). The existence of a dark exciton level below the bright exciton band has been proposed as an explanation for low quantum efficiency.9 Spataru et al. showed that this splitting has minimal effect at room temperature, and the more important effect is the thermal momentum blocking of the radiative transition. 10The relatively low values of the quantum efficiency show that it is the nonradiative decay rate that dominates over the radiative decay rate. There are several nonradiative decay mechanisms proposed in the literature. At high fluences, excitonϪexciton Auger deexcitation has been suggested. 11,12 Furthermore, excitons in doped semiconducting nanotubes can decay via electronϪphonon interactions. 13 However, for undoped nanotubes in the linear regime, the main nonradiative decay mechanism is exciton diffusion to quenching sites, such as structural defects, adsorbate molecules, or the ends of the nanotube. 14Ϫ16 Stepwise fluorescence quenching in carbon nanotubes in response to changes to the nanotube's environment 16Ϫ18 can clearly also be utilized in sensor applications, such as biological sensors, ideally capable of detecting single molecules. 19The diffusion constant is the main parameter of the diffusion model, but it is not well-known. Experimentally extracted values of the diffusion constant range over 3 orders of magnitude, from 0.1 to 100 cm 2 /s. 12,16,18,20,21 Environment, chirality variation, length distributions, sample quality, and the presence of bundling introduce complexities in the behavior of the optical properties of nanotubes. Therefore, it is important to first examine the expected behavior of an individual nanotube with wellcontrolled static or dynamic quenching defects as the only interaction with the environment.In this paper, we assume that the observed diffusive behavior arises from random walks by excitons and perform Monte Carlo simulations of these random walks to model the fluorescence from nanotubes under uniform excitation (see Detailed Methods). From these simulations, we obtain the time-resolved, spatially resolved, and integrated quantum efficiency for nanotubes in the presence of perfectly quenching defects and of varying lengths. We show

The exciton dynamics for an ensemble of individual, suspended (6,5), single-walled carbon nanotubes revealed by single color E(22) resonant pump-probe spectroscopy for a wide range of pump fluences are reported. The optically excited initial exciton population ranges from approximately 5 to 120 excitons per ∼725 nm nanotube. At the higher fluences of this range, the pump-probe signals are no longer linearly dependent on the pump intensity. A single, predictive model is described that fits all data for two decades of pump fluences and three decades of delay times. The model introduces population loss from the optically active zero momentum E(22) state to the rest of the E(22) subband, which is dark due to momentum selection rules. In the single exciton limit, the E(11) dynamics are well described by a stretched exponential, which is a direct consequence of diffusion quenching from an ensemble of nanotubes of different lengths. The observed change in population relaxation dynamics as a function of increasing pump intensity is attributed to exciton-exciton Auger de-excitation in the E(11) subband and, to a lesser extent, in the E(22) subband. From the fit to the model, an average defect density 1/ρ = 150 nm and diffusion constants D(11) = 4 cm(2)/s and D(22) = 0.2 cm(2)/s are determined.