$G^{\prime }$ band in double- and triple-walled carbon nanotubes: A Raman study

Double- and triple-walled carbon nanotubes are studied in detail by laser energy-dependent Raman spectroscopy in order to get a deeper understanding about the second-order ${\mathrm{G}}^{\prime }$ band Raman process, general nanotube properties, such as electronic and vibrational properties, and the growth method itself. In this work, the inner nanotubes from the double- and triple-walled carbon nanotubes are produced through the encapsulation of fullerene peapods with high-temperature thermal treatments. We find that the spectral features of the ${\mathrm{G}}^{\prime }$ band, such as the intensity, frequency, linewidth, and line shape are highly sensitive to the annealing temperature variations. We also discuss the triple-peak structure of the ${\mathrm{G}}^{\prime }$ band observed in an individual triple-walled carbon nanotube taken at several laser energies connecting its Raman spectra with that for the ${\mathrm{G}}^{\prime }$ band spectra obtained for bundled triple-walled carbon nanotubes.

Figure 1

The Raman spectra represent RBM (low-frequency range) and ${\mathrm{G}}^{\prime }$ band (high-frequency range) features of the host SWNTs (bottom spectrum) together with the corresponding spectra for the bundled DWNTs (other spectra), where the nanotubes are annealed at various temperatures between 1500 and $2000 {}^{\circ }\mathrm{C}$ taken with $E_{\mathrm{laser}}$ lines of (a) 1.96 and (b) 2.41 eV. The identification of peaks with specific spectral features are the host nanotubes which have ${\omega }_{\mathrm{RBM}}$ below $225 {\mathrm{cm}}^{-1}$ and for the inner nanotubes ${\omega }_{\mathrm{RBM}}$, which are between 225 and $400 {\mathrm{cm}}^{-1}$. The RBM regions of resonant $(2n\hspace{0.17em}+\hspace{0.17em}m)$ families are indicated by green (host nanotubes) and red (inner nanotubes) color identifications. The ${\mathrm{G}}^{\prime }$ band features occur above $2550 {\mathrm{cm}}^{-1}$ for the inner and host nanotubes.

Figure 2

The peak frequencies of the ${\mathrm{G}}^{\prime }$ band for the inner and the host nanotubes [(a) and (b)], and the peak intensity ratios [(c) and (d)] of the ${\mathrm{G}}^{\prime }$ bands for both the inner and host nanotubes are plotted as a function of annealing temperature. The host nanotubes in this figure are the outer nanotubes of the DWNT bundles. The error bars represent the FWHM of the peaks for the Raman spectra taken at 1.96 eV (a) and at 2.41 eV (b). The ${\mathrm{G}}^{\prime }$ band at the lower frequency belongs to the inner nanotubes (${\mathrm{G}}_{\mathrm{inner}}^{\prime }$ and as indicated in the schematic cross sectional view), and by increasing the annealing temperature this peak shifts towards higher frequencies, and hence to larger inner nanotube diameters. This tendency is also reflected through the RBM spectra shown in Fig. 1.

Figure 3

The $E_{\mathrm{laser}}$ vs ${\omega }_{{\mathrm{G}}^{\prime }}$ relations of the inner (lower four relations) and the outer (upper four relations) nanotube from bundled DWNTs are presented. The blue and black lines are, respectively, the fitted linear relations for fullerene-peapod derived DWNTs [22] and for CVD DWNTs [37]. The red lines are adapted from the Raman results for the bundled DWNTs produced with 1500 and $2000 {}^{\circ }\mathrm{C}$, and depicted in Fig. 1. Differences in the growth methods are directly reflected in a change of the ${\mathrm{G}}^{\prime }$ band dispersions.

Figure 4

The low Raman frequency range in (a) shows the resonant RBMs for the two inner nanotubes of an individual TWNT lying on a silicon ${\mathrm{Si}/\mathrm{SiO}}_2$ substrate (the Raman peak at $303 {\mathrm{cm}}^{-1}$ is from the ${\mathrm{Si}/\mathrm{SiO}}_2$ substrate). (b) depicts the ${\mathrm{G}}^{\prime }$ band spectra taken with five different laser lines in the high Raman frequency range of the individual TWNT shown in (a). Each Raman spectrum between $E_{\mathrm{laser}}$ values of 2.11 and 2.41 eV shows three well resolved ${\mathrm{G}}^{\prime }$ lines coming from the three concentric nanotubes. The inset in (b) depicts the ${\mathrm{G}}^{\prime }$ line separations ${\Delta }_{\mathrm{ih}}$ (open circles) and ${\Delta }_{\mathrm{ho}}$ (closed circles), where i, h, and o refer to the inner, host, and outer nanotube. The Raman intensity of each ${\mathrm{G}}^{\prime }$ line change, and all ${\mathrm{G}}^{\prime }$ lines shift towards higher frequencies, as well as tend to increase the ${\mathrm{G}}^{\prime }$ peak widths by increasing $E_{\mathrm{laser}}$, as indicated in the inset.

Figure 5

The colored triangles and the error bars represent the positions and FWHM of the ${\mathrm{G}}^{\prime }$ lines for the inner (red color), host (green color), and outer nanotube (blue color) of an individual TWNT. The solid lines represent the ${\mathrm{G}}^{\prime }$ peak dispersions for each concentric nanotube. We also included the experimental ${\mathrm{G}}^{\prime }$ band results from two individual CVD DWNTs at 2.33 eV (see circle and square symbols) [37]. The right panel depicts the relation A (Table 1) between ${\omega }_{{\mathrm{G}}^{\prime }}$ and $d_{\mathrm{t}}$ based on a Raman study on individual SWNTs measured at 2.41 eV [19].

Figure 6

The spectra show the ${\mathrm{G}}^{\prime }$ band of bundled TWNTs taken at $E_{\mathrm{laser}}$ between 2.10 and 2.54 eV from which we can extract important information about the lineshape differences as well as the laser energy dependencies. The ${\mathrm{G}}^{\prime }$ band spectrum together with the RBM intensities taken at 2.41 eV are shown in detail in Fig. 7.

Figure 7

The Raman spectra with the fitted Lorentzian lines show the ${\mathrm{G}}^{\prime }$ band results from bundled TWNTs and bundled DWNTs taken at 2.41 eV, where the inner nanotubes were fabricated by different annealing temperatures. The filled spectra indicate that the RBM intensities converted to the ${\omega }_{{\mathrm{G}}^{\prime }}$ values using three different ${\omega }_{\mathrm{RBM}}$ vs ${\omega }_{{\mathrm{G}}^{\prime }}$ relations [19, 20] for the inner, host, and outer nanotubes (in the case of the DWNTs: host nanotubes with large diameters). The details about the relations A, B, and C are given in Table 1. These relations are separated at ${\omega }_{\mathrm{RBM}}$ values of 144 and $258 {\mathrm{cm}}^{-1}$, which represent nanotube diameters that are larger (smaller) than 1.7 nm (0.9 nm), according to the relation [32] ${\omega }_{\mathrm{RBM}}=218.3/d_{\mathrm{t}}+15.9$. The three triangles represent the ${\mathrm{G}}^{\prime }$ band frequencies from the individual TWNT shown in Fig. 4.