Dissolution-limited reactions in solid-state synthesis

A mechanochemical approach using ball milling enables us to carry out organic reactions between solid-state reactants as well as those between liquid reactants. Under such mechanochemical conditions, a considerable reactivity difference between liquid and solid reactants is often observed, which may result from the poor-diffusivity of reactants in solids. The chemical reaction between reacting solids happens at their interface and forms a region rich in products. We here integrate the Landau theory of the solid-liquid phase transition into the Onsager’s theory of irreversible processes to theoretically predict the reaction kinetics limited by the diffusion of reactants through the heterogeneous interfacial region. Our theory predicts that in the limit of low temperature, the reaction kinetics is mostly limited by the dissolution of reactant molecules into the product-rich phase, rather than the poor diffusivity in solids, and provides a quantitative relationship between the reaction rate and the equilibrium miscibility phase diagram.