Phase field modeling of electrodeposition process in lithium metal batteries

One of the main weaknesses in long term performance of conventional lithium batteries is the growth of lithium microstructures on the electrode surface due to an electrochemical process, which can eventually lead to failure of these batteries. Suppressing this microstructure growth is a key in developing new generations of lithium metal batteries (LMBs). In this study, a two-dimensional (2D) phase field model is constructed to understand and determine the parameters controlling formation and evolution of microstructures in LMBs. A Ginzburg-Landau free energy functional, which is a function of concentration of Li + and applied voltage, and a system consisting of a pure lithium metal electrode and an electrolyte made of lithium hexafluorophosphate in a binary organic solvent of 1:1 ratio of ethylene carbonate and dimethyl carbonate. The evolution equations consist of a Cahn-Hilliard fourth-order partial differential equation (PDE) for evolution of Li+ concentration in the domain, and a Laplace's equation for charge conservation. Using COMSOL, the growth thickness and growth rate from the anode surface are simulated by applying different boundary conditions of concentration and different potentials. The proposed model is compared to existing electrodeposition models and results show that the Laplace's equation can be used in different forms proposed in literature. Assuming this battery to be a strongly anisotropic system, the Cahn-Hilliard equation is modified to include anisotropy and the simulations reveal a strong directional growth from the anode surface. The results of the developed model suggested that this phase field model is capable of quantitatively predicting the formation and growth of microstructures in LMBs and may be used to improve their life time in the future. This model can also be applied to study electrodeposition process in other material systems.