Hyperbolic subdiffusive impedance

TL;DR

This paper investigates the electrochemical impedance of subdiffusive electrolyte transport using a hyperbolic subdiffusion model with fractional derivatives, deriving impedance formulas and analyzing parameter effects on Nyquist plots.

Contribution

It introduces a hyperbolic subdiffusion equation approach to model electrolyte transport and derives impedance formulas considering general boundary conditions.

Findings

Derived formulas for electrochemical impedance in subdiffusive media.

Analyzed the impact of subdiffusion parameters on impedance spectra.

Provided insights into boundary condition effects on impedance behavior.

Abstract

We use the hyperbolic subdiffusion equation with fractional time derivatives (the generalized Cattaneo equation) to study the transport process of electrolytes in media where subdiffusion occurs. In this model the flux is delayed in a non-zero time with respect to the concentration gradient. In particular, we obtain the formula of electrochemical subdiffusive impedance of a spatially limited sample in the limit of large and of small pulsation of the electric field. The boundary condition at the external wall of the sample are taken in the general form as a linear combination of subdiffusive flux and concentration of the transported particles. We also discuss the influence of the equation parameters (the subdiffusion parameter and the delay time) on the Nyquist impedance plots.