Skip to main content
SpringerLink
Log in

Computer simulation of nanotube contact

  • Published:
Mechanics of Solids Aims and scope Submit manuscript

Abstract

We develop procedures of numerical solution of nanostructure contact problems, which are based on the time discretization of nonlinear equations of molecular mechanics. The matrices and vectors of these equations are determined by using the Morse law of covalent atomic interaction, the fictitious rod elements to take account of angular variations between neighboring atomic covalent bonds, and noncovalent Van der Waals forces to take account of contact interactions between the graphene-like nanostructures. The procedures developed were included into the computational package PIONER, which was used to solve the problem of contact/self-contact of two nanotubes under conditions of dynamic equilibrium. We showed that the type of contact interaction significantly depends on the impact velocity of nanotubes. For a relatively small impact velocity, the nanotubes “adhere” to each other with a small deformation of their walls, due to the action of the Van der Waals attractive forces. As the impact velocity increases, the nanotubes fly apart because of the action of noncovalent repulsive forces. As the impact velocity continues to increase, there is a strong deformation of nanotubes with instantaneous “adhesion” of opposite ends and further separation of tubes. We show that taking account of the noncovalent forces of interaction between the opposite parts of the nanotube walls prevents their self-intersection; in this region of the nanotube contact, ovalization of their transverse cross-sections occurs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. K. Ariga and T. Kunitake, Supramolecular Chemistry — Fundamentals and Applications (Springer, Berlin, 2006).

    Google Scholar 

  2. M. J. Buehler, Atomic Modeling of Materials Failure (Springer, New York, 2008).

    Book  Google Scholar 

  3. W. K. Liu, E. G. Karpov, and H. S. Park, Nano Mechanics and Materials: Theory, Multiscale Methods and Applications (Wiley, Chichester, 2006).

    Book  Google Scholar 

  4. H. Ralf-Tabar, Computational Physics of Carbon Nanotubes (Cambridge Univ. Press, Cambridge, 2008).

    Google Scholar 

  5. B. I. Yakobson and L. S. Couchman, Nanotubes: Supramolecular Mechanics in Dekker Encyclopedia of Nanoscience and Nanotechnology (Marcel Dekker, New York, 2004).

    Google Scholar 

  6. J. Z. Zhang, Z. L. Wang, J. Liu, et. al., Self-Assembled Nanostructures (Kluwer Acad. Publ., New York, 2004).

    Google Scholar 

  7. M. Arroyo and T. Belytschko, “Finite Element Methods for the Non-Linear Mechanics of Crystalline Sheets and Nanotubes,” Int. J. Numer. Meth. Engng 59(3), 419–456 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  8. R. C. Batra and A. Sears, “Continuum Model of Multi-Walled Carbon Nanotubes,” Int. J. Solids Struct. 44, 7577–7596 (2007).

    Article  MATH  Google Scholar 

  9. N. Hu, K. Nunoya, D. Pan, et al., “Prediction of Buckling Characteristics of Carbon Nanotubes,” Int. J. Solids Struct. 44(20), 6535–6550 (2007).

    Article  MATH  Google Scholar 

  10. A. L. Kalamkarov, A. V. Georgiades, S. K. Rokkam, et al., “Analytical and Numerical Techniques to Predict Carbon Nanotubes Properties,” Int. J. Solids Struct. 43(22/23), 6832–6854 (2006).

    Article  MATH  Google Scholar 

  11. A. Y. T. Leung, X. Guo, and X. Q. He, “Postbuckling of Carbon Nanotubes by Atomic-Scale Finite Element,” J. Appl. Phys. 99, p. 124308 (2006).

    Article  ADS  Google Scholar 

  12. R. Saito, R. Matsuo, T. Kimura, et al., “Anomalous Potential Barrier of Double-Wall Carbon Nanotube,” Chem. Phys. Lett. 348(3), 187–193 (2001).

    Article  ADS  Google Scholar 

  13. A. Sears and R. C. Batra, “Buckling of Multiwalled Carbon Nanotubes under Axial Compression,” Phys. Rev. B 73(8), 085410 (2006).

