J. Phys. Chem. C 2010, 114, 18091–18095
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Thermally Activated Interlayer Bonding in Multiwalled Carbon Nanotubes Chun Tang,*,†,‡ Yi Zhang,† Wanlin Guo,‡ and Changfeng Chen† Department of Physics and High Pressure Science and Engineering Center, UniVersity of NeVada, Las Vegas, NeVada 89154, United States, and Institute of Nano Science, Nanjing UniVersity of Aeronautics and Astronautics, Nanjing 210016, China ReceiVed: July 12, 2010; ReVised Manuscript ReceiVed: September 1, 2010
Recent experimental and theoretical results show that interlayer bonds in multiwalled carbon nanotubes (MWCNTs) play a pivotal role in improving their mechanical and electronic properties desirable for device applications. However, generation of interlayer bonds while maintaining tube structural integrity remains a key challenge. Here we demonstrate by molecular dynamics simulations that high-temperature thermal treatment can controllably activate interlayer bonding in MWCNTs and few-layer graphene systems, which leads to a significant improvement in their mechanical properties such as load carrying capacity and high-temperature tensile ductility. Moreover, first-principles calculations show that interlayer bonding opens up energy gaps in metallic MWCNTs, providing a way to produce all-semiconducting MWCNTs. These results offer new insights into the behavior of MWCNTs and raise prospects of effective thermal engineering of their structural, mechanical, and electronic properties. Introduction 1,2
The ultralow friction among adjacent layers of multiwalled carbon nanotubes (MWCNTs) represents a major obstacle for designing CNT-based superstrong nanofibers. To enhance their load carrying capacity, many strategies have been proposed. One of the promising routes is the creation of interlayer bonding in MWCNTs.3-6 Theoretical results4,5 predicted that interlayer sp3 bonds can significantly enhance the mechanical properties of MWCNTs. Recently, Peng et al.7 reported enhanced maximum sustainable loads undertaken by MWCNTs, which is attributed to irradiation-induced cross-links between adjacent walls. These demonstration-of-principle-type results raise the important issue of finding a practical way to generate interlayer sp3 bonds in MWCNTs or multilayered carbon structures in general. Many experimental efforts have been reported recently; several groups have observed interlayer sp3 bond formation in MWCNTs and multilayer graphene systems using electron irradiation or laser pulse.3,7-9 These treatments, however, are hard to scale up for practical production because they require expensive operating instruments and techniques. Meanwhile, these methods are also prone to introducing undesirable structural damage which will lower their performance in nanoelectromechanical systems (NEMSs). Therefore, it is highly desirable to search for new strategies for generating sp3 bonds in MWCNTs in a controllable manner while maintaining their structural integrity. Furthermore, the broad applications of CNTs in nanoscale electronic devices and abundant electromechanical coupling effects require that this new strategy should also be able to maintain, or possibly, improve their electronic properties. In the present work, we explore a new route to generating interlayer bonding via thermal activation in MWCNTs. Molecular dynamics simulations reveal that thermally activated interlayer bonds depend sensitively on tube-wall curvature and * To whom correspondence should be addressed. E-mail: tangchun@ physics.unlv.edu. † University of Nevada. ‡ Nanjing University of Aeronautics and Astronautics.
remain robust when annealed to low temperature, and the resulting interwall cross-links significantly enhance the load transfer capability while maintaining the strength of MWCNTs. First-principles calculations show that interlayer bonding can turn metallic MWCNTs into semiconductors while maintaining or increasing the energy gaps of semiconducting tubes. These results offer new insights into the pivotal role of interlayer bonding in modifying a broad range of behaviors of MWCNTs and raise prospects of effective thermal engineering of their properties. Methods The molecular dynamics simulations are carried out using the second-generation Tersoff-Brenner empirical bond-order potential;10,11 the long-range van der Waals interaction is described by the Lennard-Jones (L-J) potential in the form of
[( ) ( ) ]
V(rij) ) 4ε
σ rij
12
-
σ rij
6
The L-J constants used in our simulations are ε ) 51.2 K and σ ) 2.28 Å. The time step is 0.5 fs; at least 5000 steps were used for structural relaxation at each temperature or strain state. This method has been widely used in studies of CNTs and produced key insights for understanding their deformation under various loading conditions, nonlinear elastic scaling behavior, and enhanced mechanical properties.5,12-17 In particular, although it has known deficiencies,18,19 this potential is demonstrated to provide an accurate description of sp3 bond states in low-density carbon systems.12,19 Here we study thermal activation of interlayer bonding and its effects on the properties of MWCNTs. For each annealing simulation, we first heat the system from 0 K gradually to a high temperature and then cool the system back down to 300 K. The lowest temperature increment is 10 K for the low-temperature region (200 K and below) and 50 K for the high-temperature region (over 200 K). These heating
10.1021/jp106444n 2010 American Chemical Society Published on Web 10/05/2010
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Tang et al.
