The effects of impurity scattering and transport topology on trapping in quasi-one-dimensional systems: Application to excitons in molecular crystals

Abstract

A model is developed which permits a detailed examination of the effects of impurity scattering and deviations from a strictly one‐dimensional transport topology on the trapping rate and on the mean‐square displacement of mobile species in systems which are nearly one dimensional in their transport characteristics, i.e., quasi‐one‐dimensional. The model is applied specifically to Frenkel excitons in molecular crystals, but may be readily adapted to other types of systems. Both coherent (wavelike) and incoherent (diffusive) microscopic modes of exciton transport are considered. In the strictly one‐dimensional limit following pulsed optical excitation, a time‐dependent trapping rate function is obtained as opposed to the commonly employed trapping rate constant. It is demonstrated that the coherent and incoherent trapping rate functions have identical dependencies on time and on impurity concentration and the macroscopic rate of transport can be calculated. To treat deviations from strictly one‐dimensional transport topology, it is necessary to consider anisotropic walks on the system’s ’’superlattice,’’ i.e., the array of molecular chain segments which are bounded by scattering impurities. Montroll’s Green function formalism is employed to obtain solutions to various walk topologies which have not previously been reported in the literature. In the quasi‐one‐dimensional case, a time‐dependent trapping rate function is also obtained unless the walk on the superlattice is nearly isotropic. The various trapping rate functions are then employed to provide explicit expressions for the time‐dependent trap population which is proportional to the intensity of time resolved optical emission, a widely used experimental observable. Finally, the exciton mean‐square displacement for a quasi‐one‐dimensional system with scattering impurities is shown to remain basically one dimensional even in situations where exciton trapping behaves in a manner best described in terms of a three‐dimensional topology.