Daniel Jacobson, California Institute of Technology
We examine the aggregation of Brownian particles starting from a seed with a reactive boundary. Brownian dynamics simulations analyzed via the introduction of a microscopic version of the Damkohler number, the dimensionless parameter that characterizes the relative rate of reaction versus diffusion, reveal a mechanism and a corresponding analytical expression that describes the crossover from compact KPZ growth to dendritic growth in the reaction-limited regime. This crossover occurs when the time required for a particle to diffuse across the angular correlation length of the cluster exceeds the characteristic reaction time at the boundary. Scaling analysis shows that the radius of the cluster at the crossover goes as the reciprocal of the Damkohler number to the power of the KPZ dynamic exponent, which is 3/2 in two dimensions. Based on this scaling relationship, we devise a novel plating strategy that can be used to control dendritic growth in electrochemical systems. We also use large-scale simulations to confirm that the fractal dimension of the dendrites is independent of the Damkohler number as predicted from renormalization group arguments and discuss a number of technical advantages inherent to our simulation methodology. This work provides a quantitative mechanistic understanding of the crossover from compact to dendritic growth in electrochemical systems, which is a limiting factor in the commercialization of rechargeable lithium metal batteries.
Abstract Author(s): Daniel Jacobson, Thomas F. Miller III