Thermal vibration and apparent thermal contraction of single-walled carbon nanotubes

Guoxin CAO, Xi CHEN*, Jeffrey W. KYSAR

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

83 Citations (Scopus)


It is of fundamental value to understand the thermo-mechanical properties of carbon nanotubes. In this paper, by using molecular dynamics simulation, a systematic numerical investigation is carried out to explore the natural thermal vibration behaviors of single-walled carbon nanotubes and their quantitative contributions to the apparent thermal contraction behaviors. It is found that the thermo-mechanical behavior of single-walled carbon nanotubes is exhibited through the competition between quasi-static thermal expansion and dynamic thermal vibration, while the vibration effect is more prominent and induces apparent contraction in both radial and axial directions. With increasing temperature, the anharmonic interatomic potential helps to increase the bond length, which leads to thermally induced expansion. On the other hand, the higher structural entropy and vibrational entropy of the system cause the carbon nanotube to vibrate, and the apparent length of nanotube decreases due to various vibration modes. Parallel analytical and finite element analyses are used to validate the vibration frequencies and provide helpful insights. The unified multi-scale study has successfully decoupled and systematically analyzed both thermal expansion and contraction behaviors of single-walled carbon nanotube from 100 to 800 K, and obtained detailed information on various vibration modes as well as their quantitative contributions to the coefficient of thermal expansion in axial and radial directions. The results of this paper may provide useful information on the thermo-mechanical integrity of single-walled carbon nanotubes, and become important in practical applications involving finite temperature. © 2006 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)1206-1236
Number of pages31
JournalJournal of the Mechanics and Physics of Solids
Issue number6
Publication statusPublished - Jun 2006
Externally publishedYes

Bibliographical note

This work is supported in part by the Columbia University Academic Quality Fund “Columbia Nanomechanics Research Center”. XC acknowledges support from NSF CMS-0407743. JWK acknowledges support from NSF CMS-0134226. We also wish to thank the anonymous reviewer who suggested that we carefully distinguish between the classical MD approach and the quantum mechanics approach.


  • Carbon nanotube
  • Thermal property
  • Vibration


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