Influences of vacancy defects on buckling behaviors of open-tip carbon nanocones


This study investigated influences of vacancy defects on buckling behaviors of open-tip carbon nanocones (CNCs) by molecular dynamics simulations. Effects of vacancy location and temperature on the buckling behaviors were examined in the study. Some interesting findings were attained from the investigations. It was noticed that the CNC with an upper vacancy has comparable degradation in the critical strain and in the critical load with the CNC with a middle vacancy, whereas the CNC with a lower vacancy has lower degradation in the antibuckling ability than the above two CNCs. The antibuckling ability of the CNCs reduces with the growth of the temperature. This temperature effect is more apparent in the perfect CNC than in the vacancy-defect CNCs. It was also observed that the degradation in the antibuckling ability is obvious at a lower temperature, but it decreases as the temperature grows. Besides, all the CNCs (including the perfect and the vacancy-defect CNCs) exhibited a shrinking/swelling buckling mode shape at the studied temperatures. Existence of the vacancies did not alter the buckling mode shape of the CNCs.

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  1. 1.

    N. Tagmatarchis ed.: Advances in Carbon Nanomaterials: Science and Applications (Pan Stanford Publishing, Singapore, 2012).

    Google Scholar 

  2. 2.

    M. Ge and K. Sattler: Observation of fullerene cones. Chem. Phys. Lett. 220, 192–196 (1994).

    CAS  Article  Google Scholar 

  3. 3.

    A. Krishnan, E. Dujardin, M.M.J. Treacy, J. Hugdhl, S. Lynum, and T.W. Ebbesen: Graphitic cones and the nucleation of curved carbon surfaces. Nature 388, 451–454 (1997).

    CAS  Article  Google Scholar 

  4. 4.

    S.N. Naess, A. Elgsaeter, G. Helgesen, and K.D. Knudsen: Carbon nanocones: Wall structure and morphology. Sci. Technol. Adv. Mater. 10, 065002 (2009).

    Article  CAS  Google Scholar 

  5. 5.

    S. Iijima, M. Yudasaka, R. Yamada, S. Bandow, K. Suenaga, F. Kokai, and K. Taskahashi: Nanoaggregates of single-walled graphitic carbon nanohorns. Chem. Phys. Lett. 309, 165–170 (1999).

    CAS  Article  Google Scholar 

  6. 6.

    Y. Gogotsi, S. Dimovski, and J.A. Libera: Conical crystals of graphite. Carbon 40, 2263–2267 (2002).

    CAS  Article  Google Scholar 

  7. 7.

    G. Zhang, X. Jiang, and E. Wang: Tubular graphite cones. Science 300, 472–474 (2003).

    CAS  Article  Google Scholar 

  8. 8.

    Z.L. Tsakadze, I. Levchenko, K. Ostrikov, and X. Su: Plasma-assisted self-organized growth of uniform carbon nanocone arrays. Carbon 45, 2022–2030 (2007).

    CAS  Article  Google Scholar 

  9. 9.

    I. Levchenko, K. Ostrikov, J.D. Long, and S. Xu: Plasma-assisted self-sharpening of platelet-structured single-crystalline carbon nanocones. Appl. Phys. Lett. 91, 113115 (2007).

    Article  CAS  Google Scholar 

  10. 10.

    H. Terrones, T. Hayashi, M. Muñoz-Navia, M. Terrones, Y.A. Kim, N. Grobert, R. Kamalakaran, J. Dorantes-Davila, R. Escudero, M.S. Dresselhaus, and M. Endo: Graphitic cones in palladium catalysed carbon nanofibers. Chem. Phys. Lett. 343, 241–250 (2001).

    CAS  Article  Google Scholar 

  11. 11.

    M. Endo, Y.A. Kim, T. Hayashi, Y. Fukai, K. Oshida, M. Terrones, T. Yanagisawa, S. Higaki, and M.S. Dresselhaus: Structural characterization of cup-stacked-type nanofibers with an entirely hollow core. Appl. Phys. Lett. 80, 1267 (2002).

