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 nanotubes in solution and compare it to that obtained from the same starting material where the tubes are present in ordered bundles or ropes. Interestingly, the radial mode frequencies for the tubes in solution are found to be approximately 10 cm (-1) higher than those observed for tubes in a rope, in apparent contradiction to lattice dynamics predictions. We suggest that there is no such contradiction, and propose that the upshift is due rather to a decreased energy spacing of the Van Hove singularities in isolated tubes over the spacings in a rope, thereby allowing the same laser excitation to excite different diameter tubes in these two samples.