Skip to main content
SpringerLink
Log in

Thermal vibration of double-walled carbon nanotubes predicted via double-Euler-beam model and molecular dynamics

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

The paper presents how to study the thermal vibration of a double-walled carbon nanotube (DWCNT) by using a model of double-Euler beams, together with the law of energy equipartition, with the energy of van der Waals interaction between layers taken into consideration. The basic finding of the study is the relation, derived via the model of double-Euler beams and the law of energy equipartition, between the temperature and the root-of-mean-squared (RMS) amplitude of the thermal vibration at any cross section of the DWCNT. The molecular dynamics simulations of thermal vibration of the DWCNT in argon atmosphere show that the model of double-Euler beams can predict the RMS amplitude of the thermal vibration of the DWCNT reasonably well.

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. Treacy M.M.J., Ebbesen T.W., Gibson J.M.: Exceptionally high Young’s modulus observed for individual carbon nanotubes. Nature 381, 678–680 (1996)

    Article  Google Scholar 

  2. Krishnan A., Dujardin E., Ebbesen T.W., Yianilos P.N., Treacy M.M.J.: Young’s modulus of single-walled nanotubes. Phys. Rev. B 58(20), 14013 (1998)

    Article  Google Scholar 

  3. Xu Z.P., Zheng Q.S., Chen G.H.: Thermally driven large-amplitude fluctuations in carbon-nanotube-based devices: Molecular dynamics simulations. Phys. Rev. B 74(19), 195445 (2006)

    Google Scholar 

  4. Hsieh J.Y., Lu J.M., Huang M.Y., Hwang C.C.: Theoretical variations in the Young’s modulus of single-walled carbon nanotubes with tube radius and temperature: a molecular dynamics study. Nanotechnology 17, 3920–3924 (2006)

    Article  Google Scholar 

  5. Wang L.F., Hu H.Y., Guo W.L.: Thermal vibration of carbon nanotubes predicted by beam models and molecular dynamics. Proc. R. Soc. A 466(2120), 2325–2340 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Feng E.H., Jones R.E.: Equilibrium thermal vibrations of carbon nanotubes. Phys. Rev. B 81, 125436 (2010)

    Article  Google Scholar 

  7. Feng E.H., Jones R.E.: Carbon nanotube cantilevers for next-generation sensors. Phys. Rev. B 83, 125412 (2011)

    Article  Google Scholar 

  8. Qian D., Wagner G.J., Liu W.K., Yu M.F., Ruoff R.S.: Mechanics of carbon nanotubes. Appl. Mech. Rev. 55, 495–533 (2002)

    Article  Google Scholar 

  9. Yoon J., Ru C.Q., Mioduchowski A.: Non-coaxial resonance of an isolated multiwall carbon nanotube. Phys. Rev. B 66, 233402 (2002)

    Article  Google Scholar 

  10. Yoon J., Ru C.Q., Mioduchowski A.: Timoshenko-beam effects on transverse wave propagation in carbon nanotubes. Compos. Part B Eng. 35, 87 (2004)

    Article  Google Scholar 

  11. Thomson W.T.: Theory of Vibration with Applications. Prentice-Hall, Englewood Cliffs (1972)

    Google Scholar 

  12. He X.Q., Kitipornchai S., Liew K.M.: Buckling analysis of multi-walled carbon nanotubes: a continuum model accounting for van der Waals interaction. J. Mech. Phys. Solids 53, 303–326 (2005)

    Article  MATH  Google Scholar 

  13. Brenner D.W.: Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films. Phys. Rev. B 42, 9458 (1990)

    Article  Google Scholar 

  14. Rafizadeh H.A.: An analytical-potential approach to the lattice dynamics of graphite. Physica 74, 135–150 (1974)

    Article  Google Scholar 

  15. Cleary S.M., Mayne H.R.: High-symmetry global minimum geometries for small mixed Ar/Xe Lennard–Jones clusters. Chem. Phys. Lett. 418, 79–83 (2006)

    Article  Google Scholar 

  16. Yakobson B.I., Brabec C.J., Bernholc J.: Nanomechanics of carbon tubes: instabilities beyond linear response. Phys. Rev. Lett. 76, 2511 (1996)

    Article  Google Scholar 

  17. Zhang P., Huang Y., Geubelle P.H., Klein P.A., Hwang K.C.: The elastic modulus of single-wall carbon nanotubes: a continuum analysis incorporating interatomic potentials. Int. J. Solids Struct. 39, 3893 (2002)

    Article  MATH  Google Scholar 

  18. Wang J.B., Guo X., Zhang H.W., Wang L., Liao J.B.: Energy and mechanical properties of single-walled carbon nanotubes predicted using the higher order Cauchy–Born rule. Phys. Rev. B 73, 115428 (2006)

    Article  Google Scholar 

  19. Wang L.F., Hu H.Y.: Flexural wave propagation in single-walled carbon nanotubes. Phys. Rev. B 71(19), 195412 (2005)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University Aeronautics and Astronautics, Nanjing, 210016, China

    Li Feng Wang & Hai Yan Hu

Authors
  1. Li Feng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hai Yan Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Li Feng Wang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, L.F., Hu, H.Y. Thermal vibration of double-walled carbon nanotubes predicted via double-Euler-beam model and molecular dynamics. Acta Mech 223, 2107–2115 (2012). https://doi.org/10.1007/s00707-012-0694-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-012-0694-0

Keywords

Search

Navigation