    Article  ADS  Google Scholar 

  14. H. S. Shen and C. L. Zhang, “Postbuckling Prediction of Axially Loaded Double-Walled Carbon Nanotubes with Temperature Dependent Properties and Initial Defects,” Phys. Rev. B 74(3), 035410 (2006).

    Article  ADS  Google Scholar 

  15. Y. Y. Zhang, V. B. C. Tan, and C. M. Wang, “Effect of Strain Rate on the Buckling Behavior of Single- and Double-Walled Carbon Nanotubes,” Carbon 45(3), 514–523 (2007).

    Article  Google Scholar 

  16. H. W. Zhang, L. Wang, and J. B. Wang, “Computer Simulation of Buckling Behavior of Double-Walled Carbon Nanotubes with Abnormal Interlayer Distances,” Comput. Mater. Sci. 39(3), 664–672 (2007).

    Article  Google Scholar 

  17. S. Zhang, S. L. Mielke, R. Khare, et al., “Mechanics of Defects in Carbon Nanotubes: Atomic and Multiscale Simulation,” Phys. Rev. B 71(11), 115403 (2005).

    Article  ADS  Google Scholar 

  18. M. J. Buehler, Y. Kong, H. Gao, and Y. Huang, “Self-Folding and Unfolding of Carbon Nanotubes,” Trans. ASME. J. Engng Mater. Technol. 128(3), 3–10 (2006).

    Article  Google Scholar 

  19. M. Arroyo and T. Belytschko, “A Finite Deformation Membrane Based on Inter-Atomic Potentials for the Transverse Mechanics of Nanotubes,” Mech. Mater. 35(3), 193–215 (2003).

    Article  Google Scholar 

  20. G. Gao, T. Cagin, and W. A. Goddard III, “Energetics, Structure, Mechanical and Vibrational Properties of Single Walled Carbon Nanotubes,” Nanotech. 9(3), 184–191 (1998).

    Article  ADS  Google Scholar 

  21. B. Liu, H. Jiang, Y. Huang, et al., “Atomic-Scale Finite Element Method in Multiscale Computation with Applications to Carbon Nanotubes,” Phys. Rev. B 72, 035435 (2005).

    Article  ADS  Google Scholar 

  22. S. J. V. Frankland, V. M. Harik, G. M. Odegard, et al., “The Stress-Strain Behavior of Polymer-Nanotube Composites from Molecular Dynamics Simulation,” Compos. Sci. Technol. 63, 1655–1661 (2003).

    Article  Google Scholar 

  23. R. V. Goldstein and A. V. Chentsov, “Discrete-Continuous Model of a Nanotube,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 57–74 (2005) [Mech. Solids (Engl. Transl.) 40 (4), 45–59 (2005)].

  24. R. V. Goldstein, A. V. Chentsov, R. M. Kadushnikov, and N. A. Shturkin, “Methodology and Metrology for Mechanical Testing of Nano- and Microdimensional Objects, Materials, and Products of Nanotechnology,” Ross. Nanotekhnol. 3(1–2), 114–124 (2008) [Nanotechnol. Russ. (Engl. Transl.) 3 (1–2), 112–121 (2008)].

    Google Scholar 

  25. N. Hu, H. Fukanaga, C. Lu, et al., “Prediction of Elastic Properties of Carbon Nanotube Reinforced Composites,” Proc. Roy. Soc. London. Ser. A 461(2058), 1685–1710 (2005).

    Article  ADS  Google Scholar 

  26. C. Y. Li and T. W. Chou, “Modeling of Carbon Nanotubes and Their Composites,” in Nanomechanics of Materials and Structures (Springer, Berlin, 2006).

    Google Scholar 

  27. G. M. Odegard, T. S. Gates, L. M. Nicholson, and E. Wise, “Equivalent-Continuum Modeling of Nano-Structured Materials,” Compos. Sci. Technol. 62(14), 1869–1880 (2002).

