The molar extinction coefficient of single-wall carbon nanotubes (SWNTs) is determined using fluorescence tagging, as well as atomic force microscopy (AFM) imaging, which facilitate the correlation of nanotube concentrations with absorption spectra. Tagging of SWNTs is achieved using fluorescence-labeled single-strand DNA oligomers as the dispersion additive, while AFM imaging is used to determine the mass of SWNTs in the retentate of vacuum-filtered colloidal SWNT suspensions. The resulting absorption cross section for the first exciton transition of (6,5) nanotubes of 1.7 × 10–17 cm2 per C-atom corresponds to an extinction coefficient of (4400 ± 1000) M–1·cm–1, which is equivalent to an oscillator strength of 0.010 per carbon atom.

We have studied ultrafast spectral diffusion (SD) within exciton bands of semiconducting single-wall carbon nanotubes (s-SWNTs) using one-and two-dimensional, near-infrared transient hole burning spectroscopy and time-resolved fluorescence spectroscopy at temperatures between 15 K and 293 K. We find that inhomogeneous spectral broadening of 60 meV for s-SWNTs embedded in gelatin exceeds the homogeneous linewidth of 3.3 meV by over an order of magnitude. The experiments show that ultrafast spectral diffusion of excitons in gel-immobilized s-SWNTs on the 250 fs time-scale can be attributed to axial intra-tube exciton diffusion. Comparison with kinetic Monte Carlo simulations suggests that the length-scale characteristic of the granularity of the axial potential energy landscape is about 24 nm.

Electron−hole correlation lengths, also termed exciton size, for (6,5) single-wall carbon nanotubes (SWNTs) are determined using femtosecond time-resolved pump−probe spectroscopy. The phase space filling model is used to obtain the sizes of the first subband exciton in samples of isolated and of bundled SWNTs. The experiments indicate that the exciton size of (13 ± 3) nm is a factor of 6 higher than previous experimental estimates and theoretical predictions for vacuum suspended SWNTs. This surprising result may be attributed at least in part to the effect of the dielectric environment on exciton sizes and supports recent theoretical findings predicting that screening in SWNTs may enhance rather than reduce electron−hole interactions for separations larger than the tube diameter. Thereby, the work also points to the unique nature of screening and electronic correlations in one-dimensional semiconductors.T he electron−hole correlation length of excitons, sometimes also termed exciton size, is key for a better understanding of the photophysical properties of semiconductors in general and of energy transport processes in particular. In nanoscale semiconducting single-wall carbon nanotubes (s-SWNTs) the exciton size also determines the very nature of exciton transport, potentially being one-or twodimensional, depending on the exciton being smaller or larger than the nanotube diameter. Other exciton properties such as binding energy and effective mass are also profoundly affected by dimensionality because of its delicate interplay with screening and electronic correlations. 1−9 A robust experimental assessment of exciton size is thus key for improving our understanding of energy transport and screening in lowdimensional semiconductor materials.Here we present a new assessment of the size of excitons in semiconducting (6,5) SWNTs by using femtosecond timeresolved pump−probe spectroscopy. The results are contrasted with prior results from a similar study but which obtained considerably smaller exciton sizes. This discrepancy is in part attributed to recent improvements in sample preparation protocols and experimental characterization of isolated as well as aggregated s-SWNT samples. Details on sample preparation and in particular on a newly developed process for fabrication of thin gelatin matrix films with individualized and aggregated SWNTs can be found in the Supporting Information. The Supporting Information also details how these films were prepared to prevent the formation of larger SWNT floc in aggregated samples and how to further minimize excessive light scattering from such samples. The work presented here reveals that the current best estimate of electron−hole correlation lengths in (6,5) SWNTs of (13 ± 3) nm is a factor of 6 higher than previously believed. 6,10−13 This surprising finding has impact on several critical aspects of exciton photophysics in SWNTs, from energy transport over exciton stability to the determination of impurity concentrations in SWNTs.According to 14 the change of the linear optical...