Coupling of mechanical deformation and reaction in mechanochemical transformations

Driven by the promise of alternative synthetic routes to fine chemicals and pharmaceuticals, mechanochemistry is going through a period of intense growth. Mechanical forces are successfully utilized to activate chemical reactions involving an ever-growing variety of inorganic and organic substances with the aim of developing solvent-less processes to be used in the greener chemical industry of tomorrow. Down this path, the proper understanding of the relationships between processing variables, macroscopic transformation kinetics and microscopic chemistry represents one of the fundamental challenges to face. In this work, we develop a kinetic model that, taking into account the intrinsic statistical nature of the mechanical processing of powders by ball milling, combines a phenomenological description of the rheological behaviour of molecular solids with the chemistry of interface reactions. Specifically, we use discrete deformation maps to account for the co-deformation of molecular solids and the consequent increase of the interface area between initially segregated reactants. We assume that the chemical reaction only occurs, with a certain probability, when reactants come into contact due to relocations induced by shearing. No diffusion is allowed. The systematic variation of the amount of powder involved in individual impacts, the composition of powder mixtures and the reaction probability at the interface provide us with a complete overview of the kinetic scenario. In particular, we present the different kinetic curves that can be originated from interface reaction, pointing out how statistical, mixing and chemical factors affect the mechanochemical kinetics. Eventually, we suggest how experimental findings can be used to gain information on the underlying mechanochemistry based on the outcomes of our kinetic modeling.