Diameter-Selective Raman Scattering from Vibrational Modes in Carbon Nanotubes

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