Theoretical interpretation of Warburg's impedance in electrolytic cells

TL;DR

This paper provides a theoretical analysis of Warburg's impedance in electrolytic cells using the Poisson-Nernst-Planck model, highlighting conditions like differing ion diffusion coefficients and non-blocking electrodes necessary for Warburg-like behavior.

Contribution

It offers a rigorous theoretical justification for Warburg's impedance expression, correcting previous assumptions and extending analysis to more complex cell models.

Findings

Warburg impedance requires different diffusion coefficients for positive and negative ions.

Non-blocking electrodes modeled as Ohmic contacts are essential for Warburg behavior.

The analysis can be generalized to asymmetric cells and more complex charge exchange models.

Abstract

We discuss the origin of Warburg's impedance in electrolytic cells containing only one group of positive and one group of negative ions. Our analysis is based on the Poisson-Nernst-Planck model, where the generation-recombination phenomenon is neglected. We show that to observe Warburg's like impedance the diffusion coefficient of the positive ions has to differen from that of the negative one, and furthermore that the electrodes have to be not blocking. We assume that the non-blocking properties of the electrodes can be described by means of an Ohmic model, where the charge exchange between the cell and the external circuit is described by means of an electrode conductivity. For simplicity we consider a symmetric cell. However, our analysis can be easily generalized to more complicated situations, where the cell is not symmetric and the charge exchange is described by Chang-Jaffe model, or by a linearized version of Butler-Volmer equation. Our analysis allows to justify the expression for Warburg's impedance proposed previously by several groups, based on wrong assumptions.