Interface-Governed Deformation of Nanobubbles and Nanotents Formed by Two-Dimensional Materials

From Auto-Kirigami to Drumheads: Suspended, Self-Tearing, and Strained Graphene Nanostructures Formed by Nanoindentation

Nanoindentation of substrate-supported graphene can produce auto-kirigami (AK) structures: spontaneously folded and extended self-tearing nanoribbons up to several micrometers in length. However, the mechanisms governing their formation and yield are poorly understood. Here, we study graphene AK through statistical analysis of high-throughput experiments involving hundreds-fold arrays of indents on highly uniform regions of exfoliated monolayer and bilayer graphene, with no applied oscillation (in contrast with prior work). Post-mortem atomic force microscopy analysis reveals a baseline AK formation rate of 13-61% for monolayers and 0-17% for bilayers depending on inter-indent pitch. Force-distance curves of each type of nanostructure showed no appreciable differences. Moreover, graphene can remain intact after indentation, permitting formation of unbroken graphene suspended over or conformed within indents. Inter-indent pitch affects the absolute and relative formation rates of these nanostructures, attributed to indentation-induced tensile graphene strain. This advances the understanding of mechanisms for controlled formation of nanostructures, including twisted bilayers of graphene and other van der Waals materials.

Stiffer Is Stickier: Adhesion in Elastic Nanofilms

When two objects are brought into contact, separating them typically requires overcoming a detachment force. While this adhesion-induced force is vital for thin film materials in a range of nature and engineering systems, its quantitative understanding remains elusive due to the complex interplay between nonlinear deformation and adhesion. Here we perform controlled experiments and develop formal theories for the detachment force in a canonical configuration: separation of a sphere from an elastic graphene film. We observe that applying tension to the film can increase both its apparent out-of-plane stiffness and its detachment force, a behavior that cannot be explained by macroscopic adhesion theories. We attribute this unusual "stiffer-stickier" behavior to long-range intermolecular forces and demonstrate that it is a general phenomenon for elastic nanofilms, explainable through a multiscale theory that we develop. The ideas introduced here offer a generic strategy to understand the adhesion of slender structures across various length scales.

Mechanical and electromechanical properties of 2D materials studied via in situ microscopy techniques

Two-dimensional (2D) materials with van der Waals stacking have been reported to have extraordinary mechanical and electromechanical properties, which give them revolutionary potential in various fields. However, due to the atomic-scale thickness of these 2D materials, their fascinating properties cannot be effectively characterized in many cases using conventional measurement techniques. Based on typical microscopy techniques such as scanning electron microscopy (SEM), transmission electron microscopy (TEM), and atomic force microscopy (AFM), a range of in situ microscopy techniques have been developed to systematically quantify the mechanical and electromechanical properties of 2D materials. This review highlights the advancements of in situ microscopy techniques for studying elasticity and fracture, adhesion and separation, structural superlubricity, as well as c-axis piezoresistivity and rotation angle-related transport of 2D materials. The methods and results of various microscopy experiments, including nanoindentation using AFM, pressurized bubble tests, self-retraction experiments, pull-to-peel methods and so on, are compared, and their respective advantages and limitations are discussed. Finally, we summarize the current challenges in these microscopy techniques and outline development opportunities.

Many-body van der Waals interactions in multilayer structures studied by atomic force microscopy

Van der Waals interaction in multilayer structures was predicted to be of many-body character, almost in parallel with the establishment of Lifshitz theory. However, the diminishing interaction between layers separated by a finite-thickness intermediate layer prevents experimental verification of the many-body nature. Here we verify the substrate contribution at the adhesion between the atomic force microscopy tip and the supported graphene, by taking advantage of the atomic-scale proximity of two objects separated by graphene. While the pairwise dispersion theory overestimates the substrate contribution at critical adhesive pressures, the many-body dispersion theory remedies this deficiency, highlighting the non-additivity nature of substrate contribution. The many-body effect is further understood through the energy spectrum of charge density fluctuations. These findings open the door to modulating the van der Waals interaction on two-dimensional material surfaces, which would be relevant to various technologies, including microelectromechanical systems and surface molecular assembly.

Revealing the Interlayer Interaction Forces in 2D Graphene Materials by Graphene-Wrapped Nanoprobe

Understanding the interlayer interaction between 2D layered structures is critical for the construction of various micro- and nanoscale functional devices. However, both the normal and the tangential interlayer interactions between 2D layered materials have rarely been studied simultaneously. In this work, an immersion and lift-up method is proposed to wrap a layer of graphene flakes onto a plasma-pretreated atomic force microscopy (AFM) nanoprobe for the measurements of interaction forces by AFM. The normal interactions (adhesion force and adhesion energy) and tangential interactions (friction force) between two different probes (Pt-coated probe and graphene-wrapped probe) and two different 2D graphene materials [graphene and graphene oxide (GO)] were systematically measured, respectively. The adhesion energies of Pt-GO, Pt-graphene, graphene-GO, and graphene-graphene were measured to be 0.72 ± 0.05, 0.41 ± 0.03, 0.19 ± 0.02, and 0.10 ± 0.02 J m-2, respectively. The graphene-graphene contact pair showed the lowest adhesion force (5.57 ± 1.03 nN) and adhesion energy (0.10 ± 0.02 J m-2), which was attributed to the strong covalent bonds and charge density distribution. The friction coefficients of Pt-GO, graphene-GO, Pt-graphene, and graphene-graphene were determined to be 0.38, 0.14, 0.054, and 0.013. The graphene-graphene tribo-pair exhibited a superlow friction state for a long time, which was attributed to incommensurate contact and weak van der Waals interactions. These findings provide a technical route to reveal the interlayer interactions of various 2D layered materials, which can be widely applied in microelectromechanical systems.

