Spin Statistics for Triplet-Triplet Annihilation Upconversion: Exchange Coupling, Intermolecular Orientation, and Reverse Intersystem Crossing

Triplet-triplet annihilation upconversion (TTA-UC) has great potential to significantly improve the light harvesting capabilities of photovoltaic cells and is also sought after for biomedical applications. Many factors combine to influence the overall efficiency of TTA-UC, the most fundamental of which is the spin statistical factor, eta, that gives the probability that a bright singlet state is formed from a pair of annihilating triplet states. The value of eta is also critical in determining the contribution of TTA to the overall efficiency of organic light-emitting diodes. Using solid rubrene as a model system, we reiterate why experimentally measured magnetic field effects prove that annihilating triplets first form weakly exchange-coupled triplet-pair states. This is contrary to conventional discussions of TTA-UC that implicitly assume strong exchange coupling, and we show that it has profound implications for the spin statistical factor eta. For example, variations in intermolecular orientation tune eta from 2/5 to 2/3 through spin mixing of the triplet-pair wave functions. Because the fate of spin-1 triplet-pair states is particularly crucial in determining eta, we investigate it in rubrene using pump-push-probe spectroscopy and find additional evidence for the recently reported high-level reverse intersystem crossing channel. We incorporate all of these factors into an updated model framework with which to understand the spin statistics of TTA-UC and use it to rationalize the differences in reported values of eta among different common annihilator systems. We suggest that harnessing high-level reverse intersystem crossing channels in new annihilator molecules may be a highly promising strategy to exceed any spin statistical limit.