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General Elasticity Theory for Graphene Membranes Based on Molecular Dynamics

Published online by Cambridge University Press:  01 February 2011

Kaveh Samadikhah ,
Juan Atalaya ,
Caroline Huldt ,
Andreas Isacsson  and
Jari Kinaret
Kaveh Samadikhah
Affiliation:
Chalmers university of technology, applied physics, Kemigården 1, Gothenburg, SE-412 96, Sweden
Juan Atalaya
Affiliation:
juan.atalaya@chalmers.se, University of Gothenburg, Department of Physics, Kemigården 1, Gothenburg, SE-412 96, Sweden
Caroline Huldt
Affiliation:
chuldt@fy.chalmers.se, Chalmers University of Technology, Department of Applied Physics, Kemigården 1, Gothenburg, SE-41296, Sweden
Andreas Isacsson
Affiliation:
andreas.isacsson@chalmers.se, Chalmers University of Technology, Department of Applied Physics, Kemigården 1, Gothenburg, SE-41296, Sweden
Jari Kinaret
Affiliation:
jari.kinaret@chalmers.se, Chalmers University of Technology, Department of Applied Physics, Kemigården 1, Gothenburg, SE-41296, Sweden
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Abstract

We have studied the mechanical properties of suspended graphene membranes using molecular dynamics (MD) and generalized continuum elasticity theory (GE) in order to develop and assess a continuum description for graphene. The MD simulations are based on a valence force field model which is used to determine the deformation and the elastic energy of the membrane (EMD) as a function of external forces. For the continuum description, we use the expression Econt = Estretching + Ebending for the elastic energy functional. The elastic parameters (tensile rigidity and Poisson ratio) entering Econt are determined by requiring that Econt = EMD for a set of deformations.

Comparisons with the MD results show excellent agreement. We find that the elastic energy of a supported graphene sheets is typically dominated by the nonlinear stretching terms whereas a linear description is valid only for very small deflections. This implies that in some applications, i.e. NEMS, a linear description is of limited applicability.

Keywords

elastic propertiesstress/strain relationshipsimulation
Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 1057: Symposium II – Nanotubes and Related Nanostructures , 2007 , 1057-II10-20
Copyright
Copyright © Materials Research Society 2008

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References

REFERENCES

1. Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Zhang, Y., Dubonos, S.V., Grigorieva, I.V. and Firsov, A.A., Science 306, 666 (2004).Google Scholar
2. Guinea, F., Neto, A.H. Castro and Peres, N.M.R., Solid State Commun. 143, 116 (2007).Google Scholar
3. Bunch, J.S., Zande, A.M. van der, Verbridge, S.S., Frank, I.W., Tanenbaum, D.M., Parpia, J.M., Craighead, H.G. and McEuen, P.L., Science 314, 490 (2007).Google Scholar
4. Witkamp, B.; Poot, M.; van der Zant, H. S. J, Nano Lett.; (Letter); 2006; 6(12); 2904–2908.Google Scholar
5. Hwang, H.J. and Kang, J.W., Physica E 27, 163 (2005).Google Scholar
6. Li, Z.L., Dharap, P., Sharma, P., Nagarajaiah, S. and Yakobson, B.I., J. Appl. Phys. 97, 074303 (2005).Google Scholar
7. Yakobson, B.I., Brabec, C.J. and Bernholc, J., Phys. Rev. Lett. 76, 2511 (1996).Google Scholar
8. Lu, J.P., Phys. Rev. Lett. 79, 1297 (1997).Google Scholar
9. Odegard, G.M., Gates, T.S., Nicholson, L.M. and Wise, K.E., Compos. Sci. Technol. 62, 1869 (2002).Google Scholar
10. Landau, L.D. and Lifshitz, E.M., Theory of Elasticity, 1st Eng. ed. (Pergamon Press Ltd, London, 1959) p. 60–61.Google Scholar
11. Keating, P.N., Phys. Rev. 145, 637 (1966).Google Scholar
12. Lobo, C. and Martins, J.L., Z. Phys. D. 39, 159 (1997).Google Scholar
13. Atalaya, J., M.Sc. Thesis, (Göteborg University, Göteborg, Sweden, unpublished).Google Scholar
14. Chen, X. and Cao, G., Nanotechn. 17, 3884 (2006).Google Scholar
15. Timoshenko, S. and Woinowsky-Krieger, S., Theory of Plates and Shells, 2d ed. (McGraw-Hill, New York, 1959) p. 418.Google Scholar