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Stretching behavior of a carbon nanowire encapsulated in a carbon nanotube
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Scripta Materialia 60 (2009) 129–132 www.elsevier.com/locate/scriptamat
Stretching behavior of a carbon nanowire encapsulated in a carbon nanotube H. Li,a,* F.W. Sun,b K.M. Liewc and X.F. Liua a
School of Materials Science and Engineering and Key Laboratory of Liquid Structure and Heredity of Materials, Ministry of Education, Shandong University, China b Physics Department, Ocean University of China, Qingdao, China c Department of Building and Construction, City University of Hong Kong, Kowloon, Hong Kong Received 5 May 2008; revised 15 August 2008; accepted 4 September 2008 Available online 26 September 2008
Molecular dynamic simulations are performed to study the deformation behavior of nanocomposite structures formed by the insertion of a carbon nanowire (CNW) into a carbon nanotube (CNW@CNT) under tension. The simulation results indicate that insertion of the CNW into CNT makes the plastic elongation increase. A superplastic deformation behavior is observed and finally, CNW@CNT is drawn to be a very long elongated nanobridge. During the tensile deformation, pentagon–heptagon defects, octagonal defects, and higher-order rings are observed. A large hole caused by some defects accelerates the fracturing of the CNT. Crown copyright Ó 2008 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved. Keywords: Mechanical properties testing; Tension test; Nanocomposite; Plastic deformation; Molecular dynamics
Carbon nanotubes (CNTs) have attracted interest not only for their unusual electrical and mechanical properties [1,2], but also because of their hollow interior that serves as a nanometric capillary [3] in nanomaterial fabrication. Filling single-walled carbon nanotubes (SWNTs) with certain materials creates one-dimensional (1D) nanowires that have exciting applications. Nanowires have a very large surface-area/volume ratio as compared to bulk materials, and their structures and properties can be quite different from those of bulk materials [4–6]. Recent molecular dynamic (MD) simulations have offered more evidence of the formation of a stable nanobridge in metallic nanowires under tensile deformation [7]. The MD simulations of the mechanical behavior of nanowires have also been investigated [8,9]. Ji and Park [10] used the classical MD simulation to study the inelastic deformation of metallic nanowires, and demonstrated that the geometry of nanomaterials can be utilized to control the operant modes of inelastic deformation. In previous experiments, the nonlinear response of a tube under a high strain has been studied [11,12]. For instance, a carbon fiber was stretched to form a nanobridge under a high-resolution transmission electron microscope [13]. Furthermore, Zhao et al. [14] observed * Corresponding author. E-mail: [email protected]
that linear carbon chain consisting of more than 100 atoms encapsulated into CNT in the cathode deposits by the method of hydrogen arc discharge evaporation. Not only can linear CNW be embedded into CNT, but other form of carbon such as 1D periodic chains C60 fullerene molecules inside single-walled CNT, can also be observed [15,16]. As to more complex CNW structures, multi-walled CNT irradiated by Ar [17] and Si [18] ion beams showed the novel formation of amorphous carbon nanowire network. Nanocomposite materials have been one of the most promising materials for mechanical application. Danailov [19] used empirical potential and atomistic simulation to model the bending behavior of single-walled carbon nanotube encapsulating metal nanowire. Another relative study [20] showed the fracture and fatigue properties of CNT, CNT/polymer, and CNT/epoxy under load. In this study, the object is to perform a simulation about the stretching behavior of carbon nanowires that are inserted into carbon nanotubes (CNW@CNTs). CNTs are good templates for the manufacture of 1D ultra-thin wires because of hollow and cylindrical structures with nanometric sizes. Carbon atoms are first relaxed using DISCOVER module [21] to obtain the optimized structures of CNW@CNT. And then they are further optimized with another ab initio DTF methods (DMOL3). Li and Zhang [22] have used the same method
1359-6462/$ - see front matter Crown copyright Ó 2008 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved. doi:10.1016/j.scriptamat.2008.09.010
