Abstract
The confinement of excited charges in carbon nanotubes has significant effect on their optical and electronic properties. The absorption of light generates strongly correlated electron-hole pairs (excitons) in carbon nanotubes. We present a study of the decay of these photogenerated excitons in solutions of semiconducting SWNTs using the degenerate pump probe technique. Under specific experimental conditions, the exciton-exciton reactions on carbon nanotubes were found to correspond to an ideal ID coalescence-diffusion system with distinct regions of reaction-limited and diffusion-limited behaviours. We provided the first experimental evidence for such a system of ‘universal behaviour’ at longer times which exhibits a power law decay whose exponent and amplitude are independent of the initial population - one of the key characteristics of this reaction-diffusion system. We also show for the first time that exciton-exciton interactions are long-range, and further that the transition between reaction-limited and diffusion-limited regimes is much more abrupt than is predicted by existing theories. A modified theory incorporating a finite reaction length provided an excellent fit to the experimental data for a reaction length of ~7 nm. We determined the reaction rate constant of kr = (3.76±0.04) nm/ps and the diffusion coefficient of D = (8.1±0.4) nm2/ps from fitting of the asymptotic regimes with rate equations. We also provided the first experimental evidence of sub-diffusive transport of excitons in quasi 1D SWNTs through studies of exciton annihilation dynamics in HiPco and CoMoCat SWNTs, where we observed that excitons in HiPco SWNTS exhibit normal diffusive transport where decay follows a t-α power law with decay exponent (α ≈0.5), whereas excitons in CoMoCat SWNTs decay more slowly with decay exponent (α ≈0.3) as result of sub-diffusive transport. We correlate this slow decay to a higher defect concentration in CoMoCat SWNTs as compared to HiPco measured using Raman spectroscopy and X-ray photoelectron spectroscopy. The experimental results were also compared to results from a Monte Carlo simulation of 1D diffusion in a fluctuating potential landscape which shows good agreement with experiment and underlines the necessity to consider spatial aspects (separation of defects and interaction range) in theoretical approaches to the dynamics. The study of excitonic decay in single walled carbon nanotubes is very important in terms of understanding of fundamental photophysics of 1D system and their possible application in electronics and photonic devices especially in light emitting devices and non-linear optics.