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When Brownian particles (such as ions, colloids, or misfolded proteins)deposit onto a reactive cluster, the cluster undergoes a transition from acompact to a dendritic morphology. Continuum modeling reveals that the criticalradius for this compact-to-dendritic (CTD) transition should be proportional tothe particle diffusivity divided by the surface reaction rate. However,previous studies have had limited success verifying that the same scalingarises in the continuum limit of a particle-based deposition model. Thisdiscrepancy suggests that the continuum model may be missing part of themicroscopic dendrite formation mechanism, a concerning hypothesis given thatsimilar models are commonly used to study dendritic growth in electrodepositionand lithium metal batteries. To clarify the accuracy of such models, wereexamine the particle-based CTD transition using larger system sizes, up tohundreds of millions of particles in some cases, and an improved paradigm forthe surface reaction. Specifically, this paradigm allows us to converge oursimulations and to work in terms of experimentally accessible parameters. Withthese methods, we show that in both two and three dimensions, the behavior ofthe critical radius is consistent with the scaling of the continuum model. Ourresults help unify the particle-based and continuum views of the CTDtransition. In each of these cases, dendrites emerge when particles can nolonger diffuse around the cluster within the characteristic reaction timescale.Consequently, this work implies that continuum methods can effectively capturethe microscopic physics of dendritic deposition.

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