Impurity quenching of molcular excitons. III. Partially coherent excitons in linear chains

Abstract

We have extended a model of exciton quenching, previously developed for pure Frenkel excitons, to include the exciton‐phonon interaction. We introduce a mathematically tractable exciton density matrix equation that describes the motion of excitons on a finite chain quenched at both ends. From this equation we find that the excitation on the chain as a function of time exhibits several types of kinetic behavior that result from the interplay of coherent, incoherent, and quenching terms. This behavior changes as a continuous function of the strength of the incoherent terms in such a way as to define five kinetic regions, ranging from that of pure Frenkel excitons to that of completely incoherent (hopping) excitons. In each of these five regions the average excitation decay rate constant is proportional to c^p, p = 0, 1, 2, or 3, where c is the quencher concentration.