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recently to obtain the stable semiconductor nanowires encapsulated into CNT and study the electrical transport properties of them. Kang et al. [23] have also used the similar MD method (i.e. steepest descent scheme) to obtain similar structures of ultra-thin copper nanowire encapsulated into CNT. Figure 1a shows the morphology of an 11-strand CNW@CNT(9,9) (i.e., an 11-strand nanowire including 102 atoms with a helical structure that is encap˚ sulated in a CNT(9,9)). Its length and diameter are 21.9 A ˚ , respectively. The atoms that constitute the and 12.22 A CNW are colored blue for clarity. The numerical simulation is carried out by means of the classical MD method [24], in which the Newtonian equations of motion are solved numerically for a set of atoms that interact via Brenner’s ‘‘second generation’’ empirical many-body bond order potential [25]. The Brenner REBO potential contains improved analytic function and an extended database. But in the Brenner second-generation REBO potential, the fixed switching function approach is prob˚ because lematic as C–C bonds are stretched beyond 1.7 A it significantly influences the forces. So we modify the onset of interaction cut-off value to avoid this problem. Similarly, Huhtala [26] employed the adaptive intermolecular reactive empirical bond-order (AIRBO) potential [27]. The elongating behavior of the CNW@CNT is simulated by solving the equations of motions using Gear’s predictor-corrector algorithm [28]. The axial elongation of a structured CNW@CNT is achieved by applying tension at a rate of 40 m s 1 at both ends. At the same time, the atoms at both ends of the CNW@CNT are kept transparent to inter-atomic forces. The end atoms are then moved outward along the axis in small increments, followed by a conjugate gradient minimization method [29] in which the end atoms are kept fixed. In this paper, the Nose–Hoover thermostat scheme [30] is used to keep the temperature at 60K, and the time step is chosen as 1 fs. In the following paragraphs, we present an extensive set of simulation results for the CNW@CNT to elucidate the mechanical properties of this material under load. In the initial stage, the average distance between
the outer atoms of the CNW and the CNT wall is about ˚ , and thus the interaction between them is 3.16 A the long-range van der Waals potential using the Lennard–Jones potential [31]. The stretching process of an 11-strand CNW@CNT(9,9) is shown in Figure 2. There is a uniform increase in the carbon–carbon bond length. No defects are detected below the strain e = 0.22. As the strain reaches e = 0.228 the diameter of the tube apparently reduces, the necking effect [32] is observed, as shown in Figure 2a. This is mainly because pentagon–heptagon dislocation (5|7) defect [33] dispersion occurs during the stretching process. To show clearly the result, we present an atomic view of defect nucleation for CNW@CNT(9,9) in Figure 3. As diameter of the CNT decreases, the interaction between the outer atoms of the CNW and those at the tube becomes stronger. And it results in forming a more complex hybridization structure: C–C bonds can be rotated and some parts of the initial perfect hexagons are activated to form 5|7 defect during the elongation, then defect disperses all over the tube wall. With the combined effect of tension and rotation of C–C bond, some higher-order rings such as octagon and nonagon are observed. The tube tension releases its excess strain via the spontaneous formation of topological defects. The closest distance between the atom of the CNW and one of the ˚ at e = 0.38 (in general, sp3 hybridization CNT is 1.41 A ˚ [25]). Recent DFT simoccurs at the distance of 1.54 A
Figure 2. Morphological changes of the 11-strand CNW@CNT(9,9) under elongation. (a) e = 0.22, the CNT begins to break and the CNW atoms attach to the surface of the CNT wall. (b) e = 0.51, the CNT fractures completely, and the CNT atoms and CNW atoms combine. (c) e = 0.91, the CNW begins to deform into a single chain. (d) e = 1.36, the single chain is stretched and the gray atom is composed of the initial CNT. (e) At e = 2.8, the CNW@CNT reaches its critical dimension.
Figure 1. Morphologies of different CNTs encapsulating CNW. (a) CNW@CNT(9,9); (b) CNW@CNT(7,7); (c) CNW@CNT(20,0); (d) CNW@CNT(15,15); (e) CNW@CNT(30,0); (f) CNW@CNT(20,20).
Figure 3. Snapshot of the molecular dynamic simulation of the 11-strand CNW@CNT(9,9) at e = 0.228. The nucleation of the pentagon–heptagon dislocation can be seen, and much larger open rings form.
