Diffusion influenced reversible transfer of electronic excitation energy in liquid solution by long-range interaction

An approach to donor-acceptor kinetics in the presence of diffusion and reversible energy transfer due to microscopic interaction is described. A set of coupled dynamic equations for the reduced distribution functions of reactant molecules in forward and reverse steps is presented on the basis of a hierarchical system of many-body Smoluchowski equations. With a view toward treating long-range dipolar interaction mediated energy transfer kinetics, this formalism is generalized to incorporate unimolecular decay pathways. Numerical calculations of this set of equations for the excited donor decay after a delta pulse show the dependence of the result on acceptor concentration, forward and back transfer distance-dependent rates, donor and acceptor lifetime, and on their diffusive motion. Comparison with the corresponding forward and irreversible reactive dynamics provides detailed insights into the time dependence of flow of electronic excitation in donors and accepters. The irreversible Smoluchowski limit is only recovered when both the forward and the reverse reactive systems are undergoing fast molecular motion (slow reaction). In the donor-donor case the temporal profile of the excited donor decay and the evolution of ground state donor (that receives energy from the initially excited donor) is presented, along with the total excitation that resides in these two kind of donors. The total excitation in this situation is found to follow a monotonic exponential decay with its characteristic natural lifetime, as expected in a lifetime measurement experiment. (C) 1997 American Institute of Physics.