Mathematical model of the dendritic growth during lithium electrodeposition

Abstract

Dendritic growth of lithium during galvanostatic electrodeposition is modeled. The time-dependent concentration distribution near the lithium surface is computed by numerically solving the transport equation inside the diffusion boundary layer. The dendrite propagation rate, i.e., the dendrite tip current density, is calculated by analyzing the various overpotentials that develop at the dendrite tip and at the flat electrode surface. The surface overpotential at the dendrite tip due to its radius of curvature is also incorporated in the model; however, for typical dendrite tip radii, it is shown that this surface overpotential is very small. The dendrite tip propagation rate predicted by the model agrees reasonably well with experimental data from the literature. For dendritic growth under pure activation control, a simplified analytical expression for the tip current density is derived. The analytical expression shows that dendritic growth is suppressed in systems that exhibit a lower charge transfer coefficient.