We perform transmission electron microscopy, electron diffraction, and Raman scattering experiments on an individual suspended double-walled carbon nanotube (DWCNT). The first two techniques allow the unambiguous determination of the DWCNT structure: (12,8)@(16,14). However, the low-frequency features in the Raman spectra cannot be connected to the derived layer diameters d by means of the 1/d power law, widely used for the diameter dependence of the radial-breathing mode of single-walled nanotubes. We discuss this disagreement in terms of mechanical coupling between the layers of the DWCNT, which results in collective vibrational modes. Theoretical predictions for the breathing-like modes of the DWCNT, originating from the radial-breathing modes of the layers, are in a very good agreement with the observed Raman spectra. Moreover, the mechanical coupling qualitatively explains the observation of Raman lines of breathing-like modes, whenever only one of the layers is in resonance with the laser energy.

A double-walled carbon nanotube (DWNT), a coaxial composite of two singlewalled carbon nanotubes (SWNT), provide a unique model to study interactions be- microscopy (HRTEM), electron diffraction (ED) and resonant Raman scattering (RRS)experiments on the same individual suspended DWNT is the ultimate way to relate unambiguously its atomic structure, defined by the chiral indices of the coaxial outer/inner SWNTs, and its Raman-active vibration modes. This approach is used to investigate the inter-tube distance dependence of the G-modes of individual index-identified DWNTs composed of two semiconducting SWNTs. We state the main features of the dependence of the G-mode frequencies on the distance between the inner and outer layers: (i) when the inter-layer distance is larger than the nominal van der Waals distance (close to 0.34 nm), a downshift of the inner-layer G-modes in respect to the G-modes in the equivalent SWNTs is measured.(ii) the amplitude of the downshift depends on the inter-layer distance, or in other words, on the negative pressure felt by the inner layer in DWNT. (iii) no shift is observed for an inter tube distance close to 0.34 nm.