    Article  Google Scholar 

  28. Q. Wang, “Torsional Instability of Carbon Nanotubes Encapsulating C60 Fullerens,” Carbon 47(2), 507–512 (2009).

    Article  Google Scholar 

  29. N. G. Chopra, L. X. Benedict, V. H. Crespi, et al., “Fully Collapsed Carbon Nanotubes,” Nature 377, 135–138 (1995).

    Article  ADS  Google Scholar 

  30. A. M. Krivtsov, Strain and Failure of Rigid Bodies with Microstructure (Fizmatlit, Moscow, 2007) [in Russian].

    Google Scholar 

  31. T. S. Gates, G. M. Odegard, S. J. V. Frankland, and T. C. Clancy, “Computational Materials: Multi-Scale Modeling and Simulation of Nanostructured Materials,” Compos. Sci. Technol. 65(15/16), 2416–2434 (2005).

    Article  Google Scholar 

  32. S. N. Korobeynikov, “Nonlinear Equations of Deformation of Atomic Lattices,” Arch. Mech. 57(6), 457–475 (2005).

    Google Scholar 

  33. B. D. Annin, S. N. Korobeynikov, and A. V. Babichev, “Computer Simulation of a Twisted Nanotube Buckling,” Sib. Zh. Industr. Mat. 11(1), 3–22 (2008) [J. Appl. Industr. Math. (Engl. Transl.) 3 (3), 318–333 (2009)].

    Google Scholar 

  34. S. N. Korobeynikov, “TheNumerical Solution of Nonlinear Problems on Deformation and Buckling of Atomic Lattices,” Int. J. Fract. 128(1), 315–323 (2004).

    Article  Google Scholar 

  35. S. N. Korobeynikov and A. V. Babichev, “Numerical Simulation of Dynamic Deformation and Buckling of Nanostructures,” in CD ICF Interquadrennial Conference Full Papers (Institute for Problems in Mechanics, Moscow, 2007).

    Google Scholar 

  36. S. N. Korobeynikov and A. V. Babichev, “Nanotube Buckling under Sudden Application of Axial Load,” in Mathematical Modeling of Systems and Processes (Izd-vo PGTU, Perm, 2008), pp. 43–54 [in Russian].

    Google Scholar 

  37. K.M. Liew, C.H. Wong, and M. J. Tan, “Tensile and Compressive Properties of Carbon Nanotube Bundles,” Acta Mater. 54(1), 225–231 (2006).

    Article  Google Scholar 

  38. C.-L. Zhang and H.-S. Shen, “Buckling and Postbuckling Analysis of Single-Walled Carbon Nanotubes in Thermal Environments via Molecular Dynamics Simulation,” Carbon 44(13), 2608–2616 (2006).

    Article  Google Scholar 

  39. M. Arroyo and T. Belytschko, “Finite Crystal Elasticity of Carbon Nanotubes Based on the Exponential Cauchy-Born Rule,” Phys. Rev. B 69, 115415 (2004).

    Article  ADS  Google Scholar 

  40. B. Liu, Y. Huang, H. Jiang, et al., “The Atomic-Scale Finite Element Method,” Comput. Methods Appl. Mech. Engng 193(17–20), 1849–1864 (2004).

    Article  MATH  Google Scholar 

  41. N. A. Kasti, “Zigzig Carbon Nanotubes — Molecular/Structural Mechanics and Finite Element Method,” Int. J. Solids Struct. 44, 6914–6929 (2007).

    Article  MATH  Google Scholar 

  42. A. Y. T. Leung, X. Guo, X. Q. He, and S. Kitipornchai, “A Continuum Model for Zigzag Single-Walled Carbon Nanotubes,” Appl. Phys. Lett. 86, 083110 (2005).

    Article  ADS  Google Scholar 

  43. C. Y. Li and T. W. Chou, “A Structural Mechanics Approach for the Analysis of Carbon Nanotubes,” Int. J. Solids Struct. 40(10), 2487–2499 (2003).

    Article  MATH  Google Scholar 

  44. Y. Wang, C. Sun, X. Sun, et al., “2-D Nano-Scale Finite Element Analysis of a Polymer Field,” Compos. Sci. Technol. 63, 1581–1590 (2003).

