On the direct energy transfer via exchange to randomly distributed acceptors

This paper investigates the direct, incoherent energy transfer due to exchange from an excited donor to randomly distributed acceptors. Making use of a general, exact formula for the time and concentration dependent ensemble averaged decay [Blumen and Manz, J. Chem. Phys. 71,4694(1979) ] simple approximate expressions for the limiting cases, of low and high concentrations and of short and long times, also under the inclusion of the back-transfer in the pair approximation, are derived; for low acceptor concentrations and long times the results of Inokuti and Hirayama [J. Chem. Phys. 43, 1978 (1965)] generalized to arbitrary dimensions, are retrieved. The limits of validity of the different approximations are determined by a numerical evaluation of the exact formula for particular lattices of interest.