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ulation [34] indicated that carbon atoms would form covalent bonds with graphene sheets, thus affecting shell sliding. Experiments [35] also provided evidence that C– C covalent bonds can exists on the surface of a perfect nanotube. As the strain continues to increase, the cylinder of the CNT breaks (as shown in Figure 2b). Finally, the composite structure is found to be a single carbon atomic chain between the CNT’s fragments. The bonds in the linear chain are found to be of a cumulene type (i.e., all of the bond lengths are nearly equivalent), as shown in Figure 2d and e. This nanobridge structure resembles the experimental result of pulling out a long carbon nanowire at the end of a carbon nanotube [36]. And in theoretical aspect, Wang et al. [37] has also used the same MD simulation method to obtain a long stable single carbon nanowire by pulling some corner atoms of a graphite layer. Both of them obtained the stable single chain structure employing different methods. Figure 4a shows the stress–strain curves for the individual CNT, CNW, and CNW@CNT at the same stretching rate. The critical stress for the CNTs is 127 GPa, which is in good agreement with the experiment value (150 GPa) obtained by Demczyk [38]. The critical stress of the CNW and CNW@CNT are 35 GPa and 94 GPa, respectively. The strength of the CNT is much larger than the composite nanostructure made up of CNW inserted into CNT. Insertion of the CNW into CNT does not increase the critical strength of the CNT, but actually weakens it. This is mainly because during the stretching process, the atoms of the CNW attach to the defect of the CNT, causing the bond to bend. As the strain increases, the 5|7 defect becomes a large ‘‘hole” that accelerates the fracturing of the CNT. The figure of how the potential energy for CNW@CNT(9,9) varies during the elongation is also inserted in Figure 4a. It rises steadily until a few C–C bonds break and simultaneously rearrange themselves to form a 5|7 defect. As the defect becomes larger, the potential energy decreases. At the same time, the atoms of CNW attach to the breaking fragment of the CNT to form a new strong covalent bond. As the strain increases, the fracture quickly propagates along the surface of the composite structure. The latter fluctuation of the curve is mainly the result of the gliding of the carbon atoms. As an atom slips from one spot to another, the total potential changes spontaneously from a peak to a valley. Figure 4b depicts the distance between a selected pair of atoms, one of which is from the CNT and the other
is from the CNW. At e = 0.22, the potential reaches the maximum, and the distances of the four pairs of atoms ˚ . Between e = 0.22 and 0.24, the reaches about 1.54 A CNT begins to break away from the circumference of the tube, and the potential energy falls steeply. At e = 0.38, the distance between the 13 pairs of atoms ap˚ , which lead to a complex hybridization proaches 1.54 A that causes an increase in the potential energy. CNT exhibits mainly brittle behavior at high speeds, whereas the CNW@CNT shows apparent flexibility and plasticity. In contrast to our research, Marques et al. [13] predicted that under high temperatures and in the presence of defects (Stone–Wales or vacancies) the tube would exhibit mainly plastic deformation, and the stretching tube would form a single wire composed of 14 atoms. He suggested that such defects (Stone–Wales or vacancies) play an important role in the plastic dynamics of the necking and thinning of a CNT. In order to show how the vacancy defect of CNT affects the stretching behavior of CNW@CNT, we present the variety of strain energy and axial force in the tensile process in Figure 5a. The solid square curve corresponds to CNW embedded into perfect CNT(9,9). The hollow circle and triangle curves correspond to CNW embedded into CNT with one atom and two atoms vacancy, respectively. From the upper one in Figure 5a showing the strain energy as a function of strain, CNW embedded into perfect CNT needs higher energy to override the barrier than the other two types. Furthermore, the strain energy curve suffers a sharp drop after the critical point. As the atom vacancy increases, the energy barrier decreases and the curves vary smoothly after the critical point. The lower one in Figure 5a also shows the CNW embedded into perfect CNT can suffer higher axial force than the other two types. Figure 5b shows the computed force–strain relationship of the CNW@CNT under different stretching rate. The critical forces are 79.2, 88.7 ˚ 1 under the rates 5.5% ps 1, 11% ps 1 and 87.0 eV A and 22% ps 1, respectively. Furthermore, the critical strain does not decrease as the stretching rate increases. The critical strain under stretching rate 5.5% ps 1 and 11% ps 1 are 22.5%, 32.3%, respectively. This is mainly due to the thermal fluctuation effect under lower stretching rate. This interesting result is similar to the experimental result of stretching nanocrystalline copper [39]. As the stretching rate increases, some C–C bonds between atoms stretch larger in a shorter time. This abrupt
Figure 4. (a) Stress–strain curves for the CNT(9,9), 11-strand CNW, and 11-strand CNW@CNT(9,9). Potential energy versus strain for the MD simulation of the stretching of the 11-strand CNW@CNT(9,9) is inserted. (b) Distances between selected atoms from the CNW and CNT at different strains.
