Exponential and Gaussian traps in nano-TiO2 and their function in kinetics of the electron transfer to O2

Abstract

A quasi-equilibrium (QE) theoretical model is proposed to fit the slow dispersive electron relaxation of nano-TiO2 that occurs through the transfer to O2. The electron relaxation is obtained from measurement of photoinduced absorptions. By including both the traps with exponential and Gaussian distributions with respect to the energy, the electron relaxation is fully fitted with the QE model. A Monte Carlo simulation is also realized to fit the electron relaxation, which agrees well with the QE model. It is revealed that the kinetics of the electron transfer from TiO2 to O2 contains both contributions from the exponential and Gaussian traps. Their distributions are obtained from the QE model fitting. The dispersion factor of the exponential traps is ∼0.65 and the trap density is high. The Gaussian traps locate ∼0.4 eV below the conduction band and have narrow distribution. The density of the Gaussian traps is more than three orders of magnitude lower than that of the exponential traps. Despite the low density, the Gaussian traps have an important effect on the electron relaxation. The distributions of the thermal barriers for the electron relaxation are obtained for both relaxations contributed by the exponential and Gaussian traps, based on which the kinetics equations are proposed. The Gaussian trap contributed relaxation accords with mono-exponential kinetics, while the relaxation contributed from the exponential traps involves exponentially distributed weights. The apparent activation energy, kinetic time constants, and pre-exponential factor can be obtained.