Kinetic model for TiO₂ polymorphic transformation from anatase to rutile

We propose a distribution kinetics model for the polymorphic transformation (anatase to rutile) and coarsening of TiO₂. Based on population balance equations for the size distributions of the dimorphs, the simplified model applies a first-order rate expression for transformation combined with Smoluchowski coalescence for coarsening of anatase and rutile particles. Two moments of the size distributions (number and mass of particles) lead to dynamic expressions for extent of reaction and average particle diameter. The model describes the time-dependent data of Banfield and colleagues fairly accurately, and provides activation energies for anatase coalescence and transformation. The equilibrium constant for the microscopically reversible transformation, occurring without coarsening, yields a small endothermic enthalpy change per mole of TiO₂. This probably reflects contributions of the transformation enthalpy of the anhydrous phases at the given particle size, which is very close to 0, and the enthalpy associated with a small amount of dehydration (endothermic water evaporation) during transformation.