Population dynamics of driven autocatalytic reactive mixtures

Motivated by the effect of electroautocatalysis (explicit concentration dependence) on the stability of electrochemically driven phase-separating single particles, we apply the Fokker-Planck equation to describe the population dynamics of a general ensemble of chemically reactive particles. For phase-separating ensembles, we show that mosaic instability (from a homogeneous initial state to a multimodal probability distribution) may be suppressed or enhanced by autoinhibitory or autocatalytic reactions, respectively. In some cases, autocatalysis may induce two distinct populations in thermodynamically stable single-phase ensembles. Asymmetric reaction kinetics also results in qualitatively different population dynamics upon reversing the reaction direction. In the limit of negligible fluctuations, we use the method of characteristics and linearization to study the evolution of the concentration variance as well as the condition for mosaic instability, in good agreement with the full numerical solution. Applications include Li-ion batteries characterized by in situ x-ray diffraction.