Origin of the Delayed Fluorescence by Triplet–Triplet Annihilation in Solids with a Power Law Exponent of between −1/2 and −1

Triplet–triplet annihilation (TTA) merges low electronic energies in two molecules to high electronic energy in one molecule, which, following triplet sensitization, allows us to achieve high-efficiency conversion using low-intensity light. Although efficient TTA up-conversion in solutions has been reported, the TTA up-conversion in solid matrixes is preferred for practical applications. However, the emission decay kinetics after pulsed-light excitation is more complex in solids than in liquids, and the process underlying the different TTA kinetics has not yet been elucidated. Herein, we report that the complexity in the TTA kinetics in solid matrixes can originate from processes such as slow mixing of triplet excitons by migration, strong dependence on the initial distribution of triplet excitons, and an anisotropic random walk of excitons. We show theoretically that power-law fluorescence with an exponent of between −1/2 and −1 can originate from the slow diffusional mixing of excitons in one and three dimensions, where the initial exciton generation is uniformly distributed. By analyzing experimental data, we show that rich fluorescence kinetics observed experimentally by varying the temperature in molecular solids can be deeply understood in terms of bulk and nonbulk TTA under dispersive as well as normal diffusion.