Applied Surface Science 257 (2011) 10471–10476
Contents lists available at ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Diameter-dependent thermal-oxidative stability of single-walled carbon nanotubes synthesized by a floating catalytic chemical vapor deposition method Jie Ma a,∗ , Fei Yu b , Zhiwen Yuan a , Junhong Chen a,c,∗∗ a b c
State Key Laboratory of Pollution Control and Resource Reuse, School of Environmental Science and Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, China School of Environmental Science and Engineering, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai 200240, China Department of Mechanical Engineering, University of Wisconsin–Milwaukee, Milwaukee, WI 53211, USA
a r t i c l e
i n f o
Article history: Received 5 October 2010 Received in revised form 7 March 2011 Accepted 4 June 2011 Available online 26 July 2011 Keywords: Diameter-dependent Thermal stability Single-walled carbon nanotubes
a b s t r a c t In this paper, purified single-walled carbon naotubes (SWCNTs) with three different diameters were synthesized using a floating catalytic chemical vapor deposition method with ethanol as carbon feedstock, ferrocene as catalyst, and thiophene as growth promoter. The thermal-oxidative stability of differentdiameter SWCNTs was studied by using thermal analysis (TG, DTA), transmission electron microscopy (TEM), and X-ray photoelectron spectroscopy (XPS) analysis. The results indicate that small diameter SWCNTs (∼1 nm) are less stable and burn at lower temperature (610 ◦ C), however, the larger diameter SWCNTs (∼5 nm) survive after burning at higher temperature (685 ◦ C), the oxidation rate varies inversely with the tube diameter of SWCNTs, which may be concluded that the higher oxidation-resistant temperature of larger diameter SWCNTs can be attributed to the lower curvature-induced strain by rolling the planar graphene sheet for the larger diameter, so small tubes will become thermodynamically unstable. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Single-walled carbon nanotubes (SWCNTs) were first synthesized in 1993 by Iijima and Ichihara [1] and Bethune et al. [2]. Since then, numerous studies have shown that SWCNTs possess many excellent physical, chemical, magnetic, electrical, and mechanical properties [3,4]. Carbon nanotubes (CNTs) so far have been demonstrated for a wide range of applications due to a favorable combination of various unique properties such as the relatively high heat conduction performance and thermal stability [5]. Pang et al. [6] and Ajayan et al. [7] reported firstly the use of thermo gravimetric methods for CNTs in the presence of high contents of carbon nanoparticles. Pang et al. [6] reported that CNTs and nanoparticles were more resistant to oxidation than other forms of carbon, such as diamond, soot, graphite and C60 studied, under the same condition. However, CNTs exhibit very poor oxidation resistance in air at high temperatures. One influence is the metal and metallic salts which are active catalysts for graphite oxidation. The relative activities of these catalysts probably depend on the chemical nature of the catalyst particle and the localized interaction between catalyst particle and CNTs [8]. Several studies on thermal-oxidative stability of CNTs due to the presence of residual metals have been reported [9–12].
∗ Corresponding author. Tel.: +86 21 6598 1831. ∗∗ Corresponding author. Tel.: +1 414 229 2615. E-mail addresses:
[email protected] (J. Ma),
[email protected] (J. H. Chen). 0169-4332/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2011.06.164
Wu et al. [13] reported the thermal-oxidative stability of SWCNTs affected by various metal particles, such as naked metal particles, metal nanoparticles embedded inside multi-shelled graphite particles or in amorphous carbon. The results demonstrated that the presence of residual metal particles could reduce the thermal stability of SWCNTs in air by catalyzing their low-temperature oxidation. The thermal-oxidative stability of purified SWCNTs is an important issue, because these CNTs are expected to be used in composites, electronics or as sorbents that require chemical thermal robustness [14]. The thermal oxidation of SWCNTs leads to the formation of patches and circular pits on the exposed walls [15,16]. Most prior studies focused on the thermal stability of CNTs affected by purification conditions and chemical modification [17]; however, diameter-dependent thermal-oxidative stability of purified SWCNTs has been rarely reported so far. The main reason is that the present state-of-the-art technology for CNT synthesis always produces CNT samples with different diameters. More importantly, the larger diameter SWCNTs (>2 nm) cannot be readily grown with control and a narrow diameter distribution. In our previous work, different-diameter SWCNT samples have been synthesized successfully using a floating catalytic chemical vapor deposition method [18], and a highly efficient and nondestructive purification approach has been developed [19–21]. Based on our previous research results, in this paper, purified SWCNTs with three different diameters were obtained, and then the diameterdependent thermal-oxidative stability of purified SWCNTs were studied.
