The Study on Mechanical Properties of Graphene Using Molecular Mechanics
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.
[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.
[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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:70441", author = "I-Ling Chang and Jer-An Chen", title = "The Study on Mechanical Properties of Graphene Using Molecular Mechanics", 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.", volume = "9", number = "7", pages = "1261-7", }