Figure 5. (a) The upper one shows the relationship between strain energy and strain for perfect CNW@CNT and CNW@CNT with vacancy. The lower one shows the axial force as a function of strain for CNW@CNT as referred. (b) Axial forces as a function of strain under different stretching rates.
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variety in the structure leads to fracture easily. Stretching rates really affect the critical strain of CNT materials [40] and metallic nanowires [41]. We have also simulated the process of stretching CNW@CNT under experimentally accessible rate 0.1 m s 1 (0.14% ps 1) for comparison. The critical strain for it is about 20%, which is smaller than that under the strain rate 5.5% ps 1. With respect to CNT-based material in experiment, Yu et al. [42] have reported that the yield strain of multiwall CNT is as high as 12% at room temperature. The critical strain of CNW@CNT is a little larger than these experimental critical strains of CNT-based materials. Furthermore, the critical strains of Ni nanowire [41] are 11–20% under different stretching rate ranging from 0.05 to 15% ps 1, which is similar to our results. In conclusion, our results provide further insight into the stretching behavior of nanocomposite structures that are made up of a CNW inserted into a CNT. This CNW@CNT undergoes a large elongation in which a pentagon–heptagon dislocation (5|7) defect, octagonal defects and higher-order rings are observed. Insertion of the CNW into CNT increases the plastic elongation of a CNW@CNT under axial stretching. As the strain continues to increase, the composite structure is found to become a long single carbon atomic chain. Interestingly, insertion of the CNW into CNT does not increase the critical strength of the CNT but weaken. A large hole caused by (5|7) defect make the carbon tube fracture easily. We acknowledge support from the New Century Excellent Talent program of the Ministry of Education of the Government of the People’s Republic of China in the form of Grant No. NCET-05-0599. This project was also supported by Grant Nos. 50571093, 50831003 and 50871062 from the National Natural Science Foundation of China and this work was supported by a grant from National Science Fund for Distinguished Young Scholars of China (No. 50625101) and Scientific Research Foundation for Returned Scholars (JIAO WAI SI LIU2007–1108), Ministry of Education of China. We also thank the Scientific Research Foundation of Shandong University Project No. 10000067950014. We also acknowledge the City University of Hong Kong Strategic Research Grant Project No. 7002204. The work was also supported by the computing facilities provided by ACIM.. [1] S.L. Mielke, D. Troya, S. Zhang, J. Li, S. Xiao, R. Car, R.S. Ruoff, G.C. Schatz, T. Belytschko, Chem. Phys. Lett. 390 (2004) 413. [2] K.M. Liew, C.H. Wong, X.Q. He, M.J. Tan, S.A. Meguid, Phys. Rev. B 69 (2004) 115429. [3] P.M. Ajayan, O. Stephan, P. Redlich, C. Colliex, Nature 375 (1995) 564. [4] H.S. Park, J.A. Zimmerman, Scripta Mater. 54 (2006) 1127. [5] J. Diao, K. Gall, M.L. Dunn, J.A. Zimmerman, Acta Mater. 54 (2006) 643. [6] H.S. Park, C. Ji, Acta Mater. 54 (2006) 2645. [7] J. Diao, K. Gall, M.L. Dunn, Nano Lett. 4 (10) (2004) 1863.
