Crossover of limiting processes in mechanochemical reactions with flow driven by applied mechanical stress

Mechanochemical organic synthesis using ball milling leverages mechanical energy to drive chemical reactions. Comprehensive understanding of reaction kinetics is vital for the continuous development of mechanochemical synthesis. Unlike conventional solution-based reactions, however, the rate-limiting processes of mechanochemical reactions remain poorly understood due to limited knowledge of molecular dynamics at the interfacial length scales. We have recently developed a scaling theory that considers that the mechanochemical reactions of two solid reactants form a phase rich in products at their interface, where the product-rich phase is assumed to act as a fluid under the influence of a small volume of solvent added to the system. We here extend this theory to predict the rate-limiting process governing mechanochemical reactions. Our theory predicts that the rate-limiting process is determined by both the extent of the dissolution of reactant molecules into the product-rich phase and the flow driven by the applied mechanical stress in this phase. This flow retards or even suppresses the crossover to the diffusion-limited regime by accelerating the diffusion of reactant molecules in the product-rich phase. This new model incorporating both diffusion-limited and reaction-limited kinetics provides a fundamental framework for deeper understanding of mechanochemical organic reactions in ball milling.