Modeling dendrite growth during lithium electrodeposition at sub-ambient temperature

•Electrochemical model of enhanced Li dendrite growth at sub-ambient temperature.•Model combines temperature effects on Li+ diffusion and surface film formation.•Model predicts critical temperature below which dendrite formation is initiated.•Critical temperature defines the lowest temperature for safe Li-battery operation.

Increased propensity for dendritic lithium electrodeposition during sub-ambient temperature operation has been widely reported in lithium battery systems, yet is not fully understood. In the present paper, a mathematical model is developed to quantify the dendritic growth rate during lithium electrodeposition at sub-ambient temperature. This model builds on a diffusion–reaction framework presented recently by Akolkar [J. Power Sources 232 (2013) 23–28]. Using a steady-state diffusion model with a concentration-dependent diffusion coefficient, the lithium-ion concentration depletion in the stagnant Nernst diffusion boundary layer near the lithium surface is modeled. A surface electrochemical reaction model is then employed to correlate the lithium concentration depletion to the dendrite growth rate. Temperature effects on the lithium-ion transport and its electrochemical surface reaction are incorporated in the model via an Arrhenius-type temperature-dependence of the diffusion coefficient and the apparent charge transfer coefficient. It is shown that lowering the system temperature has the effect of increasing the lithium-ion diffusion resistance and decreasing the surface film thickness – conditions favorable for the formation of dendrites during lithium electrodeposition.