Gerischer impedance exhibits frequency dispersion at medium frequencies. The generalized Gerischer impedance theoretical model for a sinusoidal-shaped electrode has been developed. The impedance is presented as an expansion by the small parameter, which is equal to the ratio of the amplitude to period length of surface roughness. For the case of a weak roughness, we have derived the general expression for the complex roughness function and established its limiting behavior. It is shown that roughness does influence the value of parameters extracted from low − frequency region of an impedance measurement. In anomalous intermediate − frequency region, impedance exhibits frequency dispersion which is caused by the roughness. At high frequencies, the Gerischer impedance acts like the Warburg impedance