Kinetics of Stochastic Charge Transfer and Recombination Events in Semiconductor Colloids. Relevance to Photocatalysis Efficiency

Abstract

We report stochastic calculations in compact 2-D lattices modeling the competition between electron−hole recombination and reactive processes on the surface of illuminated TiO_2 colloidal particles. Computer simulations in which holes perform unbiased random walks, react with oxidizable donors, or neutralize stationary electrons, while the latter reduce O_2 confirm that conventional kinetic concepts and rate laws are invalid in such domains. Bimolecular carrier recombination never follows second-order kinetics:  single excitons decay exponentially and multiple pairs annihilate with second-order rate coefficients asymptotically approaching a t^(-1/2) dependence. The occurrence of discrete events at the microscopic level further implies that (1) anodic and cathodic processes do not necessarily occur synchronously and (2) the fastest, rather than the slowest, charge transfer reaction is yield-determining. We carry out a rigorous data reduction analysis of experimental recombination rates and explore photon flux, [O_2], and particle size effects on the quantum yield of photocatalytic oxidations in these systems. Under typical steady-state illumination conditions, the model predicts that primary photooxidation yields should be nearly independent of photon flux and [O_2] over wide ranges and increase with particle radius.