- Email: [email protected]
Transportation of hydrogen molecules using carbon nanotubes in torsion
1870
CARBON
4 7 ( 2 0 0 9 ) 1 8 6 7 –1 8 8 5
Singapore (NRF-CRP2–2007–02) to LJL and A*-grant (#072 101 0020) to PC. [4]
Appendix A. Supplementary data
[5]
Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.carbon.2009.03.005. [6] R E F E R E N C E S
[7]
[1] Wang Y, Di C, Liu Y, Kajiura H, Ye S, Cao L, et al. Optimizing single-walled carbon nanotube films for applications in electroluminescent devices. Adv Mater 2008;20:1–8. [2] Geng HZ, Kim KK, So KP, Lee YS, Chang Y, Lee YH. Effect of acid treatment on carbon nanotube-based flexible transparent conducting films. J Am Chem Soc 2007;129:7758–9. [3] Parekh BB, Fanchini G, Eda G, Chhowalla M. Improved conductivity of transparent single-wall carbon nanotube thin
[8]
[9]
films via stable postdeposition functionalization. Appl Phys Lett 2007;90:1219131–3. Gru¨ner G. Carbon nanotube films for transparent and plastic electronics. J Mater Chem 2006;16:3533–9. Graupner R, Abraham J, Vencelova A, Seyller T, Hennrich F, Kappes MM, et al. Doping of single-walled carbon nanotube bundles by Brønsted acids. Phys Chem Chem Phys 2003;5:5472–6. Burghard M. Electronic and vibrational properties of chemically modified single-wall carbon nanotubes. Surf Sci Rep 2005;58:1–109. Osswald S, Flahaut E, Gogotsi Y. In situ Raman spectroscopy study of oxidation of double- and single-wall carbon nanotubes. Chem Mater 2006;18:1525–33. Rakov EG, Chemistry of carbon nanotubes. In: Gogotsi Y, editor. Nanomaterials handbook, Boca Raton: Taylor & Francis; 2006. p. 105–77. Wang C, Zhou G, Wu J, Gu BL, Duan W. Effects of vacancycarboxyl pair functionalization on electronic properties of carbon nanotubes. Appl Phys Lett 2006;89:1731301–3.
Transportation of hydrogen molecules using carbon nanotubes in torsion Q. Wang* Department of Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, Manitoba, Canada R3T 5V6
A R T I C L E I N F O
A B S T R A C T
Article history:
The transportation of hydrogen molecules using carbon nanotubes subjected to torsion is
Received 28 January 2009
studied with molecular dynamics. Molecular dynamics simulations reveal that the trans-
Accepted 5 March 2009
portation in a (10, 0) carbon nanotube is a result of the van der Waals effect through the
Available online 16 March 2009
propagation of the kink initiated at the onset of the tube torsional buckling. In addition, the applied torsional loading rate has an obvious effect on the orientation of the molecular transportation. On the other hand, the motion of the molecules in a (10, 10) carbon nanotube is found to be less oriented. The mechanism of the transportation in the larger carbon nanotube is investigated through the transform of the collapsed wall of the tube in the dynamic process of the torsional buckling. Ó 2009 Elsevier Ltd. All rights reserved.
