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Kinetic Model for TiO 2 Polymorphic Transformation from Anatase to Rutile
Author(s) -
Madras Giridhar,
McCoy Benjamin J.,
Navrotsky Alexandra
Publication year - 2007
Publication title -
journal of the american ceramic society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.9
H-Index - 196
eISSN - 1551-2916
pISSN - 0002-7820
DOI - 10.1111/j.1551-2916.2006.01369.x
Subject(s) - endothermic process , enthalpy , anatase , rutile , thermodynamics , coalescence (physics) , population balance equation , particle size , materials science , population , kinetics , chemistry , physics , adsorption , organic chemistry , demography , photocatalysis , sociology , astrobiology , catalysis , quantum mechanics
We propose a distribution kinetics model for the polymorphic transformation (anatase to rutile) and coarsening of TiO 2 . 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 TiO 2 . 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.