Characteristic Vibrational Modes and Electronic Structures of Carbon

ARTICLE pubs.acs.org/JPCC

Characteristic Vibrational Modes and Electronic Structures of Carbon Nanotubes Containing Defects Minsi Xin,† Fengting Wang,† Yan Meng,† Chuanjin Tian,† Mingxing Jin,† Zhigang Wang,*,† and Ruiqin Zhang* ,†,‡ † ‡

Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China Department of Physics and Materials Science and Centre for Functional Photonics, City University of Hong Kong, Hong Kong SAR, China ABSTRACT: We investigated the geometric structures, vibrational modes, and electronic structures of models of capped (5, 5) carbon nanotubes (CNTs) with four types of defects, namely, V1, V2, V3, and V4, using density functional theory. We found that the defects cause red shifts of the highest peak in infrared (IR) spectra and the highest peak, radial mode, and breathing mode in Raman spectra. There are two IR-active modes localized at V3 and V4 defects. In contrast, the influence of the defects on the electronic structures is considerably case-dependent, with the case of V2 being very special, involving spin polarization and showing a localized feature. The defects cause energy gap change as large as 0.1 eV. By analyzing the density of states of the capped (5, 5) CNT and its four defective structures, we found that at around 7 eV there is a characteristic peak belonging to the pure CNT that could be useful for defect detections. Our results are helpful for understanding the defect effects on the properties of general single-walled CNTs.

’ INTRODUCTION As typical one-dimensional nanomaterials, carbon nanotubes (CNTs) possess many promising mechanical, electrical, and optical properties, showing potentials of wide applications in physics, chemistry, biology, and medical science.1 4 Because of the growth environment variance, joining of foreign particles, and other factors, CNTs in practice usually contain various defects.5 7 Therefore, it appears to be very important to study the influence of defects on the CNT properties. Since the discovery of defects, there has been much research conducted on related topics.8 18 Chico et al.19 found in 1996 that a defect composed of pentagon and eptagon rings could change the chirality and the electronic structures of the single wa-lled CNT. Their result, using a tight-binding method, showed that the defect performance could be viewed as a nanoscale metal/semiconductor or semiconductor/semiconductor junction. In 2004, Miyamoto et al.20 investigated the Stone Wales (SW) defect in (3, 3) CNT using resonant laser under infrared and ultraviolet conditions. They pointed out that a peak at 1962 cm 1 is the characteristic peak of the defect in CNTs. In 2007, Haskins et al.21 found in their study that the influence of defects and their locations are smaller on the Young’s modulus than on the maximum tensile strain that the CNT could withstand. Three years later, Dresselhaus et al.22 reviewed the research progress in defect-induced double resonance processes in studies of nanographite, graphene, and CNTs. Progress included research combining Raman spectroscopy and microscopy as well as theoretical modeling. Also reviewed are the ion-bombarded graphene and nanographite, which showed amorphous features due to the involvement of defects and boundaries, detectable by Raman spectroscopy for their atomic structures. For example, based on r 2011 American Chemical Society

the acoustic scattering selection rule, one can identify their zigzag and armchair edge structures. So far, the reported easily observable defects include those with topological structures composed of pentagons, heptagon, octagons, and nonagons. However, more systematic studies on them are still desirable. Issues to further address include the following. Compared with the pure CNTs, what are the characteristics of those with defects? How can one understand the differences among them? Answering these questions is significant to research on CNT structures for identifying their defect types. In this paper, we performed a systematic comparative study on a cap (5, 5) CNT using a model of (5, 5) CNT, five unit cells long, capped with two C60 half spheres at the two ends for the following cases: (1) without involving any defect; (2) with a middle surface C atom lost (called a V1 defect); (3) with a middle surface bridge site added with an additional C atom (called a V2 defect); (4) with two middle surface C atoms lost (called a V3 defect); and (5) with two middle surface C atoms shifted (called a V4 defect) .23 These structures are shown in Figure 1. Through first-principles density functional theoretical (DFT) calculations,24 we compared the differences in their structures, vibrational spectra, and electronic density of states (DOS).

’ COMPUTATIONAL DETAILS Considering that CNTs in reality are usually closed at both ends, we chose to use CNTs with both ends capped. We first constructed a CNT with the two ends capped with two half C60 Received: September 8, 2011 Revised: November 24, 2011 Published: December 02, 2011 292

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Figure 1. Models of pure cap (5, 5) CNT and the V1, V2, V3 and V4 defective CNTs.