The remarkable electrical, mechanical, and thermal properties of carbon nanotubes (CNTs) [1] enable them to be used for the development of devices for microelectromechanical and nanoelectromechanical system applications. Particularly, the morphology of their hollow tubes provides an excellent opportunity to create nanopumping devises for atomic transportation [2] and have great potential in the areas of nanorobotices, helium energetics, medical drug delivery, micropumps, chemical process control, and molecular medicine [3,4]. The effects of CNTs diameter on mass density,
molecular distribution, and molecular orientation of water molecules inside and outside of CNTs were identified for both confined and unconfined fluids using molecular dynamics [5]. Particularly, it was concluded that interaction with the CNT influence the orientation of water molecules near the carbon surface. It was demonstrated [6] that in CNTs, when the orientation of the water molecules was maintained along one direction, a net water transport along that direction can be attained due to coupling between rotational and translational motions. A novel nanopumping effect on the activation of
* Fax: +1 204 275 7507. E-mail addresses: [email protected]. 0008-6223/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2009.03.030
CARBON
4 7 ( 20 0 9 ) 1 8 6 7–18 8 5
an axial gas flow in a CNT by actuating Rayleigh traveling waves on the nanotube surface and the measurement of the flow of hydrogen and helium gases were reported [3]. Applying torsion to CNTs was recently reported for atomic transportation [7]. The transportation of helium atoms was realized with van der Waals force through the induced kink propagation. Higher environmental temperature and strain rate were found to promote the atomic transportation using CNTs. The present research reports the transportation of hydrogen molecules using CNTs subjected to torsion by molecular dynamics at room temperature. In particular, the effect of the loading rate and the CNT size on the orientation of the hydrogen molecules is investigated. In simulations, the time step used in the molecular dynamics during the loading process is chosen to be from 0.01 to 0.06 fs to make the simulations much reliable and accurate, and the time step in the dynamic process after the loading is chosen to be 0.5 fs to efficiently describe longer processes. The interatomic interactions are described by the force field of condensed-phased optimized molecular potential for atomistic simulation studies [8], which has been proven to be applicable in describing the mechanical properties of CNTs [9]. The Andersen method is employed in the thermostat to control the thermodynamic temperature and generate the correct statistical ensemble. The transportation of 64 hydrogen molecules encapsulated in a (10, 0) CNT with the length of 6.2 nm is first investigated. The molecules are installed in the CNT with a congregated pattern before any minimization process. The morphology of the CNT and the encapsulated molecules with the congregated pattern after the minimization process is shown in Fig. 1. Preliminary instability analysis shows that the CNT keeps the stable state at a torsion angle, 0.524 rad, applied to the left clamped end of the tube. Fig. 2a shows the snapshot of the structure at t ¼ 7 ps when addi-
1871
tional torsion angle, 1.222 rad, a sufficiently large angle for the transportation of the molecules, with a rate of 0.244 rad/ ps, is applied to the left end. It is clearly seen that most of the molecules are pushed rightward with only three molecules left to the left side of the kink at the current moment since the first cluster of the molecules is originally placed close to the left end of the tube. The snapshot of the CNT and hydrogen molecules at the end of the molecular dynamics process, t ¼ 45 ps, is seen in Fig. 2b. Similar to the observations of transportation of helium atoms using CNTs [7], the kink, which is initiated on the tube wall subjected a torsion angel beyond the buckling capacity of the tube, starts to expand rightward, and consequently 61 molecules are pumped out of the right end of the CNT, leaving only three molecules pushed out of the left end. The orientation of a majority of the molecules can therefore be realized by subjecting torsion with the rate, 0.245 rad/ps. The driving force for molecular transportation is from the kink propagation or expansion which, through the strong van der Waals force between the tube wall and molecules, induces motions of the encapsulated molecules towards the direction of the kink propagation. The snapshot of the same tube and molecules at t ¼ 24 ps is provided in Fig. 3a with the same dynamic process but with a lower rate, 0.067 rad/ps. Because of the lower loading rate, the accelerations of hydrogen molecules are smaller than those of the molecules in the tube subjected to a higher loading rate studied in Fig. 2 [7]. As a result, 11 molecules are locked to the left side of the kink location at the moment, while the others are pushed to move rightward with the kink propagation. With further shrink of the tube wall throughout the longitudinal direction of the tube due to the kink propagation, the hydrogen molecules are finally pushed out of the tube at t ¼ 58 ps, shown in Fig. 3b. The studies of helium atomic transportation in CNTs at lower loading rate [7]
Fig. 1 – The (10, 0) zigzag CNT containing 64 hydrogen molecules.
Fig. 2 – Molecular dynamics simulations of 64 hydrogen molecules encapsulated in the (10, 0) CNT subjected to torsion with a rate of 0.245 rad/ps at (a) 7 ps with three hydrogen molecules pushed leftward; and (b) 45 ps with all molecules out of the tube.
1872
CARBON
4 7 ( 2 0 0 9 ) 1 8 6 7 –1 8 8 5
Fig. 3 – Molecular dynamics simulations of 64 hydrogen molecules encapsulated in the (10, 0) CNT subjected to torsion with a rate of 0.067 rad/ps at (a) 24 ps with eleven hydrogen molecules pushed leftward; and (b) 58 ps with all molecules out of the tube.
