Crossover of rate-limiting processes in mechanochemical reactions under flow driven by applied mechanical stress

Mechanochemical organic synthesis using ball milling leverages mechanical energy to drive chemical reactions. A comprehensive understanding of the underlying reaction kinetics is essential for the continuous development of mechanochemical synthesis. However, the rate-limiting processes of mechanochemical reactions remain poorly understood because molecular behavior at interfacial length scales is still largely unknown. We have theoretically predicted that mechanochemical reactions of two solid reactants lead to the formation of a product-rich phase at their interface due to the instability arising from the immiscibility of product and reactant solids and that the applied mechanical stress accelerates the diffusion of reactants through the product-rich layer by decreasing the thickness of this layer. To shed light on the rate-limiting processes governing such mechanochemical reactions, we develop here a scaling theory. This theory predicts that the rate-limiting process depends on the thickness of the product-rich layer and can therefore change over time. Unlike conventional solution-based reactions, the crossover between regimes of rate-limiting processes is influenced not only by the diffusion length but also by the extent of reactant dissolution into the product-rich layer and the magnitude of the applied mechanical stress. The model developed in this study provides a fundamental framework for a deeper understanding of mechanochemical organic reactions occurring during ball milling.