DIAMETER-SELECTIVE RAMAN-SCATTERING FROM VIBRATIONAL-MODES IN CARBON NANOTUBES

Single wall carbon nanotubes (SWNTs) that are found as close-packed ar rays in crystalline ropes have been studied by using Raman scattering techniques with laser excitation wavelengths in the range from 514.5 t o 1320 nanometers. Numerous Raman peaks were observed and identified w ith vibrational modes of armchair symmetry (n, n) SWNTs. The Raman spe ctra are in good agreement with lattice dynamics calculations based on C-C force constants used to fit the two-dimensional, experimental pho non dispersion of a single graphene sheet. Calculated intensities from a nonresonant, bond polarizability model optimized for sp(2) carbon a re also in qualitative agreement with the Raman data, although a reson ant Raman scattering process is also taking place. This resonance resu lts from the one-dimensional quantum confinement of the electrons in t he nanotube.