Strain in Hybrid Organic-Inorganic Metal Halide Perovskites Microstructures by Numerical Simulations

Hybrid organic-inorganic metal halide perovskites (HOIPs) are promising materials for optoelectronics applications. Their optical and electrical properties can be controlled by strain engineering, that results from application of local elastic deformation or deposition on pre-patterned substrates acquiring a conformal 3D shape. Most interesting, their mechanical properties depend on their crystal structure, composition and dimensionality. We explore by numerical simulations the deformation of a selection of HOIPs comprising a broad range of elastic properties. We consider an axial symmetry with the formation of microdomes on flakes. Radial and vertical forces are considered, finding that the radial force is more effective to obtain large deformation. Large vertical displacement and strain is obtained for HOIPs with low stiffness. The layered nature of HOIPs, that are formed by inorganic layers of different thickness and organic spacers, is also investigated, revealing a non-monotonous trend with the proportion of inorganic to organic part.

Visualizing and Controlling of Photogenerated Electron-Hole Pair Separation in Monolayer WS2 Nanobubbles under Piezoelectric Field

The piezoelectric properties of two-dimensional semiconductor nanobubbles present remarkable potential for application in flexible optoelectronic devices, and the piezoelectric field has emerged as an efficacious pathway for both the separation and migration of photogenerated electron-hole pairs, along with inhibition of recombination. However, the comprehension and control of photogenerated carrier dynamics within nanobubbles still remain inadequate. Hence, this study is dedicated to underscore the importance of in situ detection and detailed characterization of photogenerated electron-hole pairs in nanobubbles to enrich understanding and strategic manipulation in two-dimensional semiconductor materials. Utilizing frequency modulation kelvin probe force microscopy (FM-KPFM) and strain gradient distribution techniques, the existence of a piezoelectric field in monolayer WS2 nanobubbles was confirmed. Combining w/o and with illumination FM-KPFM, second-order capacitance gradient technique and in situ nanoscale tip-enhanced photoluminescence characterization techniques, the interrelationships among the piezoelectric effect, interlayer carrier transfer, and the funneling effect for photocarrier dynamics process across various nanobubble sizes were revealed. Notably, for a WS2/graphene bubble height of 15.45 nm, a 0 mV surface potential difference was recorded in the bubble region w/o and with illumination, indicating a mutual offset of piezoelectric effect, interlayer carrier transfer, and the funneling effect. This phenomenon is prevalent in transition metal dichalcogenides materials exhibiting inversion symmetry breaking. The implication of our study is profound for advancing the understanding of the dynamics of photogenerated electron-hole pair in nonuniform strain piezoelectric systems, and offers a reliable framework for the separation and modulation of photogenerated electron-hole pair in flexible optoelectronic devices and photocatalytic applications.

Preparation and Modeling of Graphene Bubbles to Obtain Strain-Induced Pseudomagnetic Fields

It has been both theoretically predicted and experimentally demonstrated that strain can effectively modulate the electronic states of graphene sheets through the creation of a pseudomagnetic field (PMF). Pressurizing graphene sheets into bubble-like structures has been considered a viable approach for the strain engineering of PMFs. However, the bubbling technique currently faces limitations such as long manufacturing time, low durability, and challenges in precise control over the size and shape of the pressurized bubble. Here, we propose a rapid bubbling method based on an oxygen plasma chemical reaction to achieve rapid induction of out-of-plane deflections and in-plane strains in graphene sheets. We introduce a numerical scheme capable of accurately resolving the strain field and resulting PMFs within the pressurized graphene bubbles, even in cases where the bubble shape deviates from perfect spherical symmetry. The results provide not only insights into the strain engineering of PMFs in graphene but also a platform that may facilitate the exploration of the strain-mediated electronic behaviors of a variety of other 2D materials.

Mechanical Mapping of Nanoblisters Confined by Two-Dimensional Materials Reveals Complex Ridge Patterns

Understanding the mechanics of blisters confined by two-dimensional (2D) materials is of great importance for either fundamental studies or for their practical applications. In this work, we investigate the mechanical properties of nanoscale 2D material blisters using contact-resonance atomic force microscopy (CR-AFM). From the measurement results at the blister centers, the blisters' internal pressures are characterized, which are shown to be inversely proportional to the blisters' sizes. Our measurements agree considerably well with values predicted by theoretical mechanic analyses of the blisters. In addition, high-resolution mechanical mapping with CR-AFM reveals fine, complex ridge patterns of the blisters' confining membranes, which can hardly be distinguished from their topographies. The pattern complexity of a blister system is shown to increase with an increase in its bendability.

