Grain-Size-Dependent Elastic Moduli and Strengths of Polycrystalline Graphene: Atomistic Simulations

LU Ying; QIAN Jin

doi:10.21656/1000-0887.370121

Volume 37 Issue 9

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LU Ying, QIAN Jin. Grain-Size-Dependent Elastic Moduli and Strengths of Polycrystalline Graphene: Atomistic Simulations[J]. Applied Mathematics and Mechanics, 2016, 37(9): 901-914. doi: 10.21656/1000-0887.370121

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Grain-Size-Dependent Elastic Moduli and Strengths of Polycrystalline Graphene: Atomistic Simulations

doi: 10.21656/1000-0887.370121

LU Ying¹,
QIAN Jin^1,2

¹Soft Matter Research Center, Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, P.R.China;²Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province(Zhejiang University), Hangzhou 310027, P.R.China

Funds: The National Natural Science Foundation of China(11321202)

Received Date: 2016-04-18
Rev Recd Date: 2016-05-23
Publish Date: 2016-09-15

Abstract

Abstract

For polycrystalline graphene, the existence of grain boundaries might strongly influence the mechanical properties. There had been increasing experimental and numerical studies on the stiffness and strength of polycrystalline graphene, where 2 methods of nanoindentation and uniaxial tension had been widely employed for tests. However, significant discrepancies in the elastic moduli and breaking strengths from the 2 methods had been reported. Herein atomistic simulations of both the nanoindentation and the uniaxial tension were performed to explore the effects of grain sizes on the mechanical properties of polycrystalline graphene. In the simulations, the failure of polycrystalline graphene always occurred at grain boundary junctions, showing that the poly-graphene samples were weakened by the combination of grain boundary junctions, holes and topological defects. The results indicate that, the Young’s moduli and breaking strengths, from both the nanoindentation test and the uniaxial tension test, are strongly influenced by the grain sizes of poly-graphene.
- polycrystalline graphene,
- nanoindentation,
- uniaxial tension,
- elastic modulus,
- breaking strength,
- atomistic simulation

