Evaluating rates and yields of second-order, photoinitiated reactions under conditions of Gaussian-profile excitation

Interpreting rates and yields of photoinitiated reactions that follow second-order or mixed-order decay kinetics requires modeling the spatial distribution of excited states in the expressions for the reaction rates and yields. Under conditions of linear absorption, the spatial distribution of photoexcited intermediates is proportional to the incident excitation intensity pattern. A mixed-order kinetic model has been developed for interpreting the rates and yields of photoinitiated reactions under conditions of Gaussian radial profile excitation. From a numerical study, it was shown that the spatial distribution of excited states must be explicitly included in the kinetic model to acquire accurate rates and yields of second-order and mixed-order processes; it was also found that errors in fitted parameters can arise when no significant lack-of-fit can be detected. The Gaussian-weighted model is used to determine the triplet-triplet annihilation rate constant for benzophenone in acetonitrile at room temperature from its phosphorescence decay where k_TT^OBS = (1.0 ± 0.1) × 10¹⁰ M^-1 s^-1; the T-T annihilation rate constant for anthracene was determined under the same conditions by delayed fluorescence measurements where k_TT^OBS = (5.5 ± 0.5) × 10⁹ M^-1 s^-1.