Transmission line models for evaluation of impedance response of insertion battery electrodes and cells

Physics based transmission line models (TLMs) are a convenient tool for the analysis of the impedance response of electrochemical systems - the most prominent examples being double-layer capacitors, solar cells, and batteries. TLMs can provide a good quali- and quantitative evaluation of the main transport-reaction steps occurring in a given system - a a moderate mathematical effort. This mini review focuses on the theoretical development and application of TLM schemes in porous battery electrodes and other porous battery components. After a short historical overview of the main achievements in the field, we discuss in some detail the conventional TLM based on the de Levie's original proposal. Afterwards we present a couple of upgrades that address the deficiencies of the conventional model at low frequencies in which diffusion in electrolyte phases (in porous electrode and in separator) is supposed to be observed. We compare systematically the impedance responses of several TLMs and comment on their ability to simulate the measured impedance spectra. Simplifications and limitations of the discussed models are also considered. Finally, a comparison between the proposed TLMs and the output of the well-known Newman's porous electrode model is shown.