Understanding the unexpected effect of frequency on the kinetics of a covalent reaction under ball-milling conditions

We here explore how ball-mill-grinding frequency affects the kinetics of a disulfide exchange reaction. Our kinetic data show that the reaction progress is similar at all the frequencies studied (15-30 Hz), including a significant induction time before the nucleation and growth process starts. This indicates that to start the reaction an initial energy accumulation is necessary. Other than mixing, the energy supplied by the mechanical treatment has two effects: (i) reducing the crystal size and (ii) creating defects in the structure. The crystal-breaking process is likely to be dominant at first becoming less important later in the process when the energy supplied is stored at the molecular level as local crystal defects. This accumulation is taken here to be the rate-determining step. We suggest that the local defects accumulate preferentially at or near the crystal surface. Since the total area increases exponentially when the crystal size is reduced by the crystal-breaking process, this can further explain the exponential dependence of the onset time on the milling frequency.