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Scripta Materialia 60 (2009) 129–132 www.elsevier.com/locate/scriptamat
Stretching behavior of a carbon nanowire encapsulated in a carbon nanotube H. Li,a,* F.W. Sun,b K.M. Liewc and X.F. Liua a
School of Materials Science and Engineering and Key Laboratory of Liquid Structure and Heredity of Materials, Ministry of Education, Shandong University, China b Physics Department, Ocean University of China, Qingdao, China c Department of Building and Construction, City University of Hong Kong, Kowloon, Hong Kong Received 5 May 2008; revised 15 August 2008; accepted 4 September 2008 Available online 26 September 2008
Molecular dynamic simulations are performed to study the deformation behavior of nanocomposite structures formed by the insertion of a carbon nanowire (CNW) into a carbon nanotube (CNW@CNT) under tension. The simulation results indicate that insertion of the CNW into CNT makes the plastic elongation increase. A superplastic deformation behavior is observed and finally, CNW@CNT is drawn to be a very long elongated nanobridge. During the tensile deformation, pentagon–heptagon defects, octagonal defects, and higher-order rings are observed. A large hole caused by some defects accelerates the fracturing of the CNT. Crown copyright Ó 2008 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved. Keywords: Mechanical properties testing; Tension test; Nanocomposite; Plastic deformation; Molecular dynamics
Carbon nanotubes (CNTs) have attracted interest not only for their unusual electrical and mechanical properties [1,2], but also because of their hollow interior that serves as a nanometric capillary [3] in nanomaterial fabrication. Filling single-walled carbon nanotubes (SWNTs) with certain materials creates one-dimensional (1D) nanowires that have exciting applications. Nanowires have a very large surface-area/volume ratio as compared to bulk materials, and their structures and properties can be quite different from those of bulk materials [4–6]. Recent molecular dynamic (MD) simulations have offered more evidence of the formation of a stable nanobridge in metallic nanowires under tensile deformation [7]. The MD simulations of the mechanical behavior of nanowires have also been investigated [8,9]. Ji and Park [10] used the classical MD simulation to study the inelastic deformation of metallic nanowires, and demonstrated that the geometry of nanomaterials can be utilized to control the operant modes of inelastic deformation. In previous experiments, the nonlinear response of a tube under a high strain has been studied [11,12]. For instance, a carbon fiber was stretched to form a nanobridge under a high-resolution transmission electron microscope [13]. Furthermore, Zhao et al. [14] observed * Corresponding author. E-mail: [email protected]
that linear carbon chain consisting of more than 100 atoms encapsulated into CNT in the cathode deposits by the method of hydrogen arc discharge evaporation. Not only can linear CNW be embedded into CNT, but other form of carbon such as 1D periodic chains C60 fullerene molecules inside single-walled CNT, can also be observed [15,16]. As to more complex CNW structures, multi-walled CNT irradiated by Ar [17] and Si [18] ion beams showed the novel formation of amorphous carbon nanowire network. Nanocomposite materials have been one of the most promising materials for mechanical application. Danailov [19] used empirical potential and atomistic simulation to model the bending behavior of single-walled carbon nanotube encapsulating metal nanowire. Another relative study [20] showed the fracture and fatigue properties of CNT, CNT/polymer, and CNT/epoxy under load. In this study, the object is to perform a simulation about the stretching behavior of carbon nanowires that are inserted into carbon nanotubes (CNW@CNTs). CNTs are good templates for the manufacture of 1D ultra-thin wires because of hollow and cylindrical structures with nanometric sizes. Carbon atoms are first relaxed using DISCOVER module [21] to obtain the optimized structures of CNW@CNT. And then they are further optimized with another ab initio DTF methods (DMOL3). Li and Zhang [22] have used the same method
1359-6462/$ - see front matter Crown copyright Ó 2008 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved. doi:10.1016/j.scriptamat.2008.09.010
