RESEARCH PAPER: Omitted From October 2005 Issue, Special Section on Nanomaterials and Nanomechanics

Self-Folding and Unfolding of Carbon Nanotubes

[+] Author and Article Information
Markus J. Buehler

California Institute of Technology, Division of Chemistry and Chemical Engineering, Pasadena, CA 91125

Yong Kong, Huajian Gao

Max Planck Institute for Metals Research, Heisenbergstrasse 3, D-70569 Stuttgart, Germany

Yonggang Huang

Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL

J. Eng. Mater. Technol 128(1), 3-10 (Dec 27, 2005) (8 pages) doi:10.1115/1.1857938 History: Received May 30, 2004; Revised October 25, 2004; Online December 27, 2005
Copyright © 2006 by ASME
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Shell-rod wire transition of CNTs, (a) represents shell-like behavior, (b) behavior of CNTs as a rod, and (c) shows the CNT that behaves similarly as a wire. The properties of such wirelike CNTs are in the focus of this paper.
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Wirelike behavior of CNTs. Upon application of compressive loading at the ends of the tube as discussed in 14, the armchair-carbon nanotube forms a helical structure.
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Decomposition of the CNT into virtual atom types. Types 1 and 4 interact via vdW interactions (LJ potential). The type 3 is being used to pin the CNT during application of external forces in order to bring ends of the CNT into contact (see Fig. 4 and associated discussion in the text), and types 6 and 7 are utilized to apply external forces. All virtual atom types interact via the Tersoff potential with themselves and others.
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(a) Equilibrium distance of CNTs. The calculated equilibrium distance agrees with molecular statics calculations by Huang 19. Subplots (b)–(f) show the results of a computer simulation of formation of bundles of SWNTs. (b) shows the initial configuration as a square lattice, (c) shows the relaxed state. It is evident that a triangular lattice has been formed, and (d) shows the relaxed configuration (after a few nanoseconds) of a larger number of CNTs. It can be seen that several “crystal” defects have been created, such as grain boundaries between “nanograins” of CNTs, and vacancies. (e) and (f) show three-dimensional views on the larger bundle of CNTs depicted in (d).
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Application of mechanical force to bring two ends of the CNT into contact to initiate the self-alignment folding process. Once the two ends of the CNT are in contact, the system is equilibrated for some time (forces are set to zero, and ends are held fixed) until this constraint is released. This must be done with care to avoid large fluctuations due to release of potential energy into kinetic motion, thus hindering the self-folding.
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Self-folding mechanism of CNTs with aspect ratio 340. After two ends of the CNTs are brought into contact by applying small forces as shown in Fig. 4, the CNT self-aligns and forms a tennis-racket-like shape. The reason for this is the vdW interaction between different parts of the CNT. The self-folding only occurs if the CNT is sufficiently long, so that the energy gain by forming vdW bonds is larger than the energy necessary to bend the CNT. In this case, we increase the parameter ε to accelerate the folding dynamics.
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Self-folding mechanism of CNTs with aspect ratio around 500. After two ends of the CNTs are brought into contact by applying small forces as shown in Fig. 4, the CNT self-aligns and forms a tennis-racket-like shape due to the vdW interaction between different parts of the CNT. Unlike in the study shown in Fig. 6, here the parameter ε is chosen so that the correct binding energy of CNTs is achieved during the whole simulation.
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At low temperature, the CNT is thermodynamically stable and the bonded length oscillates around an equilibrium position (T=232 K). Similar studies have been carried out with longer CNTs, where correspondingly the bonded region grows.
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Unfolding of CNT due to increase in temperature (T=2,320 K). We start from the same initial condition as in the calculation shown in Fig. 7.
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Schematic phase diagram of carbon nanotube deformation mechanisms. The plot shows regions where different states or deformation mechanisms of CNTs govern, as a function of aspect ratio and temperature. For low aspect ratios, the temperature dependence of the deformation mechanism is negligible. For large aspect ratios, temperature governs if the folded state is stable or not, and for very large aspect ratios the folded state is stable until evaporation of the CNT.



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