Figure 3. Raman spectra of the five CNTs and the three classical vibrational modes of the cap (5, 5) CNT. The curves in the left-hand panel are respective the Raman vibrational spectra for the cap (5, 5), V1, V2, V3, and V4 CNTs. The right-hand panel shows the three vibrational modes, breathing, radial, and transverse, of the pure cap (5, 5) CNT.

through frequency correction with a factor of 0.983634 and their charge distributions via natural bond orbital (NBO) analysis.35 For further understanding the influence of defects on their electronic structures, we analyzed their DOS. All calculations were performed with the Gaussian 03 package.36

Figure 2. IR spectra of the five CNTs and the IR characteristic vibrational modes of V3 and V4. In the left-hand panel, the curves from bottom to top represent the IR spectra of cap (5, 5), V1, V2, V3, and V4 CNTs, respectively. The right-hand panels show the characteristic modes at 1648.66 cm 1 for V3 and at 1756.32 cm 1 for V4. They have their corresponding peaks in the left-hand panel.

spheres;25 that is, a cap (5, 5) CNT of five unit cells long. On the basis of this CNT, we further built the models of CNTs with defects, namely, V1, V2, V3, and V4.23 We adopted a spin-unrestricted local spin density functional approximation (LSDA) in density functional theory (DFT) using Slater exchange functional and VWN correlation functional.26 30 Moreover, we considered the various possible spin multiplicities including singlet and triplet. Although the LSDA method is not satisfactory in prediction of energy gap,31 it could predict similar trends as those based on the GGA-B3LYP method.24 Past practices indicate that the LSDA method can provide good results of structures and deformation of CNTs and the subsequent optical spectrum shift and other properties, consistent with experimental trends.32 Compared with the generalized gradient approximation (GGA), LSDA is less costly. Considering the large size of each model, which contains around 140 C atoms, and the required accuracy and computation efficiency, we used a double split basis set function.33 The reliability of this basis set has been proved in past research.24,32 By performing structural optimizations including singlet and triplet and vibrational spectrum analysis, we determined the stable structures of these models. We further obtained their IR and Raman spectra

’ RESULTS AND DISCUSSION By optimizing the structures and calculating their vibrational frequencies, we found that the defects could cause vibrational spectrum shifts and intensity changes of these CNTs, together with slight changes in their electronic structures. We first analyze all the singlet structures. From Figure 2, it is seen that the effect of defects on the IR spectra37 is considerably large. In the figure, the peak in the black curve at 1492.15 cm 1 is the highest for the cap (5, 5) CNT, while those at 1444.69, 1490.99, 1467.89, and 1488.58 cm 1 are the highest peaks for V1, V2, V3, and V4, respectively. These peaks correspond to the same vibrational mode. The results indicate that the presence of defects caused red shifts of the highest peak, with different shifts and intensity changes for different cases. The curves of the four defective CNTs present various characteristic peaks, among which the one at 1648.66 cm 1 for V3 and the one at 1756.32 cm 1 for V4 are remarkable. They are due to the contribution of the defects. As shown in Figure 2, the vibrational mode of the V3 defect localizes at the pentagon ring with no contribution from the octagon ring, while for the V4 case the vibrational mode totally localizes at the defect. Compared with IR spectroscopy, Raman activity is more concerned in experimental researches.26 The peaks at 193.26, 338.94, and 1525.18 cm 1 in the black curve in Figure 3 are respectively the radial, breathing, and transverse modes of the defect-free cap (5, 5) CNT. Compared with them, the radial mode of V1 involves a 15 cm 1 red shift. The symmetry of the CNT changed considerably due to the presence of the V1 defect, and its vibrational mode change is also large, losing the breathing and transverse modes. The V2 CNT is from the pure cap (5, 5) CNT plus one additional C atom at the central bridge location and thus possesses a relatively high symmetry. Its vibrational modes at 191.67, 334.52, and 1525.12 cm 1 respectively correspond to radial, breathing, and transverse modes. It can be seen 293

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Figure 4. Densities of states of the five CNT models. The curves from top to bottom in the figure are respectively the densities of states for cap (5, 5), V1, V2, V3, and V4 CNTs. The black arrows point to the HOMOs and LUMOs of these five CNTs. The dashed vertical lines indicate the Fermi levels. The shaded area shows the special peaks of the cap (5, 5) CNT, in comparison with those from the defective CNTs.

Figure 6. (a) HOMO and (b) LUMO of the cap (5, 5), V2 singlet, and V3 CNTs.