Figure 2. (A) Pulling force on the inner wall of the (17,0)/(26,0) DWCNT versus pullout distance after annealing at high temperature (2800 K) with (HTwD) or without (HTwoD) vacancy defect, compared to results at low temperature (0 K) without annealing (LT). (B) Structural snapshots of the interlayer bonds formed around the vacancy defect (outlined in bold). (C) Expanded view of the LT case.
Figure 1. (A) Cross section of the (8,0)/(17,0)/(26,0) TWCNT annealed at higher temperatures and then cooled to 300 K. (B) Strain energy of the (8,0)/(17,0)/(26,0) TWCNT at 300 K without and with annealing. (C) Snapshots of the (8,0)/(17,0)/(26,0) TWCNT under tensile strain after annealing at 2000 K.
and cooling rates were tested to produce the convergence results reported in this work. To perform a similar simulation on the time order of several seconds is beyond current computer capacity but necessary for further examining of results reported here; we expect a slight influence to be observed. We examine a series of single-, double-, and triple-walled CNTs (SWCNTs, DWCNTs, and TWCNTs) composed of (8,0), (17,0), and (26,0) tubes for benchmark results. The Berendsen thermal scheme20 was employed to control the temperature in the simulations. Results and Discussion We first show simulated annealing of the (8,0)/(17,0)/(26,0) TWCNT at high temperatures followed by a cooling down to 300 K. We observe an interesting trend in interlayer bonding formation (see Figure 1A): it starts between the innermost walls first at 800 K, and the bond concentration increases with rising temperature; it then spreads to between the outer walls at higher temperatures. This trend is attributed to the curvature-dependent strain energy in the MWCNTs: the higher curvature of the inner walls induces larger pre-existing strain energy, which makes them less stable21-23 and, therefore, more prone to thermal activation of interlayer bonding. These bonds are homogeneously distributed along the tube wall, which ensures that the MWCNTs do not lose their well-defined one-dimensional structural property. They remain stable when the system temperatures are cooled down to 300 K and persist under initial tensile loading without any severe structural damage, which bodes well for applications of MWCNTs. To study the role of interlayer bonds in modifying the elastic properties of MWCNTs, we performed tensile simulation for MWCNTs with or without thermal annealing. Simulations on DWCNTs and TWCNTs yield the same conclusions; we therefore focus our discussion on the (8,0)/(17,0)/(26,0) TWCNT as a representative example (see Figure 1B). For MWCNTs without annealing, each wall breaks separately from the inner to outer tubes (see Supporting Information Figure S1) due to their diameter-dependent elastic limit.24,25 For annealed MWCNTs, their elastic limit is reduced slightly (Figure 1B) since its strength is weakened by activation of the sp3 bonds (compared
to sp2 bonds), which also makes the tube more ductile. In most of our simulations, the elastic limit is reduced by only 1% comparing to MWCNTs without annealing, suggesting that the thermal treatment has little effect on the intrinsic strength of the individual tubes that form the MWCNTs. Meanwhile, these interlayer bonds significantly improve the overall strength of the MWCNTs by preventing intertube sliding (see below for details). A wide distribution of interlayer bonds over the tube walls also leads to a tensile deformation pattern (Figure 1C) different from that without annealing beyond the elastic limit. The annealed MWCNT becomes more ductile and exhibits improved plasticity. The monotonic increase of interlayer bonding concentration with rising temperature (Figure 1A) first improves the tube plasticity but then impedes it (see Figure 1B) due to higher defect localization at further increased concentration of interlayer bonds. These systematic trends suggest that high-temperature annealing can be used as an effective tool for thermal engineering of the structural behavior of MWCNTs. Low efficiency in load transfer between different walls of MWCNTs presents a major obstacle for their mechanical applications. Electron-beam irradiation has been used to generate cross-links within CNT bundles or different layers of MWCNTs to improve their performance.3,26 Recent studies show that such cross-links can significantly enhance the load transfer capacity of MWCNTs.3-5,7 Our simulations show that high-temperature annealing offers an effective alternative approach. We calculated the pullout force on the inner wall of the (17,0)/(26,0) DWCNT using an approach