Warburg's impedance revisited

TL;DR

This paper critically reevaluates Warburg's impedance derivation, showing that previous assumptions are incorrect and providing a more accurate model for electrochemical impedance considering diffusion and displacement currents.

Contribution

It offers a corrected derivation of electrochemical impedance that challenges traditional Warburg assumptions and extends the model to asymmetric cells with realistic boundary conditions.

Findings

Warburg's impedance assumptions are invalid under certain conditions.

Correct impedance modeling differs from Warburg's predictions at high frequencies.

The new model applies to asymmetric electrochemical cells.

Abstract

The derivation of Warburg's impedance presented in several books and scientific papers is reconsidered. It has been obtained by assuming that the total electric current across the sample is just due to the diffusion, and that the external potential applied to the electrode is responsible for an increase of the bulk density of charge described by Nernst's model. We show that these assumptions are not correct, and hence the proposed derivations questionable. A correct determination of the electrochemical impedance of a cell of an insulating material where are injected external charges of a given sign, when the diffusion and the displacement currents are taken into account, does not predict, in the high frequency region, for the real and imaginary parts of the impedance, the trends predicted by Warburg's impedance in the Nernstian approximation. The presented model can be generalized to the case of asymmetric cell, assuming boundary conditions physically sound.