Work

On the Distributed Resistor-Constant Phase Element Transmission Line in a Reflective Bounded Domain

Year: 2025

Type: article

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.

Source: Journal of The Electrochemical Society

DOI: 10.1149/1945-7111/add212

Authors: Anis Allagui, Enrique H. Balaguera, Chunlei Wang

Institutions: University of Sharjah, Florida International University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Tuning the Frequency Response of Fractional-Order Microsupercapacitors, AccelNet-Implementation: Broadening Carbon Ring