Incoherent Exciton Quenching on Lattices

Abstract

The time-dependent excitation function φ(t) for exciton quenching in lattices of any dimension is derived from a general master equation in terms of perfect lattice Green's functions. Attention is largely restricted to nearest-neighbor interactions for which the Green's functions have simple forms. The quenchers are characterized by three dimensionless rate parameters: λ, for nearest neighbor host-quencher energy transfer; μ, for back transfer from quencher to host; and Q, for irreversible degradation of excitation on the quencher. Simple expressions for the Laplace transform of φ(t) under two different initial conditions are given for low concentrations of periodically placed quenchers that have identical but arbitrary λ, μ, and Q. Randomly placed quenchers are treated by adapting the coherent potential approximation; in three dimensions, this method gives a φ(t) that is identical to that with periodic quenchers of the same low concentration. Lattices with two types of defects-one with μ = 0 and one with μ > 0, a case of particular interest in organic crystals-are treated in some detail. Finally, it is shown that energy transfer anisotropies have little effect on φ(t), unless the smallest relative transfer rate is at least as small as the quencher concentration.