Generalized Random-Walk Model for Singlet-Exciton Energy Transfer

Abstract

The usual model for singlet-exciton motion and trapping in molecular crystals is generalized to arbitrary finite trapping regions about each activator and to more than nearest-neighbor steps by the random walker. The properties of extended trapping regions, which simulate activator-induced host traps, are obtained rigorously by applying general results for three-dimensional random walks. The capacity $C\left(A\right)\mathrm{}$ of the extended trapping region is shown, by explicit calculations for a simple cubic lattice, to depend on the size and shape of the trapping region and on the anisotropy and step distribution of the random walker. The capacity controls the competition between singlet-exciton absorption (trapping and subsequent trap fluorescence) and emission (host fluorescence) observed in doped organic crystals. The model accounts qualitatively for the "anomalous" time dependence of the energy-transfer rate in tetracene-doped anthracene and in anthracene- or tetracene-doped naphthalene. The model also accounts for the reported variations in the apparent exciton hopping time, which provide strong evidence for the hypothesis of extended trapping regions.