Nature of the constant factor in the relation between radial breathing mode frequency and tube diameter for single-wall carbon nanotubes

Resonance Raman scattering is used to determine the radial breathing mode (RBM) frequency (omega(RBM)) dependence on tube diameter (d(t)) for single-wall carbon nanotubes (SWNTs). We establish experimentally the omega(RBM)=227.0/d(t) as the fundamental relation for pristine SWNTs. All the other RBM values found in the literature can be explained by an upshift in frequency due mostly to van der Waals interaction between SWNTs and environment.