Figure 5. Characteristic orbital below the HOMO of the cap (5, 5) CNT.

that the V2 defect caused different red shifts for these three modes. The radial and breathing modes of V3 are located at 191.11 and 331.10 cm 1, and the spectra in the range from 1604.21 to 1648.66 cm 1 are the modes localized at the V3 defect. The V4 defect is the well-known SW defect, being a classical model well accepted and studied for CNTs.38 42 In our work, the V4 defect is constructed in the middle of the cap (5, 5) CNT. The peaks at 186.21 and 336.77 cm 1 in the green curve in Figure 3 correspond to the radial and breathing modes, while the one at 1756.32 cm 1 is due to vibration of the two atoms in the defect center and thus is the intrinsic mode of the defect. In addition, the highest peak in Raman spectra of the cap (5, 5) CNT is located at 1315.24 cm 1, while red shifts of 92, 62, 80, and 84 cm 1 occurred for those of the V1, V2, V3, and V4 CNTs. At around 130 cm 1, each defective CNT presents a characteristic mode, the vibration of which causes both ends of the CNT to bend toward the defect. Summarizing above, we found that the influence of different defects on the highest peak in IR spectra is the same; that is, all caused red shifts. For the highest peak in the Raman spectra, the influence of the defects on the radial, breathing, and transverse modes are also the same. Then, will their influences on the energy gaps still be the same? To answer this question, in the following we will make a simple analysis of the influence of various defects on the highest occupied molecular orbital (HOMO) lowest unoccupied molecular orbital (LUMO) gaps. HOMO LUMO gaps are important data and can indicate the conductivity of the materials.43,44 In 2008, Zheng and Duley24

Figure 7. Charge distribution diagrams of the five CNTs.

compared the densities of states of zigzag carbon nanodots with different saturated ends by B3LYP calculations and concluded that the end structure can significantly alter the HOMO LUMO gaps. Considering that the calculated energy gaps of the defective CNTs are different for different theories, we focus here mainly on the influence of the various defects on the CNTs studied by the same theory. The curves in Figure 4 with various colors show the densities of states of the five CNTs. The vertical dashed lines denote their Fermi levels, and black arrows point to the HOMOs and LUMOs. We can see that the intensities of individual peaks in the DOS spectra of the five defective CNTs vary from case to case but all follow the same trend. The energy gap of the cap (5, 5) CNT is about 0.38 eV. Those of the V1 and V2 singlet states are respectively 0.12 and 0.13 eV smaller, as indicated with the blue curves in the figure, implying conductivity enhancements. The energy gaps of V3 and V4 are increased by 0.07 and 0.11 eV compared with that of the cap (5, 5) CNT, as shown with the yellow and green curves in the figure, indicating conductivity reductions. We also found an interesting feature here that at 7 eV there appears clearly a double peak feature of cap (5, 5) CNT, different from those of the four defective CNTs. In particular, the peak on the left is unique for the cap (5, 5) CNT. 294

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These peaks are highlighted in the shaded area. We found that the left peak of the cap (5, 5) CNT is from the contribution of an inner orbital below HOMO that displays a perfect symmetric delocalized orbital as seen in Figure 5. From the figure, we can see that it is due to the π bond formed along the tube axis and shows a perfect symmetric delocalized structure. It is possible that this feature could be destroyed due to the presence of any defects and thus there could be no such special peak appearing in the other four models containing defects. The results shown in Figure 4 for the four defective CNTs indeed lack this feature. To check if the finding is a general feature for pure CNTs, we additionally

investigated two capped (5, 5) CNTs of four and seven unit cells long. Still, we found that there is a π bonding feature in each case, similar to what is shown in Figure 5, being an inner orbital below HOMO formed along the tube axis and showing a perfect symmetric delocalized structure. However, because the number of atoms in the systems was changed, this orbital shifted from that of cap (5, 5) CNT five units long. Further work is on going to verify if this peak is also characteristic for all other defect-free pure CNTs so as to provide an important characteristic feature for defect detection in CNTs. Figure 6 shows the singlet state’s HOMO and LUMO of the cap (5, 5), V2, and V3 CNTs. The HOMO and LUMO of the defect-free cap (5, 5) CNT are delocalized and distributed uniformly on the tube surface.25 Those of V1 and V4 also show delocalization features similar to the cap (5, 5) CNT (not shown here), whereas the HOMO and LUMO of V3 shows clearly a localization feature, similar to those of edge hydrogen-terminated graphene nanodots.24 However, when a C atom is introduced to form the V2 defect, the orbital distribution of the CNT is totally different. The HOMO of the V2 singlet state still shows a clear delocalization feature but the LUMO mainly localizes at the defect. Figure 6 shows that the LUMO of the V2 singlet state is mainly from the contribution of the added C atom. From the result of structure optimization, the angle formed by the added atom with the two C atoms in the CNT is about 96.8
. The angle is close to the case of sp2 hybridization but involves the formation of two bonds only. The left antibonding orbital is of a higher energy and contributes to the LUMO, resulting in the obvious localization feature of the V2 singlet state. Figure 7 shows the charge (the vertical axis) averaged among the charges of C atoms within 2 Å distance around a location shown in the horizontal axis. It is clearly seen that the charge distribution of the pure cap (5, 5) CNT has good symmetry, while those of the others are obviously not symmetric due to the deformation caused by the presence of defects. Therefore, the