One-Dimensional MoS2 Nanoscrolls as Miniaturized Memories

Dimensionality of materials is closely related to their physical properties. For two-dimensional (2D) semiconductors such as monolayer molybdenum disulfide (MoS2), converting them from 2D nanosheets to one-dimensional (1D) nanoscrolls could contribute to remarkable electronic and optoelectronic properties, yet the rolling-up process still lacks sufficient controllability, which limits the development of their device applications. Herein we report a modified solvent evaporation-induced rolling process that halts at intermediate states and achieve MoS2 nanoscrolls with high yield and decent axial uniformity. The accordingly fabricated nanoscroll memories exhibit an on/off ratio of ∼104 and a retention time exceeding 103 s and can realize multilevel storage with pulsed gate voltages. Such open-end, high-curvature, and hollow 1D nanostructures provide new possibilities to manipulate the hysteresis windows and, consequently, the charge storage characteristics of nanoscale field-effect transistors, thereby holding great promise for the development of miniaturized memories.

Core/Shell-Like Localized Emission at Atomically Thin Semiconductor-Au Interface

Localized emission in atomically thin semiconductors has sparked significant interest as single-photon sources. Despite comprehensive studies into the correlation between localized strain and exciton emission, the impacts of charge transfer on nanobubble emission remains elusive. Here, we report the observation of core/shell-like localized emission from monolayer WSe2 nanobubbles at room temperature through near-field studies. By altering the electronic junction between monolayer WSe2 and the Au substrate, one can effectively adjust the semiconductor to metal junction from a Schottky to an Ohmic junction. Through concurrent analysis of topography, potential, tip-enhanced photoluminescence, and a piezo response force microscope, we attribute the core/shell-like emissions to strong piezoelectric potential aided by induced polarity at the WSe2-Au Schottky interface which results in spatial confinement of the excitons. Our findings present a new approach for manipulating charge confinement and engineering localized emission within atomically thin semiconductor nanobubbles. These insights hold implications for advancing the nano and quantum photonics with low-dimensional semiconductors.

Fine-Tuning of the Excitonic Response in Monolayer WS2 Domes via Coupled Pressure and Strain Variation

We present a spectroscopic investigation of the vibrational and optoelectronic properties of WS2 domes in the 0-0.65 GPa range. The pressure evolution of the system morphology, deduced by the combined analysis of Raman and photoluminescence spectra, revealed a significant variation in the dome's aspect ratio. The modification of the dome shape caused major changes in the mechanical properties of the system resulting in a sizable increase of the out-of-plane compressive strain while keeping the in-plane tensile strain unchanged. The variation of the strain gradients drives a nonlinear behavior in both the exciton energy and radiative recombination intensity, interpreted as the consequence of a hybridization mechanism between the electronic states of two distinct minima in the conduction band. Our results indicate that pressure and strain can be efficiently combined in low dimensional systems with unconventional morphology to obtain modulations of the electronic band structure not achievable in planar crystals.

Button shear testing for adhesion measurements of 2D materials

Two-dimensional (2D) materials are considered for numerous applications in microelectronics, although several challenges remain when integrating them into functional devices. Weak adhesion is one of them, caused by their chemical inertness. Quantifying the adhesion of 2D materials on three-dimensional surfaces is, therefore, an essential step toward reliable 2D device integration. To this end, button shear testing is proposed and demonstrated as a method for evaluating the adhesion of 2D materials with the examples of graphene, hexagonal boron nitride (hBN), molybdenum disulfide, and tungsten diselenide on silicon dioxide and silicon nitride substrates. We propose a fabrication process flow for polymer buttons on the 2D materials and establish suitable button dimensions and testing shear speeds. We show with our quantitative data that low substrate roughness and oxygen plasma treatments on the substrates before 2D material transfer result in higher shear strengths. Thermal annealing increases the adhesion of hBN on silicon dioxide and correlates with the thermal interface resistance between these materials. This establishes button shear testing as a reliable and repeatable method for quantifying the adhesion of 2D materials.

Locally Strained 2D Materials: Preparation, Properties, and Applications

2D materials are promising for strain engineering due to their atomic thickness and exceptional mechanical properties. In particular, non-uniform and localized strain can be induced in 2D materials by generating out-of-plane deformations, resulting in novel phenomena and properties, as witnessed in recent years. Therefore, the locally strained 2D materials are of great value for both fundamental studies and practical applications. This review discusses techniques for introducing local strains to 2D materials, and their feasibility, advantages, and challenges. Then, the unique effects and properties that arise from local strain are explored. The representative applications based on locally strained 2D materials are illustrated, including memristor, single photon emitter, and photodetector. Finally, concluding remarks on the challenges and opportunities in the emerging field of locally strained 2D materials are provided.

