Abstract
Mechanics at nanometer scale involves physical factors often entirely different from the familiar concepts in macroscopic mechanical engineering (elastic moduli, contact forces, friction etc.). These new features are often of chemical nature: intermolecular forces, thermal fluctuations, chemical bonds. The general aspects and issues of nanomechanics are illustrated by an overview of the properties of nanotubes: linear elastic parameters, nonlinear elastic instabilities and buckling, inelastic relaxation, yield strength and fracture mechanisms, and their kinetic theory. Atomistic scenarios of coalescence-welding and the role of non- covalent forces (supra-molecular interactions) between the nanotubes are also discussed due to their significance in potential applications. A discussion of theoretical and computational work is supplemented by brief summaries of experimental results, for the entire range of the deformation amplitudes.
Editor’s note: Nanomechanics is an area of nanoscale mechanics studying mechanical phenomena, mechanical material properties, mechanical and electro-mechanical behavior of nanoscale material systems and nanostructures of 100 nm or less in size.
An erratum of the original chapter can be found under DOI 10.1007/978-94-017-9263-9_11
An erratum to this chapter can be found at http://dx.doi.org/10.1007/978-94-017-9263-9_11
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Notes
- 1.
Editor’s notes: B. Yakobson and his colleagues were among the first to perform theoretical modeling of carbon nanotubes, i.e.,
1993/94—R.S. Ruoff and J. Tersoff team at IBM has done first theoretical modeling of carbon nanotubes and carbon nanotube crystals.
1996—M.M.J. Treacy, T.W. Ebbesen and J.M. Gibson have carried out first experimental testing of carbon nanotubes with the atomic force microscope (AFM).
1996—B.I. Yakobson, C.J. Brabec and J. Bernholc have performed molecular dynamics (MD) simulation of the axial buckling and twisting of carbon nanotubes. They have shown the shell-like behavior of carbon nanotubes.
1997—C.M. Lieber and his team at Harvard University have done similar experimental testing of vibrating carbon nanotubes.
- 2.
Editor’s notes in words of Leonardo da Vinci [about his notes on science]: “… I believe that before I am at the end of this I shall have to repeat [some of] the same things; and therefore, O reader, blame me not, because the subjects are many…” and it is important to encourage the reader.
- 3.
Editor’s notes: “Movement is created by heat and cold.” Leonardo da Vinci, Philosophy, p. 79, in The Notebooks of Leonardo da Vinci (edited by E. MacCurdy, Konecky and Konecky printing, Duckworth and Co., London, 1906).
- 4.
Editor’s notes: “Therefore O students study mathematics and do not build without foundations.” Leonardo da Vinci, Philosophy, p. 82, in The Notebooks of Leonardo da Vinci (edited by E. MacCurdy, Konecky and Konecky printing, Duckworth and Co., London, 1906).
- 5.
Editor’s notes: “He who blames the supreme certainty of mathematics feeds on confusion, and will never impose silence upon the contradictions of the sophistical sciences, which occasion a perpetual clamor.” Leonardo da Vinci, Philosophy, p. 83, in The Notebooks of Leonardo da Vinci (edited by E. MacCurdy, Konecky and Konecky printing, Duckworth and Co., London, 1906). .
- 6.
Editor’s notes: “Let no one read me who is not mathematician in my beginnings.” Leonardo da Vinci, Philosophy, p. 85, in The Notebooks of Leonardo da Vinci (edited by E. MacCurdy, Konecky and Konecky printing, Duckworth and Co., London, 1906).
- 7.
Editor’s notes: “Inequality is the cause of all local movements.” Leonardo da Vinci, Aphorisms, p. 89, in The Notebooks of Leonardo da Vinci (edited by E. MacCurdy, Konecky and Konecky printing, Duckworth and Co., London, 1906).