    CAS  Article  Google Scholar 

  12. 12.

    B. Ekşioğlu and A. Nadarajah: Structural analysis of conical carbon nanofibers. Carbon 44, 360–373 (2006).

    Article  CAS  Google Scholar 

  13. 13.

    I.C. Chen, L.H. Chen, A. Gapin, S. Jin, L. Yuan, and S.H. Liou: Iron-platinum-coated carbon nanocone probes on tipless cantilevers for high resolution magnetic force imaging. Nanotechnology 19, 075501 (2008).

    Article  CAS  Google Scholar 

  14. 14.

    J. Sripirom, S. Noor, U. Koehler, and A. Schulte: Easily made and handled carbon nanocones for scanning tunneling microscopy and electroanalysis. Carbon 49, 2402–2412 (2011).

    CAS  Article  Google Scholar 

  15. 15.

    J.Y. Hsieh, C. Chen, J.L. Chen, C.I. Chen, and C.C. Hwang: The nanoindentation of a copper substrate by single-walled carbon nanocone tips: A molecular dynamics study. Nanotechnology 20, 095709 (2009).

    Article  CAS  Google Scholar 

  16. 16.

    S.S. Yu and W.T. Zheng: Effect of N/B doping on the electronic and field emission properties for carbon nanotubes, carbon nanocones, and graphene nanoribbons. Nanoscale 2, 1069–1082 (2010).

    CAS  Article  Google Scholar 

  17. 17.

    O.O. Adisa, B.J. Cox, and J.M. Hill: Open carbon nanocones as candidates for gas storage. J. Phys. Chem. C 115, 24528–24533 (2011).

    CAS  Article  Google Scholar 

  18. 18.

    M.L. Liao: A study on hydrogen adsorption behaviors of open-tip carbon nanocones. J. Nanopart. Res. 14, 837 (2012).

    Article  CAS  Google Scholar 

  19. 19.

    N. Yang, G. Zhang, and B. Li: Carbon nanocone: A promising thermal rectifier. Appl. Phys. Lett. 93, 243111 (2008).

    Article  CAS  Google Scholar 

  20. 20.

    S.P. Jordan and V.H. Crespi: Theory of carbon nanocones: Mechanical chiral inversion of a micron-scale three-dimensional object. Phys. Rev. Lett. 93, 255504 (2004).

    Article  CAS  Google Scholar 

  21. 21.

    P.C. Tsai and T.H. Fang: A molecular dynamics study of the nucleation, thermal stability and nanomechanics of carbon nanocones. Nanotechnology 18, 105702 (2007).

    Article  CAS  Google Scholar 

  22. 22.

    K.M. Liew, J.X. Wei, and X.Q. He: Carbon nanocones under compression: Buckling and post-buckling behaviors. Phys. Rev. B 75, 195435 (2007).

    Article  CAS  Google Scholar 

  23. 23.

    J.X. Wei, K.M. Liew, and X.Q. He: Mechanical properties of carbon nanocones. Appl. Phys. Lett. 91, 261906 (2007).

    Article  CAS  Google Scholar 

  24. 24.

    M.L. Liao, C.H. Cheng, and Y.P. Lin: Tensile and compressive behaviors of open-tip carbon nanocones under axial strains. J. Mater. Res. 26, 1577–1584 (2011).

    CAS  Article  Google Scholar 

  25. 25.

    M.M.S. Fakhrabadi, N. Khani, R. Omidvar, and A. Rastgoo: Investigation of elastic and buckling properties of carbon nanocones using molecular mechanics approach. Comput. Mater. Sci. 61, 248–256 (2012).

    CAS  Article  Google Scholar 

  26. 26.

    M.M.S. Fakhrabadi, B. Dadashzadeh, V. Norouzifard, and A. Allahverdizadeh: Application of molecular dynamics in mechanical characterization of carbon nanocones. J. Comput. Theor. Nanosci. 10, 1921–1927 (2013).

    CAS  Article  Google Scholar 

  27. 27.

