Diameter-selective resonant Raman scattering in double-wall carbon nanotubes

Double-wall carbon nanotubes (DWNT’s) have been studied by Raman scattering using different excitation wavelengths and their spectra compared to those of single wall nanotubes (SWNT’s) and ${\mathrm{C}}_{60}$-SWNT peapods. Raman scattering from the radial and tangential vibrational modes of very small diameter $d\sim 0.6–0.9\hspace{0.5em}\mathrm{nm}$ secondary (interior) semiconducting tubes within the DWNT can be unambiguously identified with 647.1 and 1064 nm excitations. The frequency of the tangential displacement vibrational modes identified with these secondary (interior) tubes is found to be downshifted by $\sim 7\hspace{0.5em}{\mathrm{cm}}^{-1}$ relative to that of the larger primary (exterior) tubes that exhibit a diameter $d\sim 1.3–1.6\hspace{0.5em}\mathrm{nm}.$ This downshift strongly suggests that at small tube diameters (i.e., $d\sim 0.7\hspace{0.5em}\mathrm{nm}),$ the associated wall curvature of the nanotube may require an admixture of ${\mathrm{sp}}^3$ character in the C-C interaction. Our results also show that the value ${\gamma }_0=2.90\mathrm{}\hspace{0.5em}\mathrm{eV}$ for the nearest C-C tight binding integral is consistent with the resonant enhanced Raman scattering from DWNT’s.