Triplet-triplet exciton interactions and delayed fluorescence in single-wall carbon nanotubes

We present pump-probe-, time-correlated single photon counting and spin-sensitive photoluminescence studies of semiconducting single-wall carbon nanotubes (SWNTs) which unambiguously identify triplet-triplet annihilation as the mechanism underlying a long-lived delayed fluorescence (DF) signal. DF decays with a $t^{-0.9}$ power-law, characteristic of diffusion-limited annihilation reactions in 1-dimensional systems. The experiments allow to determine triplet diffusion constants in SWNTs to be on the order of $1\, {\rm cm^2s^{-1}}$ and the triplet lifetime which is found to be $60\pm30\, {\rm \mu s}$. The experiments indicate that the rate of diffusion-limited photo-reactions, here exemplified by triplet-triplet annihilation, can be reduced by one-dimensional confinement. A comparison of optical transients in aqueous and organic solvent environments also indicates how polaron pair dynamics can be influenced by the environment.