Abstract
We focus on understanding the kinetics of a mechanically activated Knoevenagel condensation conducted in a ball mill, that is characterized by sigmoidal kinetics and the formation of a rubber-like cohesive intermediate state coating the milling ball. The previously described experimental findings are explained using a phenomenological kinetic model. It is assumed that reactants transform into products already at the very first collision of the ball with the wall of the jar. The portion of reactants that are transformed into products during each oscillation is taken to be a fraction of the amount of material that is trapped between the ball and the wall of the jar. This quantity is greater when the reaction mixture transforms from its initial powder form to the rubber-like cohesive coating on the ball. Further, the amount of reactants processed in each collision varies proportionally with the total area of the layer coating the ball. The total area of this coating layer is predicted to vary with the third power of time, thus accounting for the observed dramatic increase of the reaction rate. Supporting experiments, performed using a polyvinyl acetate adhesive as a nonreactive but cohesive material, confirm that the coating around the ball grows with the third power of time.
Highlights
Mechanical processing by ball milling (BM) is a well established methodology in materials science [1,2]
The results presented heretofore provide significant insight into the main factors and processes underlying the kinetics of the mechanically activated Knoevenagel condensation between vanillin and barbituric acid investigated in previous work [8], and help clarify the interplay between the degree of chemical conversion and the rheological properties of the substances subjected to BM
It is worth noting that the kinetic model describes satisfactorily the initial portion of the kinetic curve without the need for a time dependent rate coefficient k
Summary
Mechanical processing by ball milling (BM) is a well established methodology in materials science [1,2]. Physical and chemical transformations are activated and driven by the transfer of mechanical energy to the particulate This activation takes place every time the particulate gets trapped between the surfaces of the milling tools (the ball and the jar walls) as they collide with each other [1,2,3,4,5,6,7]. Deformation results in the effective mixing of the solid phases on the microscopic scale, which is accompanied by the formation of extended interfaces between the reactants and the consequent enhancement of chemical reactivity [1,2,3,4,5,6,7]
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