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...

We measured the work of separation of single and few-layer MoS membranes from a SiO substrate using a mechanical blister test and found a value of 220 ± 35 mJ/m. Our measurements were also used to determine the 2D Young's modulus (E) of a single MoS layer to be 160 ± 40 N/m. We then studied the delamination mechanics of pressurized MoS bubbles, demonstrating both stable and unstable transitions between the bubbles' laminated and delaminated states as the bubbles were inflated. When they were deflated, we observed edge pinning and a snap-in transition that are not accounted for by the previously reported models. We attribute this result to adhesion hysteresis and use our results to estimate the work of adhesion of our membranes to be 42 ± 20 mJ/m.

We created graphene blisters that cover and seal an annular cylinder-shaped microcavity in a SiO2 substrate filled with a gas. By controlling the pressure difference between the gas inside and outside of the microcavity, we switch the graphene membrane between multiple stable equilibrium configurations. We carried out experiments starting from the situation where the pressure of the gas inside and outside of the microcavity is set equal to a prescribed charging pressure, p0 and the graphene membrane covers the cavity like an annular drum, adhered to the central post and the surrounding substrate due to van der Waals forces. We decrease the outside pressure to a value, pe which causes it to bulge into an annular blister. We systematically increase the charging pressure by repeating this procedure causing the annular blister to continue to bulge until a critical charging pressure pc(i) is reached. At this point the graphene membrane delaminates from the post in an unstable manner, resulting in a switch of graphene membrane shape from an annular to a spherical blister. Continued increase of the charging pressure results in the spherical blister growing with its height increasing, but maintaining a constant radius until a second critical charging pressure pc(o) is reached at which point the blister begins to delaminate from the periphery of the cavity in a stable manner. Here, we report a series of experiments as well as a mechanics and thermodynamic model that demonstrate how the interplay among system parameters (geometry, graphene stiffness (number of layers), pressure, and adhesion energy) results in the ability to controllably switch graphene blisters among different shapes. Arrays of these blisters can be envisioned to create pressure-switchable surface properties where the difference between patterns of annular versus spherical blisters will impact functionalities such as wettability, friction, adhesion, and surface wave characteristics.

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/SiO 2 interfaces. We find an average adhesion energy of 0.24 J/m 2 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.2

No abstract

We present a unique experimental configuration that allows us to determine the interfacial forces on nearly parallel plates made from the thinnest possible mechanical structures, single and few layer graphene membranes. Our approach consists of using a pressure difference across a graphene membrane to bring the membrane to within ~ 10-20 nm above a circular post covered with SiO x or Au until a critical point is reached whereby the membrane snaps into adhesive contact with the post. Continuous measurements of the deforming membrane with an AFM coupled with a theoretical model allow us to deduce the magnitude of the interfacial forces between graphene and SiO x and graphene and Au. The nature of the interfacial forces at ~ 10 -20 nm separations is consistent with an inverse fourth power distance dependence, implying that the interfacial forces are dominated by van der Waals interactions. Furthermore, the strength of the interactions is found to increase linearly with the number of graphene layers. The experimental approach can be used to measure the strength of the interfacial forces for other atomically thin two-dimensional materials, and help guide the development of nanomechanical devices such as switches, resonators, and sensors.KEYWORDS: Graphene, Interfacial forces, Nanoelectromechanical systems, Pullin instability 3 Interfacial forces act between all materials 1 . At macroscopic distances, these interfacial forces are weak and practically insignificant, but at distances approaching tens of nanometers, they become much stronger, thereby enhancing the attraction within micro/nanomechanical structures or molecules, and potentially significantly affecting the device performance 2-5 . Graphene, a 2 dimensional nanomaterial composed of carbon atoms, is a promising material with potential applications in a variety of nanomechanical, biological and electrical devices due to its exceptional properties 6-14 . Furthermore, graphene being extremely thin with a very high surface area to volume ratio is highly susceptible to interfacial forces and is an ideal candidate to study and characterize these forces 15,16 . Therefore, there is an increasing interest in studying the nature of interfacial forces on graphene 17 . Even though the adhesion strength between graphene and substrates when in contact has been experimentally measured in different ways, experimental measurements of non-contact attractive interfacial forces remains relatively unexplored [18][19][20][21] . Interfacial forces on bulk materials or other nanomaterials have been measured using a variety of configurations 1, 4, 5, 22 . Here, we demonstrate a novel experimental method to study these elusive forces on graphene with a real time observation of the induced pull in instability.Devices used in this study consist of a graphene flake suspended over an annular ring etched into a silicon oxide wafer, forming a graphene-sealed microcavity (Fig. 1a).Device configurations include graphene suspended on bare SiO x or gold-coated SiO x . The graphene memb...

No abstract

Large arrays of 3-terminal nanoelectromechanical graphene switches are fabricated. The switch is designed with a novel geometry that leads to low actuation voltages and improved mechanical integrity, while reducing adhesion forces, which improves the reliability of the switch. A finite element model including non-linear electromechanics is used to simulate the switching behavior and to deduce a scaling relation between the switching voltage and device dimensions.