Since the first successful synthesis of graphene just over a decade ago, a variety of twodimensional (2D) materials (e.g., transition metal-dichalcogenides, hexagonal boron-nitride, etc.) have been discovered. Among the many unique and attractive properties of 2D materials, mechanical properties play important roles in manufacturing, integration and performance for their potential applications. Mechanics is indispensable in the study of mechanical properties, both experimentally and theoretically. The coupling between the mechanical and other physical properties (thermal, electronic, optical) is also of great interest in exploring novel applications, where mechanics has to be combined with condensed matter physics to establish a scalable theoretical framework. Moreover, mechanical interactions between 2D materials and various substrate materials are essential for integrated device applications of 2D materials, for which the mechanics of interfaces (adhesion and friction) has to be developed for the 2D materials. Here we review recent theoretical and experimental works related to mechanics and mechanical properties of 2D materials. While graphene is the most studied 2D material to date, we expect continual growth of interest in the mechanics of other 2D materials beyond graphene.

Layered systems of 2D crystals and heterostructures are widely explored for new physics and devices. In many cases, monolayer or few-layer 2D crystals are transferred to a target substrate including other 2D crystals, and nanometer-scale blisters form spontaneously between the 2D crystal and its substrate. Such nanoblisters are often recognized as an indicator of good adhesion, but there is no consensus on the contents inside the blisters. While gas-filled blisters have been modeled and measured by bulge tests, applying such models to spontaneously formed nanoblisters yielded unrealistically low adhesion energy values between the 2D crystal and its substrate. Typically, gas-filled blisters are fully deflated within hours or days. In contrast, we found that the height of the spontaneously formed nanoblisters dropped only by 20-30% after 3 mo, indicating that probably liquid instead of gas is trapped in them. We therefore developed a simple scaling law and a rigorous theoretical model for liquid-filled nanoblisters, which predicts that the interfacial work of adhesion is related to the fourth power of the aspect ratio of the nanoblister and depends on the surface tension of the liquid. Our model was verified by molecular dynamics simulations, and the adhesion energy values obtained for the measured nanoblisters are in good agreement with those reported in the literature. This model can be applied to estimate the pressure inside the nanoblisters and the work of adhesion for a variety of 2D interfaces, which provides important implications for the fabrication and deformability of 2D heterostructures and devices.

Monolithic hierarchical nanoporous gold disks, 500 nm in diameter, 75 nm in thickness and 3.5 nm in pore radius, have been fabricated by hybrid processes. A surface-enhanced Raman scattering enhancement factor of at least 10(8) has been obtained on individual disks using benzenethiol self-assembled monolayer with 785 nm laser excitation.

Two-dimensional (2D) materials have recently been theoretically predicted and experimentally confirmed to exhibit electromechanical coupling. Specifically, monolayer and few-layer molybdenum disulfide (MoS) have been measured to be piezoelectric within the plane of their atoms. This work demonstrates and quantifies a nonzero out-of-plane electromechanical response of monolayer MoS and discusses its possible origins. A piezoresponse force microscope was used to measure the out-of-plane deformation of monolayer MoS on Au/Si and AlO/Si substrates. Using a vectorial background subtraction technique, we estimate the effective out-of-plane piezoelectric coefficient, d, for monolayer MoS to be 1.03 ± 0.22 pm/V when measured on the Au/Si substrate and 1.35 ± 0.24 pm/V when measured on AlO/Si. This is on the same order as the in-plane coefficient d reported for monolayer MoS. Interpreting the out-of-plane response as a flexoelectric response, the effective flexoelectric coefficient, μ, is estimated to be 0.10 nC/m. Analysis has ruled out the possibility of elastic and electrostatic forces contributing to the measured electromechanical response. X-ray photoelectron spectroscopy detected some contaminants on both MoS and its substrate, but the background subtraction technique is expected to remove major contributions from the unwanted contaminants. These measurements provide evidence that monolayer MoS exhibits an out-of-plane electromechanical response and our analysis offers estimates of the effective piezoelectric and flexoelectric coefficients.

