An Analytical Three-Scale Impedance Model for Porous Electrode with Agglomerates in Lithium-Ion Batteries

An analytical, three-scale impedance model is developed for porous electrodes in lithium-ion batteries. The model first mathematically describes the electrochemical reactions and species transport inside the micron-sized agglomerate consisting of submicron-sized primary particles, and then extends the agglomerate model to the whole porous electrode using the Newman's approach. Compared with the existing two-scale impedance models, the present model is featured with a refined description of the structure of the electrode/electrolyte interface at the primary active material particle, and an analytical formulation of electrochemical reactions and species transport inside the agglomerates. The model is validated using electrochemical impedance spectroscopy (EIS) data of an NMC positive electrode in a three-electrode lithium-ion cell over a wide range of SOC. The identified values of key model parameters are corroborated by results from other experiments or the literature. A parametric study reveals that the characteristic frequency of lithium ion diffusion in the electrolyte can be comparable or even smaller than that in the active material particle. As a result, EIS models capable of distinguishing between the solid phase diffusion and liquid phase diffusion should be used to extract the lithium ion diffusivities from impedance data.