Influence of packing on the vibrational properties of infinite and finite bundles of carbon nanotubes

The quantitative analysis of the vibrational properties of carbon nanotubes is a key issue for the interpretation of Raman experiments. In particular, a reliable characterization of the atomic structure of single-wall carbon nanotubes produced under various conditions is mainly based on the interpretation of low-frequency $(100\mathrm{}–300\hspace{0.5em}{\mathrm{cm}}^{-1})$ Raman spectra. In the present work, we analyze the influence of the packing of the tubes on these low-frequency modes. We find that the low-frequency spectra of crystals of single-wall carbon nanotubes present two intense Raman modes instead of a single fully symmetric $A_{1g}$ mode characteristic of isolated tubes. The second mode has a non-negligible intensity for crystals formed with nanotubes of radii larger than $7\hspace{0.5em}\AA .$ For finite number of tubes in a bundle, two breathinglike intense modes appear as a specific signature. Finally, our simulation for inhomogenous bundles made of a large number of tubes does not reveal any specific signature of the individual tubes in the low-frequency Raman spectra.