Out-of-plane deformation patterns, such as buckling, wrinkling, scrolling, and folding, formed by multilayer van der Waals materials have recently seen a surge of interest. One crucial parameter governing these deformations is bending rigidity, on which significant controversy still exists despite extensive research for more than a decade. Here, we report direct measurements of bending rigidity of multilayer graphene, molybdenum disulfide (${\mathrm{MoS}}_2$), and hexagonal boron nitride (hBN) based on pressurized bubbles. By controlling the sample thickness and bubbling deflection, we observe platelike responses of the multilayers and extract both their Young’s modulus and bending rigidity following a nonlinear plate theory. The measured Young’s moduli show good agreement with those reported in the literature ($E_{\text{graphene}}>E_{\text{hBN}}>E_{{\text{MoS}}_2}$), but the bending rigidity follows an opposite trend, $D_{\text{graphene}}<D_{\text{hBN}}<D_{{\text{MoS}}_2}$ for multilayers with comparable thickness, in contrast to the classical plate theory, which is attributed to the interlayer shear effect in the van der Waals materials.

Monolayer two-dimensional (2D) crystals exhibit a host of intriguing properties, but the most exciting applications may come from stacking them into multilayer structures. Interlayer and interfacial shear interactions could play a crucial role in the performance and reliability of these applications, but little is known about the key parameters controlling shear deformation across the layers and interfaces between 2D materials. Herein, we report the first measurement of the interlayer shear stress of bilayer graphene based on pressurized microscale bubble loading devices. We demonstrate continuous growth of an interlayer shear zone outside the bubble edge and extract an interlayer shear stress of 40 kPa based on a membrane analysis for bilayer graphene bubbles. Meanwhile, a much higher interfacial shear stress of 1.64 MPa was determined for monolayer graphene on a silicon oxide substrate. Our results not only provide insights into the interfacial shear responses of the thinnest structures possible, but also establish an experimental method for characterizing the fundamental interlayer shear properties of the emerging 2D materials for potential applications in multilayer systems.

Significance: Spontaneously formed nanoblisters are almost inevitable when transferring 2D crystals to a substrate. We hypothesize that those nanoblisters are filled with liquid according to our time-lapse atomic force microscopy scans and reasonable estimation of adhesion energy. We show that the liquid-filled nanoblisters form as a result of competition between the elastic energy of the deformed 2D crystal, the interfacial energy associated with van der Waals interactions, and surface tension of the liquid contents. Besides pointing to solutions for controlling their shape and internal pressure, our analysis provides a method to estimate the work of adhesion of 2D material interfaces by simply measuring the aspect ratios of the blisters, which is essential for the design and fabrication of 2D crystal-based applications.