Table 1. Extent of Structural Deformations of CNTs with the Five Defectsa geometry

cap (5, 5)

V1

length (Å)

0

0.05

D (Å)

0

0.15

D^(Å)

0

0.27

V2

V3

0.01

0.29

1.47 0.50

0.39 0.41

V4 0.12 0.10 0.52

a

Length is used to indicate the distance between the pentagon rings at the two tube end-caps. D is the distance from defect to the facing CNT wall at the middle of the CNT, and D^ is the diameter of the CNT in the direction perpendicular to D. The parameters of cap (5, 5) CNT were set as reference for describing the deformation extent of the other defective CNTs.

Figure 8. (a) HOMO and (b) spin density of the V2 triplet electronic state.

Figure 9. Diagrams of IR and Raman spectra and charge distribution of the defective CNTs at the V2 singlet and triplet electronic states, as well as densities of states of the V2 triplet electronic state. 295

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The Journal of Physical Chemistry C various defects influenced the charge distribution considerably. Due to the presence of the two C60 half spheres as caps at the ends of the CNT, the charge distribution in the middle of the CNT is different from that at the ends, because the curvatures and bond angles at the spheres and the tube are obviously different, though the whole system has sp2 hybridization. Furthermore, inclusion of the various defects causes the change in bonding and thus the further charge redistribution. The overall effect makes the charge distribution fluctuate obviously, as shown in Figure 7. The presence of defects could result in deformations in the CNTs. Table 1 presents the extents of deformation in the CNT due to the four defects. The length is used to indicate the distances between the pentagon rings at the two tube end-caps. D is the distance from the defect to the facing CNT wall at the middle of the CNT, and D^ is the diameter of the CNT in the direction perpendicular to D. It is seen that the effects of these defects are different, with that of V2 being the most significant, due to insertion of a C atom and thus considerable effects on D and D^. Considering the presence of unsaturated carbon atoms at the defect, we further investigated the possible electron polarization at them by studying their triplet states, by use of V1 and V2 as representatives. The results show that the singlet and triplet states of V1 and V2 are very close in geometry. The singlet state of V1 is 2.9 kcal/mol lower than the triplet without showing any spin inversion effect. In contrast, the triplet state of V2 is 2.6 kcal/ mol lower than its singlet state, showing that the triplet state is the ground state. From Figure 8, the HOMO of the triplet state of V2 is very close to the LUMO of its singlet, showing that the V2 triplet-state orbital mainly originates from the defect region. Figure 8b shows an obvious spin polarization feature. From Figure 9, it is seen that there is negligible frequency shift in the vibrational spectrum from singlet to triplet state. There are only minor changes in the spectrum intensity, as shown in the range from 1000 to 1500 cm 1. We further analyzed the charge population and found that the charge distributions of the singlet and triplet states are very similar. Moreover, the DOS at the range far from the valence band shows structure very close to the spin singlet state. Due to the electron occupation change, the electronic structure in the valence band shows an obvious difference from the spin singlet state. The energy gap of the spin triplet state was calculated by subtracting the HOMO and LUMO energies of the whole system. The energy gap of the V2 spin singlet mentioned earlier is 0.13 eV smaller than that of the cap (5, 5) CNT, and the energy gap of the V2 spin triplet about 0.11 eV smaller than that of the cap (5, 5) CNT and showing a minor change. Thus, the effect of the defect on the overall feature of the energy gap remains unchanged. Through the above study, we found that the various defects possess unique characteristics in their properties. Accordingly, one can fabricate and identify defective CNTs with such properties.

