Analysis of Warburg's impedance and its equivalent electric circuits

The derivation of Warburg's impedance is revisited and critically analyzed. We show that the original derivation where the electric current is assumed to be due only to the diffusion of ions, as proposed by Warburg, raises some fundamental questions. The roles of the drift current, in the absence of which the equilibrium is never reached in the dc case, and of the displacement current, which is important even in the low frequency region where the Warburg's impedance appears, are discussed. Finally, the utility of models based on equivalent electric circuits, ladder networks, or transmission lines in the analysis of impedance spectroscopy data is investigated.