Donor-acceptor kinetics in the presence of energy migration. Forward and reverse energy transfer

Abstract

A theoretical model for donor-acceptor kinetics in the presence of energy migration is presented. The model treats both forward and reverse energy transfer between donor and acceptor molecules, in the liquid as well as in rigid solutions. Equations for donor and acceptor fluorescence decay and respective quantum yields have been developed by applying a three-step analysis. In the first step, we introduce, on the basis of a statistical Förster treatment (averaging over spatial positions), functions describing the response of the system after δ-pulse excitation. In the second step we use a convolution method to evaluate the response of the donor and acceptor system in the presence of energy migration and forward energy transfer, using a realistic excitation profile. Finally, applying again a convolution method (averaging over time), we find donor and acceptor fluorescence decay profiles (and respective quantum yields) in the presence of forward and reverse energy transfer. The general solutions for donor and acceptor fluorescence decay profiles and quantum yields have been given in the form of Laplace transforms. We show that in rigid solution reverse energy transfer from acceptor to donor leads to a non-exponential donor decay for long times. This deviation from single-exponential decay can be studied experimentally.