Enabling dendrite-free lithium metal batteries through a constrained phase-field model

High-capacity batteries that employ lithium-metal anodes experience filamentary dendrite growth at the anode/electrolyte interface, which significantly impacts battery performance and safety. In this study, we introduce a constrained phase-field approach to model dendrite-free electro-deposition by incorporating an optimal control mechanism into the phase-field evolution. Specifically, dendrite formation is mitigated by introducing an energy functional that penalizes the formation of interfaces with high-curvature protrusions. We develop a coupled multiphysics model comprising a nonconserved Allen–Cahn equation for the metal electrode interface, a reaction–diffusion (Cahn–Hilliard-type) equation for ionic transport, and electrostatic charge conservation with Butler–Volmer boundary kinetics. The model is solved under a variational framework, yielding modified phase-field evolution equations that steers deposition away from dendritic pathways. Our findings suggest a novel paradigm for designing charging protocols and interface modifications that could enable safer dendrite-free lithium-metal batteries.