Experimental quantification of impact force and energy for mechanical activation in vibratory ball mills

Abstract

Mechanochemistry has been shown to provide a greener alternative to chemical synthesis; however, challenges in establishing clear relationships between chemical reaction yields and operational reactor parameters, such as milling frequency, milling ball material properties, vessel material properties, and reactor geometries used in a mechanochemical synthesis, make optimizing reactor efficiency difficult. This study presents a force model that relates these reactor parameters to quantifiable impact forces within a vibratory ball mill. To validate this force model, we developed a method for integrated, real-time measurement of force ensembles in the reaction vessel by embedding piezoresistive sensors with fast response to capture impact dynamics at various milling frequencies and operational settings. We measured force using preground NaCl at different fill ratios and compared it to an adjusted Hertzian contact mechanics force model with fill factor. We found agreement between the measured and modeled impact force. At the macroscale, impact acts as an ensemble of forces dynamically applied to the reactants. By simulating the mechanical activation of an illustrative mechanochemical system with known energetics, we show that there is little to no difference in effect between using the mean impact force and force ensemble on the kinetics of a straightforward mechanochemical reaction. We also demonstrate kinetic energy quantification in the Knoevenagel condensation reaction of vanillin and barbituric acid to understand what fraction of kinetic energy goes toward mechanical activation. We observed that the energetics of high-frequency milling for this reaction system entail diminishing returns, reinforcing the notion that there can be an optimal balance between collision intensity, resulting impact forces, and productive energy usage. The developed toolset and models provide a framework for understanding mechanochemical activation in vibratory ball mills and optimizing reaction parameters for scale-up to other reactors.