(321ad) Transformation of Amorphous Titania to Anatase: Kinetics and Dynamics

A novel kinetic model for the transformation of nano-sized amorphous TiO2 to anatase with associated coarsening by coalescence will be described in this presentation. Based on population balance (distribution kinetics) equations for the size distributions, the model applies a first-order rate expression for transformation combined with Smoluchowski coalescence for the coarsening particles. Size distribution moments (number and mass of particles) lead to dynamic expressions for extent of reaction and average anatase particle diameter, which are compared with experimental data in the literature. Data at different temperatures yield activation energies for coalescence and transformation rate coefficients, as well as an overall endothermic transformation energy for combined transformation and dehydration. Titanium dioxide has been extensively investigated to understand its photocatalytic, electronic, and optical properties. Applications include the photocatalytic oxidation of organic pollutants for water purification; electrical devices such as sensors, batteries, and capacitors; and pigment additives. Nanocrystalline TiO2 exists in several polymorphic forms, including amorphous and anatase. The transformation between polymorphs involves fundamental issues of kinetics and thermodynamics, and has been intensely investigated both experimentally and theoretically. TiO2 polymorph transformations occur at high temperatures and involve a solid phase reaction with attendant dehydration. Associated with the heating, coarsening by coalescence reduces the surface energy. As different polymorphs are more or less stable because of surface energy effects, the coarsening profoundly influences the transformation process. For a particular size particle, the most stable polymorph will be favored as the transformation product. We have recently investigated TiO2 transformation from anatase to rutile, which occurs at temperatures higher than the amorphous to anatase reaction. A distribution kinetics model was proposed to represent the transformation and concomitant coarsening of TiO2. Based on population balance equations for the size distributions of the dimorphs, the model applied 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) led to dynamic expressions for extent of reaction and average particle diameter. The model quantitatively described the time-dependent data reasonably accurately, and provided activation energies for anatase coalescence and transformation. The temperature dependence of the equilibrium constant for the microscopically reversible transformation revealed an endothermic enthalpy change, which was attributed to the accompanying dehydration. We have modeled the transformation of nanometer-sized amorphous TiO2 to anatase in the same manner, representing coalescence by classical Smoluchowski theory and transformation by an overall first-order reaction. The model is based on two assumptions; first, we consider that coalescence is the dominating mechanism of coarsening. Second, the microscopically reversible transformation from A (amorphous) to B (anatase) for nanoparticles is assumed independent of size. The rationale is that diffusion-limited reaction processes will be extremely rapid in ultra-small particles. The processes defining the assumed mechanism satisfy TiO2 mass conservation.