This paper reports an experimental and theoretical investigation of the indentation of a layered elastic solid, with special reference to the surface force apparatus (SFA). The contacting surfaces of the SFA comprise a 3-layer material: a thin mica surface layer on a thicker epoxy layer supported by a thick silica substrate. An existing finite element analysis of the deformation of ideal mica/epoxy/silica surfaces used in the SFA is adapted to compare with the experimental measurements of the variation of contact size with load, both with and without adhesion at the interface. This is in marked difference to the Johnson, Kendall and Roberts (JKR) theory for homogeneous solids. Experiments and finite element calculations were also carried out on the elastic indentation of a thin (5.5 µm) layer of mica on a very thick layer of epoxy (>100 µm). As input data for the calculations, the elastic moduli of the mica and epoxy were measured in separate indentation experiments. The stiffness of a layered solid can be expressed by an ‘effective modulus’ , which has been deduced from the experimental measurements and compared with the theoretical values with fair success. The work of adhesion is commonly measured in the SFA by observing the ‘pull-off force’ to separate the surfaces. The theory shows that, for a layered solid, the pull-force can vary significantly from the JKR value for a homogeneous solid. In particular, it was found that the mica surface energy, γsv, measured by SFA experiments using crossed cylinders of mean radius R, where the materials are layered and the mica/mica adhesion is high, can vary with the pull-off force Fp according to Fp/4πR < γsv < Fp/2πR, and for this particular experiment was given as γsv = Fp/3.5 πR as compared with γsv = Fp/3πR for homogeneous materials.

Understanding the process of charge generation, transfer, and diffusion between two-dimensional (2D) materials and their supporting substrates is very important for potential applications of 2D materials. Compared with the systematic studies of triboelectric charging in a bulk sample, a fundamental understanding of the triboelectrification of the 2D material/insulator system is rather limited. Here, the charge transfer and diffusion of both the SiO surface and MoS/SiO interface through contact electrification and frictional electrification are investigated systematically in situ by scanning Kelvin probe microscopy and dual-harmonic electrostatic force microscopy. Different from the simple static charge transfer between SiO and the PtSi alloy atomic force microscope (AFM) tip, the charge transfer between the tip and the MoS/SiO system is complicated. Triboelectric charges, generated by contact or frictional electrification with the AFM tip, are trapped at the MoS/SiO interface and act as floating gates. The local charge discharge processes can be obtained by monitoring the surface potential. The charge decay time (τ) of the MoS/SiO interface is one (or two) orders of magnitude larger than the decay time τ of the SiO surface. This work facilitates an understanding of the triboelectric and de-electrification of the interface between 2D materials and substrates. In addition to the charge transfer and diffusion, we demonstrate the nanopatterns of surface and interfacial charges, which have great potential for the application of self-assembly of charged nanostructures.

Symmetry is highly relevant with various quantities and phenomena in physics. While the translational symmetry breaks at the edges of two-dimensional hexagonal crystalline flakes, it is usually associated with the breaking of central inversion symmetry that is yet to be observed in terms of physical properties. Here, we report an experiment–theory joint study on in-plane compressed single-crystal monolayer WS2 flakes. Although the flakes show a hexagonal appearance with a C6 symmetry, our density functional theory calculations predict that their in-plane strain, geometric structure, work-function, energy bandgap, and mechanical modulus are nonequivalent among the triangular regions with different edge terminations at the atomic scale, and the flakes exhibit self-patterns with a C3 symmetry. Such nonequivalence of physical properties and concomitant self-patterns persist even in a 50 μm-sized monolayer WS2, observed using atomic force microscopy. This indicates that the symmetry arising from the atomic geometry could preserve up to tens of microns for both geometric and properties of the flake, regardless of its mesoscopic geometry, i.e., C6 here. Such a detectable mesoscopic scale and symmetric nano- to mesoscale patterns provide promising building blocks for 2D materials and devices and also allow edge terminations of 2D flakes to be directly distinguished.

Strain engineering plays a vital role in controlling the physical properties of two-dimensional (2D) materials. However, the nanomechanical behavior of atomically thin 2D crystals under strain has not been completely understood. Here, strain-induced hierarchical ripple nanostructures in triangular MoS2 flakes were investigated by advanced atomic force microscopy and optical spectral measurements. The hierarchical nanoripples exhibited a threefold radial pattern, and their mechanical, electronic, and optical spectra characteristics were significantly modified due to the suffering from large tensile strain. Structure evolution of these hierarchical nanoripples was further discussed based on the geometry and thickness of MoS2 flakes, and we attributed the curtain effect at the limit of a single atomic layer. Our study will be beneficial in designing nanomechanical structures and prototype electromechanical devices with 2D materials.

It is fundamentally important to understand how the interlayer interaction of neighboring graphene sheets is influenced by chemical doping. Here we investigate the interlayer coupling of multilayer graphene doped with controlled boron content via the Raman-active in-plane shear mode. The experimental results reveal a remarkable decline in the interlayer shear modulus as boron content increases, which is a direct consequence of the enlarged interlayer spacing, further supported by the molecular dynamic (MD) simulations. Nanoindentation tests were conducted to clarify the influence of interlayer coupling behaviors on nanomechanical behaviors of boron-doped bilayer graphene. As the interlayer slippage is induced under shear deformations, the weakened shear resistance would lead to the reduced energy dissipation during sliding process. Our results provide valuable insight into fundamental mechanical properties of boron-doped graphene and its interfaces and potentially allows tailoring of interlayer coupling for low energy dissipation electromechanical devices.