Axial Stiffness of Multiwalled Carbon Nanotubes as a Function of the Number of Walls

Authors

  • V. Zavalniuk I.I. Mechnikov Odesa National University

DOI:

https://doi.org/10.15407/ujpe57.9.933

Keywords:

-

Abstract

The axial stiffness of multiwalled carbon nanotubes (MWCNTs) is studied as a function of the number of walls and their parameters. It is demonstrated that the axial stiffness is determined only by several external shells (usually 3–5 and up to 15 for the extremely large nanotubes and high elongations) which is in good agreement with the experimentally observed inverse relation between the radius and the Young modulus (i.e., stiffness) of MWCNTs. Such behavior is
a consequence of the van der Waals intershell interaction. An interpolating formula for the MWCNT's actual axial stiffness as a function of the external radius and the elongation of a tube is obtained.

References

R.S. Ruoff and D.C. Lorents, Carbon 33, 925 (1995).

https://doi.org/10.1016/0008-6223(95)00021-5

S. Govindjee and J.L. Sackman, Solid State Commun. 110, 227 (1999).

https://doi.org/10.1016/S0038-1098(98)00626-7

B.I. Yakobson and Ph. Avouris, in Mechanical Properties of Carbon Nanotubes, edited by M.S. Dresselhaus, G. Dresselhaus, and Ph. Avouris, (Springer, Heidelberg, 2001), Topics in Applied Physics 80, 287.

https://doi.org/10.1007/3-540-39947-X_12

B.I. Yakobson, C.J. Brabec, and J. Bernholc, Phys. Rev. Lett. 76, 2511 (1996).

https://doi.org/10.1103/PhysRevLett.76.2511

M.F. Yu, O. Lourie, M.J. Dyer, K. Moloni, T.F. Kelly, and R.S. Ruoff, Science 287, 637 (2000).

https://doi.org/10.1126/science.287.5453.637

S. Iijima, C. Brabec, A. Maiti, and J. Bernholc, J. Chem. Phys. 104, 2089 (1996).

https://doi.org/10.1063/1.470966

D.A. Walters, L.M. Ericson, M.J. Casavant, J. Liu, D.T. Colbert, K.A. Smith, and R.E. Smalley, Appl. Phys. Lett. 74, 3803 (1999).

https://doi.org/10.1063/1.124185

M.F. Yu, B.S. Files, S. Arepalli, and R.S. Ruoff, Phys. Rev. Lett. 84, 5552 (2000).

https://doi.org/10.1103/PhysRevLett.84.5552

T.W. Tombler, C. Zhou, J. Kong, H. Dai, L. Liu, C.S. Jayanthi, M. Tang, and S.Y. Wu, Nature 405, 769 (2000).

https://doi.org/10.1038/35015519

M.M.J. Treacy, T.W. Ebbesen, and J.M. Gibson, Nature 381, 678 (1996).

https://doi.org/10.1038/381678a0

A. Krishnan, E. Dujardin, T.W. Ebbesen, P.N. Yianilos, and M.M.J. Treacy, Phys. Rev. B 58, 14013 (1998).

https://doi.org/10.1103/PhysRevB.58.14013

E.W. Wong, P.E. Sheehan, and C.M. Lieber, Science 277, 1971 (1997).

https://doi.org/10.1126/science.277.5334.1971

J.P. Salvetat, G.A. D. Briggs, J.M. Bonard, R.R. Bacsa, A.J. Kulik, T. Stöckli, N.A. Burnham, and L. Forró, Phys. Rev. Lett. 82, 944 (1999).

https://doi.org/10.1103/PhysRevLett.82.944

B.G. Demczyk, Y.M. Wang, J. Cumings, M. Hetman, W. Han, A. Zettl, and R.O. Ritchie, Mater. Sci. Eng. A 334, 173 (2002).

https://doi.org/10.1016/S0921-5093(01)01807-X

Z.W. Pan, S.S. Xie, L. Lu, B.H. Chang, L.F. Sun, W.Y. Zhou, G. Wang, and D.L. Zhang, Appl. Phys. Lett. 74, 3152 (1999).

https://doi.org/10.1063/1.124094

P. Zhang, Y. Huang, P.H. Geubelle, P.A. Klein, and K.C. Hwang, J. Solids Struct. 39, 3893 (2002).

https://doi.org/10.1016/S0020-7683(02)00186-5

Y. Wu, M. Huang, F. Wang, X.M. Henry Huang, S. Rosenblatt, L. Huang, H. Yan, S.P. O'Brien, J. Hone, and T.F. Heinz, Nano Lett. 8, 4158 (2008).

https://doi.org/10.1021/nl801563q

Z. Tu and Z. Ou-Yang, Phys. Rev. B 65, 233407 (2002).

J.P. Lu, Phys. Rev. Lett. 79, 1297 (1997).

