Blister tests are commonly used to determine the mechanical and interfacial properties of thin film materials with recent applications for graphene. This paper presents a numerical study on snap transitions of pressurized graphene blisters. A continuum model is adopted combining a nonlinear plate theory for monolayer graphene with a nonlinear traction–separation relation for van der Waals interactions. Three types of blister configurations are considered. For graphene bubble blisters, snap-through and snap-back transitions between pancake-like and dome-like shapes are predicted under pressure-controlled conditions. For center-island graphene blisters, snap transitions between donut-like and dome-like shapes are predicted under both pressure and volume control. Finally, for the center-hole graphene blisters, growth is stable under volume or N-control but unstable under pressure control. With a finite hole depth, the growth may start with a snap transition under N-control if the hole is relatively deep. The numerical results provide a systematic understanding on the mechanics of graphene blisters, consistent with previously reported experiments. Of particular interest is the relationship between the van der Waals interactions and measurable quantities in corresponding blister tests, with which both the adhesion energy of graphene and the equilibrium separation for the van der Waals interactions may be determined. In comparison with approximate solutions based on membrane analyses, the numerical method offers more accurate solutions that may be used in conjunction with experiments for quantitative characterization of the interfacial properties of graphene and other two-dimensional (2D) membrane materials.

References

References
1.
Allen
,
M. G.
, and
Senturia
,
S. D.
,
1989
, “
Application of the Island Blister Test for Thin Film Adhesion Measurement
,”
J. Adhes.
,
29
(
1–4
), pp.
219
231
.
2.
Jensen
,
H. M.
,
1991
, “
The Blister Test for Interface Toughness Measurement
,”
Eng. Fract. Mech.
,
40
(
3
), pp.
475
486
.
3.
Lai
,
Y. H.
, and
Dillard
,
D. A.
,
1994
, “
A Study of the Fracture Efficiency Parameter Blister Tests for Films and Coatings
,”
J. Adhes. Sci. Technol.
,
8
(
6
), pp.
663
678
.
4.
Xu
,
D.
, and
Liechti
,
K. M.
,
2010
, “
Bulge Testing Transparent Thin Films With Moiré Deflectometry
,”
Exp. Mech.
,
50
(
2
), pp.
217
225
.
5.
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
(
2
), p.
026104
.
6.
Koenig
,
S. P.
,
Boddeti
,
N. G.
,
Dunn
,
M. L.
, and
Bunch
,
J. S.
,
2011
, “
Ultrastrong Adhesion of Graphene Membranes
,”
Nat. Nanotechnol.
,
6
(
9
), pp.
543
546
.
7.
Boddeti
,
N. G.
,
Koenig
,
S. P.
,
Long
,
R.
,
Xiao
,
J.
,
Bunch
,
J. S.
, and
Dunn
,
M. L.
,
2013
, “
Mechanics of Adhered Pressurized Graphene Blister
,”
ASME J. Appl. Mech.
80
(
4
), p.
040909
.
8.
Cao
,
Z.
,
Wang
,
P.
,
Gao
,
W.
,
Tao
,
L.
,
Suk
,
J. W.
,
Ruoff
,
R. S.
,
Akinwande
,
D.
,
Huang
,
R.
, and
Liechti
,
K. M.
,
2014
, “
A Blister Test for Interfacial Adhesion of Large-Scale Transferred Graphene
,”
Carbon
,
69
, pp.
390
400
.
9.
Liu
,
X.
,
Boddeti
,
N. G.
,
Szpunar
,
M. R.
,
Wang
,
L.
,
Rodriguez
,
M. A.
,
Long
,
R.
,
Xiao
,
J.
,
Dunn
,
M. L.
, and
Bunch
,
J. S.
,
2013
, “
Observation of Pull-In Instability in Graphene Membranes Under Interfacial Forces
,”
Nano Lett.
,
13
(
5
), pp.
2309
2313
.
10.
Boddeti
,
N. G.
,
Liu
,
X.
,
Long
,
R.
,
Xiao
,
J.
,
Bunch
,
J. S.
, and
Dunn
,
M. L.
,
2013
, “
Graphene Blisters With Switchable Shapes Controlled by Pressure and Adhesion
,”
Nano Lett.
,
13
(
12
), pp.
6216
6221
.
11.
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
(
1
), pp.
332
337
.
12.
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
(
9
), p.
093103
.
13.
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
(
8
), pp.
2458
2462
.
14.
Herbig
,
C.
,
Ahlgren
,
E. H.
,
Schroder
,
U. A.
,
Martinez-Galera
,
A. J.
,
Arman
,
M. A.
,
Kotakoski
,
J.
,
Knudsen
,
J.
,
Krasheninnikov
,
A. V.
, and
Michely
,
T.
,
2015
, “
Xe Irradiation of Graphene on Ir(111): From Trapping to Blistering
,”
Phys. Rev. B
,
92
(
8
), p.
085429
.
15.
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
(
5991
), pp.
544
547
.
16.
Lu
,
J.
,
Castro Neto
,
A. H.
, and
Loh
,
K. P.
,
2012
, “
Transforming Moire Blisters Into Geometric Graphene Nano-Bubbles
,”
Nat. Commun.