Deformable Catalytic Material Derived from Mechanical Flexibility for Hydrogen Evolution Reaction

Deformable catalytic material with excellent flexible structure is a new type of catalyst that has been applied in various chemical reactions, especially electrocatalytic hydrogen evolution reaction (HER). In recent years, deformable catalysts for HER have made great progress and would become a research hotspot. The catalytic activities of deformable catalysts could be adjustable by the strain engineering and surface reconfiguration. The surface curvature of flexible catalytic materials is closely related to the electrocatalytic HER properties. Here, firstly, we systematically summarized self-adaptive catalytic performance of deformable catalysts and various micro-nanostructures evolution in catalytic HER process. Secondly, a series of strategies to design highly active catalysts based on the mechanical flexibility of low-dimensional nanomaterials were summarized. Last but not least, we presented the challenges and prospects of the study of flexible and deformable micro-nanostructures of electrocatalysts, which would further deepen the understanding of catalytic mechanisms of deformable HER catalyst.

Extra-High Mechanical and Phononic Anisotropy in Black Phosphorus Blisters

Strain is an effective strategy to modulate the electrical, optical, and optoelectronic properties of 2D materials. Conventional circular blisters could generate a biaxial stretching of 2D membranes with notable strain gradients along the hoop direction. However, such a deformation mode cannot be utilized to investigate mechanical responses of in-plane anisotropic 2D materials, for example, black phosphorus (BP), due to its crystallographic orientation dependence. Here, a novel rectangular-shaped bulge device is developed to uniaxially stretch the membrane, and further provide a promising platform to detect orientation-dependent mechanical and optical properties of anisotropic 2D materials. Impressively, the derived anisotropic ratio of Young's modulus of BP flakes is much higher than the values obtained via the nanoindentation method. The extra-high strain-dependent phononic anisotropy in Raman modes along different crystalline orientations is also observed. The designed rectangular budge device expands the uniaxial deformation methods available, allowing to explore the mechanical, and strain-dependent physical properties of other anisotropic 2D materials more broadly.

Local Nanostrain Engineering of Monolayer MoS2 Using Atomic Force Microscopy-Based Thermomechanical Nanoindentation

Strain engineering in two-dimensional materials (2DMs) has important application potential for electronic and optoelectronic devices. However, achieving precise spatial control, adjustable sizing, and permanent strain with nanoscale resolution remains challenging. Herein, a thermomechanical nanoindentation method is introduced, inspired by skin edema caused by mosquito bites, which can induce localized nanostrain and bandgap modulation in monolayer molybdenum disulfide (MoS2) transferred onto a poly(methyl methacrylate) film utilizing a heated atomic force microscopy nanotip. Via adjustment of the machining parameters, the strains of MoS2 are manipulated, achieving an average strain of ≤2.6% on the ring-shaped expansion structure. The local bandgap of MoS2 is spatially modulated using three types of nanostructures. Among them, the nanopit has the largest range of bandgap regulation, with a substantial change of 56 meV. These findings demonstrate the capability of the proposed method to create controllable and reproducible nanostrains in 2DMs.

Solid-liquid phase transition inside van der Waals nanobubbles: an atomistic perspective

The liquid-solid phase transition during the confinement of a van der Waals bubble is studied using molecular dynamics simulations. In particular, argon is considered inside a graphene bubble, where the outer membrane is a sheet of graphene, and the substrate is atomically flat graphite. A methodology to avoid metastable states of argon is developed and implemented to derive a melting curve of trapped argon. It is found that in the confinement, the melting curve of argon shifts toward higher temperatures, and the temperature shift is about 10-30 K. The ratio of the height to the radius of the GNB (H/R) decreases with increasing temperature. It also most likely undergoes an abrupt change through the liquid-crystal phase transition. The semi-liquid state of argon was detected in the transition region. At this state, the argon structure stays layered, but the atoms travel distances of several lattice constants.

Free-electron interactions with van der Waals heterostructures: a source of focused X-ray radiation

The science and technology of X-ray optics have come far, enabling the focusing of X-rays for applications in high-resolution X-ray spectroscopy, imaging, and irradiation. In spite of this, many forms of tailoring waves that had substantial impact on applications in the optical regime have remained out of reach in the X-ray regime. This disparity fundamentally arises from the tendency of refractive indices of all materials to approach unity at high frequencies, making X-ray-optical components such as lenses and mirrors much harder to create and often less efficient. Here, we propose a new concept for X-ray focusing based on inducing a curved wavefront into the X-ray generation process, resulting in the intrinsic focusing of X-ray waves. This concept can be seen as effectively integrating the optics to be part of the emission mechanism, thus bypassing the efficiency limits imposed by X-ray optical components, enabling the creation of nanobeams with nanoscale focal spot sizes and micrometer-scale focal lengths. Specifically, we implement this concept by designing aperiodic vdW heterostructures that shape X-rays when driven by free electrons. The parameters of the focused hotspot, such as lateral size and focal depth, are tunable as a function of an interlayer spacing chirp and electron energy. Looking forward, ongoing advances in the creation of many-layer vdW heterostructures open unprecedented horizons of focusing and arbitrary shaping of X-ray nanobeams.

