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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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)
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)
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)
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)
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)
Feng E.H., Jones R.E.: Equilibrium thermal vibrations of carbon nanotubes. Phys. Rev. B 81, 125436 (2010)
Feng E.H., Jones R.E.: Carbon nanotube cantilevers for next-generation sensors. Phys. Rev. B 83, 125412 (2011)
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)
Yoon J., Ru C.Q., Mioduchowski A.: Non-coaxial resonance of an isolated multiwall carbon nanotube. Phys. Rev. B 66, 233402 (2002)
Yoon J., Ru C.Q., Mioduchowski A.: Timoshenko-beam effects on transverse wave propagation in carbon nanotubes. Compos. Part B Eng. 35, 87 (2004)
Thomson W.T.: Theory of Vibration with Applications. Prentice-Hall, Englewood Cliffs (1972)
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)
Brenner D.W.: Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films. Phys. Rev. B 42, 9458 (1990)
Rafizadeh H.A.: An analytical-potential approach to the lattice dynamics of graphite. Physica 74, 135–150 (1974)
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)
Yakobson B.I., Brabec C.J., Bernholc J.: Nanomechanics of carbon tubes: instabilities beyond linear response. Phys. Rev. Lett. 76, 2511 (1996)
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)
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)
Wang L.F., Hu H.Y.: Flexural wave propagation in single-walled carbon nanotubes. Phys. Rev. B 71(19), 195412 (2005)
Author information
Authors and Affiliations
Corresponding author
Rights 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
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-012-0694-0