References
B.I. Yakobson, Morphology and rate of fracture in chemical decomposition of solids. Phys. Rev. Lett. 67(12), 1590–1593 (1991)
B.I. Yakobson, Stress-promoted interface diffusion as a precursor of fracture. J. Chem. Phys. 99(9), 6923–6934 (1993)
S. Iijima, Helical microtubules of graphitic carbon. Nature 354, 56–58 (1991)
R.B. Phillips, Crystals, Defects and Microstructures. (Cambridge University Press, Cambridge, 2001), p. 780
T. Hertel, R.E. Walkup, P. Avouris, Deformation of carbon nanotubes by surface van der Waals forces. Phys. Rev. B 58(20), 13870–13873 (1998)
B.I. Yakobson, R.E. Smalley, Fullerene nanotubes: C1,000,000 and beyond. Am. Scien. 85(4), 324–337 (1997)
B.I. Yakobson, P. Avouris, in Mechanical Properties of Carbon Nanotubes, ed. by M.S. Dresselhaus, G. Dresselhaus, P. Avouris, Carbon Nanotubes (Springer, Berlin, 2001), pp. 287–327
S.A. Chin, Symplectic integrators from composite operator factorizations. Phys. Lett. A 226(6), 344–348 (1997)
F. Ercolessi, M. Parinello, E. Tosatti, Simulation of gold in the glue model. Philos. Mag. A 58(1), 213–226 (1988)
M.S. Daw, Model of metallic cohesion—the embedded-atom method. Phys. Rev. B 39(11), 7441–7452 (1989)
M.W. Finnis, J.E. Sinclair, A simple empirical N-body potential for transition-metals. Philos. Mag. A 50(1), 45–55 (1984)
J. Tersoff, New empirical approach for the structure and energy of covalent systems. Phys. Rev. B 37(12), 6991–7000 (1988)
D.W. Brenner, Empirical potential for hydrocarbons for use in simulating the chemical vapor-deposition of diamond films. Phys. Rev. B 42(15), 9458–9471 (1990)
O.A. Shenderova, D.W. Brenner, A. Omeltchenko, X. Su, L.H. Yang, Atomistic modeling of the fracture of polycrystalline diamond. Phys. Rev. B 61(6), 3877–3888 (2000)
R. Car, M. Parrinello, Unified approach for molecular dynamics and density-functional theory. Phys. Rev. Lett. 55(22), 2471–2474 (1985)
O.F. Sankey, R.E. Allen, Atomic forces from electronic energies via the Hellmann-Feynman theorem, with application to semiconductor (110) surface relaxation. Phys. Rev. B 33(10), 7164–7171 (1986); O.F. Sankey, D.J. Niklewski, Ab initio multicenter tight-binding model for molecular-dynamics simulations and other applications in covalent systems. Phys. Rev. B 40(6), 3979–3995 (1989); C.M. Goringe, D.R. Bowler, E. Hernandez, Tight-binding modeling of materials. Rep. Prog. Phys. 60, 1447–1512 (1997)
S. Nose, A molecular dynamics method for simulations in the canonical ensemble. Mol. Phys. 52(2), 255–268 (1984); W. G. Hoover, Canonical dynamics: equilibrium phase-space distributions. Phys. Rev. A 31(3), 1695–1697 (1985)
R.E. Allen, Electron-ion dynamics: a technique for simulating both electronic transitions and ionic motion in molecules and materials. Phys. Rev. B 50(24), 18629–18632 (1994); R.E. Allen, T. Dumitrica, B. Torralva, in Electronic and Structural Response of Materials to Fast Intense Laser Pulses, ed. by K.T. Tsen, Ultrafast Physical Processes in Semiconductors (Academic, New York, 2001), pp. 315–388
K.N. Kudin, G.E. Scuseria, B.I. Yakobson, C2F, BN and C nano-shell elasticity by ab initio computations. Phys. Rev. B 64, 235406 (2001)
M.M.J. Treacy, T.W. Ebbesen, J.M. Gibson, Exceptionally high Young’s modulus observed for individual carbon nanotubes. Nature 381, 678–680 (1996)
E.W. Wong, P.E. Sheehan, C.M. Lieber, Nanobeam mechanics: elasticity, strength and toughness of nanorods and nanotubes. Science 277, 1971–1975 (1997)
P. Poncharal, Z.L. Wang, D. Ugarte, W.A. Heer, Electrostatic deflections and electromechanical resonances of carbon nanotubes. Science 283, 1513–1516 (1999)
B.I. Yakobson, C.J. Brabec, J. Bernholc, Nanomechanics of carbon tubes: instabilities beyond the linear response. Phys. Rev. Lett. 76(14), 2511–2514 (1996)
B.I. Yakobson, C.J. Brabec, J. Bernholc, Structural mechanics of carbon nanotubes: from continuum elasticity to atomistic fracture. J. Comput. Aided Mater. Des. 3, 173–182 (1996)
A. Garg, J. Han, S.B. Sinnott, Interactions of carbon-nanotubule proximal probe tips with diamond and graphite. Phys. Rev. Lett. 81(11), 2260–2263 (1998)
