Paper Titles
Elastic Moduli of Carbon Nanotubes Using Second Generation Improved Brenner Potential
p.1
Synthesis of Nano CuO by Polymeric Precursor Method and its Low Temperature Reduction to Stable Copper Nanoparticles
p.11
Synthesis of Fe-Co Nanobars Using Sodium Sulfite Assisted Polyol Process and their Structural and Magnetic Studies
p.21
Hydrogen Storage on Platinum-Decorated Carbon Nanotubes with Boron, Nitrogen Dopants or Sidewall Vacancies
p.29
Mechanical Properties of Glass Fibre-Epoxy Based Polymer Nanocomposites
p.41
In Situ Filling of Fe/Ni Oxide Nanowire into Carbon Nanotubes Doped with Nitrogen in CH4/H2/Air Plasma
p.51
Synthesis of Carbon Nanostructures and CaCO3 Nanoparticles by Arc Discharge in Mineral Water
p.57
Growth and Experimental Evidence of Quantum Confinement Effects in Cu2O and CuO Thin Films
p.69
On the Solid Hydrogen Intercalation in Multilayer Carbohydride-Like Graphane Nanostructures, Relevance to the Storage Applications
p.75

Elastic Moduli of Carbon Nanotubes Using Second Generation Improved Brenner Potential

Article Preview

Abstract:

Soon after the discovery of carbon nanotubes, it was realized that the theoretically predicted mechanical properties of these interesting structures could make them ideal for a wealth of technological applications. A number of computer simulation methods applied to their modeling, has led over the past decade to an improved but by no means complete understanding of the mechanics of carbon nanotubes. Tersoff potential has been widely used but it has since been modified many times. The latest is the second-generation reactive empirical bond order potential by Brenner and co workers, which is being used in this work for manipulating these tiny structures. We outline the computational approaches that have been taken. The elastic moduli of armchair, zigzag and chiral nanotubes have been computed. We generate the coordinates of carbon nanotubes of different chirality’s and size. Each and every structure thus generated is allowed to relax till we obtain minima of energy. We then apply the requisite compressions, elongations and twists to the structures and compute the elastic moduli. Young’s modulus is found to be dependent on tube radius for thinner tubes and attains a constant value of the order 1TPa. Our results of Poisson’s ratio and shear modulus are also encouraging and compare well with other theoretical and experimental work.

You might also be interested in these eBooks
Journal of Nano Research Vol. 15 View Preview

Info:

Periodical:

Journal of Nano Research (Volume 15)

Pages:

1-10

DOI:

https://doi.org/10.4028/www.scientific.net/JNanoR.15.1

Citation:

Cite this paper

Online since:

September 2011

Authors:

Dinesh Kumar, Veena Verma, Keya Dharamvir

Keywords:

Carbon Nanotube (CN), Poisson’s Ratio (ν), REBO, Shear Modulus (G), Young’s Modulus (Y)

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

© 2011 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

References

[10] has reported the moduli of quite a good range of radii and our results show the same trends. Experiments have shown that Y of CNTs is in order of 1Tpa. [13, 18-21]. In addition to the resistance to yield and fracture [22] Young's modulus Y can be used to measure the strength of materials and great number of works have been devoted to determining the Young's Modulus of CNTs using the empirical MD [11, 23-27], tight binding [28-30] or ab initio [31-33]. The value of Poisson ratio is 0. 28 as reported by Lu [11] and 0. 19 by Yakobson et al using Tersoff- Brenner potential [34]. Using finite element method, Sun et. al. [35] have calculated the value of Poisson ratio to lie in the range of 0. 31 to 0. 35. Our values of Poisson ratio for (5, 5), (10, 10), (8, 4), (12, 6) nanotubes match well with ref [10] but our values are higher for (9, 0) and (17, 0) nanotubes and match well with ref [11]. The shear Modulus for CNTs lies in the range of 300 Gpa. Our value of shear modulus for (5, 5), (10, 10), (9, 0), (17, 0), (8, 4), (12, 6), (20, 10) matches well with S. Gupta et. al. [10]. Values calculated by J.P. Lu [11] for shear modulus are little higher. Our results for shear modulus are in good agreement with ref [36]. The second generation reactive empirical bond order (REBO) potential with modified parameters reproduces the Y values, Poisson's ratios n and Shear Modulus G for CNTs. We look forward to others also to check the validity of this potential for other nanostructures as well. Acknowledgements: Authors are thankful to Dr. H.S. Bhatti, Professor and Head, Department of Physics, Punjabi University, Patiala for guiding and providing necessary facilities to bring this work in the present form. References.

Google Scholar

[1] B.L. Yakobson and Ph. Avorius, Mechanical properties of Carbon nanotubes, in topics in Applied Physics: Carbon nanotubes synthesis. Structure, properties and applications. M.S. Dresselhaus, G. Dresselhaus and Ph. Avorius . eds. Springer. New York (2001).

DOI: 10.1007/978-3-540-72865-8

Google Scholar

[2] P.M. Ajayan and R. Vijtai, Properties and applications of Nanotubes, Materials Science Aspects NATO ASI seminar (2001).

Google Scholar

[3] R.S. Rouff, and D.C. Lorents, Mechanical and Thermal Properties of Carbon nanotubes, Carbon 33(7) (1995) 925-930.

DOI: 10.1016/0008-6223(95)00021-5

Google Scholar

[4] Hone, James, Phonons and thermal properties of Carbon nanotubes, in topics in applied physics: Carbon nanotubes synthesis. Structure, properties and applications. M.S. Dresselhaus, G. Dresselhaus and Ph. Avorius . eds. Springer. New York (2001).