    Article  Google Scholar 

  45. H. W. Zhang, L. Wang, J. B. Wang, and H. F. Ye, “Parametric Variational Principle and Quadratic Programming Method for van der Waals Force Simulation of Parallel and Cross Nanotubes,” Int. J. Solids Struct. 44(9), 2783–2801 (2007).

    Article  MATH  Google Scholar 

  46. H. W. Zhang, Z. Yao, J. B. Wang, and W. X. Zhong, “Phonon Dispersion Analysis of Carbon Nanotubes Based on Inter-Belt Model and Symplectic Solution Method,” Int. J. Solids Struct. 44(20), 6428–6449 (2007).

    Article  MATH  Google Scholar 

  47. MARC Users Guide, Vol.C: Program Input (MSC. Software Corporation, Santa Ana, 2007).

  48. L. A. Girifalco, M. Hodak, and R. S. Lee, “Carbon Nanotubes, Buckyballs, Ropes, and a Universal Graphitic Potential,” Phys. Rev. B 62(19), 13104–13110 (2000).

    Article  ADS  Google Scholar 

  49. A. S. Kravchuk, “On Models and Solution of Problems of Nanocontact Mechanics,” in Mathematical Modeling of Systems and Processes (Izd-vo PGTU, Perm, 2007), pp. 123–141 [in Russian].

    Google Scholar 

  50. S. N. Korobeynikov, Nonlinear Strain of Rigid Bodies (Sib. otdel. RAN, Novosibirsk, 2000) [in Russian].

    Google Scholar 

  51. S. N. Korobeynikov, V. P. Agapov, M. I. Bondarenko, and A. N. Soldatkin, “The General Purpose Nonlinear Finite Element Structural Analysis Program PIONER,” in Proc. Int. Conf. Numerical Methods and Applications (Publ. House of the Bulgarian Acad. of Sci., Sofia, 1989), pp. 228–233.

    Google Scholar 

  52. S. B. Sinnott, O. A. Shenderova, C. T. White, and D. W. Brenner, “Mechanical Properties of Nanotubule Fibers and Composites Determined from Theoretical Calculations and Simulations,” Carbon 36(1–2), 1–9 (1998).

    Article  Google Scholar 

  53. PATRAN Users Guide (MSC.Software Corporation, Santa Ana, 2007).

  54. A. V. Babichev, “Automating Model Construction and Visualization of Results of Numerical Simulation of Deformation of Nanostructures,” Vych. Mekh. Sploshn. Sred 1(4), 21–27 (2008).

    Google Scholar 

  55. E. G. Rakov, Nanotubes and Fullerens (Logos, Moscow, 2006) [in Russian].

    Google Scholar 

  56. T. Belytschko, S. P. Xiao, G. C. Schatz, and R. S. Ruoff, “Atomic Simulations of Nanotube Fracture,” Phys. Rev. B 65, 235430 (2002).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lavrentyev Institute of Hydrodynamics, Siberian Branch of Russian Academy of Sciences, pr-t akad. Lavrentyeva 15, Novosibirsk, 630090, Russia

    B. D. Annin, V. V. Alekhin & S. N. Korobeynikov

  2. Sobolev Institute of Geology and Mineralogy, Siberian Branch of Russian Academy of Sciences, pr-t akad. Koptyuga 3, Novosibirsk, 630090, Russia

    A. V. Babichev

Authors
  1. B. D. Annin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. V. Alekhin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. V. Babichev
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. N. Korobeynikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. D. Annin.

Additional information

Original Russian Text © B.D. Annin, V.V. Alekhin, A.V. Babichev, S.N. Korobeynikov, 2010, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2010, No. 3, pp. 56–76.

About this article

Cite this article

Annin, B.D., Alekhin, V.V., Babichev, A.V. et al. Computer simulation of nanotube contact. Mech. Solids 45, 352–369 (2010). https://doi.org/10.3103/S0025654410030064

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0025654410030064

Key words

Search

Navigation