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Torsional buckling analysis of chiral multi-walled carbon nanotubes based on an accurate molecular mechanics model

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Abstract

This study is concerned with the torsional buckling behavior of chiral multi-walled carbon nanotubes (MWCNTs) based on a molecular mechanics model. An analytical solution is carried out to calculate the elastic critical buckling shear strain of MWCNTs with different types of chirality. To determine the force constants used in the molecular mechanics model, on the basis of quantum mechanics, density functional theory is employed. Through comparison of the results obtained from the present molecular mechanics model and ones from available molecular dynamics simulations, the validity of the present approach is assessed. The influence of chirality on the critical buckling shear strain of nanotubes is then investigated. It is indicated that nanotubes with (n, n/2) chirality buckle at lower values of critical buckling shear strain compared with zigzag and armchair nanotubes.

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References

  1. Iijima S.: Helical microtubes of graphitic carbon. Nature (London) 354, 56–58 (1991)

    Article  Google Scholar 

  2. Wong E.W., Sheehan P.W., Lieber C.M.: Nanobeam mechanics: elasticity, strength, and toughness of nanorods and nanotubes. Science 277, 1971–1975 (1997)

    Article  Google Scholar 

  3. Salvetal J.P., Briggs G.A.D., Bonard J.M., Bacsa R.R., Kulik A.J., Stockli T., Burnham N.A., Forro L.: Elastic and shear moduli of single-walled carbon nanotube ropes. Phys. Rev. Lett. 82, 944–947 (1999)

    Article  Google Scholar 

  4. Yakobson B.I., Brabec C.J., Bernholc J.: Nanomechanics of carbon tubes: instabilities beyond linear response. Phys. Lett. A 76, 2511–2514 (2000)

    Article  Google Scholar 

  5. Srivastava D., Menon M., Cho K.: Nanoplasticity of single-wall carbon nanotubes under uniaxial compression. Phys. Rev. Lett. 83, 2973–2976 (1999)

    Article  Google Scholar 

  6. Pantano A., Boyce M.C., Parks D.M.: Mechanics of axial compression of single and multi-wall carbon nanotubes. ASME J. Eng. Mater. Technol. 126, 279–284 (2004)

    Article  Google Scholar 

  7. Lu W.B., Wu J., Feng X., Hwang K.C., Huang Y.: Buckling analyses of double-wall carbon nanotubes: a shell theory based on the interatomic potential. ASME J. Appl. Mech. 77, 061016 (2010)

    Article  Google Scholar 

  8. Ansari R., Sahmani S., Rouhi H.: Rayleigh–Ritz axial buckling analysis of single-walled carbon nanotubes with different boundary conditions. Phys. Lett. A 375, 1255–1263 (2011)

    Article  Google Scholar 

  9. Kiani K.: Axial buckling analysis of vertically aligned ensembles of single-walled carbon nanotubes using nonlocal discrete and continuous models. Acta Mech. 225, 3569–3589 (2014)

    Article  MathSciNet  Google Scholar 

  10. Vodenitcharova T., Zhang L.C.: Effective wall thickness of a single-walled carbon nanotubes. Phys. Rev. B 68, 165401 (2003)

    Article  Google Scholar 

  11. Zhou X., Zhou J., Ou-Yang Z.C.: Strain energy and young’s modulus of single-wall carbon nanotubes calculated from electronic energy-band theory. Phys. Rev. B 62, 13692–13696 (2000)

    Article  Google Scholar 

  12. Chang T., Gao H.: Size-dependent elastic properties of a single-walled carbon nanotube via a molecular mechanics model. J. Mech. Phys. Solids 51, 1059–1074 (2003)

    Article  Google Scholar 

  13. Chang T., Li G., Guo X.: Elastic axial buckling of carbon nanotubes via a molecular mechanics model. Carbon 43, 287–294 (2005)

    Article  Google Scholar 

  14. Chang T., Guo W., Guo X.: Buckling of multiwalled carbon nanotubes under axial compression and bending via a molecular mechanics model. Phys. Rev. B 72, 064101 (2005)

    Article  Google Scholar 

  15. Chang T., Geng J., Guo X.: Chirality- and size-dependent elastic properties of single-walled carbon nanotubes. Appl. Phys. Lett. 87, 251929 (2005)

    Article  Google Scholar 

  16. Chang T., Geng J., Guo X.: Prediction of chirality- and size-dependent elastic properties of single-walled carbon nanotubes via a molecular mechanics model. Proc. R. Soc. A 462, 2523–2540 (2006)

    Article  Google Scholar 

  17. Chang T.: A molecular based anisotropic shell model for single-walled carbon nanotubes. J. Mech. Phys. Solids 58, 1422–1433 (2010)

    Article  MathSciNet  Google Scholar 

  18. Meo M., Rossi M.: Prediction of young’s modulus of single wall carbon nanotubes by molecular-mechanics based finite element modeling. Compos. Sci. Technol. 66, 1597–1605 (2006)

    Article  Google Scholar 

  19. Wang X., Yang H.K., Dong K.: Torsional buckling of multi-walled carbon nanotubes. Mater. Sci. Eng. A 404, 314–322 (2005)

    Article  Google Scholar 

  20. Lu Y.J., Wang X.: Combined torsional buckling of multi-walled carbon nanotubes. J. Phys. D Appl. Phys. 39, 3380–3387 (2006)

    Article  Google Scholar 

  21. Yang H.K., Wang X.: Torsional buckling of multi-wall carbon nanotubes embedded in an elastic medium. Compos. Struct. 77, 182–192 (2007)

