Hot spot generation, reactivity, and decay in mechanochemical reactors

In this work, a bottom-up modeling approach to describe the reactive conditions in mechanochemical reactors is presented. The approach is focused on the creation of hot spots as the mechanism of enhanced reaction. In this model, energy dissipated during a collision is converted to heat in the milling media, and the reaction proceeds thermochemically. The first step of the model, determining the energy dissipated during the collision, is done by treating the ball and powder bed as viscoelastic materials and using a Kelvin Voigt model. The energy dissipation profile from the collision model is imported into a COMSOL (R) simulation. The heat transfer through the powder bed, treated as a continuous medium, is calculated, providing the temperature, volume, and time needed to calculate reaction rates. The final result of the model is the extent of reaction over a single collision. To verify the approach, the mechanochemical decomposition of calcium carbonate is studied. The real-time CO2 production under varying milling frequencies is measured using an in-line mass spectrometer. The ball and mill velocities, as well as, collision frequencies is determined by analyzing high speed video of a transparent milling vessel. The model describes hot spots with temperatures exceeding 1000 K that persist for tens of milliseconds.