similar to that of ref 4; we fixed the left end of the outer wall during the simulation, and the pulling force was measured on the right end of the inner wall, as sketched in Figure 2B. The results (see Figure 2A and 2C) show that hightemperature annealing produces a two-order-of-magnitude increase in pulling force compared to that without annealing. We also calculated the stress distribution by pulling one end of the outer layer only while keeping the other end of both layers fixed (see Supporting Information Figure S2). The stress undertaken by the inner layer almost equals that by the outer layer before the interlayer bonds break. The stiffness is therefore roughly doubled compare to MWCNTs without thermally activated sp3 bonds, suggesting excellent load transfer capability, which agrees well with Peng et al.’s experiments.7 These results demonstrate a significant improvement in the load transfer capacity by thermally activated interlayer bonding. Moreover, our simulations reveal a distinct advantage of high-temperature annealing in its ability to mitigate the structural weakness associated with pre-existing vacancy defects that are commonly
Interlayer Bonding in Multiwalled Carbon Nanotubes
Figure 3. (A) Pulling force vs pulling distance for a bilayer graphene at difference temperatures. (Inset) Schematic of calculating the pulling force in simulation. The bilayer graphene structutre is annealed at 2800 K; interlayer bonds are shown in black; edge atoms are saturated by hydrogen atoms. (B) Pulling force vs pulling distance for a trilayer graphene annealed at 2000 K; the pull loadings are applied to the middle layer of the trilayer graphene.
induced during synthesis or by irradiation. The calculated pulling force on the annealed DWCNT with a pre-existing vacancy defect shows a surprising increase by another factor of 3 compared to that for defect-free DWCNT (see Figure 2A). It is attributed to the dangling bonds around the vacancy site (see Figure 2B) that are more reactive and form stronger links (than sp3 type) with the adjacent layer, thus producing higher load transfer capability. Considering the fact that defects inevitably exist in MWCNTs either through the synthesis process or during their application in nanoscale mechanical devices, our result thus offers a practical strategy for overcoming the defect-induced weakening of their strength via thermal treatment. This mechanism is also expected to play a key role in modifying the structural properties of multilayered covalent materials. The experimental finding of temperature-driven strength enhancement of graphite27,28 has been a long-standing puzzle and remains poorly understood.29 The load transfer enhancement by thermally activated interlayer bonding suggests a plausible mechanism. At high temperatures, thermally activated crosslinks among different graphitic layers and at grain boundaries can greatly improve the load transfer efficiency, thus allowing the bulk sample to undertake larger loading. Direct simulations of such a complex problem are beyond current computing capability. We instead conducted simulations on few-layer graphene and found that high-temperature annealing indeed activates interlayer cross-links similar to those found in MWCNTs (see Figure 3). These cross-links produce a significant increase in the pulling force. For the bilayer graphene, a twoorders-of-magnitude improvement is observed. We also conducted simulation on a trilayer graphene. The pulling force exerted on the middle layer reaches 0.9 nN/atom, which is 3 orders of magnitude higher than that without thermal annealing. This is due to the increased sp3 bond concentration in the trilayer graphene, suggesting that structural confinement would have a considerable impact on interlayer bonding formation and loading transfer capacity in multilayer graphene. It should be noted that these interlayer bonds, however, appear at higher temperatures (above 1300 K) compared to those in MWCNTs and are less stable against perturbations in thermal (temperature reduction) and/or mechanical (pulling) conditions. This is observed by
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Figure 4. Strain energy at 2000 K for (A) the (8,0)/(17,0) DWCNT and (B) the (8,0)/(17,0)/(26,0) TWCNT. The inset in B shows the local structure with interlayer fusion. Black bonds denote those formed between different layers. (C) Snapshots of the TWCNT under tensile loading. (D) Activation and evolution of intralayer topological defects driven by interlayer bonds in the TWCNT. The associated bond rotations are indicated by pairs of small arrows.
