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Research Papers

Mechanics of Adhered, Pressurized Graphene Blisters

[+] Author and Article Information
J. Scott Bunch

Department of Mechanical Engineering,
University of Colorado at Boulder,
Boulder, CO 80309

Martin L. Dunn

Singapore University of Technology and Design,
Singapore 138682

1Current address: Department of Mechanical Engineering, University of Alberta, Edmonton, AB T6G 2G8, Canada.

Manuscript received January 23, 2013; final manuscript received March 15, 2013; accepted manuscript posted April 18, 2013; published online May 31, 2013. Editor: Yonggang Huang.

J. Appl. Mech 80(4), 040909 (May 31, 2013) (8 pages) Paper No: JAM-13-1043; doi: 10.1115/1.4024255 History: Received January 23, 2013; Revised March 15, 2013; Accepted April 18, 2013

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.

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Figures

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Fig. 1

Schematic cross sections of test structures illustrating (a) the initial configuration of the system, charged to a pressure p0 in a pressure chamber—the shaded region under the graphene membrane indicates trapped gas (change from darker to lighter shade indicates decreasing pressure); possible final configurations when the external pressure is reduced with graphene membranes deformed due to the expanding gas molecules (b) with and (c) without delamination from the substrate

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Fig. 2

Variation of free energy with blister radius at a fixed pressure p0 with (a) a0 = 2 μm and h = 0.25 μm, (b) a0 = 3 μm and h = 0.25 μm, and (c) a0 = 2 μm and h = 1.25 μm

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Fig. 3

(a) and (d) Maximum deflection, δ; (b) and (e) blister radius, a; and (c) and (f) final equilibrium microchamber pressure, pi, plotted as functions of the input pressure, p0, with Γ = 0.2 J/m2. The cavity dimensions are (a)–(c) a0 = 2 μm and h = 0.25 μm and (d)–(f) a0 = 2 μm and h = 1.25 μm.

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Fig. 6

(a) Three-dimensional rendering of AFM height scan of a graphene blister pressurized to 2.4 MPa (chip 2). The maximum height is about 520 nm; (b) cross sections of the AFM height measurements (chip 2) at different input pressures in increasing order, p0—0.48 MPa, 1.32 MPa, 1.83 MPa, and 2.40 MPa. The dashed curves are the deflection profiles from Hencky's solution, with the maximum deflection fit to the measured value.

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Fig. 7

(a) Maximum deflection, (b) blister radius, and (c) final internal pressure. The point symbols are from measurements, and the solid curves are from the analysis with no delamination and delamination for different values of adhesion energy: Γ = 0.2 J/m2 (dashed), Γ = 0.24 J/m2 (solid), and Γ = 0.28 J/m2 (long dashed). The square symbols are those that were used to determine the adhesion energies in Fig. 5.

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Fig. 8

(a) AFM amplitude image (40 × 40 μm) of a graphene membrane that has undergone large-scale delamination at p0 = 2.8 MPa with a0 ≈ 2.2 μm and h ≈ 5 μm. Assuming the adhesion energy is between 0.2 and 0.4 J/m2 and the graphene has eight layers, the critical pressure is between 1.9 and 3.15 MPa.

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Fig. 4

Critical pressure for the onset of delamination as a function of: (a) cavity depth, (b) cavity radius, and (c) adhesion energy for the constant pressure (bottom curves) and constant N blister tests (top curves). When not being varied, h = 400 nm, a0 = 2 μm, and Γ = 0.2 J/m2.

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Fig. 5

Adhesion energies for monolayer graphene membranes on two different SiO2 substrates/chips. The average adhesion energy is 0.44 J/m2 for chip 1 and 0.24 J/m2 for chip 2.

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