Plastic bending and shape-memory effect of double-wall carbon nanotubes

Hideki Mori, Shigenobu Ogata, Ju Li, Seiji Akita, and Yoshikazu Nakayama

Phys. Rev. B 76, 165405 – Published 3 October 2007

Abstract

Plastic bending of (5,5)@(10,10) double-wall carbon nanotube is analyzed using nudged elastic band minimum energy path calculations. At lower applied bending curvature, only the outer tube deforms plastically. However, at higher bending curvature, both the inner and outer tubes deform plastically. We find that the plastic deformation of the outer tube is more difficult than that of isolated single-wall carbon nanotube of the same diameter due to tube-tube interactions. In contrast, the plastic deformation of the inner tube is not strongly affected by the presence of the outer tube. We also analyze the shape-memory effect (SME) discovered experimentally, which is a thermal recovery process from the plastically bent state to the straight defect-free state, which can be repeated multiple times. We analyze the physics behind SME of carbon nanotubes, which is quite different from that of traditional shape-memory alloys.

Received 30 March 2007

DOI:https://doi.org/10.1103/PhysRevB.76.165405

Authors & Affiliations

Hideki Mori¹, Shigenobu Ogata¹, Ju Li², Seiji Akita³, and Yoshikazu Nakayama^4,*

¹Department of Mechanical Science and Bioengineering, Osaka University, Osaka 560-8531, Japan
²Department of Materials Science and Engineering, Ohio State University, Columbus, Ohio 43210, USA
³Department of Physics and Electronics, Osaka Prefecture University, Osaka 599-8531, Japan
⁴Department of Mechanical Engineering, Osaka University, Osaka 565-0871, Japan

^*nakayama@mech.eng.osaka-u.ac.jp

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Vol. 76, Iss. 16 — 15 October 2007

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Images

Figure 1
(Color online) (a) The back and belly positions of a bent CNT, (b) plastic deformation accomplished by bond rotation (adapted from Ref. 18), and (c) plastic deformation accomplished by bond rotation, first nucleation event in (5,5) armchair SWNT. Labels “ND” and “SW” mean the defect-free state and the state with the 5-7-7-5 defect, respectively; the numeral labels are the split step of the 5-7 (+ dislocation) and 7-5 (− dislocation) defect pairs.Reuse & Permissions
Figure 2
The effect of boundary condition on the energetics of 5-7-7-5 defect nucleation and 5-7 defect migration in (a) outer tube and (b) inner tube. Filled circle means that all ends are fixed. Open circle means that both ends of the outer tube are fixed; one end of the inner tube is fixed and the other end is free.Reuse & Permissions
Figure 3
(Color online) (a) Atomic configuration of an elastically bent (5,5)@(10,10) DWNT at a bending curvature $ρ = 0.16 {nm}^{- 1}$ . The energetics map of DWNT for 5-7-7-5 defect nucleation and 5-7 pairs migration on (5,5)@(10,10) DWNT at bending curvature (b) $ρ = 0 {nm}^{- 1}$ , (c) $ρ = 0.08 {nm}^{- 1}$ , and (d) $ρ = 0.16 {nm}^{- 1}$ . Labels ND and SW mean the defect-free state and the state with the 5-7-7-5 defect, respectively. $x$ axis and $y$ axis are the split steps of the two pairs of dislocations on the inner and outer tubes, respectively. Arrow shows minimum energy path.Reuse & Permissions
Figure 4
Formation energies of the defective configuration as a function of the bending curvature $ρ$ in (a) outer tube, (b) (10,10) SWNT, (c) inner tube, and (d) (5,5) SWNT. For the formation energy of the inner tube, we chose the value where the plastic deformation of the outer tube has been completed (after gliding eight times). Solid lines are the linear interpolations. Dashed lines mean the buckling regime.Reuse & Permissions
Figure 5
Activation energies of 5-7-7-5 defect nucleation as a function of the bending curvature $ρ$ in (a) outer tube, (b) (10,10) SWNT, (c) inner tube, and (d) (5,5) SWNT. For the activation energy of the inner tube, we chose the value where the plastic deformation of the outer tube has been completed. Solid line and dashed line are the linear interpolations. Dashed lines mean the buckling regime.Reuse & Permissions
Figure 6
The NEB optimized recovery energetics of (a) DWNT at zero stress ( $x$ axis and $y$ axis are the split step of the 5-7 pair on the inner and outer tubes, respectively) and (b) that of (10,10) SWNT. Labels ND and SW mean the defect-free state and the state with the 5-7-7-5 defect, respectively. The zero-energy point on the map and MEP correspond to the plastically bent state. On the map, it is at $x = 8$ and $y = 4$ . Arrow shows minimum energy path.Reuse & Permissions

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