Raman characteristic peaks induced by the topological defects of carbon nanotube intramolecular junctions

The vibrational modes of some single-wall carbon nanotube (SWNT) intramolecular junctions (IMJs) have been calculated using the latest Brenner reactive empirical bond order (REBO) potential, based on which their nonresonant Raman spectra have been further calculated using the empirical bond polarizability model. It is found that the Raman peaks induced by pentagon defects lie out of the $G$-band of the SWNTs; thus, the high-frequency part of the Raman spectra of the SWNT IMJs can be used to experimentally determine their detailed geometrical structures. Also, the intensity of the Raman spectra has a close relation with the number of pentagon defects in the SWNT IMJs. Following the Descartes-Euler polyhedral formula, the number of heptagon defects in the SWNT IMJs can also be determined. The first-principles calculations are also performed, verifying the results obtained by the REBO potential. The $G$ band width of the SWNT IMJ can reflect the length of its transition region between the pentagon and heptagon rings.

Figure 1

(Color online) The phonon dispersion relationship and vibrational density of states of armchair (10, 10) and zigzag (17, 0) SWNTs, calculated by REBO potential. Left part is for (10, 10) tube, and right one is for (17, 0) tube.

Figure 2

(Color online) (10, 10)-(17, 0) SWNT IMJ. The optimized structure is shown in the left panel and the periodic structure is shown in right panel. Only one pair of pentagon-heptagon rings is used to connect the different tubes.

Figure 3

(Color online) The nonresonant Raman spectrum of the (10, 10)-(17, 0) SWNT IMJ: (a) Low-frequency part and (b) high-frequency part. (c) and (d) show the low- and high-frequency parts of the Raman spectra of (10, 10) and (17, 0) tubes, respectively. In (a), $\left(i\right)$ and $\left(c\right)$ indicate that the modes come from the in-phase and counterphase combinations of the original Raman modes in the perfect SWNTs, respectively.

Figure 4

(Color online) The atomic vibrations of the Raman active modes at frequencies of 25.2 and $34.3{\mathrm{cm}}^{-1}$, which come from the combinations of the basic Raman active modes of the (10, 10) and (17, 0) SWNTs.

Figure 5

(Color online) The atomic vibrations of the Raman active modes at frequencies of 65.5, 85.7, and $108.4{\mathrm{cm}}^{-1}$, which come from the atomic vibrations of the junction part.

Figure 6

(Color online) The atomic vibrations of the Raman active modes beyond $1800{\mathrm{cm}}^{-1}$ for the (10, 10)-(17, 0) SWNT IMJ.

Figure 7

(Color online) The atomic vibrations of the localized states on the heptagon defect of the (10, 10)-(17, 0) SWNT IMJ. Here only the strongest two states are shown.

Figure 8

(Color online) Some localized states caused by pentagon defects on a graphene.

Figure 9

(Color online) Some localized states caused by heptagon defects on a graphene.

Figure 10

(Color online) Some states localized on the whole SW defects of a graphene.

Figure 11

(Color online) Two different structures of the (5, 5)-(10, 10) SWNT IMJs, viewed from different directions. (a)–(c) are the high-symmetry structures. (d)–(f) are the low-symmetry structures.

Figure 12

(Color online) The high-frequency part of the Raman spectra of the two SWNT IMJs. The upper and lower panels are for the high- and low-symmetry SWNT IMJ, respectively.