10472
J. Ma et al. / Applied Surface Science 257 (2011) 10471–10476
2. Experimental
peak energies were calibrated by placing the major C1s peak at 284.6 eV.
The present SWCNT samples were prepared by a floating catalytic chemical vapor deposition method [18,19]. Ethanol was used as carbon feedstock, ferrocene was used as catalyst, and thiophene was used as growth promoter. Ferrocene and thiophene were dissolved in ethanol with different concentrations. The concentration of ferrocene ranged from 6.7 to 20 mg mL−1 , and the thiophene concentration ranged from 0 to 5% (vol.%, the same hereafter). The solution was sonicated for 10 min and then transferred to a reservoir for spray pyrolysis. A quartz tube of 3 cm in diameter and 1 m in length was heated up to temperatures between 1000 and 1150 ◦ C using a tubular furnace with a heating length of 70 cm. In raising the temperature, Ar flow was initiated in the quartz tube in order to purge oxygen from the reaction chamber. After 15 min holding at a desired temperature, the ethanol solution dissolved with ferrocene and thiophene was supplied by an electronic squirming pump at a rate of 0.4 mL min−1 and sprayed through a nozzle with an Ar flow of 160 L h−1 . After several hours of pyrolysis, the supply of ethanol was terminated, and the sample was collected from a glass bottle connected to the quartz tube. The morphology and microstructure of the sample were studied using high resolution transmission electron microscopy (HRTEM) (JEOL 2100F, accelerating voltage of 200 kV). To do this, the sample was dispersed in ethanol by means of a sonicator and scooped up with a holey amorphous carbon film. Raman spectroscopy (JOBINYVON T64000) was used to further characterize the structural integrity of the purified samples. Thermal gravimetric analysis (Pyrisdiamond TG/DTA) was used to quantitatively characterize the as-prepared and purified SWCNTs. X-ray photoelectron spectroscopy (XPS) analysis was carried out in a Kratos Axis Ultra DLD spectrometer, using monochromated Al Ka X-rays, at a base pressure of 1 × 10−9 Torr. Survey scans determined between 1100 and 0 eV revealed the overall elemental compositions of the sample and regional scans for specific elements were also performed. The
3. Results and discussion In this study, SWCNTs were synthesized by spray pyrolysis of alcohol with the addition of different amounts of ferrocene and thiophene. Fig. 1 illustrates the TEM images of the as-grown samples synthesized at 1150 ◦ C with additions of 0.1% and 1% thiophene, respectively. Apparently, these samples were composed of small-diameter SWCNTs (with 0.1% thiophene addition). The obtained sample is thus defined as “SD-SWCNTs”, which contains bundles of SWCNTs with small diameters of ∼1 nm (Fig. 1a). With the increase of the sulphur addition, the diameter of SWCNTs increased. With the addition of 1% thiophene, the obtained sample contained mainly individual SWCNTs (Fig. 1c and d), which is defined as “LD-SWCNTs”, and bundles composed of a large number of tubes were not observed. Furthermore, the individual, separate SWCNTs usually have diameters larger than 3 nm. The obtained sample was defined as “MD-SWCNTs” with the addition of 0.5% thiophene. Comparing SD-SWCNTs (Fig. 1b) with LD-SWCNTs (Fig. 1d) shows some distinct characteristics. Firstly, the diameter of SWCNT has increased from 1 nm to 5.8 nm. Secondly, the diameter of SWCNT bundles decreased; moreover, single separated SWCNT has been found. It is well known that such CNTs tend to form bundles as a result of the strong van der Waals surface forces between small-diameter (SD) CNTs [22]. Previous studies on properties and applications of SWCNTs were limited to those with SDs (mostly less than 2 nm). The individual, separated SWCNTs with larger diameters may find new applications [23,24]. Micro-Raman spectra, especially the radial breathing mode (RBM), can be effectively employed to study properties of SWCNTs. Low-frequency micro-Raman spectra for SD-SWCNTs, MD-SWCNTs, and LD-SWCNTs are shown in Fig. 2a, which were measured with a laser excitation wavelength of 514.5 nm. The
Fig. 1. TEM images of the samples synthesized at 1150 ◦ C containing SD-SWCNTs (a, b) and LD-SWCNTs (c, d).
