Transmission Line Model of Battery Cell's Impedance: Theory Vs. Experiments

Abstract

Electrochemical impedance spectroscopy (EIS) is arguably the most accurate electrochemical technique. It often appears as the main or, more commonly, an additional approach in experimental investigation of advanced batteries. To a large extent, the popularity of impedance technique is probably due to fully automized, easy-to-use modern devices and, also, due to user-friendly softwares that facilitate the basic analysis of measured spectra in terms of equivalent circuit fitting. On the negative side, the final result of such a standard approach is a set of parameters (resistors, capacitors, inductors) which are difficult to interpret in terms of physical processes occurring in the measured cell. In the worst case, assignment of equivalent circuit parameters to physical processes is carried out arbitrarily which frequently leads to erroneous intepretation of cell’s physics.Interpretation of measured EIS spectra gets much more reliable if instead the equivalent circuit approach one relies on physical-chemical models that describe transport and reaction phenomena in given cell. The linearized physical-chemical models of electrochemical cells can be solved in three ways: (i) by finding an analytical solution, (ii) using conventional numerical procedures, (iii) using the transmission line approach which transcribes the physical equations into a large number of spatially distributed discrete visual elements that resemble the usual resistors and capacitors.In this presentation we will demonstrate the power of transmission line approach when trying to resolve the physical meaning of measured impedance features of advanced battery cells. After explaining the transmission line methodology on conventional battery electrodes, such as LiCoO2, NMC, LiFePO4, the general applicability of the approach will be demonstrated on state of the art electrodes such as sulfur cathode, lithium rich fcc and magnesium batteries. In all cases discussed we will compare the actual measured spectra with theoretical predictions of the corresponding transmission line model. We will show that the latter is able to accurately predict the trends in both sizes and shapes of measured spectra when changing the experimental conditions (electrode thickness, concentration of salt, state of charge, cycle number, surface treatment of electrode, porosity of electrode etc.). Furthemore, the proposed model is also able to capture peculiar small details of measured impedance responses, some of which will be discussed and explained in order to further elucidate processes taking place in modern battery components.