We study the mechanics of pressurized graphene membranes using an experimental configuration that allows the determination of the elasticity of graphene and the adhesion energy between a substrate and a graphene (or other two-dimensional solid) membrane. The test consists of a monolayer graphene membrane adhered to a substrate by surface forces. The substrate is patterned with etched microcavities of a prescribed volume and, when they are covered with the graphene monolayer, it traps a fixed number (N) of gas molecules in the microchamber. By lowering the ambient pressure and thus changing the pressure difference across the graphene membrane, the membrane can be made to bulge and delaminate in a stable manner from the substrate. This is in contrast to the more common scenario of a constant pressure membrane blister test, where membrane delamination is unstable, and so this is not an appealing test to determine adhesion energy. Here, we describe the analysis of the membrane/substrate as a thermodynamic system and explore the behavior of the system over representative experimentally accessible geometry and loading parameters. We carry out companion experiments and compare them to the theoretical predictions and then use the theory and experiments together to determine the adhesion energy of graphene/SiO2 interfaces. We find an average adhesion energy of 0.24 J/m2, which is lower but in line with our previously reported values. We assert that this test—which we call the constant N blister test—is a valuable approach to determine the adhesion energy between two-dimensional solid membranes and a substrate, which is an important but not well-understood aspect of behavior. The test also provides valuable information that can serve as the basis for subsequent research to understand the mechanisms contributing to the observed adhesion energy. Finally, we show how, in the limit of a large microcavity, the constant N test approaches the behavior observed in a constant pressure blister test, and we provide an experimental observation that suggests this behavior.

References

References
1.
Geim
,
A. K.
,
2009
, “
Graphene: Status and Prospects
,”
Science
,
324
(
5934
), pp.
1530
1534
.10.1126/science.1158877
2.
Lin
,
Y.-M.
,
Dimitrakopoulos
,
C.
,
Jenkins
,
K. A.
,
Farmer
,
D. B.
,
Chiu
,
H.-Y.
,
Grill
,
A.
, and
Avouris
,
Ph.
,
2010
, “
100-GHz Transistors From Wafer-Scale Epitaxial Graphene
,”
Science
,
327
(
5966
), pp.
662
.10.1126/science.1184289
3.
Bunch
,
J. S.
,
van der Zande
,
A. M.
,
Verbridge
,
S. S.
,
Frank
, I
. W.
,
Tanenbaum
,
D. M.
,
Parpia
,
J. M.
,
Craighead
,
H. G.
, and
McEuen
,
P. L.
,
2007
, “
Electromechanical Resonators From Graphene Sheets
,”
Science
,
315
, pp.
490
493
.10.1126/science.1136836
4.
Chen
,
S.
,
Brown
,
L.
,
Levendorf
,
M.
,
Cai
,
W.
,
Ju
,
S.-Y.
,
Edgeworth
,
J.
,
Li
,
X.
,
Magnuson
,
C. W.
,
Velamakanni
,
A.
,
Piner
,
R. D.
,
Kang
,
J.
,
Park
,
J.
, and
Ruoff
,
R. S.
,
2011
, “
Oxidation Resistance of Graphene-Coated Cu and Cu/Ni Alloy
,”
ACS Nano
,
5
(
2
), pp.
1321
1327
.10.1021/nn103028d
5.
El-Kady
,
M. F.
,
Strong
, V
.
,
Dubin
,
S.
, and
Kaner
,
R. B.
,
2012
, “
Laser Scribing of High-Performance and Flexible Graphene-Based Electrochemical Capacitors
,”
Science
,
335
(
6074
), pp.
1326
1330
.10.1126/science.1216744
6.
Zhu
,
Y.
,
Li
,
L.
,
Zhang
,
C.
,
Casillas
,
G.
,
Sun
,
Z.
,
Yan
,
Z.
,
Ruan
,
G.
,
Peng
,
Z.
,
Raji
,
A. O.
,
Kittrell
,
C.
,
Hauge
,
R. H.
, and
Tour
,
J. M.
,
2012
, “
A Seamless Three-Dimensional Carbon Nanotube Graphene Hybrid Material
,”
Nat. Commun.
,
3
, p. 1225.10.1038/ncomms2234
7.
Low
,
T.
,
Perebeinos
, V
.
,
Tersoff
,
J.
, and
Avouris
,
P.
,
2012
, “
Deformation and Scattering in Graphene Over Substrate Steps
,”
Phys. Rev. Lett.
,
108
(
9
), p.
096601
.10.1103/PhysRevLett.108.096601
8.
Scharfenberg
,
S.
,
Rocklin
,
D. Z.
,
Chialvo
,
C.
,
Weaver
,
R. L.
,
Goldbart
,
P. M.
, and
Mason
,
N.
,
2011
, “
Probing the Mechanical Properties of Graphene Using a Corrugated Elastic Substrate
,”
Appl. Phys. Lett.
,
98
(
9
), p.
091908
.10.1063/1.3553228
9.
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
.10.1126/science.1191700
10.
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
, p. 893.10.1038/srep00893
11.
Meyer
,
J. C.
,
Geim
,
A. K.
,
Katsnelson
,
M. I.
,
Novoselov
,
K. S.
,
Booth
,
T. J.
, and
Roth
,
S.
,
2007
, “
The Structure of Suspended Graphene Sheets
,”
Nature
,
446
, pp.
60
63
.10.1038/nature05545
12.
Kim
,
K.
,
Lee
,
Z.
,
Malone
,
B. D.
,
Chan
,
K. T.
,
Alemán
,
B.
,
Regan
,
W.