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recently to obtain the stable semiconductor nanowires encapsulated into CNT and study the electrical transport properties of them. Kang et al. [23] have also used the similar MD method (i.e. steepest descent scheme) to obtain similar structures of ultra-thin copper nanowire encapsulated into CNT. Figure 1a shows the morphology of an 11-strand CNW@CNT(9,9) (i.e., an 11-strand nanowire including 102 atoms with a helical structure that is encap˚ sulated in a CNT(9,9)). Its length and diameter are 21.9 A ˚ , respectively. The atoms that constitute the and 12.22 A CNW are colored blue for clarity. The numerical simulation is carried out by means of the classical MD method [24], in which the Newtonian equations of motion are solved numerically for a set of atoms that interact via Brenner’s ‘‘second generation’’ empirical many-body bond order potential [25]. The Brenner REBO potential contains improved analytic function and an extended database. But in the Brenner second-generation REBO potential, the fixed switching function approach is prob˚ because lematic as C–C bonds are stretched beyond 1.7 A it significantly influences the forces. So we modify the onset of interaction cut-off value to avoid this problem. Similarly, Huhtala [26] employed the adaptive intermolecular reactive empirical bond-order (AIRBO) potential [27]. The elongating behavior of the CNW@CNT is simulated by solving the equations of motions using Gear’s predictor-corrector algorithm [28]. The axial elongation of a structured CNW@CNT is achieved by applying tension at a rate of 40 m s 1 at both ends. At the same time, the atoms at both ends of the CNW@CNT are kept transparent to inter-atomic forces. The end atoms are then moved outward along the axis in small increments, followed by a conjugate gradient minimization method [29] in which the end atoms are kept fixed. In this paper, the Nose–Hoover thermostat scheme [30] is used to keep the temperature at 60K, and the time step is chosen as 1 fs. In the following paragraphs, we present an extensive set of simulation results for the CNW@CNT to elucidate the mechanical properties of this material under load. In the initial stage, the average distance between
the outer atoms of the CNW and the CNT wall is about ˚ , and thus the interaction between them is 3.16 A the long-range van der Waals potential using the Lennard–Jones potential [31]. The stretching process of an 11-strand CNW@CNT(9,9) is shown in Figure 2. There is a uniform increase in the carbon–carbon bond length. No defects are detected below the strain e = 0.22. As the strain reaches e = 0.228 the diameter of the tube apparently reduces, the necking effect [32] is observed, as shown in Figure 2a. This is mainly because pentagon–heptagon dislocation (5|7) defect [33] dispersion occurs during the stretching process. To show clearly the result, we present an atomic view of defect nucleation for CNW@CNT(9,9) in Figure 3. As diameter of the CNT decreases, the interaction between the outer atoms of the CNW and those at the tube becomes stronger. And it results in forming a more complex hybridization structure: C–C bonds can be rotated and some parts of the initial perfect hexagons are activated to form 5|7 defect during the elongation, then defect disperses all over the tube wall. With the combined effect of tension and rotation of C–C bond, some higher-order rings such as octagon and nonagon are observed. The tube tension releases its excess strain via the spontaneous formation of topological defects. The closest distance between the atom of the CNW and one of the ˚ at e = 0.38 (in general, sp3 hybridization CNT is 1.41 A ˚ [25]). Recent DFT simoccurs at the distance of 1.54 A
Figure 2. Morphological changes of the 11-strand CNW@CNT(9,9) under elongation. (a) e = 0.22, the CNT begins to break and the CNW atoms attach to the surface of the CNT wall. (b) e = 0.51, the CNT fractures completely, and the CNT atoms and CNW atoms combine. (c) e = 0.91, the CNW begins to deform into a single chain. (d) e = 1.36, the single chain is stretched and the gray atom is composed of the initial CNT. (e) At e = 2.8, the CNW@CNT reaches its critical dimension.
Figure 1. Morphologies of different CNTs encapsulating CNW. (a) CNW@CNT(9,9); (b) CNW@CNT(7,7); (c) CNW@CNT(20,0); (d) CNW@CNT(15,15); (e) CNW@CNT(30,0); (f) CNW@CNT(20,20).
Figure 3. Snapshot of the molecular dynamic simulation of the 11-strand CNW@CNT(9,9) at e = 0.228. The nucleation of the pentagon–heptagon dislocation can be seen, and much larger open rings form.
