Time-Fractional Approach to the Electrochemical Impedance: The Displacement Current

TL;DR

This paper develops a time-fractional model for electrochemical impedance that ensures current conservation and predicts constant phase element behavior in anomalous diffusion, linking fractional order to impedance characteristics.

Contribution

It establishes conditions for a time-fractional Poisson-Nernst-Planck model to accurately describe electrochemical impedance with current solenoidality.

Findings

Model predicts constant phase element behavior at low frequencies.

The slope of reactance versus resistance curve equals the fractional derivative order.

Ensures total current remains solenoidal in fractional models.

Abstract

We establish, in general terms, the conditions to be satisfied by a time-fractional approach formulation of the Poisson-Nernst-Planck model in order to guarantee that the total current across the sample be solenoidal, as required by the Maxwell equation. Only in this case the electric impedance of a cell can be determined as the ratio between the applied difference of potential and the current across the cell. We show that in the case of anomalous diffusion, the model predicts for the electric impedance of the cell a constant phase element behaviour in the low frequency region. In the parametric curve of the reactance versus the resistance, the slope coincides with the order of the fractional time derivative.