D. Srivastava, M. Menon, K. Cho, Nanoplasticity of single-wall carbon nanotubes under uniaxial compression. Phys. Rev. Lett. 83(15), 2973–2976 (1999)
B.I. Yakobson, M.P. Campbell, C.J. Brabec, J. Bernholc, High strain rate fracture and C-Chain unraveling in carbon nanotubes. Comput. Mater. Sci. 8, 341–348 (1997)
R.S. Ruoff et al., Radial deformation of carbon nanotubes by van der Waals forces. Nature 364, 514–516 (1993)
N.G. Chopra et al., Fully collapsed carbon nanotubes. Nature 377, 135–138 (1995)
J.F. Despres, E. Daguerre, K. Lafdi, Flexibility of graphene layers in carbon nanotubes. Carbon 33(1), 87–92 (1995)
S. Iijima, C.J. Brabec, A. Maiti, J. Bernholc, Structural flexibility of carbon nanotubes. J. Chem. Phys. 104(5), 2089–2092 (1996)
B.I. Yakobson, in Dynamic Topology and Yield Strength of Carbon Nanotubes. Fullerenes, Electrochemical Society (ECS, Paris, Pennington, 1997)
R.E. Smalley, B.I. Yakobson, The future of the fullerenes. Solid State Commun. 107(11), 597–606 (1998)
J.Z. Liu, Q. Zheng, Q. Jiang, Effect of a rippling mode on resonances of carbon nanotubes. Phy. Rev. Lett. 86, 4843–4846 (2001)
B.I. Yakobson, Mechanical relaxation and ‘intramolecular plasticity’ in carbon nanotubes. Appl. Phys. Lett. 72(8), 918–920 (1998)
B.I. Yakobson, Physical Property Modification of Nanotubes. U.S. Patent 6,280,677 B1, 2001
M.B. Nardelli, B.I. Yakobson, J. Bernholc, Mechanism of strain release in carbon nanotubes. Phys. Rev. B 57, R4277 (1998)
M.B. Nardelli, B.I. Yakobson, J. Bernholc, Brittle and ductile behavior in carbon nanotubes. Phys. Rev. Lett. 81(21), 4656–4659 (1998)
B.I. Yakobson, G. Samsonidze, G.G. Samsonidze, Atomistic theory of mechanical relaxation in fullerene nanotubes. Carbon 38, 1675 (2000)
G.G. Samsonidze, G.G. Samsonidze, B.I. Yakobson, Kinetic theory of symmetry-dependent strength in carbon nanotubes. Phys. Rev. Lett. 88, 065501 (2002)
L. Chico et al., Pure carbon nanoscale devices: nanotube heterojunctions. Phys. Rev. Lett. 76(6), 971–974 (1996)
P.G. Collins et al., Nanotube nanodevice. Science 278, 100–103 (1997)
D. Tekleab, D.L. Carroll, G.G. Samsonidze, B.I. Yakobson, Strain-induced electronic property heterogeneity of a carbon nanotube. Phys. Rev. B 64, 035419 (2001)
P. Zhang, Y. Huang, H. Gao, K.C. Hwang, Fracture nucleation in SWNT under tension: a continuum analysis incorporating interatomic potential. ASME Trans. J. Appl. Mech. (2002) (in press)
H. Bettinger, T. Dumitrica, G.E. Scuseria, B.I. Yakobson, Mechanically induced defects and strength of BN nanotubes. Phys. Rev. B 65(Rapid Comm.), 041406 (2002)
P. Zhang, V.H. Crespi, Plastic deformations of boron-nitride nanotubes: an unexpected weakness. Phys. Rev. B 62, 11050 (2000)
D. Srivastava, M. Menon, K.J. Cho, Anisotropic nanomechanics of boron nitride nanotubes: nanostructured “skin” effect. Phys. Rev. B 63, 195413 (2001)
G.G. Samsonidze, G.G. Samsonidze, B.I. Yakobson, Energetics of Stone-Wales defects in deformations of monoatomic hexagonal layers. Comp. Mater. Sci. 23, 62–72 (2000)
T. Dumitrica, H. Bettinger, B.I. Yakobson, Stone-Wales barriers and kinetic theory of strength for nanotubes. (2002) (in progress)
C. Wei, K.J. Cho, D. Srivastava, private communication. xxx.lanl.gov/abs/cond-mat/0202513
Y. Zhao, B.I. Yakobson, R.E. Smalley, Dynamic topology of fullerene coalescence. Phys. Rev. Lett. 88, 185501 (2002)
P. Nikolaev et al., Diameter doubling of single-wall nanotubes. Chem. Phys. Lett. 266, 422 (1997)
M. Terrones et al., Coelescence of single-walled carbon nanotubes. Science 288, 1226–1229 (2000)
R. Martel, H.R. Shea, P. Avouris, Rings of single-wall carbon nanotubes. Nature 398, 582 (1999)
B.I. Yakobson, L.S. Couchman. Persistence length and nanomechanics of random coils and bundles of nanotubes. (2002) (submitted)
V.M. Harik, Ranges of applicability of the continuum beam models in the mechanics of carbon nanotubes. Solid State Comm. 120, 331 (2001)
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Yakobson, B.I., Dumitrică, T. (2014). Retracted: Nanomechanics: Physics Between Engineering and Chemistry. In: Harik, V. (eds) Trends in Nanoscale Mechanics. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9263-9_4
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