J. Ma et al. / Applied Surface Science 257 (2011) 10471–10476
10473
Fig. 2. Raman spectra of purified SWCNTs (a) low frequency, and diameter distribution of SWCNTs, using data obtained from HRTEM images, (b) SD-SWCNTs, (c) MD-SWCNTs and (d) LD-SWCNTs.
peak positions for the SD-SWCNTs are at 200–270 cm−1 , and those for the LD-SWCNTs are at 45–85 cm−1 . With the increasing thiophene addition amount, the peak position has shifted to a lower frequency. Such a difference is a piece of clear evidence that the diameters of SWCNTs are significantly enlarged with more addition of thiophene. The observed peaks correspond to the RBMs, whose frequencies ωRBM depend on the diameter of SWCNTs d by ωRBM =
A +B d
(1)
where A and B are two constants. For typical SWCNTs, A = 234 cm−1 nm and B = 10 cm−1 have been found [25,26]. Based on Eq. (1) and the observed peaks at low frequencies, the diameters are calculated to be in the range of 0.91–1.56 nm for SD-SWCNTs but in the range of 3.2–7.0 nm for LD-SWCNTs. The diameter distributions for different products were shown in Fig. 2b–d, with the diameter distribution of the present SWCNTs determined directly from HRTEM images. It can be found that the average diameter of SWCNTs is ∼1.2 nm for SD-SWCNTs with a narrow distribution, ∼2.3 nm for MD-SWCNTs, ∼5.8 nm for LD-SWCNTs. And the average diameter of SWCNTs increased from ∼1 nm to ∼5 nm from SD-SWCNTs, MD-SWCNTs to LD-SWCNTs with the increasing thiophene addition amount. These three kinds of different-diameter representative samples (SD-, MD-, LD-SWCNTs) have been selected to study the thermaloxidative stability detailed in the following content. TG and DTA have been widely utilized to make qualitative and quantitative studies on the oxidative behaviour of various materials. Here, main thermal event temperature (Tm ) for chemical oxidative reaction, can be defined and measured precisely and is associated with burning of SWCNTs. Firstly, the thermal analytic curves of as-prepared samples are presented in Fig. 3a. The residual weights (%) after the
heating process show the presence of metallic impurities in pristine samples. Assuming that all carbonaceous materials have been oxidized and Fe particles were oxidized to Fe2 O3 , the amount of Fe in each sample can be estimated. Fig. 3a shows that SD-SWCNTs contain the nearly 21% Fe in weight, attributed to catalyst Fe nanoparticles. The LD-SWCNTs sample contains 39% Fe in weight, which is more than that of MD-SWCNTs (around 30%). The weightloss behaviour of purified samples is shown in Fig. 3c. The purified samples contain a residual weight of Fe about 2%. This indicates that there were far fewer catalytic particles left in the purified samples as confirmed by HRTEM, suggesting efficient removal of catalyst particles. The temperatures at which the main thermal events took place (Tm ) during the whole oxidation process may be identified from the DTA curves (Fig. 3b and d). For the purified SD-SWCNT sample, the events might occur at temperatures from 550 ◦ C to 650 ◦ C with the main thermal oxidation taking place at ∼610 ◦ C. Main thermal events occurred at ∼685 ◦ C for the LD-SWCNTs sample, which has undergone high temperature treatment. Comparing as-prepared sample (Fig. 3b) with purified sample (Fig. 3d), it is clearly seen that Tm goes up with decreasing residual metal weight content, as also shown in Table 1. The trend indicates that the metal content strongly affects the thermal-oxidative stability of SWCNTs. The higher metal content is, the lower the thermal-oxidative stability of SWCNTs is, which is in good agreement with previous reports [27,28]. Comparing the line (a), (b) and (c) of Fig. 3d, it is also clearly seen that the Tm goes up from 610 ◦ C to 685 ◦ C with the increasing tube diameter. The results indicate that small diameter SWCNTs (∼1 nm) are less stable and can burn at a lower temperature; however, the larger diameter SWCNTs (∼5 nm) can survive after burning at a higher temperature. The peak shape of Fig. 3d shows that the oxidation rate varies inversely with the tube diameter
10474
J. Ma et al. / Applied Surface Science 257 (2011) 10471–10476
Fig. 3. TG curves of different-diameter SWCNTs (a) pristine SWCNTs, (c) purified SWCNTs, DTA curves of different-diameter SWCNTs, (b) pristine SWCNTs and (d) purified SWCNTs.