Effect of Temperatures and Graphene on the Mechanical Properties of the Aluminum Matrix: A Molecular Dynamics Study

Graphene has become an ideal reinforcement for reinforced metal matrix composites due to its excellent mechanical properties. However, the theory of graphene reinforcement in graphene/aluminum matrix composites is not yet well developed. In this paper, the effect of different temperatures on the mechanical properties of the metal matrix is investigated using a classical molecular dynamics approach, and the effects of the configuration and distribution of graphene in the metal matrix on the mechanical properties of the composites are also described in detail. It is shown that in the case of a monolayer graphene-reinforced aluminum matrix, the simulated stretching process does not break the graphene as the strain increases, but rather, the graphene and the aluminum matrix have a shearing behavior, and thus, the graphene "pulls out" from the aluminum matrix. In the parallel stretching direction, the tensile stress tends to increase with the increase of the graphene area ratio. In the vertical stretching direction, the tensile stress tends to decrease as the percentage of graphene area increases. In the parallel stretching direction, the tensile stress of the system tends to decrease as the angle between graphene and the stretching direction increases. It is important to investigate the effect of a different graphene distribution in the aluminum matrix on the mechanical properties of the composites for the design of high-strength graphene/metal matrix composites.

Hoop compression driven instabilities in spontaneously formed multilayer graphene blisters over a polymeric substrate

The blistering of elastic membranes is prone to elastic-solid as well as substrate-based mechanical instabilities. The solid-based instabilities have been well-explored in the mechanically indented blisters of elastic membranes over the rigid/solid substrates, but an integrated study illustrating the underlying mechanism for the onset of solid as well as substrate-based instabilities in the spontaneous blistering of a 2D material is still lacking in the literature. In this article, an extensive experimental as well as analytical analysis of the spontaneous blister-formation in the multilayer graphene (MLG) flakes over a polymeric substrate is reported, which elucidates the involved mechanism and the governing parameters behind the development of elastic-solid as well as viscoelastic-substrate based instabilities. Herein, a 'blister-collapse model' is proposed, which infers that the suppression of the hoop compression, resulting from the phase-transition of the confined matter, plays a crucial role in the development of the instabilities. The ratio of blister-height to flake-thickness is a direct consequence of the taper-angle of the MLG blister and the thickness-dependent elasticity of the upper-bounding MLG flake, which shows a significant impact on the growth-dynamics of the viscous fingering pattern (viscoelastic-substrate based instability) under the MLG blister.

In-situ atomic level observation of the strain response of graphene lattice

Strain is inevitable in two-dimensional (2D) materials, regardless of whether the film is suspended or supported. However, the direct measurement of strain response at the atomic scale is challenging due to the difficulties of maintaining both flexibility and mechanical stability at low temperature under UHV conditions. In this work, we have implemented a compact nanoindentation system with a size of [Formula: see text] 160 mm[Formula: see text] [Formula: see text] 5.2 mm in a scanning tunneling microscope (STM) sample holder, which enables the reversible control of strain and gate electric field. A combination of gearbox and piezoelectric actuator allowed us to modulate the depth of the indentation continuously with nanometer precision. The 2D materials were transferred onto the polyimide film. Pd clamp was used to enhance the strain transfer from the polyimide from to the 2D layers. Using this unique technique, strain response of graphene lattice were observed at atomic precision. In the relaxed graphene, strain is induced mainly by local curvature. However, in the strained graphene with tented structure, the lattice parameters become more sensitive to the indentor height change and stretching strain is increased additionally. Moreover, the gate controllability is confirmed by measuring the dependence of the STM tip height on gate voltage.

Pull-to-Peel of Two-Dimensional Materials for the Simultaneous Determination of Elasticity and Adhesion

The flexible and clinging nature of ultrathin films requires an understanding of their elastic and adhesive properties in a wide range of circumstances from fabrications to applications. Simultaneously measuring both properties, however, is extremely difficult as the film thickness diminishes to the nanoscale. Here we address such difficulties through peeling by pulling thin films off from the substrates (we thus refer to it as "pull-to-peel"). Particularly, we perform in situ pull-to-peel of graphene and MoS₂ films in a scanning electron microscope and achieve simultaneous determination of their Young's moduli and adhesions to gold substrates. This is in striking contrast to other conceptually similar tests available in the literature, including indentation tests (only measuring elasticity) and spontaneous blisters (only measuring adhesion). Furthermore, we show a weakly nonlinear Hooke's relation for the pull-to-peel response of two-dimensional materials, which may be harnessed for the design of nanoscale force sensors or exploited in other thin-film systems.

