Interlayer interactions and radial breathing mode in double- and triple-walled carbon nanotube bundles

A double-walled carbon nanotube (DWNT) can be considered a inner single-walled carbon nanotube (SWNT) protected by an outer SWNT. Likewise, a triple-walled carbon nanotube (TWNT) can considered an inner DWNT encapsulated by an outer SWNT. The signature in resonant Raman spectroscopy for carbon nanotubes is the radial breathing mode (RBM). For radial breathing modes (RBM), double- and triple-walled carbon nanotubes can be considered as coupled oscillators. The RBM frequency, ω_RBM, is senstive to environmental factors and interlayer interactions. For interlayer interactions, it is necessary to take into account curvature effects, particularly for smaller tubes, whether the constituent tubes are commensurate, and whether the inner tubes are really isolated from the environment from the outer tubes. Another matter of interest is how do the magnitudes of the interlayer interactions compare. Resonant Raman spectra of a DWNT bundle and TWNT bundle were taken. From those spectra, chiral indices were assigned and tube diameters calculated. Then, a comparison to the SWNT ω_RBM was made and the questions presented above answered.