Exciton annihilation in molecular crystals at high exciton densities

Abstract

Suna's kinematic equations describing exciton annihilation in aromatic crystals are solved for higher exciton densities $n$, i.e., where $n\ensuremath{\ge}\frac{\ensuremath{\beta}}{\ensuremath{\gamma}}$, where $\ensuremath{\beta}$ is the monomolecular decay rate and $\ensuremath{\gamma}$ is the bimolecular annihilation rate constant. It is found that in case of diffusion-limited annihilation, $\ensuremath{\gamma}$ is a function of the exciton density $n$ even for $n$ small compared to the lattice site density. In general $\ensuremath{\gamma}$ is then a monotonically increasing function of $n$ and these density effects depend on the dimensionality of the exciton motion. For both triplet and singlet excitons, $\ensuremath{\gamma}$ is a function of $n$ in one-dimensional and two-dimensional systems only. In the case of singlet excitions, $\ensuremath{\gamma}$ depends on $n$ even in three-dimensional systems if reabsorption is a dominant mechanism of exciton motion. Some materials are suggested in which such effects could be experimentally observable.