noticing the frequent drop in the pulling force of annealed fewlayer graphene (see Figure 3), corresponding to gradual breaking of the interlayer cross-links. The transient nature of the interlayer bonds between graphitic layers is consistent with their curvaturedependent behavior discussed above. Interestingly, simulations on bilayer graphene with a vacancy defect show that the dangling bonds around the defect do not lead to formation of interlayer bonds as in DWCNTs but self-heals with their intralayer neighbors, forming a 5-6-6-5 defect dipole instead (see Supporting Information Figure S3). As a result, the pulling force is not notably enhanced. This again demonstrates that the curvature-induced strain energy plays a key role in interlayer bonding formation and stability. Recent experiments observed8 formation of transient sp3 bonds between graphite sheets and established a lower bound for the critical (lattice) temperature of 1000 K for their activation, which is in good agreement with our simulation results and lends strong support to the present computational approach. We next explore the behavior of MWCNTs under tensile loading at high temperatures motivated by recent observation of high-temperature superplasticity.30 A key outstanding issue is how the interlayer bonds affect the plastic dynamics of MWCNTs. Simulation results at 2000 K (Figure 4A) show that, unlike at 300 K, the two walls of the (8,0)/(17,0) DWCNT neck simultaneously at a site of high concentration of sp3 interlayer bonds that have weakened the structure compared to other segments with stronger sp2 C-C bonds. The strain energy curve for the TWCNT (Figure 4B) shows two peaks corresponding to the yielding of the inner two walls and the outer wall, respectively. The three walls do not neck simultaneously here because the higher concentration of interlayer bonds between the inner walls leads to their earlier necking. Upon further tensile loading, interlayer bonds between the outer two walls produce different types of deformation, namely, intralayer Stone-Wales deformation assisted by the interlayer bonding and interlayer fusion as shown in Figure 4B-D, with enhanced tensile ductility. We identify two main atomistic mechanisms for the deformation modes driven by interlayer bonding. The first is activation of intralayer Stone-Wales defects assisted by the interlayer bonding, which weakens the intralayer C-C bonds and provides
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Figure 5. Calculated electronic band structure of the (8,0)/(17,0) and (6,0)/(15,0) DWCNT with and without interlayer bonds (IB). Insets in B, C, and E show the band structure near the Fermi energy.