Strain and Interference Synergistically Modulated Optical and Electrical Properties in ReS2/Graphene Heterojunction Bubbles

Two-dimensional (2D) material bubbles, as a straightforward method to induce strain, represent a potentially powerful platform for the modulation of different properties of 2D materials and the exploration of their strain-related applications. Here, we prepare ReS₂/graphene heterojunction bubbles (ReS₂/gr heterobubbles) and investigate their strain and interference synergistically modulated optical and electrical properties. We perform Raman and photoluminescence (PL) spectra to verify the continuously varying strain and the microcavity induced optical interference in ReS₂/gr heterobubbles. Kelvin probe force microscopy (KPFM) is carried out to explore the photogenerated carrier transfer behavior in both strained ReS₂/gr heterobubbles and ReS₂/gr interfaces, as well as the oscillation of surface potential caused by optical interference under illumination conditions. Moreover, the switching of in-plane crystal orientation and the modulation of optical anisotropy of ReS₂/gr heterobubbles are observed by azimuth-dependent reflectance difference microscopy (ADRDM), which can be attributed to the action of both strain effect and interference. Our study proves that the optical and electrical properties can be effectively modulated by the synergistical effect of strain and interference in a 2D material bubble.

Strong and Localized Luminescence from Interface Bubbles Between Stacked hBN Multilayers

Extraordinary optoelectronic properties of van der Waals (vdW) heterostructures can be tuned via strain caused by mechanical deformation. Here, we demonstrate strong and localized luminescence in the ultraviolet region from interface bubbles between stacked multilayers of hexagonal boron nitride (hBN). Compared to bubbles in stacked monolayers, bubbles formed by stacking vdW multilayers show distinct mechanical behavior. We use this behavior to elucidate radius- and thickness-dependent bubble geometry and the resulting strain across the bubble, from which we establish the thickness-dependent bending rigidity of hBN multilayers. We then utilize the polymeric material confined within the bubbles to modify the bubble geometry under electron beam irradiation, resulting in strong luminescence and formation of optical standing waves. Our results open a route to design and modulate microscopic-scale optical cavities via strain engineering in vdW materials, which we suggest will be relevant to both fundamental mechanical studies and optoelectronic applications.

Dynamic, Spontaneous Blistering of Substrate-Supported Graphene in Acidic Solutions

We report that for monolayer and few-layer graphene on common silicon and glass substrates, acidic solutions induce fast, spontaneous generation of solution-enclosing blisters/bubbles. Using interference reflection microscopy, we monitor the blister-generating process in situ and show that at pH < ∼2, nanoscale to micrometer-sized graphene blisters, up to ∼100 nm in height, are universally generated with high surface coverages on hydrophilic, but not hydrophobic, surfaces. The spontaneously generated blisters are highly dynamic, with growth, merging, and reconfiguration occurring at second-to-minute time scales. Moreover, we show that in this dynamic system, graphene behaves as a semipermeable membrane that allows the relatively free passing of water, impeded passing of the NaCl solute, and no passing of large dye molecules. Consequently, the blister volumes can be fast and reversibly modulated by the solution osmotic pressure.

Polymer curing assisted formation of optically visible sub-micron blisters of multilayer graphene for local strain engineering

The local or global straining techniques are used to modulate the electronic, vibrational and optical properties of the two-dimensional (2D) materials. However, manipulating the physical properties of a 2D material under a local strain is comparatively more challenging. In this work, we demonstrate an easy and efficient polymer curing assisted technique for the formation of optically visible multilayer graphene (MLG) blisters of different shapes and sizes. The detailed spectroscopic and morphological analyses have been employed for exploring the dynamics of the confined matter inside the sub-micron blisters, which confirms that the confined matter inside the blister is liquid (water). From further analyses, we find the nonlinear elastic plate model as an acceptable model under certain limits for the mechanical analyses of the MLG blisters over the (poly)vinyl alcohol (PVA) polymer film to estimate the MLG-substrate interfacial adhesion energy and confinement pressure inside the blisters. The findings open new pathways for exploiting the technique for the formation of sub-micron blisters of the 2D materials for local strain-engineering applications, as well as the temperature-controlled release of the confined matter.

Universal shape of graphene nanobubbles on metallic substrate

Graphene nanobubbles (GNBs) are formed from matter trapped between a two-dimensional material and a substrate. Such structures exhibit a wide range of new fundamental phenomena and are promising for nanoelectronic applications. However, a central part of the synthesis methods leads to the formation of GNBs with undetermined matter composition. Moreover, none of the GNBs' synthesis methods allow one to control the type of trapped matter. In a recent paper [K. M. Zahra, PCCP, 22,7606 (2020)], the authors proposed a new approach that allows the production of GNBs on a copper substrate with pure nitrogen inside in a controlled manner. In this work, we continue this research by studying the geometry of the GNBs in detail and indirectly measuring the internal pressure, which depends on the van der Waals adhesion energy and elastic properties of the graphene membrane. In agreement with other studies, we observe that dome-shaped bubbles exhibit universal scaling law, i.e., constant height to radius ratio. However, the measured height to radius ratio differs significantly from the known results of experiments and computer simulations. This deviation is explained by applying the membrane theory and taking into account the high adhesion of the copper substrate and graphene sheet. The adhesion energy calculated based on experimental data is close to the measurements performed by other experimental techniques.