https://doi.org/10.1103/PhysRevLett.79.1297

P. Poncharal, Z.L. Wang, D. Ugarte, and W.A. de Heer, Science 283, 1513 (1999).

https://doi.org/10.1126/science.283.5407.1513

N. Yao and V. Lordi, J. Appl. Phys. 84, 1939 (1998).

https://doi.org/10.1063/1.368323

Z. Xin, Z. Jianjun, and O.-Y. Zhong-can, Phys. Rev. B 62, 13692 (2000).

https://doi.org/10.1103/PhysRevB.62.13692

C. Li and T.W. Chou, Composit. Sci. Techn. 63 1517 (2003).

https://doi.org/10.1016/S0266-3538(03)00072-1

J.-Y. Hsieh, J.-M. Lu, M.-Y. Huang, and C.-C. Hwang, Nanotechn. 17, 3920 (2006).

https://doi.org/10.1088/0957-4484/17/15/051

Z. Peralta-Inga, S. Boyd, J.S. Murray, C.J. O'Connor, and P. Politzer, Struct. Chem. 14, 431 (2003).

https://doi.org/10.1023/B:STUC.0000004487.72835.13

V. Adamyan and V. Zavalniuk, J. Phys.: Condens. Matter 23, 015402 (2010).

https://doi.org/10.1088/0953-8984/23/1/015402

L.A. Girifalco, M. Hodak, and R.S. Lee, Phys. Rev. B 62, 013104 (2000).

https://doi.org/10.1103/PhysRevB.62.13104

D. Baowan and J.M. Hill, Z. angew. Math. Phys. 58, 857 (2007).

https://doi.org/10.1007/s00033-006-6098-z

D. Baowan, N. Thamwattana, and J.M. Hill, Commun. Nonlin. Sci. Numer. Simul. 13, 1431 (2008).

https://doi.org/10.1016/j.cnsns.2007.01.002

V. Zavalniuk and S. Marchenko, Low Temp. Phys. 37 337 (2011).

https://doi.org/10.1063/1.3592692

J. Cumings and A. Zettl, Science 289 602 (2000).

https://doi.org/10.1126/science.289.5479.602

J.L. Rivera, C. McCabe, and P.T. Cummings, Nanotechn. 16, 186 (2005).

https://doi.org/10.1088/0957-4484/16/2/003

S.B. Legoas, V.R. Coluci, S.F. Braga, P.Z. Coura, S.O. Dantas, and D.S. Galvao, Nanotechn. 15, 184 (2004).

https://doi.org/10.1088/0957-4484/15/4/012

O.L. Blakslee, D.G. Proctor, E.J. Seldin, G.B. Spence, and T. Weng, J. Appl. Phys. 41, 3373 (1970).

https://doi.org/10.1063/1.1659428

D. Sánchez-Portal, E. Artacho, J.M. Soler, A. Rubio, and P. Ordejón, Phys. Rev. B 59, 12678 (1999).

https://doi.org/10.1103/PhysRevB.59.12678

J.-W. Jiang, J.-S. Wang, and B. Li, Phys. Rev. B 80, 113405 (2009).

https://doi.org/10.1103/PhysRevB.80.113405

B.I. Yakobson, C.J. Brabec, and J. Bernholc, Phys. Rev. Lett. 76, 2511 (1996).

https://doi.org/10.1103/PhysRevLett.76.2511

A. Sears and R.C. Batra, Phys. Rev. B 69, 235406 (2004).

https://doi.org/10.1103/PhysRevB.69.235406

V.N. Popov, V.E. Van Doren, and M. Balkanski, Phys. Rev. B 61, 3078 (2000).

https://doi.org/10.1103/PhysRevB.61.3078

Y.Jin and F.G. Yuan, Composit. Sci. Techn. 63, 1507 (2003). https://doi.org/10.1016/S0266-3538(03)00074-5

J.P. Salvetat, A.J. Kulik, J.M. Bonard, G.A.D. Briggs, T. Stöckli, K. Méténier, S. Bonnamy, F. Béguin, N.A. Burnham, and L. Forró, Adv. Mater. 11, 161 (1999). https://doi.org/10.1002/(SICI)1521-4095(199902)11:2<161::AID-ADMA161>3.0.CO;2-J

N.R. Raravikar, P. Keblinski, A.M. Rao, M.S. Dresselhaus, L.S. Schadler, and P.M. Ajayan, Phys. Rev. B 66, 235424 (2002). https://doi.org/10.1103/PhysRevB.66.235424

A.V. Dolbin, V.B. Esel'son, V.G. Gavrilko, V.G. Manzhelii, N.A. Vinnikov, and S.N. Popov, Fiz. Nizk. Temp. 34, 860 (2008). https://doi.org/10.1063/1.2967518

Downloads

Published

2012-09-30

How to Cite

Zavalniuk, V. (2012). Axial Stiffness of Multiwalled Carbon Nanotubes as a Function of the Number of Walls. Ukrainian Journal of Physics, 57(9), 933. https://doi.org/10.15407/ujpe57.9.933

Issue

Section

Nanosystems