DOI: 10.1007/3-540-39947-x_11

Google Scholar

[5] Jerzy Bernholc, Christopher Roland and Boris I Yakobson Nanotubes, Solid–state & Matrials Science 2 (1997) 706-715.

Google Scholar

[6] Yao, Z., Dekker et al., Electrical Transport through Single-walled carbon nanotubes, in topics in applied physics: Carbon nanotubes synthesis, Structure, properties and applications. M.S. Dresselhaus, G. Dresselhaus and Ph. Avorius . eds. Springer. New York. (2001).

DOI: 10.1007/3-540-39947-x_7

Google Scholar

[7] Sumio Iijima, and Toshinari Ichihashi, Nature 363 (1993) 603-605.

Google Scholar

[8] D. W. Brenner, O. A Shenderova, J. A Harrison, S. J Stuart, B. Ni and S. B Sinnott, J. Phys.: Condens. Matter 14 (2002) 783-802.

DOI: 10.1088/0953-8984/14/4/312

Google Scholar

[9] J. Tersoff, Phys. Rev. Lett. 61 (1988) 2879-2882.

Google Scholar

[10] S. Gupta, K. Dharamvir and V. K. Jindal, Phys. Rev. B 72(2005) 165428-165443.

Google Scholar

[11] J.P. Lu, Phys. Rev. Lett. 79 (1997) 1297-1300.

Google Scholar

[12] A. Krishnan, E. Dujardin, T. W. Ebbesen, P. N. Yanilos, M. M. J. Treacy, Phys. Rev. B58 (20) (1998) 14013-14019.

DOI: 10.1103/physrevb.58.14013

Google Scholar

[13] E W Wong, P E Sheehan and CM Lieber, Science 277 (1997) 1971-(1975).

Google Scholar

[14] Robertson, D.H., D.W. Brenner and J.W. Mintmire, Phys. Rev. B 45(21) (1992) 45-48.

Google Scholar

[15] Cornwell, C.F. and L.T. Wille, Solid State Communications, 101(8) (1997) 555-558.

Google Scholar

[16] Yao, N. and V. Lordi, Journal of Applied Physics, 84(4) (1998) 1939-(1943).

Google Scholar

[17] Zhou, X., J. Zhou and Z. Ou-Yang, Phys. Rev. B, 62(20) (2000) 13692-13696.

Google Scholar

[18] A. Krishnan, E. Dujardin, M.M.J. Treacy, J. Hugdhal, S. Lynum and T.W. Ebbesen, Nature 388(1997) 451-454.

DOI: 10.1038/41284

Google Scholar

[19] M.M. Treacy, T.W. Ebbesen, J.M. Gibson, Nature (London) 381(1996) 678-680.

Google Scholar

[20] O. Lourie, H.D. wagner, J. Mater. Res. 13 (1998) 2418-2422.

Google Scholar

[21] J. Muster, M. Burghard, S. Roth, G.S. Duesberg, E. hernandz, A. Rubio, J. Vac. Sci. Technol B16 (1998) 2796-2801.

Google Scholar

[22] Traian Dumitrica, Ming Hua, Boris I. Yakobson, Proceedings of National Academy of Sciences. U.S.A. 103 (2006), 6105-6109.

Google Scholar

[23] D.H. Robertson, D.W. Brenner, and J.W. Mintmire, Phys. Rev. B 45 (1992) 12592-12595.

Google Scholar

[24] G. Oerney, W. Zhong, D. Tomanek, Z. Phys. D: At. Mol. Clusters 27 (1993) 93.

Google Scholar

[25] C.F. Cornwell, L.T. Wille, Solid State Communications 101 (1997) 555-558.

Google Scholar

[26] N. Yao, V. Lordi, J. Appl. Phys. 84 (1998) 1939-(1943).

Google Scholar

[27] T. Belytschko, S.P. Xiao, G.C. Schatz, R.S. Ruoft, Phys. Rev. B 65 (2002) 235430-235437.

Google Scholar

[28] E. Hernandez, C. Goze, P. Bernier, A. Rubio, Appl. Phys. A: Material Science Process 68 (1999) 287-292.

Google Scholar

[29] G. Dereli, C. Ozdogan, Phys. Rev. B 67 (2003) 035416-035421.

Google Scholar

[30] Z. Xin, Z. Jianjun, 0. Zhong-can, Phys. Rev. B 62 (2000) 13692-13696.

Google Scholar

[31] Daniel Sanchez-Portal, Emilio Artacho, Jose M. Soler, Angel Rubio, Pablo Ordejon, Phys. Rev. B 59 (1999) 12678-12688.

Google Scholar

[32] G. Van Lier, C. Van Alsenoy, V Van Doren, P. Geerlings, Chem. Phys. Lett. 326(1, 2) (2000) 181-185.

DOI: 10.1016/s0009-2614(00)00764-8

Google Scholar

[33] Shigenobu Ogata, Yoji Shibutani, Phys. Rev. B 68 (2003) 165409-165412.

Google Scholar

[34] B.I. Yakobson, C.J. Brabec, and J. Bernholc, Phys. Rev. Lett. 76 (1996) 2511-2514.

Google Scholar

[35] X. Sun, W. Zhao, Material Science and Engineering A 390(3) (2005) 366-371.

Google Scholar

[36] D. -B. Zhang and T. Dumitrica, Appl. Phys. Lett. 93 (2008) 031919.

Google Scholar