    Article  Google Scholar 

  22. Sun C.Q., Liu K.X.: Torsional buckling of multi-walled carbon nanotubes under combined axial and radial loadings. J. Phys. D Appl. Phys. 41, 205404 (2008)

    Article  Google Scholar 

  23. Hao M.J., Guo X.M., Wang Q.: Small-scale effect on torsional buckling of multi-walled carbon nanotubes. Eur. J. Mech. A-Solids 29, 49–55 (2010)

    Article  MathSciNet  Google Scholar 

  24. Zhang Y.Y., Wang C.M.: Torsional responses of double-walled carbon nanotubes via molecular dynamics simulations. J. Phys. Condens. Matter 20, 455214 (2008)

    Article  Google Scholar 

  25. Hai-Yang S., Li-Feng L., Feng F.: Torsional behaviour of carbon nanotubes with abnormal interlayer distances. J. Phys. D Appl. Phys. 42, 055414 (2009)

    Article  Google Scholar 

  26. Leach, A.R.: Molecular Modeling Principles and Applications. Addison Wesley Longman Limited, London, pp. 131–210 (1996)

  27. Perdew J.P., Burke K., Ernzerhof M.: Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996)

    Article  Google Scholar 

  28. Perdew J.P., Burke K., Wang Y.: Generalized gradient approximation for the exchange-correlation hole of a many-electron system. Phys. Rev. B 54, 16533–16539 (1996)

    Article  Google Scholar 

  29. Baroni, S., Corso, D.A., Gironcoli, S., Giannozzi, P., Cavazzoni, C., Ballabio, G., Scandolo, S., Chiarotti, G., Focher, P., Pasquarello, A., Laasonen, K., Trave, A., Car, R., Marzari, N., Kokalj, A.: http://www.pwscf.org/

  30. Zhao K., Zhao M., Wang Z., Fan Y.: Tight-binding model for the electronic structures of SiC and BN nanoribbons. Phys. Rev. E 43, 440–445 (2010)

    Google Scholar 

  31. Grosso G., Parravicini G.P.: Solid State Physics. Academic Press, London (2000)

    Google Scholar 

  32. Hohenberg P., Kohn W.: Inhomogeneous electron gas. Phys. Rev. B 136, 864–871 (1964)

    Article  MathSciNet  Google Scholar 

  33. Kohn W., Sham L.J.: Self-consistent equations including exchange and correlation effects. Phys. Rev. A 140, 1133–1138 (1965)

    Article  MathSciNet  Google Scholar 

  34. Hamann D.R., Schlüter M., Chiang C.: Norm-conserving pseudopotentials. Phys. Rev. Lett. 43, 1494–1497 (1979)

    Article  Google Scholar 

  35. Troullier N., Martins J.L.: Efficient pseudopotentials for plane-wave calculations. Phys. Rev. B 43, 1993–2006 (1991)

    Article  Google Scholar 

  36. Topsakal M., Cahangirov S., Ciraci S.: The response of mechanical and electronic properties of graphane to the elastic strain. Appl. Phys. Lett. 96, 091912 (2010)

    Article  Google Scholar 

  37. Monkhorst H.J., Pack J.D.: Special points for brillouin-zone integrations. Phys. Rev. B 13, 5188–5192 (1976)

    Article  MathSciNet  Google Scholar 

  38. Lee C., Wei X., Kysar J.W., Hone J.: Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321, 385–388 (2008)

    Article  Google Scholar 

  39. Liu F., Ming P., Li J.: Ab initio calculation of ideal strength and phonon instability of graphene under tension. Phys. Rev. B 76, 064120 (2007)

    Article  Google Scholar 

  40. Arroyo M., Belytschko T.: Finite crystal elasticity of carbon nanotubes based on the exponential Cauchy–Born rule. Phys. Rev. B 69, 115415 (2004)

    Article  Google Scholar 

  41. Lu Q., Arroyo M., Huang R.: Elastic bending modulus of monolayer graphene. J. Phys. D App. Phys. 42, 102002 (2009)

    Article  Google Scholar 

  42. Leung A.Y.T., Wu Y., Zhong W.: Computation of young’s moduli for chiral single-walled carbon nanotubes. Appl. Phys. Lett. 88, 251908 (2006)

    Article  Google Scholar 

  43. Fang S.C., Chang W.J., Wang Y.H.: Computation of chirality- and size-dependent surface young’s moduli for single-walled carbon nanotubes. Phys. Lett. A 371, 499–503 (2007)

    Article  Google Scholar 

  44. Rossi M., Meo M.: On the estimation of mechanical properties of single-walled carbon nanotubes by using a molecular-mechanics based FE approach. Compos. Sci. Technol. 69, 1394–1398 (2009)

    Article  Google Scholar 

  45. Khademolhosseini F., Rajapakse R.K.N.D., Nojeh A.: Torsional buckling of carbon nanotubes based on nonlocal elasticity shell models. Comput. Mater. Sci. 48, 382–388 (2010)

    Article  Google Scholar 

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Correspondence to R. Ansari or H. Rouhi.

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Ansari, R., Mirnezhad, M. & Rouhi, H. Torsional buckling analysis of chiral multi-walled carbon nanotubes based on an accurate molecular mechanics model. Acta Mech 226, 2955–2972 (2015). https://doi.org/10.1007/s00707-015-1358-7

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  • DOI: https://doi.org/10.1007/s00707-015-1358-7

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