Size Dependence of the Kinetic Rate Constant for Phase Transformation in TiO₂ Nanoparticles

The temperature dependence of a kinetic rate constant for a phase transformation is usually described by the Arrhenius equation, which comprises a preexponential factor multiplied by an exponential term involving the activation energy and temperature . In this work we show that particle size is another factor that is needed in the description of kinetics of phase transformations in nanoparticles. For the phase transformation in nanocrystalline titania (TiO 2 ) proceeding via nucleation at particle−particle contacts, the activation energy varies slightly with particle size but the preexponential factor is inversely proportional to the approximately fourth power of the particle size. We attribute the large preexponential factor primarily to the high concentration of nucleation sites at particle−particle interfaces in nanomaterials compared to bulk materials. We proposed a kinetic equation that incorporates the dependence of the rate constant on the particle size for phase transformation via interface nucleation in nanoparticles.