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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Iijima  S (1991), Helical microtubules of graphitic carbon, Nature (London) 354, 56–58.
Iijima  S (1993), Single-shell carbon nanotubes of 1-nm diameter, Nature (London) 363, 603–605.
Bethune  DS, Kiang  CH, Devries  MS, Gorman  G, Savoy  R, Vazquez  J, and Beyers  R (1993), Cobalt-catalyzed growth of carbon nanotubes with single-atomic-layerwalls, Nature (London) 363, 605–607.
Saito R, Dresselhaus G, and Dresselhaus MS (1998), Physical Properties of Carbon Nanotubes, Imperial College Press, London.
Dresselhaus MS, Dresselhaus G, and Avouris Ph (eds) (2001), Carbon Nanotubes: Synthesis, Structure, Properties, and Applications, Springer-Verlag Berlin, Heidelberg.
Allen MP and Tildsley DJ (1987), Computer Simulations of Liquids, Oxford Science Publications, Oxford.
Brenner DW, Shenderova OA, and Areshkin DA (1998), Reviews in Computational Chemistry, KB Lipkowitz and DB Boyd (eds), 213, VCH Publishers, New York.
Garrison  BJ and Srivastava  D (1995), Potential-energy surfaces for chemical-reactions at solid-surfaces, Ann. Rev. Phys. Chem. 46, 373–394.
Srivastava D and Barnard S (1997), Molecular dynamics simulation of large scale carbon nanotubes on a shared memory archi-tecture, Proc. IEEE Supercomputing97 (SC’97 cd-rom), [Published]. [Paper No].
Harrison WA (1980), Electronic Structure and the Properties of Solids, Freeman, San Francisco.
Menon  M and Subbaswamy  KR (1997), Nonorthogonal tight-binding molecular dynamics scheme for silicon with improved transferability, Phys. Rev. B 55, 9231–9234.
Menon  M (2001), Generalized tight-binding molecular dynamics scheme for heteroatomic systems: Application to SimCn clusters, J. Chem. Phys. 114, 7731–7735.
Payne  MC, Teter  MP, Allan  DC, Arias  TA, and Joannopoulos  JD (1992), Iterative minimization techniques for abinitio total-energy calculations: molecular-dynamics and conjugate gradients, Rev. Mod. Phys. 68, 1045–1097.
Hohenberg  P and Kohn  W (1964), Inhomogeneous electron gas, Phys. Rev. B 136, B864.
Kohn  W and Sham  LJ (1965), Self-consistent equations including exchange and correlation effects, Phys. Rev. 140, A1133.
Check the web site for the details, http://cms.mpi.univie.ac.at/vasp/.
Srivastava  D, Menon  M, and Cho  K (2001), Computational nanotechnology with carbon nanotubes and fullerenes, (Special Issue on Nanotechnology) Computing in Engineering and Sciences 3(4), 42–55.
Robertson  DH, Brenner  DW, and Mintmire  JW (1992), Energetics of nanoscale graphitic tubules, Phys. Rev. B 45, 12592–12595.
Tibbetts  GG (1984), Why are carbon filaments tubular, J. Cryst. Growth 66, 632–638.
Yakobson  BI, Brabec  CJ, and Bernholc  J (1996), Nanomechanics of carbon tubes: Instabilities beyond linear response, Phys. Rev. Lett. 76, 2511–2514.
Lu  JP (1997), Elastic properties of carbon nanotubes and nanoropes, Phys. Rev. Lett. 79, 1297–1300.
Hernandez  E, Goze  C, Bernier  P, and Rubio  A (1998), Elastic properties of C and BxCyNz composite nanotubes, Phys. Rev. Lett. 80, 4502–4505.
Sanchez-Portal  D, Artacho  E, Solar  JM, Rubio  A, and Ordejon  P (1999), Ab initio structural, elastic, and vibrational properties of carbon nanotubes, Phys. Rev. B 59, 12678–12688.
Srivastava  D, Menon  M, and Cho  K (2001), Anisotropic nanomechanics of boron nitride nanotubes: Nanostructured “skin” effect, Phys. Rev. B 63, 195413–195416.
Ru  CQ (2000), Effective bending stiffness of carbon nanotubes, Phys. Rev. B 62, 9973–9976.
Harik  VM (2001), Ranges of applicability for the continuum beam model in the mechanics of carbon nanotubes and nanorods, Solid State Commun. 120, 331–335.
Landau LD and Lifschitz EM (1986), Theory of Elasticity, 3rd Edition, Pergamon Press, Oxford [Oxfordshire], New York.
Poncharal  P, Wang  ZL, Ugarte  D, and deHeer  WA (1999), Electrostatic deflections and electromechanical resonances of carbon nanotubes, Science 283, 1513–1516.
Iijima  S, Brabec  C, Maiti  A, and Bernholc  J (1996), Structural flexibility of carbon nanotubes, J. Chem. Phys. 104, 2089–2092.
Treacy  MMJ, Ebbesen  TW, and Gibson  JM (1996), Exceptionally high Young’s modulus observed for individual carbon nanotubes, Nature (London) 381, 678–680.