Mechanical sensors based on two-dimensional materials: Sensing mechanisms, structural designs and wearable applications

Compared with bulk materials, atomically thin two-dimensional (2D) crystals possess a range of unique mechanical properties, including relatively high in-plane stiffness and large bending flexibility. The atomic 2D building blocks can be reassembled into precisely designed heterogeneous composite structures of various geometries with customized mechanical sensing behaviors. Due to their small specific density, high flexibility, and environmental adaptability, mechanical sensors based on 2D materials can conform to soft and curved surfaces, thus providing suitable solutions for functional applications in future wearable devices. In this review, we summarize the latest developments in mechanical sensors based on 2D materials from the perspective of function-oriented applications. First, typical mechanical sensing mechanisms are introduced. Second, we attempt to establish a correspondence between typical structure designs and the performance/multi-functions of the devices. Afterward, several particularly promising areas for potential applications are discussed, following which we present perspectives on current challenges and future opportunities

Elastocapillary cleaning of twisted bilayer graphene interfaces

Although layered van der Waals (vdW) materials involve vast interface areas that are often subject to contamination, vdW interactions between layers may squeeze interfacial contaminants into nanopockets. More intriguingly, those nanopockets could spontaneously coalesce into larger ones, which are easier to be squeezed out the atomic channels. Such unusual phenomena have been thought of as an Ostwald ripening process that is driven by the capillarity of the confined liquid. The underlying mechanism, however, is unclear as the crucial role played by the sheet’s elasticity has not been previously appreciated. Here, we demonstrate the coalescence of separated nanopockets and propose a cleaning mechanism in which both elastic and capillary forces are at play. We elucidate this mechanism in terms of control of the nanopocket morphology and the coalescence of nanopockets via a mechanical stretch. Besides, we demonstrate that bilayer graphene interfaces excel in self-renewal phenomena.

Here, the authors investigate the long-range interaction and coalescence mechanism of water and ethanol nanopockets encapsulated in twisted bilayer graphene, showing the complete recovery of moiré patterns after the motion of the contaminants.

Experimental Adhesion Energy in van der Waals Crystals and Heterostructures from Atomically Thin Bubbles

The formation of gas-filled bubbles on the surface of van der Waals crystals provides an ideal platform whereby the interplay of the elastic parameters and interlayer forces can be suitably investigated. Here, we combine experimental and numerical efforts to study the morphology of the bubbles at equilibrium and highlight unexpected behaviors that contrast with the common assumptions. We exploit such observations to develop an accurate analytical model to describe the shape and strain of the bubbles and exploit it to measure the adhesion energy between a variety of van der Waals crystals, showing sizable material-dependent trends.

Indentation of solid membranes on rigid substrates with van der Waals attraction

We revisit the indentation of a thin solid sheet of size R_{sheet} suspended on a circular hole of radius R≪R_{sheet} in a smooth rigid substrate, addressing the effects of boundary conditions at the hole's edge. Introducing a basic theoretical model for the van der Waals (vdW) sheet-substrate attraction, we demonstrate the dramatic effect of replacing the clamping condition (Schwerin model) with a sliding condition, whereby the supported part of the sheet is allowed to slide towards the indenter and relax the induced hoop compression through angstrom-scale deflections from the thermodynamic equilibrium (determined by the vdW potential). We highlight the possibility that the indentation force F may not exhibit the commonly anticipated cubic dependence on the indentation depth (F∝δ^{3}), in which the proportionality constant is governed by the sheet's stretching modulus and the hole's radius R, but rather a pseduolinear response F∝δ, whereby the proportionality constant is governed by the bending modulus, the vdW attraction, and the sheet's size R_{sheet}≫R.

Recent development in friction of 2D materials: from mechanisms to applications

Two-dimensional (2D) materials with a layered structure are excellent candidates in the field of lubrication due to their unique physical and chemical properties, including weak interlayer interaction and large specific surface area. For the last few decades, graphene has received lots of attention due to its excellent properties. Besides graphene, various new 2D materials (including MoS₂, WS₂, WSe₂, NbSe₂, NbTe₂, ReS₂, TaS₂and h-BN etc.) are found to exhibit a low coefficient of friction at the macro- and even micro-scales, which may lead to widespread application in the field of lubrication and anti-wear. This article focuses on the latest development trend in 2D materials in the field of tribology. The review begins with a summary of widely accepted nano-scale friction mechanisms contain surface friction mechanism and interlayer friction mechanism. The following sections report the applications of 2D materials in lubrication and anti-wear as lubricant additives, solid lubricants, and composite lubricating materials. Finally, the research prospects of 2D materials in tribology are presented.

Van der Waals interaction affects wrinkle formation in two-dimensional materials

Nonlinear mechanics of solids is an exciting field that encompasses both beautiful mathematics, such as the emergence of instabilities and the formation of complex patterns, as well as multiple applications. Two-dimensional crystals and van der Waals (vdW) heterostructures allow revisiting this field on the atomic level, allowing much finer control over the parameters and offering atomistic interpretation of experimental observations. In this work, we consider the formation of instabilities consisting of radially oriented wrinkles around mono- and few-layer "bubbles" in two-dimensional vdW heterostructures. Interestingly, the shape and wavelength of the wrinkles depend not only on the thickness of the two-dimensional crystal forming the bubble, but also on the atomistic structure of the interface between the bubble and the substrate, which can be controlled by their relative orientation. We argue that the periodic nature of these patterns emanates from an energetic balance between the resistance of the top membrane to bending, which favors large wavelength of wrinkles, and the membrane-substrate vdW attraction, which favors small wrinkle amplitude. Employing the classical "Winkler foundation" model of elasticity theory, we show that the number of radial wrinkles conveys a valuable relationship between the bending rigidity of the top membrane and the strength of the vdW interaction. Armed with this relationship, we use our data to demonstrate a nontrivial dependence of the bending rigidity on the number of layers in the top membrane, which shows two different regimes driven by slippage between the layers, and a high sensitivity of the vdW force to the alignment between the substrate and the membrane.

