Compact-to-Dendritic Transition in the Reactive Deposition of Brownian Particles

Abstract

When Brownian particles (such as ions, colloids, or misfolded proteins) deposit onto a reactive cluster, the cluster undergoes a transition from a compact to a dendritic morphology. Continuum modeling reveals that the critical radius for this compact-to-dendritic (CTD) transition should be proportional to the particle diffusivity divided by the surface reaction rate. However, previous studies have had limited success verifying that the same scaling arises in the continuum limit of a particle-based deposition model. This discrepancy suggests that the continuum model may be missing part of the microscopic dendrite formation mechanism, a concerning hypothesis given that similar models are commonly used to study dendritic growth in electrodeposition and lithium metal batteries. To clarify the accuracy of such models, we reexamine the particle-based CTD transition using larger system sizes, up to hundreds of millions of particles in some cases, and an improved paradigm for the surface reaction. Specifically, this paradigm allows us to converge our simulations and to work in terms of experimentally accessible parameters. With these methods, we show that in both two and three dimensions, the behavior of the critical radius is consistent with the scaling of the continuum model. Our results help unify the particle-based and continuum views of the CTD transition. In each of these cases, dendrites emerge when particles can no longer diffuse around the cluster within the characteristic reaction timescale. Consequently, this work implies that continuum methods can effectively capture the microscopic physics of dendritic deposition.

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