Pressurized graphene bubbles have been observed in experiments, which can be used to determine the mechanical and adhesive properties of graphene. A nonlinear plate theory is adapted to describe the deformation of a graphene monolayer subject to lateral loads, where the bending moduli of monolayer graphene are independent of the in-plane Young's modulus and Poisson's ratio. A numerical method is developed to solve the nonlinear equations for circular graphene bubbles, and the results are compared to approximate solutions by analytical methods. Molecular dynamics simulations of nanoscale graphene bubbles are performed, and it is found that the continuum plate theory is suitable only within the limit of linear elasticity. Moreover, the effect of van der Waals interactions between graphene and its underlying substrate is analyzed, including large-scale interaction for nanoscale graphene bubbles subject to relatively low pressures.
Issue Section:
Research Papers
References
References
1.
Stolyarova
, E.
, Stolyarov
, D.
, Bolotin
, K.
, Ryu
, S.
, Liu
, L.
, Rim
, K. T.
, Klima
, M.
, Hybertsen
, M.
, Pogorelsky
, I.
, Pavlishin
, I.
, Kusche
, K.
, Hone
, J.
, Kim
, P.
, Stormer
, H. L.
, Yakimenko
, V.
, and Flynn
, G.
, 2009
, “Observation of Graphene Bubbles and Effective Mass Transport Under Graphene Films
,” Nano Lett.
, 9
, pp. 332
–337
.10.1021/nl803087x2.
Georgiou
, T.
, Britnell
, L.
, Blake
, P.
, Gorbachev
, R. V.
, Gholinia
, A.
, Geim
, A. K.
, Casiraghi
, C.
, and Novoselov
, K. S.
, 2011
, “Graphene Bubbles With Controllable Curvature
,” Appl. Phys. Lett.
, 99
, p
. 093103.10.1063/1.36316323.
Levy
, N.
, Burke
, S. A.
, Meaker
, K. L.
, Panlasigui
, M.
, Zettl
, A.
, Guinea
, F.
, Castro Neto
, A. H.
, and Crommie
, M. F.
, 2010
, “Strain-Induced Pseudo-Magnetic Fields Greater Than 300 Tesla in Graphene Nanobubbles
,” Science
, 329
, pp. 544
–547
.10.1126/science.11917004.
Lu
, J.
, Castro Neto
, A. H.
, and Loh
, K. P.
, 2012
, “Transforming Moire Blisters Into Geometric Graphene Nano-Bubbles
,” Nature Communications
, 3
, p
. 823.10.1038/ncomms18185.
Zabel
, J.
, Nair
, R. R.
, Ott
, A.
, Georgiou
, T.
, Geim
, A. K.
, Novoselov
, K. S.
, and Casiraghi
, C.
, 2012
, “Raman Spectroscopy of Graphene and Bilayer Under Biaxial Strain: Bubbles and Balloons
,” Nano Lett.
, 12
, pp. 617
–621
.10.1021/nl203359n6.
Bunch
, J. S.
, Verbridge
, S. S.
, Alden
, J. S.
, van der Zande
, A. M.
, Parpia
, J. M.
, Craighead
, H. G.
, and McEuen
, P. L.
, 2008
, “Impermeable Atomic Membranes From Graphene Sheets
,” Nano Lett.
, 8
, pp. 2458
–2462
.10.1021/nl801457b7.
Koenig
, S. P.
, Boddeti
, N. G.
, Dunn
, M. L.
, and Bunch
, J. S.
, 2011
, “Ultrastrong Adhesion of Graphene Membranes
,” Nature Nanotechnol.
, 6
, pp. 543
–546
.10.1038/nnano.2011.1238.
Yue
, K.
, Gao
, W.
, Huang
, R.
, and Liechti
, K. M.
, 2012
, “Analytical Methods for the Mechanics of Graphene Bubbles
,” J. Appl. Phys.
, 112
, p
. 083512.10.1063/1.47591469.
Hencky
, H.
