Direct Nonradiative Energy Transfer in Polymer Interphases: Fluorescence Decay Functions from Concentration Profiles Generated by Fickian Diffusion

Abstract

A model is presented describing direct nonradiative energy transfer (DET) occurring between energy donors and acceptors attached to polymer chains diffusing across a planar interface. The model considers the fact that each donor is surrounded by a nonuniform concentration of acceptors. Previous models of energy transfer in slowly diffusing systems have considered that both the donors and acceptors are distributed according to concentration profiles generated through diffusion but have simplified the problem by assuming that, in any thin slice through the profile, the acceptor concentration can be taken to be uniform. We show that this mean local concentration model provides a good description of the system when the concentration gradients are broad, but it fails when the concentration gradients are steep or when R 0 , the critical Forster distance, is large. The proposed model is expected to be particularly important for the description of the early stages of the diffusion process where one may wish to distinguish reptation effects from Fickian diffusion.