Contact mechanics correction of activation volume in mechanochemistry

Point-contact studies of interfacial chemical reactions have revealed that activation barriers can depend strongly on applied stress. However, discrepancies exist in reported values of the activation volume $\mathrm{\ensuremath{\Delta}}V$---the rate at which stress alters activation barriers---hindering its physical interpretation. We show that two contact mechanics effects---the spatially nonuniform stress, and the effect of load on reaction area---can lead to large errors. We derive a corrected model for Hertzian contacts as an example, and validate it using the growth kinetics of zinc dialkyldithiophosphate tribofilms. The model fully resolves disagreements in $\mathrm{\ensuremath{\Delta}}V$ between microscale and nanoscale atomic force microscope experiments. Our findings permit more accurate measurement of $\mathrm{\ensuremath{\Delta}}V$, which is crucial for understanding the stress-assisted thermal activation kinetics involved in mechanochemistry and tribochemistry.