Fig. 4 – Molecular dynamics simulations of 64 hydrogen molecules encapsulated in the (10, 10) CNT subjected to torsion with a rate of 1.745 rad/ps at (a) 2 ps with a left-side view when the tube cross section starts shrinking from a triangle shape; and (b) 10 ps when the cross section keeps shrinking and consequently some molecules are squeezed outside of the left end of the tube; (c) 20 ps when the cross section transforms to an elliptical shape with more molecules squeezed outside of the tube; and (d) 40 ps with a left-side view when the cross section completely transform to the elliptical shape with almost all molecules out of both ends of the tube.
CARBON
4 7 ( 20 0 9 ) 1 8 6 7–18 8 5
showed that some helium atoms were finally remained in the tube and could not be pumped out of the tube. However, since hydrogen is the lightest atom, the molecules to the left side of the kink are also found to be prone to move when the tube wall continues to shrink, and finally 11 molecules are observed to be pushed out of the left end of the tube, while the others are out of the right end of the tube. The simulations in Fig. 3a–b indicate that the orientation of the molecular transportation in the CNT is dependent upon the loading rate. Although all the molecules could be pushed out of the tube, the orientation of a majority of the molecules along an assigned direction could not be fulfilled for the transportation of hydrogen molecules at a lower rate. To investigate the orientation of the transportation in a larger CNT, molecular dynamics simulations of 64 hydrogen molecules encapsulated in a (10, 10) CNT with the length of 8.2 nm, subjected to a torsion angle of 0.873 rad with the rate of 1.745 rad/ps, are conducted. Fig. 4a displays the snapshot of the tube and molecules along longitudinal direction and a left-side view at t ¼ 2 ps after the torsion is applied. It shows the tube cross section starts shrinking from a triangle shape. At the current moment, the van der Waals force between the molecular clusters and the tube wall is still very weak due to the larger diameter of the tube. Therefore, the accelerations of the molecules are very small and almost all the molecules are found to only vibrate around their original locations. At t ¼ 10 ps shown in Fig. 4b, the cross section of the tube keeps shrinking and consequently some molecules to the left side of the kink start to move and are squeezed out of the left end of the tube, while the other molecules to the right side of the kink still stay in the tube as the right portion of the tube remains a virtually circular shape. Fig. 4c reveals further shrink of the cross section and its transition from the triangle shape to an elliptical one with more molecules squeezed out of the tube at t ¼ 20 ps. Finally, Fig. 4d shows a complete transform of the cross section to the elliptical shape, seen from the side view, with almost all molecules pushed out of both ends of the tube at t ¼ 40 ps. In the
1873
two figures, the kink finally expands to the whole tube, and consequently all the molecules are accelerated to move to the two ends of the tube due to increasing van der Waals force through the shrinking wall. It is clearly seen that the orientation of the transportation along the direction of the kink propagation cannot be efficiently fulfilled with the larger CNT.
Acknowledgement This research was undertaken, in part, thanks to funding from the Canada Research Chairs Program (CRC) and the National Science and Engineering Research Council (NSERC).
R E F E R E N C E S
[1] Iijima S. Helical microtubules of graphitic carbon. Nature 1991;354(6348):56–8. [2] Kra´l1 P, Toma´nek D. Laser-driven atomic pump. Phys Rev Lett 1999;82(26):5373–6. [3] Insepov Z, Wolf D, Hassanein A. Nanopumping using carbon nanotubes. Nano Lett 2006;6(9):1893–5. [4] Thorsen T, Marrkl SJ, Quake SR. Microfluidic large-scale integration. Science 2002;298(5593):580–4. [5] Thomas JA, McGaughey AJH. Density, distribution, and orientation of water molecules inside and outside carbon nanotubes. J Chem Phys 2008;128(8):084715. [6] Joseph S, Aluru NR. Pumping of confined water in carbon nanotubes by rotation–translation coupling. Phys Rev Lett 2008;101(6):064502. [7] Wang Q. Atomic transportation via carbon nanotubes. Nano Lett 2009;9(1):245–9. [8] Rigby D, Sun H, Eichinger BE. Computer simulations of poly(ethylene oxide): force field, PVT diagram and cyclization behaviour. Polym Int 1997;44(3):311–30. [9] Wang Q. Torsional buckling of double-walled carbon nanotubes. Carbon 2008;46(8):1172–4.
