Raman modes of index-identified freestanding single-walled carbon nanotubes.

Using electron diffraction on freestanding single-walled carbon nanotubes, we have determined the structural indices (n,m) of tubes in the diameter range from 1.4 to 3 nm. On the same freestanding tubes, we have recorded Raman spectra of the tangential modes and the radial breathing mode. For the smaller diameters (1.4-1.7 nm), these measurements confirm previously established radial breathing mode frequency versus diameter relations and would be consistent with the theoretically predicted proportionality to the inverse diameter. However, for extending the relation to larger diameters, either a yet unexplained environmental constant has to be assumed, or the linear relation has to be abandoned.