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defect also results in the energy gap change of the cap (5, 5) CNT. However, different defects cause very different influences on the energy gaps. V1 and V2 reduce the gaps and thus enhance the conductivity, while V3 and V4 increase the gap and reduce the conductivity. Most importantly, there is a characteristic peak appearing in the DOS curve belong to the pure CNT, providing an important feature for identifying the presence of defects in CNTs. The presence of defect can also change the orbital distribution, with the V2 triplet state’s HOMO showing a clear localization feature. In addition, the presence of defects causes a certain influence on the charge distribution of the CNTs. Our work would be helpful for understanding the effect of defects in general single-walled CNTs.

’ AUTHOR INFORMATION Corresponding Author

*E-mail [email protected] (Z.W.), [email protected] (R.Z.).

’ ACKNOWLEDGMENT The work described in this paper is supported by grants from the National Science Foundation of China (11004076, 11034003) and Centre for Functional Photonics (CFP) of City University of Hong Kong. ’ REFERENCES (1) Iijima, S. Nature 1991, 354, 56–58. (2) Jorio, A.; Pimenta, M. A.; Souza, A. G.; Saito, R.; Dresselhaus, G.; Dresselhaus, M. S. New J. Phys. 2003, 139, 1–17. (3) Ajayan, P. M. Chem. Rev. 1999, 99, 1787–1799. (4) Ebbesen, T. W.; Lezec, H. J.; Hiura, H.; Bennett, J. W.; Ghaemi, H. F.; Thio, T. Nature 1996, 382, 54–56. (5) Hashimoto, A.; Suenaga, K.; Gloter, A.; Urita, K.; Lijima, S. Nature 2004, 430, 870–873. (6) Saito, R.; Dresselhaus, G.; Dresselhaus, M. S. Chem. Phys. Lett. 1992, 195, 537–542. (7) Iijima, S.; Ichihashi, T.; Ando, Y. Nature 1992, 356, 776–778. (8) Nardelli, M. B.; Yakobson, B. I.; Bernholc, J. Phys. Rev. B 1998, 57, 4277. (9) Krasheninnikov, A. V.; Nordlund, K.; Keinonen, J. Phys. Rev. B 2002, 65, No. 165423. (10) Ishigami, M.; Choi, H. J.; Aloni, S.; Louie, S. G.; Cohen, M. L.; Zettl, A. Phys. Rev. Lett. 2004, 93, No. 196803. (11) Kim, G.; Jeong, B. W.; Ihm, J. Appl. Phys. Lett. 2006, 88, No. 193107. (12) Wu, G.; Dong, J. Phys. Rev. B. 2006, 73, No. 245414. (13) Andzelm, J.; Govind, N.; Maiti, A. Chem. Phys. Lett. 2006, 421, 58–62. (14) Liu, P.; Gao, H. J.; Zhang, Y. W. Appl. Phys. Lett. 2008, 93, No. 083107. (15) Kalbac, M.; Hsieh, Y. P.; Farhat, H.; Kavan, L.; Hofmann, M.; Kong, J. Nano Lett. 2010, 10, 4619–4626. (16) Jeng, Y. R.; Tsai, P. C.; Fang, T. H. J. Phys. Chem. Solids 2004, 65, 1849–1856. (17) Lahiri, J.; Lin, Y.; Bozkurt, P.; Oleynik, I.; Batzill, M. Nat. Nanotechnol. 2010, 5, 326–329. (18) Guo, W.; Zhong, W.; Dai, Y.; Li, S. Phys. Rev. B 2005, 72, 075409. (19) Chico, L.; Crespi, V. H.; Benedict, L. X.; Louie, S. G.; Cohen, M. L. Phys. Rev. Lett. 1996, 76, 971–974. (20) Miyamoto, Y.; Rubio, A.; Berber, S.; Yoon, M.; Toma’nek, D. Phys. Rev. B. 2004, 69, No. 121413. (21) Haskins, R. W.; Maier, R. S.; Ebeling, R. M.; Marsh, C. P.; Majure, D. L.; Bednar, A. J.; Welch, C. R.; Barker, B. C.; Wu, D. T. J. Chem. Phys. 2007, 127, No. 074708.

’ CONCLUSION Comparative studies of the structures, vibrational spectroscopy, and electronic density of states of defect-free cap (5, 5) CNT and its V1, V2, V3, and V4 defective structures reveal the influences of the defects. The presence of the defect causes significant influence on the IR and Raman spectra. In addition to the creation of some characteristic peaks due to the defects, the vibrational strengths are also affected. For the highest peaks in IR and Raman spectra, the influences on the different vibrational modes are the same; that is, red shifts occur. The presence of the 296

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