additional pulling force, making it easier for the 90° bond rotation as demonstrated in Figure 4C. The interlayer bonds between the outer two walls (at 12.48% strain) facilitate the rotation of the C-C bond connected to them, leading to formation of a 5-7-7-5 defect dipole (at 12.86% strain). This process generates another interlayer bond nearby which, in turn, induces rotation of another intralayer C-C bond connected to a heptagon ring, yielding formation of a 5-7-8-5 defect (at 13.23% strain). This is followed by a second process, namely, fusion of adjacent layers of the MWCNTs driven by the bond rotation in the interlayer cross-links. We observe a large number of such interlayer bond rotations under tensile loading which drive adjacent walls to fuse into a common layer. The fused layer maintains well-preserved structural integrity (see inset in Figure 4B), allowing sustained plastic deformation that is substantially larger than that at 300 K (see Figure 1 for results on the TWCNT). This fusion process combined with intralayer dislocation propagation provides a new mechanism for large plastic elongation of MWCNTs. Finally, we explore the influence of interlayer bonding on electronic properties by density functional theory calculations on two representative DWCNTs: a (6,0)/(15,0) and a (8,0)/(17,0) DWCNT, which are metallic and semiconducting, respectively, in the absence of interlayer bonding. The calculations were performed using the VASP code31 with ultrasoft pseudopotentials32 for the core region and LDA for the exchange-correlation potential. We used a kinetic energy cutoff of 400 eV and sampled up to 60 k points along the tube axis. The calculations were performed on shorter (4.23 Å) tubes due to high computational costs; they provide sufficient evidence to demonstrate the sensitive response of the electronic structure to interlayer bonding and suggest viability of tuning the energy gap of MWCNTs via thermal engineering. A vacuum region of 16 Å in the direction perpendicular to the tube axis is introduced in the supercell to avoid self-interaction. Structural configurations obtained from molecular dynamics simulations were taken as the initial structures that were relaxed using the conjugate gradient method until the force is less than 0.01 eV/ Å/atom. It is seen from Figure 5 that interlayer bonding leads to an initial reduction in the energy gap of the (8,0)/(17,0) DWCNT, which is attributed to the radial deformation with nonspherical tube cross sections induced by the stress generated by these bonds. This is in agreement with the previously observed trend in radially deformed CNTs.33,34 At higher concentrations, interlayer bonds play a dominant role and overcome the effect of radial deformation, leading to energy gap increase (Figure 5C) as expected for a sp3 bonding carbon network. Meanwhile, the presence of interlayer bonds opens up a gap in the originally metallic (6,0)/(15,0) DWCNT (Figure 5E). It is because the sp3 hybridization enhances overlap of the π orbital at the Fermi level; the increased degeneracy of the π and π* bands split consequently and form an energy gap. Due
Tang et al. to the high computational cost, similar calculations on TWCNTs with interlayer sp3 bonds were not performed. However, we expect a similar behavior to occur as they follow the same underlying mechanism. As LDA calculations usually underestimate the energy gap, this result presents a convincing case for the metal-semiconductor transition in CNTs via the interlayer bonding mechanism. It raises the prospect of addressing a major problem in nanoelectronic applications of CNTs, namely, the coexistence of metallic and semiconducting tubes in as-grown CNT arrays, by introducing interlayer bonds via thermal activation. It has been reported recently that highly enriched DWCNT arrays with average diameters of no more than 1.6 nm can be produced.35 Our results reported in the present paper are expected to stimulate further research on band gap engineering of MWCNTs via thermal activation of interlayer bonding. Conclusions In summary, we proposed thermal treatment as a new and effective strategy for generating interlayer bonding in MWCNTs and few-layer graphene systems. Our molecular dynamics simulations demonstrate that formation of interlayer bonding is sensitive to tube curvature, which allows effective thermal engineering via controllable introduction of interwall cross-links along the radial direction by annealing at appropriate temperatures. We show that thermally activated interlayer bonding leads to a significant improvement in the load carrying capacity of MWCNTs and graphene layers without reducing their intrinsic strength; thermal treatment also has a positive impact on preexisting vacancy defects in MWCNTs and few-layer graphene systems, resulting in further enhanced mechanical performance (than defect free systems). The defect dynamics (rebonding or self-healing) upon heat treatment are also sensitive to tube curvature. Moreover, the interlayer bonds open up energy gaps in metallic MWCNTs, suggesting a new route to synthesizing all-semiconducting MWCNTs. These findings offer new insights into the experimental observation of profound effects of interlayer bonding on the properties of MWCNTs and graphite and may stimulate further research on thermal activation of interlayer bonding networks in a broad class of layered covalent materials. Acknowledgment. This work was supported by DOE Cooperative Agreement DE-FC52-06NA26274 at UNLV and 973 Program (2007CB936204), NSF (10732040), and MOE (705021, IRT0534) of China at NUAA. Supporting Information Available: Tensile behaviors of SWCNTs and MWCNTs at room temperature; vacancy reconstruction in bilayer graphene upon annealing at high temperatures; load transfer in annealed DWCNTs. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Cummings, J.; Zettl, A. Low-friction nanoscale linear bearing realized from multiwall carbon nanotubes. Science 2000, 289, 602. (2) Estili, M.; Kawasaki, A. Engineering Strong Intergraphene Shear Resistance in Multi-Walled Carbon Nanotubes and Dramatic Tensile Improvements. AdV. Mater. 2010, 22, 107. (3) Kis, A.; Csa´nyi, G.; Salvetat, J.; Lee, T.; Couteau, E.; Kulik, A. J.; Benoit, W.; Brugger, J.; Forro´, L. Reinforcement of single-walled carbon nanotube bundles by intertube bridging. Nat. Mater. 2004, 3, 153. (4) Xia, Z. H.; Guduru, P. R.; Curtin, W. A. Enhancing Mechanical Properties of Multiwall Carbon Nanotubes via sp3 Interwall Bridging. Phys. ReV. Lett. 2007, 98, 245501.
