Nanomechanics of carbon nanotubes and composites

[+] Author and Article Information
Deepak Srivastava, Chenyu Wei

Computational Nanotechnology, NASA Ames Research Center, Moffett Field, California 94035-1000; deepak@nas.nasa.gov

Kyeongjae Cho

Department of Mechanical Engineering, Stanford University, Stanford, California 93045

Appl. Mech. Rev 56(2), 215-230 (Mar 04, 2003) (16 pages) doi:10.1115/1.1538625 History: Online March 04, 2003
Copyright © 2003 by ASME
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a) A graphene sheet made of C atoms placed at the corners of hexagons forming the lattice with arrows AA and ZZ denoting the rolling direction of the sheet to make b) an (5,5) armchair and (c) a (10,0) zigzag nanotubes, respectively.
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Young’s modulus as a function of the tube diameter for C, BN, BC3, BC2N from tight binding simulation 22.
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Young’s modulus verse tube diameter for ab initio simulation. Open symbols for the multiwall CNT geometry and solid symbols for the single wall tube with crystalline-rope configuration. The experimental value of the elastic modulus of graphite is also shown 23.
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Bending stiffness as a function of tube diameter from MD simulation with Tersoff-Brenner potential. The stiffness is scaled as D2.93, closed to the cubic dependence on diameter D predicted from continuum elastic theory.
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a) Bending modulus as a function of tube diameter. Solid circles are from Poncharal et al. 28; others are from other experiments as referred in Poncharal et al.’s paper. The dropping in the bending modulus is attributed to the onset of a wavelike distortion in lateral direction as shown in b).b) High–resolution TEM image of a bent nanotube (Radius of curvature ≈400 nm), showing the wavelike distortion and the magnified views 28.
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HREM images of kink structures formed in bent CNTs. Shown on left is a single kink in a SWCNT with diameter 1.2nm; Shown on right is a kink on a MWCNT with diameter 8 nm 29.
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The torsion stiffness as a function of tube diameter for a series of zigzag and armchair SWNTs calculated with Tersoff-Brenner potential. The stiffness is scaled as D3.01 for D>0.8 nm, in agreement with the prediction from continuum elastic theory.
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a) The strain energy of a compressed 6 nm long (7,7) CNT, from Tersoff-Brenner potential, has four singularities corresponding to the buckled structures with shapes shown in b to e. The CNT is elastic up to 15% compression strain despite of the highly deformed structures. The MD study was conducted at T=0 K 20.
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TEM image of fractured multiwalled carbon nanotubes under compression within a polymeric film. The enlarged image is shown on right 52.
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Shown on top from a to d are four stages of spontaneous plastic collapse of the 12% compressed (8,0) CNT, with diamond like structures formed at the location of the collapse 35.
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Five stages of spontaneous plastic collapse of the 14.25% compressed (8,0) BN nanotube. a) Nucleation of deformations near the two ends, b-d anisotropic strain release in the central compressed section and plastic buckling near the right end of the tube, and e) the final anisotropically buckled structure where all the deformation is transferred toward the right end of the tube. The cross section of each structure is shown on right.
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The Stone Wales bond rotation on a zigzag and an armchair CNT, resulting pentagon-heptagon pairs, can lengthen a nanotube, with the greatest lengthening for an armchair tube 38.
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A heptagon-pentagon pair appeared on a 10% tensile strain (10,10) CNT at T=2000 K. Plastic flow behavior of the Pentagon-heptagon pairs after 2.5ns at T=3000 K on a 3% tensile strained CNT. The shaded region indicates the migration path of the (5-7) edge dislocation 36.
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Top: Eight stress versus strain curves obtained from the tensile-loading experiments on individual SWCNT ropes. The Young’s modulus is ranged from 320GPa to 1470 GPa. The breaking strain was found at 5.3% or lower 41. Bottom: Plot of stress versus strain curves for individual MWCNTs. The Young’s modulus is ranged form 270GPa to 950 GPa, with breaking strain around 12% (one sample showed a 3% breaking strain) 42.
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The yielding strain of a 6nm long (10,0) CNT is plotted as functions of strain rate and temperature. Stone-Wales bond rotations appear first resulting in heptagon and pentagon ring; then larger C rings generated around such defects followed by the necking of the CNT; and the CNT is broken shortly after (from MD simulations with Tersoff-Brenner potential).
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Left: A 9% tensile strained (5,5) CNT with numerous Stone-Wales bond rotation defects at 2400K, and the following breaking of the tube. Right: An 11.5% tensile strained (10,0) with a group of pentagon and heptagon centered by an octagon at 1600K, and the following breaking of the tube (from MD simulation with Tersoff-Brenner potential).
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A 12% compressed (10,0) CNT at T=1600 K. A Stone-Wales dislocation defect can be seen at the upper section of the CNT. Several sp3 bonds formed in the buckled region (from MD simulation with Tersoff-Brenner potential).
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Density as a function of temperature for a polyethylene system (50 chains with Np=10), and a CNT-polyethylene composite (2nm long capped (10,0) CNT) The CNT composite has an increase of thermal expansion above Tg. (From a MD simulation with Van der Waals potential between CNT and matrix. Dihedral angle potential and torsion potential were used for the polyethylene matrix, and Tersoff-Brenner potential was used for carbon atom on the CNT.)
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Plot of the stress versus strain curve for pure polyethylene matrix and CNT composite (8 vol%) at small strain region (T=50 K). Young’s modulus is increased 30% for the composite (from MD simulation).




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