Raman-modes of index-identified free-standing single-walled carbon nanotubes

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Abstract
Using electron diffraction on free-standing single-walled carbon nanotubes we have determined the structural indices (n,m) of tubes in the diameter range from 1.4 to 3nm. On the same free-standing tubes we have recorded Raman spectra of the tangential modes and the radial breathing mode. For the smaller diameters (1.4-1.7nm) 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.