Geminate Exciton Fusion Fluorescence as a Probe of Triplet Exciton Transport after Singlet Fission

The geminate annihilation of two triplet excitons created by singlet exciton fission is affected by the dimensionality of transport as determined by typically anisotropic triplet exciton mobilities in organic molecular crystals. We analyze this process using a random-walk model where the time-dynamics of the geminate annihilation probability is determined by the average exciton hopping times along the crystallographic directions. The model is then applied to the geminate fluorescence dynamics in rubrene, where the main channel for triplet-triplet annihilation is via triplet fusion and subsequent photon emission, and we identify the transitions between transport in one, two, and three dimensions.