Effect of energetic disorder on triplet-triplet annihilation in organic semiconductors

We present a model for the triplet-triplet annihilation in organic phosphorescent host-guest systems that considers the effect of the energetic disorder on the kinetics of the annihilation. Nonequilibrium (time-dependent) transport of the triplets that arises from the progressive relaxation of triplets in the energy landscape is taken into account in the model. Triplet excitons are considered to move between the guest sites (dye molecules) via the thermally activated tunneling mechanism; the annihilation step, however, takes place through the Forster mechanism. Based on the model developed, and by calculating the time evolution of the triplet concentration, we investigate the effect of the various parameters on the effective annihilation coefficient. At low dye concentrations, it is shown that relaxation of the triplets is not completed during their lifetimes, and therefore, the annihilation process occurs entirely in the nonequilibrium. We also address the competition between two pathways for the annihilation process: single-step, long-range annihilation, and diffusion-assisted annihilation. By a quantitative comparison with experimental data reported in the literature, we demonstrate certain conditions in which there is a considerable contribution from the diffusion to the total annihilation rate. The model presented in this work can also be used for the excitons that diffuse by the Forster mechanism.