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ulation [34] indicated that carbon atoms would form covalent bonds with graphene sheets, thus affecting shell sliding. Experiments [35] also provided evidence that C– C covalent bonds can exists on the surface of a perfect nanotube. As the strain continues to increase, the cylinder of the CNT breaks (as shown in Figure 2b). Finally, the composite structure is found to be a single carbon atomic chain between the CNT’s fragments. The bonds in the linear chain are found to be of a cumulene type (i.e., all of the bond lengths are nearly equivalent), as shown in Figure 2d and e. This nanobridge structure resembles the experimental result of pulling out a long carbon nanowire at the end of a carbon nanotube [36]. And in theoretical aspect, Wang et al. [37] has also used the same MD simulation method to obtain a long stable single carbon nanowire by pulling some corner atoms of a graphite layer. Both of them obtained the stable single chain structure employing different methods. Figure 4a shows the stress–strain curves for the individual CNT, CNW, and CNW@CNT at the same stretching rate. The critical stress for the CNTs is 127 GPa, which is in good agreement with the experiment value (150 GPa) obtained by Demczyk [38]. The critical stress of the CNW and CNW@CNT are 35 GPa and 94 GPa, respectively. The strength of the CNT is much larger than the composite nanostructure made up of CNW inserted into CNT. Insertion of the CNW into CNT does not increase the critical strength of the CNT, but actually weakens it. This is mainly because during the stretching process, the atoms of the CNW attach to the defect of the CNT, causing the bond to bend. As the strain increases, the 5|7 defect becomes a large ‘‘hole” that accelerates the fracturing of the CNT. The figure of how the potential energy for CNW@CNT(9,9) varies during the elongation is also inserted in Figure 4a. It rises steadily until a few C–C bonds break and simultaneously rearrange themselves to form a 5|7 defect. As the defect becomes larger, the potential energy decreases. At the same time, the atoms of CNW attach to the breaking fragment of the CNT to form a new strong covalent bond. As the strain increases, the fracture quickly propagates along the surface of the composite structure. The latter fluctuation of the curve is mainly the result of the gliding of the carbon atoms. As an atom slips from one spot to another, the total potential changes spontaneously from a peak to a valley. Figure 4b depicts the distance between a selected pair of atoms, one of which is from the CNT and the other
is from the CNW. At e = 0.22, the potential reaches the maximum, and the distances of the four pairs of atoms ˚ . Between e = 0.22 and 0.24, the reaches about 1.54 A CNT begins to break away from the circumference of the tube, and the potential energy falls steeply. At e = 0.38, the distance between the 13 pairs of atoms ap˚ , which lead to a complex hybridization proaches 1.54 A that causes an increase in the potential energy. CNT exhibits mainly brittle behavior at high speeds, whereas the CNW@CNT shows apparent flexibility and plasticity. In contrast to our research, Marques et al. [13] predicted that under high temperatures and in the presence of defects (Stone–Wales or vacancies) the tube would exhibit mainly plastic deformation, and the stretching tube would form a single wire composed of 14 atoms. He suggested that such defects (Stone–Wales or vacancies) play an important role in the plastic dynamics of the necking and thinning of a CNT. In order to show how the vacancy defect of CNT affects the stretching behavior of CNW@CNT, we present the variety of strain energy and axial force in the tensile process in Figure 5a. The solid square curve corresponds to CNW embedded into perfect CNT(9,9). The hollow circle and triangle curves correspond to CNW embedded into CNT with one atom and two atoms vacancy, respectively. From the upper one in Figure 5a showing the strain energy as a function of strain, CNW embedded into perfect CNT needs higher energy to override the barrier than the other two types. Furthermore, the strain energy curve suffers a sharp drop after the critical point. As the atom vacancy increases, the energy barrier decreases and the curves vary smoothly after the critical point. The lower one in Figure 5a also shows the CNW embedded into perfect CNT can suffer higher axial force than the other two types. Figure 5b shows the computed force–strain relationship of the CNW@CNT under different stretching rate. The critical forces are 79.2, 88.7 ˚ 1 under the rates 5.5% ps 1, 11% ps 1 and 87.0 eV A and 22% ps 1, respectively. Furthermore, the critical strain does not decrease as the stretching rate increases. The critical strain under stretching rate 5.5% ps 1 and 11% ps 1 are 22.5%, 32.3%, respectively. This is mainly due to the thermal fluctuation effect under lower stretching rate. This interesting result is similar to the experimental result of stretching nanocrystalline copper [39]. As the stretching rate increases, some C–C bonds between atoms stretch larger in a shorter time. This abrupt
Figure 4. (a) Stress–strain curves for the CNT(9,9), 11-strand CNW, and 11-strand CNW@CNT(9,9). Potential energy versus strain for the MD simulation of the stretching of the 11-strand CNW@CNT(9,9) is inserted. (b) Distances between selected atoms from the CNW and CNT at different strains.
