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

2022/01/03 by G. Barbero, Barbero, G., L. R. Evangelista +3
Chemistry · Physics and Astronomy · #Applied Physics (physics.app-ph) #Chemical Physics (physics.chem-ph) #Electrostatics and Colloid Interactions #FOS: Physical sciences #Force Microscopy Techniques and Applications #Materials Science (cond-mat.mtrl-sci) #Surface and Thin Film Phenomena #cond-mat.mtrl-sci #physics.app-ph #physics.chem-ph

paper · pdf · doi:10.48550/arxiv.2201.00731

arxiv created 2022/01/03 · openalex publication_date 2022/01/03 · arxiv updated 2022/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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