Theory of Impedance Spectroscopy for Lithium Batteries

In this article, we derive and discuss a physics-based model for impedance\nspectroscopy of lithium batteries. Our model for electrochemical cells with\nplanar electrodes takes into account the solid-electrolyte interphase (SEI) as\nporous surface film. We present two improvements over standard impedance\nmodels. Firstly, our model is based on a consistent description of lithium\ntransport through electrolyte and SEI. We use well-defined transport\nparameters, e.g., transference numbers, and consider convection of the\ncenter-of-mass. Secondly, we solve our model equations analytically and state\nthe full transport parameter dependence of the impedance signals. Our\nconsistent model results in an analytic expression for the cell impedance\nincluding bulk and surface processes. The impedance signals due to\nconcentration polarizations highlight the importance of electrolyte convection\nin concentrated electrolytes. We simplify our expression for the complex\nimpedance and compare it to common equivalent circuit models. Such simplified\nmodels are good approximations in concise parameter ranges. Finally, we compare\nour model with experiments of lithium metal electrodes and find large\ntransference numbers for lithium ions. This analysis reveals that lithium-ion\ntransport through the SEI has solid electrolyte character.\n