Coherence in singlet-exciton motion in anthracene crystals

Abstract

We investigate the question of the transport coherence of singlet excitons by carrying out a theoretical analysis of some recently reported transient-grating experiments in pure crystals of anthracene. We calculate the coherence time and the mean free path of the exciton at 20, 10, and 1.8 K from the reported observations, and conclude that the latter indicate exciton motion in anthracene to be quite coherent at low temperatures. The mean free path is found to be of the order of 100 intersite distances at 20 K and more than 1500 intersite distances at 1.8 K. We suggest further experiments, give explicit predicted signals for specific values of the fringe spacing of the grating, and show that, on the basis of the reported values of the diffusion constant, one may expect a clearly nonexponential time dependence—with oscillations—in the signal at 1.8 K for fringe spacings as large as 1 μm. Signals without oscillations but with clearly discernible nonexponential character are shown to be expected for 1 μm fringe spacings at 10 K. We also present estimates of the mean free path of triplet excitons in several crystals including anthracene based on diffusion constants measured through Ronchi ruling experiments. They show coherence to be lost within distances of the order of a lattice constant for the temperatures studied, which are all above 100 K.