Interlayer Bonding in Multiwalled Carbon Nanotubes (5) Byrne, E.; McCarthy, M.; Xia, Z.; Curtin, W. Multiwall Nanotubes Can Be Stronger than Single Wall Nanotubes and Implications for Nanocomposite Design. Phys. ReV. Lett. 2009, 103, 045502. (6) Tombler, T.; Zhou, C.; Alexeyev, L.; Kong, J.; Dai, H.; Liu, W.; Jayanthi, C.; Tang, M.; Wu, S. Reversible electro-mechanical characteristics of carbon nanotubes under local-probe manipulation. Nature 2000, 405, 769. (7) Peng, B.; Locascio, M.; Zapol, P.; Li, S.; Mielke, S.; Schatz, G.; Espinosa, H. Measurements of near-ultimate strength for multiwalled carbon nanotubes and irradiation-induced crosslinking improvements. Nat. Nanotechnol. 2008, 3, 626. (8) Raman, R. K.; Murooka, Y.; Ruan, C.; Yang, T.; Berber, S.; Tomanek, D. Direct Observation of Optically Induced Transient Structures in Graphite Using Ultrafast Electron Crystallography. Phys. ReV. Lett. 2008, 101, 077401. (9) Kanasaki, J.; Inami, E.; Tanimura, K.; Ohnishi, H.; Nasu, K. Formation of sp3-Bonded Carbon Nanostructures by Femtosecond Laser Excitation of Graphite. Phys. ReV. Lett. 2009, 102, 087402. (10) Brenner, D. W. Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films. Phys. ReV. B 1990, 42, 9458. (11) Brenner, D. W.; Shenderova, S. A.; Harisson, J. A.; Stuart, S. J.; Ni, B.; Sinnott, S. B. A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys.: Condens. Matter 2002, 14, 783. (12) Guo, W. L.; Zhu, C.; Yu, T.; Woo, C.; Zhang, B.; Dai, Y. Formation of sp3 Bonding in Nanoindented Carbon Nanotubes and Graphite. Phys. ReV. Lett. 2004, 93, 245502. (13) Elliott, J.; Sandler, J.; Windle, A.; Young, R.; Shaffer, M. Collapse of Single-Wall Carbon Nanotubes is Diameter Dependent. Phys. ReV. Lett. 2004, 92, 095501. (14) Kutana, A.; Giapis, K. Transient Deformation Regime in Bending of Single-Walled Carbon Nanotubes. Phys. ReV. Lett. 2006, 97, 245501. (15) Li, X.; Yang, W.; Liu, B. Bending Induced Rippling and Twisting of Multiwalled Carbon Nanotubes. Phys. ReV. Lett. 2007, 98, 205502. (16) Arias, I.; Arroyo, M. Size-Dependent Nonlinear Elastic Scaling of Multiwalled Carbon Nanotubes. Phys. ReV. Lett. 2008, 100, 085503. (17) Tang, C.; Guo, W. L.; Chen, C. F. Mechanism for Superelongation of Carbon Nanotubes at High Temperatures. Phys. ReV. Lett. 2008, 100, 175501. (18) Pastewka, L.; Pou, P.; Pe´rez, R.; Gumbsch, P.; Moseler, M. Describing bond-breaking processes by reactive potentials: Importance of an environment-dependent interaction range. Phys. ReV. B 2008, 78, 161402. (19) Marks, N. A.; Cooper, N. C.; McKenzie, D. R.; McCulloch, D. G.; Bath, P.; Russo, S. P. Comparison of density-cunctional, tight-binding, and
