Förster resonance energy transfer in finite length systems and porous media

Forster Resonance Energy Transfer (FRET) is a mechanism widely used to describe the luminescent behavior of a great variety of systems. However, there is a strong need for a complete model of Forster theory to understand donor-acceptor interactions in different confinement geometries and their effects on the luminescent dynamics. Here, a methodology based on Forster theory that allows finding the probability distribution of donors and acceptors in systems of any geometry is presented. We have considered the particular cases of lines with finite length, finite cylinders, and bi-dimensional arrangements of lines and cylinders. Furthermore, using our results, we calculate the quantum yield as a function of the geometric parameters of the structures. Our numerical results show that this methodology is useful to calculate and predict the donor luminescent dynamics in structures of finite length. We find that our model explains the decrease of the transferred energy from donors to acceptors with the separation between lines or cylinders, this behavior is physically consistent. The model presented here extends the use of FRET to the study of structures with bi-dimensional arrays of lines or cylinders (as could be the case of porous media), and finite cylinder structures (as could be the case of nanotubes). In our knowledge, this work is the first theoretical approach to describe the donor-acceptor luminescent dynamics in this kind of systems.