Figure 5. (a) The upper one shows the relationship between strain energy and strain for perfect CNW@CNT and CNW@CNT with vacancy. The lower one shows the axial force as a function of strain for CNW@CNT as referred. (b) Axial forces as a function of strain under different stretching rates.
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variety in the structure leads to fracture easily. Stretching rates really affect the critical strain of CNT materials [40] and metallic nanowires [41]. We have also simulated the process of stretching CNW@CNT under experimentally accessible rate 0.1 m s 1 (0.14% ps 1) for comparison. The critical strain for it is about 20%, which is smaller than that under the strain rate 5.5% ps 1. With respect to CNT-based material in experiment, Yu et al. [42] have reported that the yield strain of multiwall CNT is as high as 12% at room temperature. The critical strain of CNW@CNT is a little larger than these experimental critical strains of CNT-based materials. Furthermore, the critical strains of Ni nanowire [41] are 11–20% under different stretching rate ranging from 0.05 to 15% ps 1, which is similar to our results. In conclusion, our results provide further insight into the stretching behavior of nanocomposite structures that are made up of a CNW inserted into a CNT. This CNW@CNT undergoes a large elongation in which a pentagon–heptagon dislocation (5|7) defect, octagonal defects and higher-order rings are observed. Insertion of the CNW into CNT increases the plastic elongation of a CNW@CNT under axial stretching. As the strain continues to increase, the composite structure is found to become a long single carbon atomic chain. Interestingly, insertion of the CNW into CNT does not increase the critical strength of the CNT but weaken. A large hole caused by (5|7) defect make the carbon tube fracture easily. We acknowledge support from the New Century Excellent Talent program of the Ministry of Education of the Government of the People’s Republic of China in the form of Grant No. NCET-05-0599. This project was also supported by Grant Nos. 50571093, 50831003 and 50871062 from the National Natural Science Foundation of China and this work was supported by a grant from National Science Fund for Distinguished Young Scholars of China (No. 50625101) and Scientific Research Foundation for Returned Scholars (JIAO WAI SI LIU2007–1108), Ministry of Education of China. We also thank the Scientific Research Foundation of Shandong University Project No. 10000067950014. We also acknowledge the City University of Hong Kong Strategic Research Grant Project No. 7002204. The work was also supported by the computing facilities provided by ACIM.. [1] S.L. Mielke, D. Troya, S. Zhang, J. Li, S. Xiao, R. Car, R.S. Ruoff, G.C. Schatz, T. Belytschko, Chem. Phys. Lett. 390 (2004) 413. [2] K.M. Liew, C.H. Wong, X.Q. He, M.J. Tan, S.A. Meguid, Phys. Rev. B 69 (2004) 115429. [3] P.M. Ajayan, O. Stephan, P. Redlich, C. Colliex, Nature 375 (1995) 564. [4] H.S. Park, J.A. Zimmerman, Scripta Mater. 54 (2006) 1127. [5] J. Diao, K. Gall, M.L. Dunn, J.A. Zimmerman, Acta Mater. 54 (2006) 643. [6] H.S. Park, C. Ji, Acta Mater. 54 (2006) 2645. [7] J. Diao, K. Gall, M.L. Dunn, Nano Lett. 4 (10) (2004) 1863.
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