CARBON
4 7 ( 2 0 0 9 ) 1 8 6 7 –1 8 8 5
Singapore (NRF-CRP2–2007–02) to LJL and A*-grant (#072 101 0020) to PC. [4]
Appendix A. Supplementary data
[5]
Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.carbon.2009.03.005. [6] R E F E R E N C E S
[7]
[1] Wang Y, Di C, Liu Y, Kajiura H, Ye S, Cao L, et al. Optimizing single-walled carbon nanotube films for applications in electroluminescent devices. Adv Mater 2008;20:1–8. [2] Geng HZ, Kim KK, So KP, Lee YS, Chang Y, Lee YH. Effect of acid treatment on carbon nanotube-based flexible transparent conducting films. J Am Chem Soc 2007;129:7758–9. [3] Parekh BB, Fanchini G, Eda G, Chhowalla M. Improved conductivity of transparent single-wall carbon nanotube thin
[8]
[9]
films via stable postdeposition functionalization. Appl Phys Lett 2007;90:1219131–3. Gru¨ner G. Carbon nanotube films for transparent and plastic electronics. J Mater Chem 2006;16:3533–9. Graupner R, Abraham J, Vencelova A, Seyller T, Hennrich F, Kappes MM, et al. Doping of single-walled carbon nanotube bundles by Brønsted acids. Phys Chem Chem Phys 2003;5:5472–6. Burghard M. Electronic and vibrational properties of chemically modified single-wall carbon nanotubes. Surf Sci Rep 2005;58:1–109. Osswald S, Flahaut E, Gogotsi Y. In situ Raman spectroscopy study of oxidation of double- and single-wall carbon nanotubes. Chem Mater 2006;18:1525–33. Rakov EG, Chemistry of carbon nanotubes. In: Gogotsi Y, editor. Nanomaterials handbook, Boca Raton: Taylor & Francis; 2006. p. 105–77. Wang C, Zhou G, Wu J, Gu BL, Duan W. Effects of vacancycarboxyl pair functionalization on electronic properties of carbon nanotubes. Appl Phys Lett 2006;89:1731301–3.
Transportation of hydrogen molecules using carbon nanotubes in torsion Q. Wang* Department of Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, Manitoba, Canada R3T 5V6
A R T I C L E I N F O
A B S T R A C T
Article history:
The transportation of hydrogen molecules using carbon nanotubes subjected to torsion is
Received 28 January 2009
studied with molecular dynamics. Molecular dynamics simulations reveal that the trans-
Accepted 5 March 2009
portation in a (10, 0) carbon nanotube is a result of the van der Waals effect through the
Available online 16 March 2009
propagation of the kink initiated at the onset of the tube torsional buckling. In addition, the applied torsional loading rate has an obvious effect on the orientation of the molecular transportation. On the other hand, the motion of the molecules in a (10, 10) carbon nanotube is found to be less oriented. The mechanism of the transportation in the larger carbon nanotube is investigated through the transform of the collapsed wall of the tube in the dynamic process of the torsional buckling. Ó 2009 Elsevier Ltd. All rights reserved.