of SWCNTs. This is an indication that the LD-SWCNTs were more oxidation-resistant than MD-SWCNTs and SD-SWCNTs. Sawada and Hamada [29] calculated the value of the bondbending energy (Ebend ) of carbon naonotube for optimized atomic configuration of each structure using Tersoff’s potential. They found the Ebend almost depends only on a single parameter, the diameter ˚ which can be expressed in a of the tubule d: for d larger than 10 A, relation derivable from a continuum elastic theory: Ebend = C1
1 2
(2)
d
˚ the deviation from the continuum elastic For d smaller than 10 A, theory appears, and the relation is modified as: Ebend = C1
1 2 d
+ C2
1 4
(3)
d
where C1 and C2 are two constants. C1 = 5.64 eV A˚ 2 , and C2 = 25.1 eV A˚ 2 . The coefficient C1 does not depend on the helix pitch due to the six-fold symmetry of a graphite sheet. Based on Eqs. (2) and (3), the Ebend of different-diameter SWCNTs are calculated to be 0.0392 eV for the SD-SWCNTs, 0.0107 eV for the MD-SWCNTs and 0.0017 eV for LD-SWCNTs, respectively. As shown in Table 1, the calculation results show that the larger-diameter
SWCNTs have lower curvature-induced strain by rolling the planar graphene sheet. Our research results of the oxidation rate varying inversely with the tube diameter of SWCNTs are also in agreement with the calculation results. Because the destruction of structure and surface modification may affect the thermal-oxidative stability of SWCNTs, Raman and XPS analysis have been studied further the structure and surface modification of SWCNTs. The Raman peaks appear at high frequencies has been shown in Fig. 4. The G peak at 1585 cm−1 is related to E2g graphite mode [30,31]. The strong intensity of this peak indicates good graphitization of SWCNTs. The D-line at around 1345 cm−1 is induced by defective structures. These could include minor amorphous carbon and some hollow graphite particles in the sample. The intensity ratio of the G and D peaks (IG /ID ) is an indicator for estimating the purity and structure quality of SWCNTs [32]. As shown in Fig. 4, the higher IG /ID ratio means a higher structure quality and purity after the purification treatment process. In our previous work [18,19], it is also evidenced strongly that the purification process did not alter the SWCNTs excellent structure to any significant extent. In order to study deeply the surface modification of SWCNTs in the purification process, The FT-IR spectra of the SD-SWCNTs and LD-SWCNTs have also been obtained, as shown in figure S1. Both
Table 1 Fe content, Tm and Ebend of as-prepared and purified SWCNTs. Sample
Fe content of as-prepared SWCNTs (%)
Fe content of purified SWCNTs (%)
Tm of as-prepared SWCNTs (◦ C)
Tm of purified SWCNTs (◦ C)
Ebend (ev) of SWCNTs
SD-SWCNTs MD-SWCNTs LD-SWCNTs
21 30 39
3 3 3
525 519 525
610 655 685
0.0392 0.0107 0.0017
J. Ma et al. / Applied Surface Science 257 (2011) 10471–10476
Fig. 4. Raman spectra of purified SWCNTs at high frequency.
