Dendrite formation is a major obstacle to developing next-generation lithium metal batteries. However, the mechanism that drives dendrite formation is not well understood. Here, we study this phenomenon using a simple model: the deposition of Brownian particles onto a reactive cluster. The cluster in this model switches from a compact to a dendritic morphology when it reaches a critical radius, but the mechanism for this transition is unclear, hindering comparisons with experiments. We revisit a proposed mechanism: that the transition occurs when the cluster radius approaches the reaction-diffusion length – the distance a particle can diffuse in the characteristic reaction time. A key quantitative prediction of this hypothesis is that the critical radius converges to a constant in the continuum limit, the limit as the particle size is taken to zero. Previous studies, however, found the continuum limit behavior to be inconsistent with this prediction. We use extensive Brownian dynamics simulations and a more accurate methodology based on direct measurements of the critical radius to show that the continuum limit does in fact converge, thus confirming the reaction-diffusion mechanism. Our simulations also show that the dendritic transition becomes infinitely sharp in the continuum limit, similar to a phase transition. Finally, we briefly explore the implications of the reaction-diffusion length mechanism for lithium metal batteries. In particular, this mechanism suggests that the solid-electrolyte interphase actually promotes dendrite formation by lowering the lithium ion diffusivity.