J. Phys. Chem. C, Vol. 114, No. 42, 2010 18095 empirical methods for the simulation of amorphous carbon. Phys. ReV. B 2002, 65, 075411. (20) Berendsen, H.; Postma, J.; Gunsteren, W.; DiNola, A.; Haak, J. Molecular dynamics with coupling to an external bath. J. Chem. Phys. 1984, 81, 3684. (21) Zhao, X.; Liu, Y.; Inoue, S.; Suzuki, T.; Jones, R. O.; Ando, Y. Smallest Carbon Nanotube Is 3 Å in Diameter. Phys. ReV. Lett. 2004, 92, 125502. (22) Sun, L. F.; Xie, S. S.; Liu, W.; Zhou, W. Y.; Liu, Z. Q.; Tang, D. S.; Wang, G.; Qian, L. X. Materials: Creating the narrowest carbon nanotubes. Nature 2000, 403, 384. (23) Mao, Y. L.; Yan, X. H.; Xiao, Y.; Xiang, J.; Yang, Y. R.; Yu, H. L. First-principles study of the (2,2) carbon nanotube. Phys. ReV. B 2005, 71, 033404. (24) Zhang, P. H.; Lammert, P. E.; Crespi, V. H. Plastic Deformations of Carbon Nanotubes. Phys. ReV. Lett. 1998, 81, 5346–5349. (25) Tang, C.; Guo, W.; Chen, C. Molecular dynamics simulation of tensile elongation of carbon nanotubes: Temperature and size effects. Phys. ReV. B 2009, 79, 155436. (26) Pregler, S. K.; Sinnott, S. B. Molecular dynamics simulations of electron and ion beam irradiation of multiwalled carbon nanotubes: The effects on failure by inner tube sliding. Phys. ReV. B 2006, 73, 224106. (27) Malmstrom, C.; Keen, R.; Green, L. Some Mechanical Properties of Graphite at Elevated Temperatures. J. Appl. Phys. 1951, 22, 593. (28) Wagner, P.; Oriesner, A. R.; Haskin, L. A. High-Temperature Properties of Graphite. II. Creep in Tension. J. Appl. Phys. 1959, 30, 152. (29) Huang, J. Y.; Chen, S.; Ren, Z. F.; Wang, Z.; Wang, D.; Vazin, M.; Chen, G.; Dresselhaus, M. S. Kink Formation and Motion in Carbon Nanotubes at High Temperatures. Phys. ReV. Lett. 2006, 97, 075501. (30) Huang, J. Y.; Chen, S.; Ren, Z. F.; Wang, Z.; Kempa, K.; Naughton, M. J.; Chen, G.; Dresselhaus, M. S. Enhanced Ductile Behavior of TensileElongated Individual Double-Walled and Triple-Walled Carbon Nanotubes at High Temperatures. Phys. ReV. Lett. 2007, 98, 185501. (31) Kresse, G.; Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. ReV. B 1993, 47, 558. (32) Vanderbilt, D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys. ReV. B 1990, 41, 7892. (33) Shan, B.; Lakatos, G. W.; Peng, S.; Cho, K. First-principles study of band-gap change in deformed nanotubes. Appl. Phys. Lett. 2005, 87, 173109. (34) Barboza, A. P. M.; Gomes, A.; Archanjo, B.; Araujo, P.; Jorio, A.; Ferlauto, A.; Mazzoni, M.; Chacham, H.; Neves, B. Deformation Induced Semiconductor-Metal Transition in Single Wall Carbon Nanotubes Probed by Electric Force Microscopy. Phys. ReV. Lett. 2008, 100, 256804. (35) Green, A.; Hersam, M. Processing and properties of highly enriched double-wall carbon nanotubes. Nat. Nanotechnol. 2009, 4, 64.
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