Table 2 XPS survey scans data of purified SWCNTs. Sample
Position (C1s, eV)
FWHM (C1s, eV)
C/O
SD-SWCNTs MD-SWCNTs LD-SWCNTs
284.75 285 284.45
4.5 1.5 2
8.34 9 7.9
SD-SWCNTs and LD-SWCNTs show characteristic peaks at 1091, 1618.8 and 3439.6 cm−1 , which could be attributed to –C–O, –C O and O–H stretching, respectively. Typical XPS survey scans of the SWCNTs are shown in Fig. 5a, and the XPS survey scans data of purified SWCNTs are shown in Table 2. The asymmetric nature and area of the C1s peak remain almost unchanged among SD-, MDand LD-SWCNTs (Fig. 5b). The XPS examination of three samples
10475
suggested ∼10 at.% of oxygen (Fig. 5), which is present as functional groups on the nanotube surface. This result reveals that the oxygen contents on the surfaces of SD-, MD-and LD-SWCNTs with different tube diameters are the same. These groups may result from the purification procedure as well as from the storage of the SWCNTs in laboratory air. The relative atomic concentrations (C/O) ratio of element content do not show obvious difference among SD-, MD-and LD-SWCNTs either. So we can conclude that the structure of three kinds of different-diameter SWCNTs have been modified by oxygen surface functional group to the same extent during the purification process. The TEM and Raman results indicated that different-diameter SWCNTs have been prepared, the diameters of SWCNTs have increased dramatically from ∼1 nm to ∼5 nm with the addition of thiophene, and the as-prepared samples have been purified by a highly efficient and nondestructive approach. The Raman analysis reveals that the different-diameter purified SWCNTs have excellent structure quality and purity after the purification process. Further XPS analysis showed that three different-diameter samples have been modified by oxygen surface functional group to the same extent during the purification process. The thermal analysis results indicate that small diameter SWCNTs (∼1 nm) are less stable and burn at a lower temperature (∼610 ◦ C); however, the larger diameter SWCNTs (∼5 nm) can survive after burning at a high temperature (∼685 ◦ C) and the oxidation rate varies inversely with the tube diameter of SWCNTs. Based on the above results, it may be concluded that the higher oxidation-resistant temperature of larger diameter SWCNTs can be attributed to the lower curvature-induced strain by rolling the planar graphene sheet with a larger diameter and smaller tubes become thermodynamically unstable. The thermodynamic stability of carbon nanotubes is determined by a competition between the increase in energy due to the bondbending strain introduced by rolling the planar graphene sheet into a tube and the decrease in energy due to the dangling bonds on the edges of the graphene sheet bonding together upon the formation of the tube. Since the strain energy within continuum
Fig. 5. XPS survey scans of purified SWCNTs (a), XPS for C1s region (b), for O1s region.
10476
J. Ma et al. / Applied Surface Science 257 (2011) 10471–10476
elasticity theory is expected to vary inversely with the square of the tube diameter [33], small tubes will become thermodynamically unstable, a simple Tersoff-like atomic potential [34] predicting a critical tube diameter of 0.4 nm [29]. Some or all of tube diameter effects may be responsible for conflicting statements in the literature. One reference [35] reported that small tubes burn first due to curvature-induced strain, smaller tubes are less stable and burn at lower temperature, and only the largest diameter tubes survive after burning at high temperatures, which is in agreement with our results. However, another study reported that large diameter tubes are less stable due to a higher defect density [36]. In this paper, a non-destructive purified approach has been adopted, so the excellent graphite structure has been retained. The higher oxidation-resistant temperature of LD-SWCNTS may be attributed to the high graphite quality and lower curvature-induced strain at a larger diameter. Therefore, our results can reconciliate these two conflicting studies. 4. Conclusion In this paper, three kinds of different-diameter purified SWCNTs were obtained based on our previous research results, and then the thermal-oxidative stability of purified different-diameter SWCNTs were studied. The results indicate that small diameter SWCNTs are less stable and burn at a lower temperature; however, the larger diameter SWCNTs can survive after burning at a high temperature and the oxidation rate varies inversely with the tube diameter of SWCNTs. The Raman and XPS analysis suggested that different-diameter SWCNTs have been modified by the oxygen surface functional groups to the same extent and have excellent structure quality and purity after the purification process. It may be concluded that the higher oxidation resistant temperature of LDSWCNTS can be attributed to lower curvature-induced strain with a larger diameter and excellent graphite structure. Acknowledgement This research is supported by The National Natural Science Foundation of China (51072135), Specialized Research Fund for the Doctoral Program of Higher Education (20100072110033), and Program for Young Excellent Talents at Tongji University (2010KJ026). We are also thankful to anonymous reviewers for their valuable comments to improve this manuscript.
