Excluded volume effect within the continuous model for the fluorescence energy transfer.

We consider and discuss the transfer of electronic energy between donor and acceptor molecules, both continuously distributed in an infinite space. In particular, the ensemble-average fluorescence intensity decay for the donor was calculated, taking into account the excluded volume. The latter may be associated either with finite molecular size or any other spatial restrictions, which are imposed on fluorophore distribution by a superstructure. Results show that in a system using excluded volume, the time dependence in donor decay is more complex compared to that predicted by a simplified stretched exponential model. We identify a crossover between two distinct time regimes in the refined decay and demonstrate its correlation with two competing parameters: r(m), which characterizes the minimal distance between interacting molecules, and R(0), which is related to the strength of the molecular interactions. In this context, the "apparent dimensionality" of the energy transfer recovered from the stretched exponential model ignores the crossover, and may be quite misleading. Basic theoretical considerations to that end are provided.