,
3
, p.
823
.
17.
Pan
,
W.
,
Xiao
,
J.
,
Zhu
,
J.
,
Yu
,
C.
,
Zhang
,
G.
,
Ni
,
Z.
,
Watanabe
,
K.
,
Taniguchi
,
T.
,
Shi
,
Y.
, and
Wang
,
X.
,
2012
, “
Biaxial Compressive Strain Engineering in Graphene/Boron Nitride Heterostructures
,”
Sci. Rep.
,
2
, no. 893.
18.
Qi
,
Z.
,
Kitt
,
A. L.
,
Park
,
H. S.
,
Pereira
,
V. M.
,
Campbell
,
D. K.
, and
Castro Neto
,
A. H.
,
2014
, “
Pseudomagnetic Fields in Graphene Nanobubbles of Constrained Geometry: A Molecular Dynamics Study
,”
Phys. Rev. B
,
90
(
12
), p.
125419
.
19.
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
(
2
), pp.
617
621
.
20.
Yue
,
K.
,
Gao
,
W.
,
Huang
,
R.
, and
Liechti
,
K. M.
,
2012
, “
Analytical Methods for the Mechanics of Graphene Bubbles
,”
J. Appl. Phys.
,
112
(
8
), p.
083512
.
21.
Wang
,
P.
,
Gao
,
W.
,
Cao
,
Z.
,
Liechti
,
K. M.
, and
Huang
,
R.
,
2013
, “
Numerical Analysis of Circular Graphene Bubbles
,”
J. Appl. Mech.
,
80
(
4
), p.
040905
.
22.
Arroyo
,
M.
, and
Belytschko
,
T.
,
2004
, “
Finite Crystal Elasticity of Carbon Nanotubes Based on the Exponential Cauchy-Born Rule
,”
Phys. Rev. B
,
69
(
11
), p.
115415
.
23.
Lu
,
Q.
, and
Huang
,
R.
,
2009
,“
Nonlinear Mechanics of Single-Atomic-Layer Graphene Sheets
,”
Int. J. Appl. Mech.
,
1
(03), pp.
443
467
.
24.
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
(
23
), p.
235406
.
25.
Huang
,
Y.
,
Wu
,
J.
, and
Hwang
,
K. C.
,
2006
, “
Thickness of Graphene and Single-Wall Carbon Nanotubes
,”
Phys. Rev. B
,
74
(
24
), p.
245413
.
26.
Lu
,
Q.
,
Arroyo
,
M.
, and
Huang
,
R.
,
2009
, “
Elastic Bending Modulus of Monolayer Graphene
,”
J. Phys. D: Appl. Phys.
,
42
(
10
), p.
102002
.
27.
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
(
12
), p.
123531
.
28.
Gao
,
W.
,
Xiao
,
P.
,
Henkelman
,
G.
,
Liechti
,
K. M.
, and
Huang
,
R.
,
2014
, “
Interfacial Adhesion Between Graphene and Silicon Dioxide by Density Functional Theory With van der Waals Corrections
,”
J. Phys. D: Appl. Phys.
,
47
(
25
), p.
255301
.
29.
Na
,
S. R.
,
Suk
,
J. W.
,
Ruoff
,
R. S.
,
Huang
,
R.
, and
Liechti
,
K. M.
,
2014
, “
Ultra Long-Range Interactions Between Large Area Graphene and Silicon
,”
ACS Nano
,
8
(
11
), pp.
11234
11242
.
30.
Yoon
,
T.
,
Shin
,
W. C.
,
Kim
,
T. Y.
,
Mun
,
J. H.
,
Kim
,
T.-S.
, and
Cho
,
B. J.
,
2012
, “
Direct Measurement of Adhesion Energy of Monolayer Graphene As-Grown on Copper and Its Application to Renewable Transfer Process
,”
Nano Lett.
,
12
(
3
), pp.
1448
1452
.
31.
Na
,
S. R.
,
Suk
,
J. W.
,
Tao
,
L.
,
Akinwande
,
D.
,
Ruoff
,
R. S.
,
Huang
,
R.
, and
Liechti
,
K. M.
,
2015
, “
Selective Mechanical Transfer of Graphene From Seed Copper Foil Using Rate Effects
,”
ACS Nano
9
(
2
), pp.
1325
1335
.
32.
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
(
6
), pp.
1643
1648
.
33.
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
(
12
), pp.
2667
2673
.
34.
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
(
2
), pp.
868
873
.
35.
Springman
,
R. M.
, and
Bassani
,
J. L.
,
2008
, “
Snap Transitions in Adhesion
,”
J. Mech. Phys. Solids
,
56
(
6
), pp.
2358
2380
.
36.
Li
,
T.
, and
Zhang
,
Z.
,
2010
, “
Snap-Through Instability of Graphene on Substrates
,”
Nanoscale Res. Lett.
,
5
(
1
), pp.
169
173
.
37.
Hencky
,
H.
,
1915
, “
On the Stress State in Circular Plates With Vanishing Bending Stiffness
,”
Z. Math. Phys.
,
63
, pp.
311
317
.
You do not currently have access to this content.