Investigation of the relationship between elastic properties of a single-walled carbon nanotubes and graphene

The investigation shows the research results of relationship between elastic properties of single-layer graphene which is assumed to be isotropic in the plane of hexagonal cells and a single-walled carbon nanotube formed from graphene as a cylindrical shell. This nanotube is assumed to have transverse isotropy about the longitudinal axis. The results for a single-walled carbon nanotube with chirality indices (4, 4) are given.

References

[1] Overney G., Zhong W., Tomanek D.Z. Structural rigidity and low frequency vibrational modes of long carbon tubules. Zeitschrift fur Physik D. Atoms, Molecules and Clusters, 1993, vol. 27, no. 1, pp. 93-96. DOI: 10.1007/BF01436769

[2] Yakobson B.I., Brabec C.J., Bernholc J. Nanomechanics of carbon tubes: Instabilities beyond linear response. Phys. Rev. Lett., 1996, vol. 76, no. 14, p. 2511.

[3] Treacy M.M.J., Ebbesen T.W., Gibson J.M. Exceptionally high Young’s modulus observed for individual carbon nanotubes. Nature, 1996, no. 381, pp. 678-680.

[4] Krishnan A., Dujardin E., Ebbesen T.W., Yianilos P.N., Treacy M.M.J. Young’s modulus of single-walled nanotubes. Phys. Rev. B, 1998, no. 58, pp. 14013-14019.

[5] Lourie O., Wagner H.D. Evaluation of Young’s modulus of carbon nanotubes by micro-Raman spectroscopy. Journal of Materials Research, 1998, no. 13, pp. 2418-2422.

[6] Pan Z.W., Xie S.S., Lu L., Chang B.H., Sun L.F., Zhou W.Y., Wang G., Zhang D.L. Tensile tests of ropes of very long aligned multiwall carbon nanotubes. Applied Physics Letters, 1999, no. 74, pp. 3152-3154.

[7] Tarasova E.S. The Study of Mechanical Properties of Composites Reinforced with Carbon Nanotubes. Molodezhnyy nauch.-tekh. vestnik: elektron. zhurn., 2014, no. 7. Available at: http://sntbul.bmstu.ru/doc/728018.html

[8] Mikitaev A.K., Kozlov G.V. The Efficiency of Polymer Nanocomposites Reinforcement by Disperse Nanoparticles. Materials Physics and Mechanics, 2014, no. 21, pp. 51-57 (in Russ.). Available at: http://www.ipme.ru/e-journals/MPM/no_12114/MPM121_06_kozlov.pdf

[9] Mikitaev A.K., Kozlov G.V. Perkolyatsionnaya model’ usileniya nanokompozitov polimer/uglerodnye nanotrubki. Materials Physics and Mechanics, 2015, no. 22, pp. 101-106 (in Russ.). Available at: http://www.ipme.ru/e-journals/MPM/no_22215/MPM222_01_mikitaev.pdf

[10] Eletskiy A.V., Iskandarova I.M., Knizhnik A.A., Krasikov D.N. Graphene: fabrication methods and thermophysical properties. Physics-Uspekhi, 2011, vol. 54, no. 3, pp. 227-258. DOI: 10.3367/UFNe.0181.201103a.0233

[11] Sorokin P.B., Chernozatonskiy L.A. Graphene-based semiconductor nanostructures. Physics-Uspekhi, 2013, vol. 56, no. 2, pp. 105-122. DOI: 10.3367/UFNe.0183.201302a.0113

[12] Antonova I.V. Chemical vapor deposition growth of graphene on copper substrates: current trends. Physics-Uspekhi, 2013, vol. 56, no. 10, pp. 1013-1020. DOI: 10.3367/UFNe.0183.201310i.1115

[13] Samaei A.T., Aliha M.R.M., Mirsayar M.M. Frequency analysis of agraphene sheet embedded in an ekastic medium with consideration of small scale. Materials Physics and Mechanics, 2015, no. 22, pp. 125-135.

[14] Galashev A.E., Rakhmanova O.R. Mechanical and thermal stability of graphene and graphene-based materials. Physics-Uspekhi, 2014, vol. 57, no. 10, pp. 970-989. DOI: 10.3367/UFNe.0184.201410c.1045

[15] Galashev A.E., Dubovik S.Yu. Molecular dynamics simulation of compression of single-layer graphene. Physics of the Solid State, 2013, vol. 55, iss. 9, pp. 1976-1983. Available at: http://link.springer.com/article/10.1134/S1063783413090102

[16] Wooster W.A. Tensors and group theory for the physical properties of crystals. Oxford, Clarendon Press, 1973. 344 p.

[17] Sirotin Yu.N., Shaskol’skaya M.P. Osnovy kristallofiziki [Fundamentals of crystal physics]. Moscow, Nauka Publ., 1979. 640 p.

[18] Novoselov K.S. Graphene: materials in the Flatland. Physics-Uspekhi, 2011, vol. 57, no. 12. Available at: http://ufn.ru/en/articles/2011/12/s/

[19] Zarubin V.S., Kuvyrkin G.N. Matematicheskie modeli mekhaniki i elektrodinamiki sploshnoy sredy [Mathematical models of mechanics and electrodynamics of continuous media]. Moscow, MGTU im. N.E. Baumana Publ., 2008. 512 p.

[20] Zarubin V.S. Prikladnye zadachi termoprochnosti elementov konstruktsiy [Applied problems of thermal strength of structural elements]. Moscow, Mashinostroenie Publ., 1985. 292 p.

[21] Eletskiy A.V. Carbon nanotubes. Physics-Uspekhi, 1997, vol. 40, no. 9, pp. 899-924. DOI: 10.1070/PU1997v040n09ABEH000282

[22] Eletskiy A.V. Carbon nanotubes and their emission properties. Physics-Uspekhi, 2002, vol. 45, no. 4, pp. 369-402. DOI: 10.1070/PU2002v045n04ABEH001033

[23] Prabhu S., Shubrajit Bhaumik, Vinayagam B.K. Finite element modeling and analysis of zigzag and armchair type single wall carbon nanotube. Journal of Mechanical Engineering Research, 2012, vol. 4 (8), pp. 260-266.

[24] Bowman J.C., Krumhansl J.A. The Low-Temperature Specific Heat of Graphite. J. Phys. Chem. Solids, 1958, vol. 6, no. 4, pp. 367-379.