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Radial buckling of multi-walled carbon nanotubes under hydrostatic pressure

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Abstract

Radial buckling stresses of carbon nanotubes (CNTs) need to be studied in high-pressure resonance Raman scattering spectrum. In this work, the closed-form expression of the critical buckling stress of multi-walled carbon nanotubes (MWCNTs) under hydrostatic pressure is derived that can be conveniently employed. Using the derived formulae, the critical buckling stresses of single-walled carbon nanotubes and double-walled carbon nanotubes with different diameters are calculated. The results are in good agreement with other reported literatures. In addition, the critical buckling stresses of each layer of a quintuple-walled CNT in different buckling modes are predicted, showing that the buckling instability can occur not only in the outermost rolled layer, but also in other rolled layer of MWCNTs by considering different diameters and buckling modes.

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References

  1. S. Iijima, Nature 354, 56 (1991)

    Article  ADS  Google Scholar 

  2. S. Iijima, T. Ichihashi, Nature 363, 603 (1993)

    Article  ADS  Google Scholar 

  3. S. Reich, C. Thomsen, J. Maultzsch, Carbon nanotubes: basic concepts and physical properties (WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, 2004)

    Google Scholar 

  4. I. Loa, J. Raman Spectrosc. 34, 611 (2003)

    Article  ADS  Google Scholar 

  5. U.D. Venkateswaran, A.M. Rao, E. Richter, M. Menon, A. Rinzler, R.E. Smalley, P.C. Ecklund, Phys. Rev. B 59(10), 928 (1999)

    Google Scholar 

  6. P. Puech, A. Ghandour, A. Sapelkin, C. Tinguely, E. Flahaut, D.J. Dunstan, W. Basca, Phys. Rev. B 78, 045413 (2008)

    Article  ADS  Google Scholar 

  7. L. Alvarez, J.L. Bantignies, R. Le Parc, R. Aznar, J.L. Sauvajol, A. Merlen, D. Machon, A. San Miguel, Phys. Rev. B 82, 205403 (2010)

    Article  ADS  Google Scholar 

  8. A.L. Aguiar, A. San-Miguel, E.B. Barros, M. Kalbáč, D. Machon, Y.A. Kim, H. Muramatsu, M. Endo, A.G. Souza Filho, Phys. Rev. B 86, 195410 (2012)

    Article  ADS  Google Scholar 

  9. J. Tang, L.C. Qin, T. Sasaki, M. Yudasaka, A. Matsushita, S. Iijima, Phys. Rev. Lett. 85, 1887 (2000)

    Article  ADS  Google Scholar 

  10. J.F. Waters, L. Riester, M. Jouzi, P.R. Guduru, J.M. Xu, Appl. Phys. Lett. 85, 1787 (2004)

    Article  ADS  Google Scholar 

  11. Y.R. Jeng, P.C. Tsai, T.H. Fang, Appl. Phys. Lett. 90, 161913 (2007)

    Article  ADS  Google Scholar 

  12. H.W. Yap, R.S. Lakes, R.W. Carpick, Nano Lett. 7, 1149 (2007)

    Article  ADS  Google Scholar 

  13. P.R. Guduru, Z. Xia, Exp. Mech. 47, 153 (2007)

    Article  Google Scholar 

  14. D.Y. Khang, J. Xiao, C. Kocabas, S. MacLaren, T. Banks, H. Jiang, Y.Y. Huang, J.A. Rogers, Nano Lett. 8, 124 (2008)

    Article  ADS  Google Scholar 

  15. P.C. Tsai, Y.R. Jeng, Y.X. Huang, K.T. Wu, Appl. Phys. Lett. 103, 053119 (2013)

    Article  ADS  Google Scholar 

  16. Q. Wang, K.M. Liew, X.Q. He, Y. Xiang, Appl. Phys. Lett. 91, 093128 (2007)

    Article  ADS  Google Scholar 

  17. Q. Wang, K.M. Liew, V.K. Varadan, Appl. Phys. Lett. 92, 043120 (2008)

    Article  ADS  Google Scholar 

  18. T. Natsuki, N. Fujita, Q.Q. Ni, M. Endo, J. Appl. Phys. 106, 084310 (2009)

    Article  ADS  Google Scholar 

  19. J.X. Shi, T. Natsuki, X.W. Lei, Q.Q. Ni, ASME J. Nanotechnol. Eng. Med. 3, 020903 (2012)

    Article  Google Scholar 

  20. S.C. Pradhan, G.K. Reddy, Comp. Mater. Sci. 50, 1052 (2011)

    Article  Google Scholar 

  21. X. Huang, W. Liang, S. Zhang, Nanoscale Res. Lett. 6, 53 (2011)

    Article  ADS  Google Scholar 

  22. B. Motevalli, A. Montazeri, J.Z. Liu, H. Rafii-Tabar, Comp. Mater. Sci. 79, 619 (2013)

    Article  Google Scholar 

  23. D.D.T.K. Kulathunga, K.K. Ang, Comp. Mater. Sci. 81, 233 (2014)

    Article  Google Scholar 

  24. D. Qian, G.J. Wagner, W.K. Liu, M.F. Yu, R.S. Ruoff, Appl. Mech. Rev. 55, 495 (2002)

    Article  ADS  Google Scholar 

  25. R. Ansari, R. Gholami, S. Sahmani, Appl. Phys. A 113, 145 (2013)

    Article  ADS  Google Scholar 

  26. H. Shima, Materials 5, 47 (2012)

    Article  ADS  Google Scholar 

  27. E. Ventsel, T. Krauthammer, Thin plates and shells (Marcel Dekker Inc, New York, 2001)

    Book  Google Scholar 

  28. X.Q. He, S. Kitipornchai, K.M. Liew, J. Mech. Phys. Solids 53, 303 (2005)

    Article  MATH  ADS  Google Scholar 

  29. R. Saito, R. Matsuo, T. Kimura, G. Dresselhaus, M.S. Dresselhaus, Chem. Phys. Lett. 348, 187 (2001)

    Article  ADS  Google Scholar 

  30. S. Timoshenko, S. Woinowsky-Keieger, Theory of plates and shells (McGraw-Hill Book Co., Singapore, 1959)

    Google Scholar 

  31. X. Wang, G. Lu, Y.J. Lu, Int. J. Solids Struct. 44, 336 (2007)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Interdisciplinary Graduate School of Science and Technology, Shinshu University, 3-15-1 Tokida, Ueda-shi, Nagano, 386-8567, Japan

    Jin-Xing Shi

  2. Faculty of Textile Science and Technology, Shinshu University, 3-15-1 Tokida, Ueda-shi, Nagano, 386-8567, Japan

    Toshiaki Natsuki & Qing-Qing Ni

  3. Institute of Carbon Science and Technology, Shinshu University, 4-17-1 Wakasato, Nagano-shi, Nagano, 380-8553, Japan

    Toshiaki Natsuki

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  1. Jin-Xing Shi
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  2. Toshiaki Natsuki
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  3. Qing-Qing Ni
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Correspondence to Toshiaki Natsuki.

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Shi, JX., Natsuki, T. & Ni, QQ. Radial buckling of multi-walled carbon nanotubes under hydrostatic pressure. Appl. Phys. A 117, 1103–1108 (2014). https://doi.org/10.1007/s00339-014-8564-3

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  • DOI: https://doi.org/10.1007/s00339-014-8564-3

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