This paper studies the decay law of the excitation of a donor molecule, due to its microscopic long range interactions with moving acceptor molecules. Particular attention is given to the case of acceptor molecules randomly dispersed in a host liquid. From a general approach we derive an exact ensemble averaged formula for the decay of the donor excitation as a function of the molecular motion. The expression obtained is valid for all types of microscopic molecular interactions and for arbitrary ratios of acceptors to inert molecules; from this formula we determine the energy decay for motions which are slow or rapid relatively to the microscopic energy transfer times. If the motion is frozen, we retrieve the decay law valid for acceptors imbedded randomly in a solid matrix [A. Blumen and J. Manz, J. Chem. Phys. (to be published)]. For slow molecular displacements, which obey the Langevin equations of Brownian motion, the diffusion dependent decay law is presented; in the case of low acceptor concentration and multipolar interactions the expression reduces to the Yokota and Tanimoto result [J. Phys. Soc. Jpn 22, 779 (1967)], generalized to spaces of arbitrary dimensions. In the case of rapid motion, the decay becomes motion independent, and is not diffusion controlled. © 1980 American Institute of Physics.