The remarkable electrical, mechanical, and thermal properties of carbon nanotubes (CNTs) [1] enable them to be used for the development of devices for microelectromechanical and nanoelectromechanical system applications. Particularly, the morphology of their hollow tubes provides an excellent opportunity to create nanopumping devises for atomic transportation [2] and have great potential in the areas of nanorobotices, helium energetics, medical drug delivery, micropumps, chemical process control, and molecular medicine [3,4]. The effects of CNTs diameter on mass density,
molecular distribution, and molecular orientation of water molecules inside and outside of CNTs were identified for both confined and unconfined fluids using molecular dynamics [5]. Particularly, it was concluded that interaction with the CNT influence the orientation of water molecules near the carbon surface. It was demonstrated [6] that in CNTs, when the orientation of the water molecules was maintained along one direction, a net water transport along that direction can be attained due to coupling between rotational and translational motions. A novel nanopumping effect on the activation of
* Fax: +1 204 275 7507. E-mail addresses: [email protected]. 0008-6223/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2009.03.030
CARBON
4 7 ( 20 0 9 ) 1 8 6 7–18 8 5
an axial gas flow in a CNT by actuating Rayleigh traveling waves on the nanotube surface and the measurement of the flow of hydrogen and helium gases were reported [3]. Applying torsion to CNTs was recently reported for atomic transportation [7]. The transportation of helium atoms was realized with van der Waals force through the induced kink propagation. Higher environmental temperature and strain rate were found to promote the atomic transportation using CNTs. The present research reports the transportation of hydrogen molecules using CNTs subjected to torsion by molecular dynamics at room temperature. In particular, the effect of the loading rate and the CNT size on the orientation of the hydrogen molecules is investigated. In simulations, the time step used in the molecular dynamics during the loading process is chosen to be from 0.01 to 0.06 fs to make the simulations much reliable and accurate, and the time step in the dynamic process after the loading is chosen to be 0.5 fs to efficiently describe longer processes. The interatomic interactions are described by the force field of condensed-phased optimized molecular potential for atomistic simulation studies [8], which has been proven to be applicable in describing the mechanical properties of CNTs [9]. The Andersen method is employed in the thermostat to control the thermodynamic temperature and generate the correct statistical ensemble. The transportation of 64 hydrogen molecules encapsulated in a (10, 0) CNT with the length of 6.2 nm is first investigated. The molecules are installed in the CNT with a congregated pattern before any minimization process. The morphology of the CNT and the encapsulated molecules with the congregated pattern after the minimization process is shown in Fig. 1. Preliminary instability analysis shows that the CNT keeps the stable state at a torsion angle, 0.524 rad, applied to the left clamped end of the tube. Fig. 2a shows the snapshot of the structure at t ¼ 7 ps when addi-
1871
tional torsion angle, 1.222 rad, a sufficiently large angle for the transportation of the molecules, with a rate of 0.244 rad/ ps, is applied to the left end. It is clearly seen that most of the molecules are pushed rightward with only three molecules left to the left side of the kink at the current moment since the first cluster of the molecules is originally placed close to the left end of the tube. The snapshot of the CNT and hydrogen molecules at the end of the molecular dynamics process, t ¼ 45 ps, is seen in Fig. 2b. Similar to the observations of transportation of helium atoms using CNTs [7], the kink, which is initiated on the tube wall subjected a torsion angel beyond the buckling capacity of the tube, starts to expand rightward, and consequently 61 molecules are pumped out of the right end of the CNT, leaving only three molecules pushed out of the left end. The orientation of a majority of the molecules can therefore be realized by subjecting torsion with the rate, 0.245 rad/ps. The driving force for molecular transportation is from the kink propagation or expansion which, through the strong van der Waals force between the tube wall and molecules, induces motions of the encapsulated molecules towards the direction of the kink propagation. The snapshot of the same tube and molecules at t ¼ 24 ps is provided in Fig. 3a with the same dynamic process but with a lower rate, 0.067 rad/ps. Because of the lower loading rate, the accelerations of hydrogen molecules are smaller than those of the molecules in the tube subjected to a higher loading rate studied in Fig. 2 [7]. As a result, 11 molecules are locked to the left side of the kink location at the moment, while the others are pushed to move rightward with the kink propagation. With further shrink of the tube wall throughout the longitudinal direction of the tube due to the kink propagation, the hydrogen molecules are finally pushed out of the tube at t ¼ 58 ps, shown in Fig. 3b. The studies of helium atomic transportation in CNTs at lower loading rate [7]
Fig. 1 – The (10, 0) zigzag CNT containing 64 hydrogen molecules.
Fig. 2 – Molecular dynamics simulations of 64 hydrogen molecules encapsulated in the (10, 0) CNT subjected to torsion with a rate of 0.245 rad/ps at (a) 7 ps with three hydrogen molecules pushed leftward; and (b) 45 ps with all molecules out of the tube.
1872
CARBON
4 7 ( 2 0 0 9 ) 1 8 6 7 –1 8 8 5
Fig. 3 – Molecular dynamics simulations of 64 hydrogen molecules encapsulated in the (10, 0) CNT subjected to torsion with a rate of 0.067 rad/ps at (a) 24 ps with eleven hydrogen molecules pushed leftward; and (b) 58 ps with all molecules out of the tube.
