The Study on Mechanical Properties of Graphene Using Molecular Mechanics

Authors: I-Ling Chang, Jer-An Chen

Abstract:

The elastic properties and fracture of two-dimensional graphene were calculated purely from the atomic bonding (stretching and bending) based on molecular mechanics method. Considering the representative unit cell of graphene under various loading conditions, the deformations of carbon bonds and the variations of the interlayer distance could be realized numerically under the geometry constraints and minimum energy assumption. In elastic region, it was found that graphene was in-plane isotropic. Meanwhile, the in-plane deformation of the representative unit cell is not uniform along armchair direction due to the discrete and non-uniform distributions of the atoms. The fracture of graphene could be predicted using fracture criteria based on the critical bond length, over which the bond would break. It was noticed that the fracture behavior were directional dependent, which was consistent with molecular dynamics simulation results.

Keywords: Energy minimization, fracture, graphene, molecular mechanics.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1107638

References:

[1] A.K. Geim, K.S. Novoselov, “The rise of graphene,” Nat. Mater., vol. 6, pp. 183-191, 2007.
[2] M. Ariza, M. Ortiz, “Discrete dislocations in graphene,” J. Mech. and Phys. Solids, vol. 58, pp. 710-734, 2010.
[3] T. Chang, “A molecular based anisotropic shell model for single-walled carbon nanotubes,” J. Mech. and Phys. Solids, vol. 58, pp. 1422-1433, 2010.
[4] K.S. Novoselov, A.K. Geim, S. Morozov, D. Jiang, Y. Zhang, S. Dubonos, et al., “Electric field effect in atomically thin carbon films,” Science, vol. 306, pp. 666-669, 2004.
[5] K. Novoselov, D. Jiang, F. Schedin, T. Booth, V. Khotkevich, S. Morozov, et al., “Two-dimensional atomic crystals,” P. Natl. Acad. Sci. USA, vol. 102 pp. 10451-10453, 2005.
[6] B.F. Machado, P. Serp, “Graphene-based materials for catalysis,” Catal. Sci. Tech., vol. 2, pp. 54-75, 2012.
[7] J. Wu, Y. Wei, “Grain misorientation and grain-boundary rotation dependent mechanical properties in polycrystalline graphene,” J. Mech. and Phys. Solids, vol. 61, pp. 1421-1432, 2013.
[8] J.S. Bunch, S.S. Verbridge, J.S. Alden, A.M. van der Zande, J.M. Parpia, H.G. Craighead, et al., “Impermeable atomic membranes from graphene sheets,” Nano Lett., vol. 8, pp. 2458-2462, 2008.
[9] J.S. Bunch, A.M. Van Der Zande, S.S. Verbridge, I.W. Frank, D.M. Tanenbaum, J.M. Parpia, et al., “Electromechanical resonators from graphene sheets,” Science, vol. 315, pp. 490-493, 2007.
[10] X. Liu, T.H. Metcalf, J.T. Robinson, B.H. Houston, F. Scarpa, “Shear modulus of monolayer graphene prepared by chemical vapor deposition,” Nano Lett., vol. 12, pp. 1013-1017, 2012.
[11] M.M. Shokrieh, R. Rafiee, “Prediction of Young’s modulus of graphene sheets and carbon nanotubes using nanoscale continuum mechanics approach,” Mater. Design, vol. 31, pp. 790-795, 2010.
[12] C. Hwu, Y.-K. Yeh, “Explicit expressions of mechanical properties for graphene sheets and carbon nanotubes via a molecular-continuum model,” Appl. Phys. A, vol. 116, pp. 125-140, 2014.
[13] C. Li, T.-W. Chou, “A structural mechanics approach for the analysis of carbon nanotubes,” Int. J. Solids Struct., vol. 40, pp. 2487-2499, 2003.
[14] Y.Z. Cheng, G.Y. Shi, “The prediction of mechanical properties of graphene by molecular mechanics and structural mechanics method,” Adv. Mat. Res., vol. 583, pp. 403-407, 2012.
[15] F. Liu, P. Ming, J. Li, “Ab initio calculation of ideal strength and phonon instability of graphene under tension,” Phys. Rev. B, vol. 76, pp. 064120, 2007.
[16] M. Neek-Amal, F. Peeters, “Nanoindentation of a circular sheet of bilayer graphene,” Phys. Rev. B, vol. 81, pp. 235421, 2010.
[17] K. Min, N. Aluru, “Mechanical properties of graphene under shear deformation,” Appl. Phys. Lett., vol. 98, pp. 013113, 2011.
[18] B. Mortazavi, Y. Rémond, S. Ahzi, V. Toniazzo, “Thickness and chirality effects on tensile behavior of few-layer graphene by molecular dynamics simulations,” Comp. Mater. Sci., vol. 53, pp. 298-302, 2012.
[19] Z. Ni, H. Bu, M. Zou, H. Yi, K. Bi, Y. Chen, “Anisotropic mechanical properties of graphene sheets from molecular dynamics,” Physica B, vol. 405, pp. 1301-1306, 2010.
[20] W.D. Cornell, P. Cieplak, C.I. Bayly, I.R. Gould, K.M. Merz, D.M. Ferguson, et al., “A second generation force field for the simulation of proteins, nucleic acids, and organic molecules,” J. Am. Chem. Soc., vol. 117, pp. 5179-5197, 1995.