Effect of van der Waals interactions on the Raman modes in single walled carbon nanotubes

We have measured the Raman spectrum of individual single walled carbon nano tubes in solution and compare it to that obtained from the same starting ma terial where the tubes are present in ordered bundles or ropes. Interesting ly, the radial mode frequencies for the tubes in solution are found to be s imilar to 10 cm(-1) higher than those observed for tubes in a rope, in appa rent contradiction to lattice dynamics predictions. We suggest that there i s no such contradiction, and propose that the upshift is due rather to a de creased energy spacing of the Van Hove singularities in isolated tubes over the spacings in a rope, thereby allowing the same laser excitation to exci te different diameter tubes in these two samples.