The Kramers-Kronig relations for usual and anomalous Poisson-Nernst-Planck models

TL;DR

This paper verifies that electrochemical impedance models based on Poisson-Nernst-Planck equations, including anomalous diffusion, are consistent with Kramers-Kronig relations, ensuring their physical validity and interpretability of experimental data.

Contribution

It analytically demonstrates the compliance of both usual and anomalous Poisson-Nernst-Planck impedance models with modified Kramers-Kronig relations in finite-length systems.

Findings

Impedance expressions satisfy modified KK relations.

Models successfully interpret experimental electrochemical data.

Theoretical validation of anomalous diffusion models.

Abstract

The consistency of the frequency response predicted by a class of electrochemical impedance expressions is analytically checked by invoking the Kramers-Kronig (KK) relations. These expressions are obtained in the context of Poisson-Nernst-Planck usual (PNP) or anomalous (PNPA) diffusional models that satisfy Poisson's equation in a finite-length situation. The theoretical results, besides being successful in interpreting experimental data, are also shown to obey the KK relations when these relations are modified accordingly