Ultrastrong adhesion of graphene membranes

Abstract

As mechanical structures enter the nanoscale regime, the influence of van der Waals forces increases. Graphene is attractive for nanomechanical systems 1,2 because its Young's modulus and strength are both intrinsically high, but the mechanical behavior of graphene is also strongly influenced by the van der Waals force 3,4 . For example, this force clamps graphene samples to substrates, and also holds together the individual graphene sheets in multilayer samples. Here we use a pressurized blister test to directly measure the adhesion energy of graphene sheets with a silicon oxide substrate. We find an adhesion energy of 0.45 ± 0.02 J/m 2 for monolayer graphene and 0.31 ± 0.03 J/m 2 for samples containing 2-5 graphene sheets. These values are larger than the adhesion energies measured in typical micromechanical structures and are comparable to solid/liquid adhesion energies [5][6][7] . We attribute this to the extreme flexibility of graphene, which allows it to conform to the topography of even the smoothest substrates, thus making its interaction with the substrate more liquidlike than solid-like. Figure 1a shows optical images of the devices used for this study. Graphene sealed microcavities were fabricated by the mechanical exfoliation of graphene over predefined wells (diameter ~5 um) etched in a SiO 2 substrate (See Methods). Two exfoliated graphene flakes were used, yielding membranes with between 1 and 5 graphene layers, which were suspended over the wells and clamped to the SiO 2 substrate by the van der Waals force. After exfoliation the internal pressure in the microcavity, p int , is equal to the external pressure, p ext , which is atmospheric pressure. In this state the membrane is flat, adhered to the substrate, and it confines N gas molecules inside the microcavity.To create a pressure difference across the graphene membrane, we put the sample in a pressure chamber and use nitrogen gas to increase p ext to p 0 . Devices are left in the pressure chamber at p 0 for between 4 and 6 days in order for p int to equilibrate to p 0 (Fig. 1b). This is thought to take place through the slow diffusion of gas through the SiO 2 substrate 3 . We then remove the device from the pressure chamber, and the pressure difference (p int > p ext ) causes the membrane to bulge upwards and the volume of the cavity to increase (Fig. 1c). We use an atomic force microscope (AFM) to measure the shape of the graphene membrane, which we parameterize by its maximum deflection, δ, and its radius, a (Fig. 1d).This technique allows us to measure δ and a for different values of p 0 . Figure 1e shows a series of AFM line cuts through the center of a mono-layer membrane as p 0 is increased. At low p 0 , the membrane is clamped to the substrate by the van der Waals force and δ increases with increasing p 0 . At higher p 0 (e.g., p 0 > 2 MPa) in addition to an increased deflection, we also observe delamination of the graphene from the SiO 2 substrate which leads to an increase in a (Fig. 1e). In Fig. 2a, we plot δ vs. p 0 for all the bi...

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