, 1915
, “On the Stress State in Circular Plates With Vanishing Bending Stiffness,” Z. Math. Phys.
, 63
, pp. 311
–317
.10.
Lu
, Q.
, and Huang
, R.
, 2009
, “Nonlinear Mechanics of Single-Atomic-Layer Graphene Sheets
,” Int. J. Appl. Mech.
, 1
, pp. 443
–467
.10.1142/S175882510900022811.
Lee
, C.
, Wei
, X.
, Kysar
, J. W.
, and Hone
, J.
, 2008
, “Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene
,” Science
, 321
, pp. 385
–388
.10.1126/science.115799612.
Wei
, X.
, Fragneaud
, B.
, Marianetti
, C. A.
, and Kysar
, J. W.
, 2009
, “Nonlinear Elastic Behavior of Graphene: Ab Initio Calculations to Continuum Description
,” Phys. Rev. B
, 80
, p. 205407
.10.1103/PhysRevB.80.20540713.
Lu
, Q.
, Gao
, W.
, and Huang
, R.
, 2011
, “Atomistic Simulation and Continuum Modeling of Graphene Nanoribbons Under Uniaxial Tension
,” Modell. Simul. Mater. Sci. Eng.
, 19
, p. 054006
.10.1088/0965-0393/19/5/05400614.
Helfrich
, W.
, 1973
, “Elastic Properties of Lipid Bilayers—Theory and Possible Experiments
,” Z. Naturforsch. C
, 28
, pp. 693
–703
.15.
Timoshenko
, S.
, 1940
, Theory of Plates and Shells
, McGraw-Hill
, New York
, pp. 333
–337
.16.
Kudin
, K. N.
, Scuseria
, G. E.
, and Yakobson
, B. I.
, 2001
, “C2F, BN, and C Nanoshell Elasticity From Ab Initio Computations
,” Phys. Rev. B
, 64
, p. 235406
.10.1103/PhysRevB.64.23540617.
Arroyo
, M.
, and Belytschko
, T.
, 2004
, “Finite Crystal Elasticity of Carbon Nanotubes Based on the Exponential Cauchy-Born Rule
,” Phys. Rev. B
, 69
, p. 115415
.10.1103/PhysRevB.69.11541518.
Huang
, Y.
, Wu
, J.
, and Hwang
, K. C.
, 2006
, “Thickness of Graphene and Single-Wall Carbon Nanotubes
,” Phys. Rev. B
, 74
, p. 245413
.10.1103/PhysRevB.74.24541319.
Lu
, Q.
, Arroyo
, M.
, and Huang
, R.
, 2009
, “Elastic Bending Modulus of Monolayer Graphene
,” J. Phys. D: Appl. Phys.
, 42
, p. 102002
.10.1088/0022-3727/42/10/10200220.
Koskinen
, P.
, and Kit
, O. O.
, 2010
, “Approximate Modeling of Spherical Membranes
,” Phys. Rev. B
, 82
, p. 235420
.10.1103/PhysRevB.82.23542021.
Brenner
, D. W.
, 1990
, “Empirical Potential for Hydrocarbons for Use in Simulating the Chemical Vapor Deposition of Diamond Films
,” Phys. Rev. B
, 42
, pp. 9458
–9471
.10.1103/PhysRevB.42.945822.
Brenner
, D. W.
, Shenderova
, O. A.
, Harrison
, J. A.
, Stuart
, S. J.
, Ni
, B.
, and Sinnott
, S. B.
, 2002
, “A Second-Generation Reactive Empirical Bond Order (REBO) Potential Energy Expression for Hydrocarbon
,” J. Phys. Condens. Matter
, 14
, pp. 783
–802
.10.1088/0953-8984/14/4/31223.
Stuart
, S. J.
, Tutein
, A. B.
, and Harrison
, J. A.
, 2000
, “A Reactive Potential for Hydrocarbons With Intermolecular Interactions
,” J. Chem. Phys.
112
, pp. 6472
–6486
.10.1063/1.48120824.
Plimpton
, S.
