Detailed analysis of the mean diameter and diameter distribution of single-wall carbon nanotubes from their optical response

We report a detailed analysis of the optical properties of single-wall carbon nanotubes (SWCNT's) with different mean diameters as produced by laser ablation. From a combined study of optical absorption, high-resolution electron energy-loss spectroscopy in transmission, and tight-binding calculations we were able to accurately determine the mean diameter and diameter distribution in bulk SWCNT samples. In general, the absorption response can be well described assuming a Gaussian distribution of nanotube diameters and the predicted inverse proportionality between the nanotube diameter and the energy of the absorption features. A detailed simulation enabled not only a determination of the mean diameter of the nanotubes, but also gives insight into the chirality distribution of the nanotubes. The best agreement between the simulation and experiment is observed when only nanotubes within 15degrees of the armchair axis are considered. The mean diameters and diameter distributions from the optical simulations are in very good agreement with the values derived from other bulk sensitive methods such as electron diffraction, x-ray diffraction, and Raman scattering.