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arXiv · 2411.17368

On the distributed resistor-constant phase element transmission line in a reflective bounded domain

Anis Allagui·Enrique H. Balaguera·Chunlei Wang
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Abstract

In this work we derive and study the analytical solution of the voltage and current diffusion equation for the case of a finite-length resistor-constant phase element (CPE) transmission line (TL) network that can represent a model for porous electrodes in the absence of any Faradic processes. The energy storage component is considered to be an elemental CPE per unit length of impedance $z_c(s)={1}/{(c_α s^α)}$ with constant parameters $(c_α,α)$ instead of the ideal capacitor of impedance $z(s)={1}/{(c\, s)}$ usually assumed in TL modeling. The problem becomes a time-fractional diffusion equation for the voltage that we solve under galvanostatic charging, and derive from it a reduced impedance function of the form $z_α(s_n)=s_n^{-α/2}\coth({s_n^{α/2}})$, where $s_n = jω_n$ is a normalized frequency. We also derive the system's step response, and the distribution function of relaxation times associated with it. The analysis can be viewed and used as a support for the fractal finite-length Warburg model.

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Anis Allagui, Enrique H. Balaguera, Chunlei Wang. 2025-04-04. On the distributed resistor-constant phase element transmission line in a reflective bounded domain. https://arxiv.org/abs/2411.17368

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