In general, fabrication of 2D electronic systems involves transferring the 2D material from one substrate to another in a process called transfer printing. [ 12,13 ] This process relies heavily on the interactions between the 2D material and the various surfaces that it contacts. Adhesion values must allow for the transfer from one substrate to another. By gaining a better understanding of the adhesion energy between 2D materials and the various substrates involved, the transfer process can be improved to allow for the picking up and printing of 2D materials onto arbitrary fl exible and stretchable substrates.Adhesion of 2D materials is also a controlling parameter for device mechanics. As a component in an integrated device, a 2D material will have to make secure contact with supporting substrates, metallic interconnects, other 2D materials, encapsulation layers, and other elements of a complete system. The mechanical interaction between 2D materials and their neighbors is an important parameter that governs the mechanical integrity of the device during thermal and mechanical loadings. Mechanical loading is often prominent during the operation of fl exible 2D devices. For example, strain engineering of 2D materials on polymer substrates can be achieved by deforming the substrate, [ 14 ] but any slippage between 2D materials and the substrate would weaken the strain transfer to the 2D materials and hence limit the tunability. Moreover, slippage between 2D materials and their polymer substrates when the substrate is deformed may lead to buckle delaminations or wrinkles when the substrate is unloaded, [ 15 ] resulting in device degradation.Because of the signifi cance of adhesion, many experimental studies have been carried out to measure the adhesion energy between graphene and stiff substrates, as summarized in a recent review paper. [ 16 ] For example, adhesion energy between exfoliated monolayer graphene and SiO 2 has been measured to be 450 mJ m −2 by a pressurized blister method, [ 17 ] while adhesion of chemical vapor deposited (CVD) monolayer graphene to Si measured by double cantilever peeling method is found to be 357 mJ m −2 . Adhesion between CVD graphene and seed copper has been measured to be 720 mJ m −2 using cantilever method [ 18 ] whereas after transferring CVD graphene to a foreign copper surface, the interface adhesion was found to be only 510 mJ m −2 using a blister test. [ 19 ] 2D systems have great promise as next generation electronic materials but require intimate knowledge of their interactions with their neighbors for device fabrication and mechanical manipulation. Although adhesion between 2D materials and stiff substrates such as silicon and copper has been measured, adhesion between 2D materials and soft polymer substrates remains diffi cult to characterize due to the large deformability of the polymer substrates. In this work, a buckling-based metrology for measuring the adhesion energy between few layer molybdenum disulfi de (MoS 2 ) and soft elastomeric substrates is proposed and de...

18Nanoblisters such as nanobubbles and nanotents formed by two-dimensional (2D) materials have been 19 extensively exploited for strain engineering purposes as they can produce self-sustained, non-uniform in-20 plane strains through out-of-plane deformation. However, deterministic measure and control of strain 21 fields in these systems are challenging because of the atomic thinness and unconventional interface 22 behaviors of 2D materials. Here, we experimentally characterize a simple and unified power law for the 23 profiles of a variety of nanobubbles and nanotents formed by 2D materials such as graphene and MoS 2 24 layers. Using membrane theory, we analytically unveil what sets the in-plane strains of these blisters 25 regarding their shape and interface characteristics. Our analytical solutions are validated by Raman 26 spectroscopy measured strain distributions in bulged graphene bubbles supported by strong and weak 27 shear interfaces. We advocate that both the strain magnitudes and distributions can be tuned by the 2D 28 material-substrate interface adhesion and friction properties. 29 30

A zinc oxide thin film transistor is developed and optimized that simultaneously functions as a transistor and a force sensor, thus allowing for scalable integration of sensors into arrays without the need for additional addressing elements. Through systematic material deposition, microscopy, and piezoelectric characterization, it is determined that an O2 rich deposition condition improves the transistor performance and pressure sensing characteristics. With these optimizations, a sensitivity of 4 nA kPa−1 and a latency of below 1 ms are achieved, exceeding the criteria for successful commercialization of arrayed pressure sensors. The functionality of 16 × 16 pressure sensor arrays on thin bendable glass substrates for integrated low weight and flexible touchscreen displays is fabricated and demonstrated and read‐out electronics to interface with the arrays and to record their response in real‐time are developed. Finally, the application of these sensors for mobile displays via their operation with an existing commercial touch integrated circuit controller is demonstrated.

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