The Raman shifts as functions of pressure were measured for the radial breathing mode and tangential modes in carbon nanoropes containing ͑10,10͒ and ͑17,0͒ single-walled tubes. An abrupt decrease in the rate of change of the Raman shift with pressure for the tangential modes, and the disappearance of the radial breathing mode, were observed at approximately 1.7 GPa. These changes in the Raman spectrum result from a structural phase transition as the nanoropes are compressed. Theoretical calculations using the empirical force method confirm this transition, as indicated by a calculated discontinuity in the lattice constants and unit cell volume at 1.7 GPa.

The vibrational modes of carbon nanotubes and nanoropes are studied. The Raman and infrared active modes are determined for armchair, zigzag, and chiral nanotubes. High-energy Raman and infrared modes exhibit distinct characteristic patterns for armchair, zigzag, and chiral tubes. In the nanorope the intertube interactions shifts the energy of certain vibrational modes dramatically. This has implications when using the vibrational spectra to identify tubes. In the nanorope we find Raman modes exhibit shifts under a change in pressure which differ from the corresponding shifts found in graphite. ͓S0163-1829͑99͒06133-0͔ PHYSICAL REVIEW B

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The effect of van der Waals interaction modeling on the vibration characteristics of multiwalled carbon nanotubesThe properties of nanoscale spheres and tubes are of recent interest due to the discovery of the fullerene molecule and the carbon nanotube. These carbon structures can be modeled as nanoscale spherical or cylindrical shells. In this article, these nanostructures are treated in the thin shell approximation with the elastic properties taken to be those of the graphene sheet. A quantization prescription is applied to the classical elastic modes to facilitate the first calculations of the quantum-mechanical normalizations of selected modes. These modes are shown to be amenable to the study of electron-phonon interactions. Indeed, electron-phonon interaction Hamiltonians are derived. Moreover, it is shown for such a tube of finite length that the electron-phonon interaction strength depends on the axial position. As a special case it is shown that the dispersion relation for the clamped tube depends on the length of the tube. In this article we consider both the vibrational frequencies and the mode quantization for both spherical shell and the nanotube using realistic material parameters.

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