Identification of inner and outer shells of double-wall carbon nanotubes using high-pressure Raman spectroscopy

The high-pressure Raman response of double-wall carbon nanotubes (DWCNTs) in the radial breathing mode (RBM) frequency region can be used for the identification of both the inner and their respective outer tubes. A simple anharmonic model of this system demonstrates that the pressure response of the inner tube in a DWCNT is uniquely defined by the inner-outer tube spacing. Consequently, a plot of the normalized pressure coefficients of the inner tube RBM frequencies as a function of their ambient pressure frequency serves as a map which allows the identification of unknown DWCNTs. The present experimental results form the basis of such a plot.

Figure 1

Raman spectra of DWCNTs in the RBM frequency region of the inner tubes for various excitation lines at ambient conditions. RBM peaks belonging to each of the five data distributions presented in Fig. 2 are labeled by the letters a–e, accordingly.

Figure 2

(Color online) Normalized pressure slopes, ${\Gamma }_i=(1∕{\omega }_i)(\partial {\omega }_i∕\partial P)$, of the inner tube RBMs in DWCNTs as a function of their frequency for various excitation lines (different symbols). The solid lines through the data emphasize their grouping in five distributions, labeled by the letters a–e. The star symbols correspond to data obtained from Ref. 24 with excitation at 514.5 (solid stars) and $647.1\mathrm{nm}$ (open star). All the carbon nanotubes with diameters of $0.55–0.90\mathrm{nm}$ along with their chiral indices $(n,m)$ are appropriately included in the lower part of the figure by means of the frequency-diameter relations given by Fantini et al. (Ref. 7). The vertical lines mark the tubes which are in resonance with the red (solid lines) or the green excitation (dotted lines).

Figure 3

(Color online) Normalized pressure slopes, ${\Gamma }_i=(1∕{\omega }_i)(\partial {\omega }_i∕\partial P)$, of the RBLMs of the single ring (solid symbols) and the inner rings comprising the double-ring model system (open symbols). The thick solid lines group data originating from the same inner ring of diameter $d_{\mathrm{in}}$ combined with outer rings of different diameters $d_{\mathrm{out}}$, while the dotted lines delineate ${\Gamma }_i$ values for inner-outer pairs of constant $\Delta d=d_{\mathrm{out}}-d_{\mathrm{in}}$. All lengths are expressed in nanometers. Inset: RBLM and GLM of a single ring.