Scaling theory for the kinetics of mechanochemical reactions with convective flow†

Deep understanding of reaction kinetics in mechanochemical conditions is crucial to further advance this field of solid-state chemistry. However, a formidable challenge owing to the complexity of these systems, in particular the kinetic effects of mechanical stress, makes this problem very complex. In this study, we developed a scaling theory to understand the kinetics of mechanochemical reactions by considering convective flows driven by applied mechanical stress, with the assumption that the product behaves as a fluid with the applied mechanical stress in a ball mill. This theory predicts that the rates of mechanochemical reactions are regulated by the dissolution of reactants in the product-rich phase formed between two reactants, and that mechanical force-induced convective flows enhance reaction rates by reducing the thickness of the product-rich phase. This scaling model provides a fundamental approach to understanding the effect of mechanical stress on mechanochemical organic reactions in ball milling.