Photokinetics of Bimolecular Reactions: Analytically Solvable Rate Laws

Light-induced bimolecular reactions occur in many naturally and artificially (laboratory or industrial) designed processes. The quantification of these reactions is generally performed by kinetics. In particular, the kinetic data of bimolecular photoreactions are often treated by second-order kinetic models. If this situation is effectively ubiquitous in practice, it remains that the underlying hypothesis, assuming that photoreactions obey the same kinetics as thermal transformations, is not consistent with the physical photosystem considered. In fact, it has been proven that unimolecular (mono-reactant) photoreactions are effectively modelled by Φ-order kinetics. The latter model is formalised by a logarithmic function bearing an exponential in its argument. Hence, Φ-order kinetics is mathematically different from the thermal reaction models. In the case of the bimolecular photoreactions that are described by different rate laws than those used for the thermal reactions, i.e., involving both radiation intensity and light absorption, there have been no reported solutions in the literature that were based on analytical integration. So much so, no kinetic order has ever been assigned to any bimolecular photoreaction. In the current situation, it is perhaps sensible to proceed, in a first step, by defining among the bimolecular photoreactions those whose rate laws can be solved analytically and establish the corresponding solutions by closed-form integration. Following such a strategy, the present paper unravels the first model equations for the kinetics of bimolecular photoreactions. The findings are part of an effort to standardise photokinetics along the same principles used in thermal kinetics.