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References

[1]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A. Electric field effect in atomically thin carbon films[J].Science,2004,306(5696): 666-669.
[2]	Mayorov A S, Elias D C, Mucha-Kruczynski M, Gorbachev R V, Tudorovskiy T, Zhukov A, Morozov S V, Katsnelson M I, Fal’ko V I, Geim A K, Novoselov K S. Interaction-driven spectrum reconstruction in bilayer graphene[J].Science,2011,333(6044): 860-863.
[3]	Lee C, Wei X, Kysar J W, Hone J. Measurement of the elastic properties and intrinsic strength of monolayer graphene[J].Science,2008,321(5887): 385-388.
[4]	Lee G H, Cooper R C, An S J, Lee S, Van der Zande A, Petrone N, Hammerberg A G, Lee C, Crawford B, Oliver W, Kysar J W, Hone J. High-strength chemical-vapor-deposited graphene and grain boundaries[J].Science,2013,340(6136): 1073-1076.
[5]	Biró L P, Lambin P. Grain boundaries in graphene grown by chemical vapor deposition[J].New Journal of Physics,2013,15: 035024.
[6]	Reina A, Jia X, Ho J, Daniel N, Son H, Bulovic V, Dresselhaus M S, Kong J. Layer area, few-layer graphene films on arbitrary substrates by chemical vapor deposition[J].Nano Letters,2009,9(8): 3087.
[7]	Ruiz-Vargas C S, Zhuang H L, Huang P Y, Van der Zande A M, Garg S, McEuen P L, Muller D A, Hennig R G, Park J. Softened elastic response and unzipping in chemical vapor deposition graphene membranes[J].Nano Letters,2011,11(6): 2259-2263.
[8]	Wang S, Suzuki S, Hibino H. Raman spectroscopic investigation of polycrystalline structures of CVD-grown graphene by isotope Labeling[J].Nanoscale,2014,6(22): 13838-13844.
[9]	Podila R, Anand B, Spear J T, Puneet P, Philip R, Sai SS, Rao A M. Effects of disorder on the optical properties of CVD grown polycrystalline graphene[J].Nanoscale,2012,4(5): 1770-1775.
[10]	Song Z, Artyukhov V I, Yakobson B I, Xu Z. Pseudo hall-petch strength reduction in polycrystalline graphene[J].Nano Letters,2013,13(4): 1829-1833.
[11]	Mortazavi B, Cuniberti G. Atomistic modeling of mechanical properties of polycrystalline graphene[J].Nanotechnology,2014,25(21): 215704.
[12]	Chen M Q, Quek S S, Sha Z D, Chiu C H, Pei Q X, Zhang Y W. Effects of grain size, temperature and strain rate on the mechanical properties of polycrystalline graphene—a molecular dynamics study[J].Carbon,2015,85: 135-146.
[13]	Becton M, Zeng X, Wang X. Computational study on the effects of annealing on the mechanical properties of polycrystalline graphene[J].Carbon,2015,86: 338-349.
[14]	Yang Z, Huang Y, Ma F, Sun Y, Xu K, Chu P K. Size-dependent deformation behavior of nanocrystalline graphene sheets[J].Materials Science & Engineering B: Advanced Functional Solid-State Materials,2015,198: 95-101.
[15]	Sha Z D, Wan Q, Pei Q X, Quek S S, Liu Z, Zhang Y, Shenoy V B. On the failure load and mechanism of polycrystalline graphene by nanoindentation[J].Scientific Reports,2014,4: 7437. doi: 10.1038/srep07437.
[16]	Yu Q, Jauregui L A, Wu W, Colby R, Tian J, Su Z, Cao H, Liu Z, Pandey D, Wei D, Chung T F, Peng P, Guisinger N P, Stach E A, Bao J, Pei S S, Chen Y P. Control and characterization of individual grains and grain boundaries in graphene grown by chemical vapour deposition[J].Nature Materials,2011,10(6): 443-449.
[17]	Brostow W, Dussault J P, Fox B L. Construction of Voronoi polyhedra[J].Journal of Computational Physics,1978,29(1): 81-92.
[18]	Finney J L. A procedure for the construction of Voronoi polyhedra[J].Journal of Computational Physics,1979,32(1): 137-143.
[19]	Plimpton S. Fast parallel algorithms for short-range molecular dynamics[J].Journal of Computational Physics,1995,117(1): 1-19.
[20]	Jones J E. On the determination of molecular fields—II: from the equation of state of a gas[C]// Proceedings of the Royal Society of London, Series A, Containing Papers of a Mathematical and Physical Character,1924,106(738): 463-477.
[21]	Ruoff R S, Hickman A P. Van der Waals binding to fullerenes to a graphite plane[J].Journal of Physical Chemistry,1993,97(11): 2494-2496.
[22]	Stuart S J, Tutein A B, Harrison J A. A reactive potential for hydrocarbons with intermolecular interactions[J].Journal of Chemical Physics,2000,112(14): 6472-6486.
[23]	Evans D J, Holian B L. The Nose-Hoover thermostat[J].Journal of Chemical Physics,1985,83(8): 4069-4074.
[24]	Nose S. A molecular dynamics method for simulations in the canonical ensemble[J].Molecular Physics,1984,52(2): 255-268.
[25]	Hoover W G. Canonical dynamics: equilibrium phase-space distributions[J].Physical Review A,1985,31(3): 1695-1697.
[26]	Wei Y, Wu J, Yin H, Shi X, Yang R, Dresselhaus M. The nature of strength enhancement and weakening by pentagon-heptagon defects in graphene[J].Nature Materials,2012,11(9): 759-763.
[27]	Thurston R N, Brugger K. Third-order elastic constants and the velocity of small amplitude elastic waves in homogeneously stressed media[J].Physical Review,1964,135(6A): 1604-1610.
[28]	Liu F, Ming P, Li J. Ab initio calculation of ideal strength and phonon instability of graphene under tension[J].Physical Review B,2007,76(6): 064120.
[29]	Khare R, Mielke S L, Paci J T, Zhang S, Ballarini R, Schatz G C, Belytschko T. Coupled quantum mechanical/molecular mechanical modeling of the fracture of defective carbon nanotubes and graphene sheets[J].Physical Review B,2007,75(7): 075412.
[30]	Komaragiri U, Begley M R, Simmonds J G. The mechanical response of freestanding circular elastic films under point and pressure loads[J].Journal of Applied Mechanics,2005,72(2): 203-212.
[31]	Begley M R, Mackin T J. Spherical indentation of freestanding circular thin films in the membrane regime[J].Journal of the Mechanics and Physics of Solids,2004,52(9): 2005-2023.
[32]	Wan K T, Guo S, Dillard D A. A theoretical and numerical study of a thin clamped circular film under an external load in the presence of a tensile residual stress[J].Thin Solid Films,2003,425(1/2): 150-162.
[33]	Landau L D, Lifshitz E M, Pitaevskii L P, Kosevich A M.Theory of Elasticity [M]. Oxford: Pergamon Press, 1986.
[34]	Neek-amal M, Peeters F M. Nanoindentation of a circular sheet of bilayer graphene[J].Physical Review B,2010,81(23): 235421.
[35]	靳从睿. 圆薄膜受中心集中力的大变形[J]. 应用数学和力学, 2008,29(7): 806-812.(JIN Cong-rui. Large deflection of circular membrane under concentrated force[J].Applied Mathematics and Mechanics,2008,29(7): 806-812.(in Chinese))
[36]	Tan X J, Wu J, Zhang K, Peng X, Sun L, Zhong J. Nanoindentation models and Young’s modulus of monolayer graphene: a molecular dynamics study[J].Applied Physics Letters,2013,102(7): 071908.
[37]	Bhatia M M, Nachbar W. Finite indentation of an elastic membrane by a spherical indenter[J].International Journal of Non-Linear Mechanics,1968,3(3): 307-324.