    J.W. Yan, K.M. Liew, and L.H. He: A mesh-free computational framework for predicting buckling behaviors of single-walled carbon nanocones under axial compression based on the moving kriging interpolation. Comput. Methods Appl. Mech. Eng. 247, 103–112 (2012).

    Article  Google Scholar 

  28. 28.

    J.W. Yan, K.M. Liew, and L.H. He: Buckling and post-buckling of single-wall carbon nanocones upon bending. Compos. Struct. 106, 793–798 (2013).

    Article  Google Scholar 

  29. 29.

    M.L. Liao: Buckling behaviors of open-tip carbon nanocones at elevated temperatures. Appl. Phys. A 117, 1109–1118 (2014).

    CAS  Article  Google Scholar 

  30. 30.

    R. Andrews, D. Jacques, D. Qian, and E.C. Dickey: Purification and structural annealing of multiwalled carbon nanotubes at graphitization temperatures. Carbon 39, 1681–1687 (2001).

    CAS  Article  Google Scholar 

  31. 31.

    N. Pierard, A. Fonseca, Z. Konya, I. Willems, G. Van Tendeloo, and J.B. Nagy: Production of short carbon nanotubes with open tips by ball milling. Chem. Phys. Lett. 335, 1–8 (2001).

    CAS  Article  Google Scholar 

  32. 32.

    B. Ni and S.B. Sinnott: Chemical functionalization of carbon nanotubes through energetic radical collisions. Phys. Rev. B 61, R16343 (2000).

    CAS  Article  Google Scholar 

  33. 33.

    C.A. Cooper, S.R. Cohen, A.H. Barber, and H.D. Wagner: Detachment of nanotubes from a polymer matrix. Appl. Phys. Lett. 81, 3873–3875 (2002).

    CAS  Article  Google Scholar 

  34. 34.

    M. Sammalkorpi, A. Krasheninnikov, A. Kuronen, K. Nordlund, and K. Kaski: Mechanical properties of carbon nanotubes with vacancies and related defects. Phys. Rev. B 70, 245416 (2004).

    Article  CAS  Google Scholar 

  35. 35.

    H. Xin, Q. Han, and X.H. Yao: Buckling and axially compressive properties of perfect and defective single-walled carbon nanotubes. Carbon 45, 2486–2495 (2007).

    CAS  Article  Google Scholar 

  36. 36.

    M. Eftekhari, S. Mohammadi, and A.R. Khoei: Effect of defects on the local shell buckling and post-buckling behavior of single and multi-walled carbon nanotubes. Comput. Mater. Sci. 79, 736–744 (2013).

    CAS  Article  Google Scholar 

  37. 37.

    S. Sharma, R. Chandra, P. Kumar, and N. Kumar: Effect of Stone-Wales and vacancy defects on elastic moduli of carbon nanotubes and their composites using molecular dynamics simulation. Comput. Mater. Sci. 86, 1–8 (2014).

    CAS  Article  Google Scholar 

  38. 38.

    J. Tersoff: New empirical model for the structural properties of silicon. Phys. Rev. Lett. 56, 632–635 (1986).

    CAS  Article  Google Scholar 

  39. 39.

    J. Tersoff: Modeling solid-state chemistry: Interatomic potentials for multi-component systems. Phys. Rev. B 39, 5566–5568 (1989).

    CAS  Article  Google Scholar 

  40. 40.

    D.C. Rapaport: The Art of Molecular Dynamics Simulations (Cambridge University Press, Cambridge, 2004).

    Google Scholar 

  41. 41.

    J.M. Haile: Molecular Dynamics Simulation: Elementary Method (John Wiley & Sons, New York, 1997).

    Google Scholar 

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The author gratefully acknowledges the support provided to this research by the Ministry of Science and Technology of Taiwan under Project Grant No. NSC 103-2923-E-006-004-MY3. The author also thanks the editor and referees for their helpful recommendations to make this study more readable.

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Correspondence to Ming-Liang Liao.

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Liao, ML. Influences of vacancy defects on buckling behaviors of open-tip carbon nanocones. Journal of Materials Research 30, 896–903 (2015).

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