,
Gannett
,
W.
,
Crommie
,
M. F.
,
Cohen
,
M. L.
, and
Zettl
,
A.
,
2011
, “
Multiply Folded Graphene
,”
Phys. Rev. B
,
83
, p.
245433
.10.1103/PhysRevB.83.245433
13.
Li
,
T.
, and
Zhang
,
Z.
,
2010
, “
Substrate-Regulated Morphology of Graphene
,”
J. Phys. D: Appl. Phys.
,
43
, p.
075303
.10.1088/0022-3727/43/7/075303
14.
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
.10.1063/1.3437642
15.
Lu
,
Z.
, and
Dunn
,
M. L.
,
2010
, “
van der Waals Adhesion of Graphene Membranes
,”
J. Appl. Phys.
,
96
, p.
111902
.10.1063/1.3270425
16.
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
.10.1063/1.3631632
17.
Lee
,
C. G.
,
Wei
,
X. D.
,
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.1157996
18.
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
.10.1063/1.3294960
19.
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/nl801457b
20.
Koenig
,
S. P.
,
Boddeti
,
N. G.
,
Dunn
,
M. L.
, and
Bunch
,
J. S.
,
2011
, “
Ultrastrong Adhesion of Graphene Membranes
,”
Nat. Nanotechnol.
,
6
, pp.
543
546
.10.1038/nnano.2011.123
21.
Jiang
,
L. Y.
,
Huang
,
Y.
,
Jiang
,
H.
,
Ravichandran
,
G.
,
Gao
,
H.
,
Hwang
,
K. C.
, and
Liu
,
B.
,
2006
, “
A Cohesive Law for Carbon Nanotube/Polymer Interfaces Based on the Van Der Waals Force
,”
J. Mech. Phys. Solids
,
54
, pp.
2436
2452
.10.1016/j.jmps.2006.04.009
22.
Tang
,
T.
,
Jagota
,
A.
, and
Hui
,
C. Y.
,
2005
, “
Adhesion Between Single-Walled Carbon Nanotubes
,”
J. Appl. Phys.
,
97
, p.
074304
.10.1063/1.1871358
23.
DelRio
,
F.
,
Dunn
,
M. L.
,
Phinney
,
L. M.
,
Bourdon
,
C. J.
, and,
de Boer
,
M. P.
,
2007
, “
Rough Surface Adhesion in the Presence of Capillary Condensation
,”
Appl. Phys. Lett.
,
90
, p.
163104
.10.1063/1.2723658
24.
DelRio
,
F.
,
Dunn
,
M. L.
, and,
de Boer
,
M. P.
,
2008
, “
Capillary Adhesion Model for Contacting Micromachined Surfaces
,”
Scr. Mater.
,
59
, pp.
916
920
.10.1016/j.scriptamat.2008.02.037
25.
Yue
,
K.
,
Gao
,
W.
,
Huang
,
R.
, and
Liechti
,
K. M.
,
2012
, “
Analytical Methods for Mechanics of Graphene Bubbles
,”
J. Appl. Phys.
,
112
(
8
), p.
083512
.10.1063/1.4759146
26.
Wan
,
K.-T.
, and
Mai
,
Y.-W.
,
1995
, “
Fracture Mechanics of a New Blister Test With Stable Crack Growth
,”
Acta Metall. Mater.
,
43
(
11
), pp.
4109
4115
.10.1016/0956-7151(95)00108-8
27.
Gent
,
A. N.
, and
Lewandowski
,
L. H.
,
1987
, “
Blow-Off Pressures for Adhering Layers
,”
J. Appl. Polym. Sci.
,
33
(
5
), pp.
1567
1577
.10.1002/app.1987.070330512
28.
Hencky
,
H.
,
1915
, “
Über den Spannungszustand in Kreisrunden Platten mit Verschwindender Biegungssteiflgkeit
,”
Z. Math. Phys.
,
63
, pp.
311
317
.
29.
Williams
,
J. G.
,
1997
, “
Energy Release Rates for the Peeling of Flexible Membranes and the Analysis of Blister Tests
,”
Int. J. Fract.
,
87
, pp.
265
288
.10.1023/A:1007314720152
30.
Fichter
,
W. B.
,
1997
, “
Some Solutions for the Large Deflections of Uniformly Loaded Circular Membranes
,” NASA Technical Paper No. 3658.
31.
Campbell
,
J. D.
,
1956
, “
On the Theory of Initially Tensioned Circular Membranes Subjected to Uniform Pressure
,”
Q. J. Mech. Appl. Math.
,
9
(
1
), pp.
84
93
.10.1093/qjmam/9.1.84
32.
Wang
,
L.
,
Travis
,
J. J.
,
Cavanagh
,
A. S.
,
Liu
,
X.
,
Koenig
,
S. P.
,
Huang
,
P. Y.
,
George
,
S. M.
, and
Bunch
,
J. S.
,
2012
, “
Ultrathin Oxide Films by Atomic Layer Deposition on Graphene
,”
Nano Lett.
,
12
(
7
), pp.
3706
3710
.10.1021/nl3014956
33.
Barton
,
R. A.
,
Ilic
,
B.
,
van der Zande
,
A. M.
,
Whitney
,
W. S.
,
McEuen
,
P. L.
,
Parpia
,
J. M.
, and
Craighead
,
H. G.
,
2011
, “
High, Size-Dependent Quality Factor in an Array of Graphene Mechanical Resonators
,”
Nano Lett.
,
11
(
3
), pp.
1232
1236
.10.1021/nl1042227
34.
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
.10.1063/1.1659428
You do not currently have access to this content.