Wong  EW, Sheehan  PE, and Lieber  CM (1997), Nanobeam mechanics: Elasticity, strength, and toughness of nanorods and nanotubes, Science 277, 1971–1975.
Krishnan  A, Dujardin  E, Ebbesen  TW, Yianilos  PN, and Treacy  MMJ (1998), Young’s modulus of single-walled nanotubes, Phys. Rev. B 58, 14013–14019.
Salvetat  JP, Briggs  GAD, Bonard  JM, Bacsa  RR, Kulik  AJ, Stockli  T, Burnham  NA, and Forro  L (1999), Elastic and shear moduli of single-walled carbon nanotube ropes, Phys. Rev. Lett. 82, 944–947.
Lourie  O, Cox  DM, and Wagner  HD (1998), Buckling and collapse of embedded carbon nanotubes, Phys. Rev. Lett. 81, 1638–1641.
Srivastava  D, Menon  M, and Cho  K (1999), Nanoplasticity of single-wall carbon nanotubes under uniaxial compression, Phys. Rev. Lett. 83, 2973–2676.
Nardelli  MB, Yakobson  BI, and Bernholc  J (1998), Brittle and ductile behavior in carbon nanotubes, Phys. Rev. Lett. 81, 4656–4659.
Nardelli  MB, Yakobson  BI, and Bernholc  J (1998), Mechanism of strain release in carbon nanotubes Phys. Rev. B 57, 4277–4280.
Zhang  PH, Lammert  PE, and Crespi  VH (1998), Plastic deformations of carbon nanotubes, Phys. Rev. Lett. 81, 5346–5349.
Yakobson  BI, Campbell  MP, Brabec  CJ, and Bernholc  J (1997), High strain rate fracture and C-chain unraveling in carbon nanotubes, Comput. Mater. Sci. 8, 341–348.
Walters  DA, Ericson  LM, Casavant  MJ, Liu  J, Colbert  DT, Smith  KA, and Smalley  RE (1999), Elastic strain of freely suspended single-wall carbon nanotube ropes, Appl. Phys. Lett. 74, 3803–3805.
Yu  MF, Files  BS, Arepalli  S, and Ruoff  RS (2000), Tensile loading of ropes of single wall carbon nanotubes and their mechanical properties, Phys. Rev. Lett. 84, 5552–5555.
Yu  MF, Lourie  O, Dyer  MJ, Moloni  K, Kelly  TF, and Ruoff  RS (2000), Strength and breaking mechanism of multiwalled carbon nanotubes under tensile load, Science 287, 637–640.
Wei  CY, Cho  K, and Srivastava  D (2002), Tensile strength of carbon nanotubes under realistic temperature and strain rate, http://xxx.lanl.gov/abs/condmat/0202513.
Wei C, Cho K, and Srivastava D (2001), Temperature and strain-rate dependent plastic deformation of carbon nanotube, MRS Symp Proc677 , AA6.5.
Wei  CY, Srivastava  D, and Cho  K (2002), Molecular dynamics study of temperature dependent plastic collapse of carbon nanotubes under axial compression, Computer Modeling in Engineering and Sciences 3, 255–261.
Vigolo  B, Penicaud  A, Coulon  C, Sauder  C, Pailler  R, Journet  C, Bernier  P, and Poulin  P (2000), Macroscopic fibers and ribbons of oriented carbon nanotubes, Science 290, 1331–1334.
Schadler  LS, Giannaris  SC, and Ajayan  PM (1998), Load transfer in carbon nanotube epoxy composites, Appl. Phys. Lett. 73, 3842–3844.
Andrews  R, Jacques  D, Rao  AM, Rantell  T, Derbyshire  F, Chen  Y, Chen  J, and Haddon  RC (1999), Nanotube composite carbon fibers, Appl. Phys. Lett. 75, 1329–1331.
Osman  MA, and Srivastava  D (2001), Temperature dependence of the thermal conductivity of single-wall carbon nanotubes, Nanotechnology 12, 21–24.
Wei  CY, Srivastava  D, and Cho  K (2002), Thermal expansion and diffusion coefficients of carbon nanotube-polymer composites, Nano Lett. 2, 647–650.
Frankland SJV, Caglar A, Brenner DW, and Griebe M (2000, Fall), Reinforcement mechanisms in polymer nanotube composites: simulated non-bonded and cross-linked systems MRS Symp Proc, A14 .17.
Wagner  HD, Lourie  O, Feldman  Y, and Tenne  R (1998), Stress-induced fragmentation of multiwall carbon nanotubes in a polymer matrix, Appl. Phys. Lett. 72, 188–190.
Lourier  O, and Wagner  HD (1998), Transmission electron microscopy observations of fracture of single-wall carbon nanotubes under axial tension, Appl. Phys. Lett. 73, 3527–3529.
Qian  Q, Dickey  EC, Andrews  R, and Rantell  T (2000), Load transfer and deformation mechanisms in carbon nanotube-polystyrene composites, Appl. Phys. Lett. 76, 2868–2870.


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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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