Derivation of Transmission Line Model from the Concentrated Solution Theory (CST) for Porous Electrodes

Abstract

It has been shown previously that the governing equations defining continuum level processes in electrochemical cells can be mapped into appropriate extended equivalent circuits, also known as transmission line models (TLMs). Here we present a derivation which results in direct construction of a TLM from the widely used concentrated solution theory (CST) for porous electrodes originally proposed by Newman. The final result of derivation is a set of equations that directly connect the main parameters of CST for porous electrode (electrolyte conductivity, transport number, concentration, thermodynamic factor, chemical diffusion coefficient, porosity) and the main elements of corresponding TLM (resistances of active and inactive ions and chemical capacitance). The constructed TLM is applied to three standard porous electrode cases found in devices such as batteries, fuel cell and supercapacitors: insertion electrodes, faradic reaction at electrode-electrolyte interface and blocking electrodes. For all three cases, the derived TLMs are justified by a direct comparison of their output with the output of the corresponding analytical expression for impedance response of CST for porous electrodes.