Excitation energy transfer from a fluorophore to single-walled carbon nanotubes

We study the process of electronic excitation energy transfer from a fluorophore to the electronic energy levels of a single-walled carbon nanotube. The matrix element for the energy transfer involves the Coulombic interaction between the transition densities on the donor and the acceptor. In the Forster approach, this is approximated as the interaction between the corresponding transition dipoles. For energy transfer from a dye to a nanotube, one can use the dipole approximation for the dye, but not for the nanotube. We have therefore calculated the rate using an approach that avoids the dipole approximation for the nanotube. We find that for the metallic nanotubes, the rate has an exponential dependence if the energy that is to be transferred, variant Planck's over 2piOmega is less than a threshold and a d(-5) dependence otherwise. The threshold is the minimum energy required for a transition other than the k(i, perpendicular)=0 and l=0 transition. Our numerical evaluation of the rate of energy transfer from the dye pyrene to a (5,5) carbon nanotube, which is metallic leads to a distance of approximately 165 A up to which energy transfer is appreciable. For the case of transfer to semiconducting carbon nanotubes, apart from the process of transfer to the electronic energy levels within the one electron picture, we also consider the possibility of energy transfer to the lowest possible excitonic state. Transfer to semiconducting carbon nanotubes is possible only if variant Planck's over 2piOmega > or = epsilon(g)-epsilon(b). The long range behavior of the rate of transfer has been found to have a d(-5) dependence if variant Planck's over 2piOmega > or = epsilon(g). But, when the emission energy of the fluorophore is in the range epsilon(g) > variant Planck's over 2piOmega > or = epsilon(g)-epsilon(b), the rate has an exponential dependence on the distance. For the case of transfer from pyrene to the semiconducting (6,4) carbon nanotube, energy transfer is found to be appreciable up to a distance of approximately 175 A.