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.apsusc.2011.06.164. References [1] S. Iijima, T. Ichihara, Nature 363 (1993) 603. [2] D.S. Bethune, C.H. Kiang, M.S. De Vries, G. Gorman, R. Savoy, J. Vazquez, R. Beyers, Nature 363 (1993) 605. [3] Y.S. Zhou, W. Xiong, Y. Gao, M. Mahjouri-Samani, M. Mitchell, L. Jiang, Y.F. Lu, Nanotechnology 31 (2010) 315601. [4] J.S. Shim, Y.H. Yun, W.D. Cho, V. Shanov, M.J. Schulz, C.H. Ahn, Langmuir 14 (2010) 11642. [5] Q.S. Zhu, X.L. Qiu, C.W. Ma, Carbon 37 (1999) 1475. [6] L.S.K. Pang, J.D. Saxby, S.P. Chatfield, J. Phys. Chem. B 97 (1993) 6941–6942. [7] P.M. Ajayan, T.W. Ebbesen, T. Ichihashi, S. Iijima, K. Tanigaki, H. Hiura, Nature 362 (1993) 522–525. [8] Z. Klusek, P.K. Datta, W. Kozlowski, Corros. Sci. 45 (2003) 1383–1393. [9] M.F.L. Aline, W.M. Anthony, H.W. Liu, R.W. Eric, G.S. Glaura, J. Therm. Anal. Calorim. 1 (2009) 257. [10] A.R. Adhikari, M.B. Huang, H. Bakhru, R. Vajtai, C.Y. Ryu, P.M. Ajayan, J. Appl. Phys. 100 (2006) 64315. [11] R. Brukh, S. Mitra, J. Mater. Chem. 17 (2007) 619. [12] R. Brukh, O. Sae-Khow, S. Mitra, Chem. Phys. Lett. 459 (2008) 149. [13] C.X. Wu, J.X. Xu, J.X. Li, G.F. Dong, L.H. Guan, Physica E 41 (2009) 1591. [14] C. Saridara, R. Brukh, Z. Iqbal, S. Mitra, Anal. Chem. 77 (2005) 1183. [15] X. Chu, L.D. Schmidt, Surf. Sci. 268 (1992) 325. [16] X. Chu, L.D. Schmidt, Ind. Eng. Chem. Res. 32 (1993) 1359. [17] S. Kundu, Y.M. Wang, W. Xia, M. Muhler, Phys. Chem. C 43 (2008) 16869. [18] J. Ma, J.N. Wang, X.X. Wang, J. Mater. Chem. 19 (2009) 3033. [19] J. Ma, J.N. Wang, Chem. Mater. 20 (2008) 2895. [20] J. Ma, F. Yu, J.N. Wang, J. Mater. Chem. 20 (2010) 5742. [21] J. Ma, J.N. Wang, C.J. TSAI3, Nussinov, R. Ma, B.Y. Front, Mater. Sci. China. 1 (2010) 17. [22] T. Hertel, R.E. Walkup, P. Avouris, Phys. Rev. B 58 (1998) 13870. [23] J.G. Duque, A.N. Parra-Vasquez, N. Behabtu, M.J. Green, ACS Nano 6 (2010) 3063. [24] A. Javey, M. Shim, H. Dai, Appl. Phys. Lett. 80 (2002) 1064. [25] M. Milnera, J. Kürti, M. Hulman, H. Kuzmany, Phys. Rev. Lett. 84 (2000) 1324. [26] A. Jorio, R. Saito, J.H. Hafner, C.M. Lieber, M. Hunter, T. McClure, G. Dresselhaus, M.S. Dresselhaus, Phys. Rev. Lett. 86 (2001) 1118. [27] E. Illekova, K. Csomorova, J. Therm. Anal. Calorim. 80 (2005) 103. [28] B.J. Landi, C.D. Cress, C.M. Evans, R.P. Raffaelle, Chem. Mater. 17 (2005) 6819. [29] S. Sawada, N. Hamada, Solid State Commun. 83 (1992) 917. [30] M.S. Dresselhaus, G. Dresselhaus, A. Jorio, A.G. Souza Filho, R. Saito, Carbon 40 (2002) 2043. [31] A.G. Souza Filho, A. Jorio, G.G. Samsonidze, G. Dresselhaus, M.A. Pimenta, M.S. Dresselhaus, A.K. Swan, R. Saito, Phys. Rev. B 67 (2003) 354271. [32] A. Grüneis, R. Saito, T. Kimura, L.G. Canc¸ado, M.A. Pimenta, A. Jorio, A.G. Souza Filho, G. Dresselhaus, M.S. Dresselhaus, Phys. Rev. B 65 (2002) 155405. [33] D.H. Robertson, D.W. Brenner, J.W. Mintmire, Phys. Rev. B 12 (1992) 592. [34] J. Tersoff, Phys. Rev. Lett. 61 (1988) 2879. [35] W. Zhoua, Y.H. Ooia, R. Russoa, P. Papaneka, D.E. Luzzia, J.E. Fischer, M.J. Bronikowskib, P.A. Willisb, R.E. Smalleyb, Chem. Phys. Lett. 1–2 (2001) 6. [36] Y. Zhang, Z. Sh i, Z. Gu, S. Iijima, Carbon 38 (2000) 2055.