Dipole-dipole electronic energy transfer. Fluorescence decay functions for arbitrary distributions of donors and acceptors .2. Systems with spherical symmetry

Many interesting systems of nanometer dimensions form spherically symmetric domains, either by design or through spontaneous self-assembly. The technique of direct nonradiative resonance energy transfer (DET) can be used to characterize the morphology of such structures on a nanometer scale. One needs to label the domain of interest with appropriate donor and acceptor dye moieties. One measures the fluorescence decay of the donors (I-D(t)) in the presence of accepters. The underlying geometry and physics of the system dictate how the dyes distribute themselves along the radial axis R of the system, according to concentration profiles (C-D(R), and C-A(R)) which need not be uniform. Because DET is sensitive to the distribution of dye interdistances, I-D(t) contains information about the underlying morphology. In this work we obtain an analytic expression relating I-D(t) to the donor/acceptor concentration profiles. This extends our previous contribution for systems with a plane of symmetry. The expression developed is general and capable of handling geometries in both extended and/or restricted spaces. It does not require a specific spatial locus for the donors nor does it require prior calculation of the pair-distribution function of the donor-acceptor distances. The development also provides one with an analytic expression for the evaluation of the interdistance distribution functions.