, 1995
, “Fast Parallel Algorithms for Short-Range Molecular Dynamics
,” J. Comput. Phys.
, 117
, pp. 1
–19
.10.1006/jcph.1995.103925.
Blakslee
, O. L.
, Proctor
, D. G.
, Seldin
, E. J.
, Spence
, G. B.
, and Weng
, T.
, 1970
, “Elastic Constants of Compression-Annealed Pyrolytic Graphite
,” J. Appl. Phys.
, 41
, pp. 3373
–3382
.10.1063/1.165942826.
Aitken
, Z. H.
, and Huang
, R.
, 2010
, “Effects of Mismatch Strain and Substrate Surface Corrugation on Morphology of Supported Monolayer Graphene
,” J. Appl. Phys.
, 107
, p. 123531
.10.1063/1.343764227.
Ishigami
, M.
, Chen
, J. H.
, Cullen
, W. G.
, Fuhrer
, M. S.
, and Williams
, E. D.
, 2007
, “Atomic Structure of Graphene on SiO2
,” Nano Lett.
, 7
, pp. 1643
–1648
.10.1021/nl070613a28.
Gupta
, A.
, Chen
, G.
, Joshi
, P.
, Tadigadapa
, S.
, and Eklund
, P. C.
, 2006
, “Raman Scattering From High-Frequency Phonons in Supported n-Graphene Layer Films
,” Nano Lett.
, 6
, pp. 2667
–2673
.10.1021/nl061420a29.
Sonde
, S.
, Giannazzo
, F.
, Raineri
, V.
, and Rimini
, E.
, 2009
, “Dielectric Thickness Dependence of Capacitive Behavior in Graphene Deposited on Silicon Dioxide
,” J. Vac. Sci. Technol. B
, 27
, pp. 868
–873
.10.1116/1.308189030.
Zong
, Z.
, Chen
, C.-L.
, Dokmeci
, M. R.
, and Wan
, K.-T.
, 2010
, “Direct Measurement of Graphene Adhesion on Silicon Surface by Intercalation of Nanoparticles
,” J. Appl. Phys.
, 107
, p. 026104
.10.1063/1.329496031.
Martoňák
, R.
, Molteni
, C.
, and Parrinello
, M.
, 2000
, “Ab Initio Molecular Dynamics With a Classical Pressure Reservoir: Simulation of Pressure-Induced Amorphization in a Si35H36 Cluster
,” Phys. Rev. Lett.
, 84
, pp. 682
–685
.10.1103/PhysRevLett.84.68232.
Hoover
, W. G.
, Ross
, M.
, Johnson
, K. W.
, Henderson
, D.
, Barker
, J. A.
, and Brown
, B. C.
, 1970
, “Soft-Sphere Equation of State
,” J. Chem. Phys.
, 52
, pp. 4931
–4941
.10.1063/1.167272833.
Clausius
, R.
, 1870
, “On a Mechanical Theory Applicable to Heat
,” Philos. Mag.
, 40
, pp. 122
–127
.34.
Zhao
, H.
, and Aluru
, N. R.
, 2010
, “Temperature and Strain-Rate Dependent Fracture Strength of Graphene
,” J. Appl. Phys.
, 108
, p. 064321
.10.1063/1.348862035.
Chen
, S.
, and Chrzan
, D. C.
, 2011
, “Monte Carlo Simulation of Temperature-Dependent Elastic Properties of Graphene
,” Phys. Rev. B
, 84
, p. 195409
.10.1103/PhysRevB.84.19540936.
Hutchinson
, J. W.
, and Evans
, A. G.
, 2000
, “Mechanics of Materials: Top-Down Approaches to Fracture
,” Acta Mater.
, 48
, pp. 125
–135
.10.1016/S1359-6454(99)00291-837.
Springman
, R. M.
, and Bassani
, J. L.
, 2008
, “Snap Transitions in Adhesion
,” J. Mech. Phys. Solids
, 56
, pp. 2358
–2380
.10.1016/j.jmps.2007.12.009
You do not currently have access to this content.
