The statistical probability factor in triplet mediated photon upconversion: a case study with perylene

Triplet-triplet annihilation photon upconversion (TTA-UC) is a process where two low-energy photons are converted into one higher-energy photon. A crucial component for an efficient upconversion process is the statistical probability factor (f), defined as the probability of the formation of a high-energy singlet state upon coupling of two low-energy triplet states. Theoretically, f depends on the energy level distribution, molecular orientation, inter-triplet exchange coupling of triplet dyads, and spin-mixing of resulting spin states (singlet, triplet, and quintet). However, experimental values of f for acene-based annihilators have been subject to large variations due to many factors that have resulted in the reporting of different f values for the same molecule. In this work, we discuss these factors by studying perylene as a case study annihilator, for which by far the largest variation in f = 16 to 100% has been reported. We systematically investigated the TTA-UC of PdTPBP:perylene, as a sensitizer-annihilator pair and obtained the experimental f = 17.9 +/- 2.1% for perylene in THF solution. This limits the maximum TTA-UC quantum yield to 9.0% (out of 50%) for this annihilator. We found that such a low f value for perylene is largely governed by the energy-gap law where higher non-radiative losses due to the small energy gap between 2 x T-1 and T-2 affect the probability of singlet formation. Interestingly, we found this observation true for other acene-based annihilators whose emission ranges from the UV to the yellow region, thus providing a blueprint for future design of efficient TTA-UC systems