Exciton trapping and sensitized luminescence: A generalized theory for all trap concentrations

The generalized-master-equation theory of sensitized luminescence in molecular crystals is extended to cover arbitrary guest concentrations by making use of a recently introduced formalism. Central to the formalism is a quantity termed the $\nu$ function, which is an ensemble average of the sum of host propagators over guest-influenced host sites. A variety of experimentally relevant sensitized luminescence observables, such as the host (and guest) luminescence intensity, the quantum yields, and the energy-transfer rates are simply related to the $\nu$ function. It is shown how the latter can be calculated for exciton motion possessing an arbitrary degree of coherence, dimensionality, and other transport characteristics, and for guest-molecule placement represented by any given pair correlation function. Specific cases are treated and results, some exact and others approximate, are presented for experimental observables.