A Consistent Derivation of the Impedance of a Lithium-Ion Battery Electrode and its Dependency on the State-of-Charge

A derivation of the fundamental impedance of a Lithium-Ion battery electrode is given, exemplarily conducted for a solid thin-film electrode. The focus of this derivation is not on developing a model which is able to reproduce the exact behaviour of a given electrode, but rather on deriving its fundamental characteristics from few and intuitive assumptions in a simple and transparent way. It is thus shown, that the fundamental impedance of a solid thin-film electrode consists of an RC-element for charge-transfer, a Finite-Length Warburg element for diffusion in the electrolyte and a Finite-Space Warburg element for diffusion in the solid-state. The use of a Finite-Length Warburg element with a serially connected capacitor for modelling diffusion in the solid-state is thus indicated to be physically questionable. In addition, the theoretically expected behaviour of charge-transfer and solid-state diffusion on the degree of lithiation (State-of-Charge) is derived and discussed.