Redshift and optical anisotropy of collective π -volume modes in multiwalled carbon nanotubes

A combined study concerning localized electron energy-loss spectroscopy (EELS) and modeling of collective π -volume modes in multiwalled carbon nanotubes (MWCNT) is presented. The changing line width and eigenfrequency of the π -volume mode can be ascribed solely to optical anisotropy and "cylindrical anisotropy." Optical anisotropy results from the weighting of various nearly degenerate and nondegenerate states allowed for the E c and E c polarizations. Cylindrical anisotropy arises from a lowering of the symmetry arising from the nanotube geometry. The eigenfrequency of the π -volume mode corresponds to polarization eigenmodes of graphite, and not to new maxima in the joint density of states, since momentum transfer Δ qπ →0. Results are also included from multiwalled hexagonal-boron nitride nanotubes (MWBNNT). An accurate description of the π -volume mode in multiwalled nanotubes has not been attempted so far, and is essential to resolve coupled MWCNT π -surface features, which are usually obscured in spectra obtained in penetrating-beam geometry. Volume mode-extracted EEL spectra demonstrate eigenfrequency modification of coupled π -surface features in the presence of a MWCNT dielectric filling. It was found, owing to dielectric screening effects and smearing of the dipole mode, that aloof-beam EELS which is conventionally applied to surface plasmon investigations, cannot give this information.