Theoretical Analysis of Reaction Inhomogeneity and Lithium Plating Onset at Fast Charge Rates

Inhomogeneous lithium intercalation of porous electrodes can lead to lithium plating during fast charging. Previous work has demonstrated the effects of inhomogeneous reactions in cathodes and anodes, both on particle and macroscale (i.e., cell) length scales. The effects of mass transport, ionic transport, electrode thermodynamic behavior and reaction kinetic behavior on lithium plating have been studied in the context of reaction inhomogeneity; however, a complete theoretical understanding on how these effects interplay to accelerate lithium metal plating has not been established at high C-rates. Here, analytical and numerical analysis is used to develop a more complete understanding on how these coupled, nonlinear physical and electrochemical effects act together to cause lithium plating. Specifically, it is shown that analytical solutions, which are functions of several nondimensional numbers (the “reaction inhomogeneity parameter” in particular), can predict onset of lithium plating at high C-rates in half-cell anodes. This analytical prediction of lithium plating exhibits surprising accuracy against a calibrated graphite half-cell model, which has highly non-linear behavior (e.g., in the open circuit voltage). These results are compared against <i>in situ </i>and <i>ex situ</i> experimental observations of lithium plating onset during fast charging. Applications for design and optimization of electrodes with complex architectures are discussed. This work attempts to clarify and unify findings in complicated numerical models to provide guidance in mitigating Li metal plating at high rates.