Fig. 4 – Molecular dynamics simulations of 64 hydrogen molecules encapsulated in the (10, 10) CNT subjected to torsion with a rate of 1.745 rad/ps at (a) 2 ps with a left-side view when the tube cross section starts shrinking from a triangle shape; and (b) 10 ps when the cross section keeps shrinking and consequently some molecules are squeezed outside of the left end of the tube; (c) 20 ps when the cross section transforms to an elliptical shape with more molecules squeezed outside of the tube; and (d) 40 ps with a left-side view when the cross section completely transform to the elliptical shape with almost all molecules out of both ends of the tube.
CARBON
4 7 ( 20 0 9 ) 1 8 6 7–18 8 5
showed that some helium atoms were finally remained in the tube and could not be pumped out of the tube. However, since hydrogen is the lightest atom, the molecules to the left side of the kink are also found to be prone to move when the tube wall continues to shrink, and finally 11 molecules are observed to be pushed out of the left end of the tube, while the others are out of the right end of the tube. The simulations in Fig. 3a–b indicate that the orientation of the molecular transportation in the CNT is dependent upon the loading rate. Although all the molecules could be pushed out of the tube, the orientation of a majority of the molecules along an assigned direction could not be fulfilled for the transportation of hydrogen molecules at a lower rate. To investigate the orientation of the transportation in a larger CNT, molecular dynamics simulations of 64 hydrogen molecules encapsulated in a (10, 10) CNT with the length of 8.2 nm, subjected to a torsion angle of 0.873 rad with the rate of 1.745 rad/ps, are conducted. Fig. 4a displays the snapshot of the tube and molecules along longitudinal direction and a left-side view at t ¼ 2 ps after the torsion is applied. It shows the tube cross section starts shrinking from a triangle shape. At the current moment, the van der Waals force between the molecular clusters and the tube wall is still very weak due to the larger diameter of the tube. Therefore, the accelerations of the molecules are very small and almost all the molecules are found to only vibrate around their original locations. At t ¼ 10 ps shown in Fig. 4b, the cross section of the tube keeps shrinking and consequently some molecules to the left side of the kink start to move and are squeezed out of the left end of the tube, while the other molecules to the right side of the kink still stay in the tube as the right portion of the tube remains a virtually circular shape. Fig. 4c reveals further shrink of the cross section and its transition from the triangle shape to an elliptical one with more molecules squeezed out of the tube at t ¼ 20 ps. Finally, Fig. 4d shows a complete transform of the cross section to the elliptical shape, seen from the side view, with almost all molecules pushed out of both ends of the tube at t ¼ 40 ps. In the
1873
two figures, the kink finally expands to the whole tube, and consequently all the molecules are accelerated to move to the two ends of the tube due to increasing van der Waals force through the shrinking wall. It is clearly seen that the orientation of the transportation along the direction of the kink propagation cannot be efficiently fulfilled with the larger CNT.
Acknowledgement This research was undertaken, in part, thanks to funding from the Canada Research Chairs Program (CRC) and the National Science and Engineering Research Council (NSERC).
R E F E R E N C E S
[1] Iijima S. Helical microtubules of graphitic carbon. Nature 1991;354(6348):56–8. [2] Kra´l1 P, Toma´nek D. Laser-driven atomic pump. Phys Rev Lett 1999;82(26):5373–6. [3] Insepov Z, Wolf D, Hassanein A. Nanopumping using carbon nanotubes. Nano Lett 2006;6(9):1893–5. [4] Thorsen T, Marrkl SJ, Quake SR. Microfluidic large-scale integration. Science 2002;298(5593):580–4. [5] Thomas JA, McGaughey AJH. Density, distribution, and orientation of water molecules inside and outside carbon nanotubes. J Chem Phys 2008;128(8):084715. [6] Joseph S, Aluru NR. Pumping of confined water in carbon nanotubes by rotation–translation coupling. Phys Rev Lett 2008;101(6):064502. [7] Wang Q. Atomic transportation via carbon nanotubes. Nano Lett 2009;9(1):245–9. [8] Rigby D, Sun H, Eichinger BE. Computer simulations of poly(ethylene oxide): force field, PVT diagram and cyclization behaviour. Polym Int 1997;44(3):311–30. [9] Wang Q. Torsional buckling of double-walled carbon nanotubes. Carbon 2008;46(8):1172–4.