Quantitative characterization of carbon nanotube (CNT) dispersions is critical for developing various CNTbased applications, e.g., transparent conducting thin films, CNT thin film transistors, CNT-reinforced composites, etc. Using both of the preparative ultracentrifuge and absorption spectrum measurements, this paper presents a simple, easy-to-use, and reproducible method to experimentally determine the sedimentation function of carbon nanotube dispersions. This information can then be used for the semiquantitative characterization of the dispersion of CNT in various liquid media. Theoretical analysis of the sedimentation function based upon the conventional ultracentrifugation model allows for the determination of the apparent sedimentation and diffusion coefficients for a specific SWNT dispersion. As demonstrated in the examples, this method, along with dynamic light scattering, was used for studying the processing-structure relationship of SWNT/H 2 O dispersions. In brief: (1) size reduction of SWNT bundles due to exfoliation (diameter reduction) and shortening/cutting (length reduction) occurs simultaneously during the sonication process; power-law dependence of the diameter and length reduction on the sonication duration were observed; (2) size reduction of SWNT bundles reflected by the sedimentation function strongly depends upon the amount of dispersion being processed; for the same sonication conditions, the greater the amount of the dispersion, the less efficient the exfoliation of the SWNT bundles is; (3) under the same sonication conditions, the sedimentation coefficient of sodium dodecylbenzenesulfonate (SDBS) assisted SWNT/H 2 O is significantly smaller than that of Triton X-100, which indicates the superior dispersing capability of the former surfactant.

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INTRODUCTIONSince O'Connell et al. 1 discovered the near-infrared photoluminescence (PL) of semiconducting tubes, significant progress has been made in the fundamental research of single-walled carbon nanotube (SWCNT) photophysics. 2À7 In parallel with the fundamental research on the photophysical behaviors of SWCNTs, various SWCNT based optical and optoelectronic applications have also been proposed and developed, 5,7 such as saturable optical absorbers, 8 single-photon emitters, 9 photodetector and sensors, 10À12 molecular optical wires, 13 and fluorescent-dye labeling in biological systems. 14,15 In the fundamental investigation and technological application of the photophysical properties of SWCNTs, one of the major concerns is the photoluminescence quantum yield (PL QY). Subject to the sample preparation protocols and methods used for QY evaluation, the PL QY of SWCNTs reported in the literature varies significantly from ∼0.01% in refs 16À18 to ∼0.1À1% in refs 19À21 to ∼1À3% in refs 22 and 23 to 7À20% in refs 24À26 to greater than 30% in ref 27. Exciton, an excited state formed by the Coulomb binding of an excited electron to a hole, has been identified to play a critical role to dominate the optical behaviors of SWCNTs. 2,6,28,29 On the basis of the excitonic picture, theoretical and experimental research efforts have been made in studying the intrinsic 24,30À33 and extrinsic 20,34À36 factors that are critical to understand the PL QY of SWCNTs. The radiative lifetime of the exciton in semiconducting SWCNTs has been theoretically estimated in the range of 1À10 ns. 30,31 Multiphonon decay (MPD) and phonon-assisted indirect exciton ionization (PAIEI) were proposed as the efficient pathways for the nonradiative decay of the excited tubes to explain the low QYs of SWCNTs. 32 At high excitation fluence, the excitonÀ exciton Auger recombination has been identified as the key mechanism in limiting the QYs of SWCNTs. 24,33 Rajan et al. 34 proposed a simple and attractive 1D exciton diffusion model to understand the SWCNT length dependent QYs. They considered the tube ends as quenching sites to solve the 1D exciton diffusion problems and derived an infinite series solution for the QYs of defect-free SWCNT with finite length. The diffusional motion of exciton in SWCNTs was confirmed by the PL stepwise quenching experiments recently reported by Cognet et al. 35 Taking into account both the tube ends and sidewall defects as the quenching sites, Hertel et al. 20 recently reported an analytical solution for the QY of defective SWCNTsIn eq 1, l is the tube length, D is the exciton diffusion coefficient, τ r is the radiative lifetime of the exciton, and d qH is the average quenching site distance in the absence of end quenching. For later discussion, we redefine the average quenching site distance d q equal to 1/(1/d qH + 1/l). Unlike d qH , d q is calculated without differentiating the quenching sites sitting in the interior of the tube from the one on the ends. Upon applying eq 1 to the lengthdependent QYs and exciton ...

Numerical simulations are performed to study the diffusion behaviors of rigid rods examined by dynamic light scattering (DLS). It was identified that the apparent diffusion coefficient, Dp, determined by DLS obeys a universal relationship Dp/DG = f(qL) = 1.1804 + 0.1764 × tanh [11.799× tan−1(qL) ‐17.169], where DG, L, and q are the mass‐of‐center diffusion coefficient, length of the rod, and scattering vector, respectively. This relationship delineates the DLS experiments into weak (qL < 4.0), intermediate (4.0 < qL < 20.0), and strong translation–rotation coupling regime (qL > 20.0). In weak (strong) coupling regime, Dp is a measure of DG (D// ‐ longitudinal diffusion coefficient) of the rods. In addition, if DLS is performed in the intermediate coupling regime, the rod length can be determined by solving Dp/DG = f(qL).