(531f) Hierarchical Multiphase Porous Electrode Theory -- a Case Study of Porous Graphite Electrode

The porous graphite electrode is the most widely used anode in lithium-ion battery and its secondary structure such as porosity and specific surface area of particle can vary. In general, the specific surface area of a fresh graphite electrode is relatively low (~ 1 m²/g) after coating and chemical treatment to reduce the capacity loss due to formation of solid-electrolyte interface(SEI). However, it still allows the electrolyte to fill up the nanopores and provides reactions on the internal surface of each secondary particle. The Damköhler numbers in both electrode scale and particle scale suggest that their concentration polarization are comparable and thus can not be ignored. Classic porous electrode theory assumes the active material to be compact and oversimplifies the flux of lithium ion in a secondary particle purely as a solid diffusion, therefore the diffusion coefficients extracted from experiments can sometimes vary several orders of magnitude. We combine the phase-field approach and a hierarchical porous electrode theory to capture the dynamics of reaction and transport in both the electrode scale and particle scale. The model is validated against the lithiation dynamics of porous graphite anode measured in-operando, capturing both the spatial and temporal nonuniformity. We then parameterize the model to a Li/Graphite half-cell setup and fit it into multiple data sets found in literature. The model respects the reaction kinetics and transport in a phase-separating material, thus transferable, and can guide the design of electrode and characterization methods for state of charge estimation and early detection of lithium plating.