Out-of-Plane Deformations Determined Mechanics of Vanadium Disulfide (VS2) Sheets

The rapid development of two-dimensional (2D) materials has significantly broadened the scope of 2D science in both fundamental scientific interests and emerging technological applications, wherein the mechanical properties play an indispensably key role. Nevertheless, particularly challenging is the ultrathin nature of 2D materials that makes their manipulations and characterizations considerably difficult. Herein, thanks to the excellent flexibility of vanadium disulfide (VS₂) sheets, their susceptibility to out-of-plane deformation is exploited to realize the controllable loading and enable the accurate measurements of mechanical properties. In particular, the Young's modulus is estimated to be 44.4 ± 3.5 GPa, approaching the lower limit for 2D transition metal dichalcogenides (TMDs). We further report the first measurement of thickness-dependent bending rigidity of VS₂, which deviates from the prediction of the classical continuum mechanics theory. Additionally, a deeper understanding of the mechanics within two dimensions also facilitates the modulation of strain-coupled physics at the nanoscale. Our Raman measurements showed the Grüneisen parameters for VS₂ were determined for the first time to be γ_E2g¹ ≈ 0.83 and γ_A1g ≈ 0.32.

Construction of Position-Controllable Graphene Bubbles in Liquid Nitrogen with Assistance of Low-Power Laser

Graphene bubbles (GBs) are of significant interest owing to their distinguished electrical, optical, and magnetic properties. GBs can also serve as high-pressure reaction vessels to numerous chemical reactions. However, previous strategies to produce GBs are relatively elaborate and random. Therefore, their potential applications are severely restricted. Here, a facile and effective protocol is proposed to construct position-controllable GBs in liquid nitrogen (LN) with the assistance of laser and graphene wrinkles. Specifically, a film of graphene mounted on a SiO₂ substrate (G@SiO₂) is subjected to irradiation by a low-power laser in LN and then many GBs emerge from the surface of G@SiO₂. Most impressively, the domain where GBs arise is the position of the laser beam spot. Hence, we demonstrated that the high collimation of laser facilitates the position definition of GBs. The microscopic results indicate that some GBs split into three parts when they were subjected to irradiation by an electron. Meanwhile, some GBs degenerate into pores with a diameter of 500 nm when they are exposed to air. To grasp the properties of GBs in depth, the molecular dynamics (MD) simulations are performed, and the corresponding results indicate that temperature has very little impact on the GBs' shape. A phase transition process of the substance inside GBs is also revealed. Moreover, a two-dimensional (2D) solid nitrogen is discovered by MD simulations. The simplicity of our protocol paves the way to engineer high-pressure microreaction vessels and fabricate porous graphene membranes.

Preparation of Twisted Bilayer Graphene via the Wetting Transfer Method

Assembling monolayers into a bilayer system unlocks the rotational free degree of van der Waals (vdW) homo/heterostructure, enabling the building of twisted bilayer graphene (tBLG) which possesses novel electronic, optical, and mechanical properties. Previous methods for preparation of homo/heterstructures inevitably leave the polymer residue or hexagonal boron nitride (h-BN) mask, which usually obstructs the measurement of intrinsic mechanical and surface properties of tBLG. Undoubtedly, to fabricate the designable tBLG with clean interface and surface is necessary but challenging. Here, we propose a simple and handy method to prepare atomically clean twisted bilayer graphene with controllable twist angles based on wetting-induced delamination. This method can transfer tBLG onto a patterned substrate, which offers an excellent platform for the observation of physical phenomena such as relaxation of moiré pattern in marginally tBLG. These findings and insight should ultimately guide the designable packaging and atomic characterization of the two-dimensional (2D) materials.

Heterogeneous deformation of two-dimensional materials for emerging functionalities

Atomically thin 2D materials exhibit strong intralayer covalent bonding and weak interlayer van der Waals interactions, offering unique high in-plane strength and out-of-plane flexibility. While atom-thick nature of 2D materials may cause uncontrolled intrinsic/extrinsic deformation in multiple length scales, it also provides new opportunities for exploring coupling between heterogeneous deformations and emerging functionalities in controllable and scalable ways for electronic, optical, and optoelectronic applications. In this review, we discuss (i) the mechanical characteristics of 2D materials, (ii) uncontrolled inherent deformation and extrinsic heterogeneity present in 2D materials, (iii) experimental strategies for controlled heterogeneous deformation of 2D materials, (iv) 3D structure-induced novel functionalities via crumple/wrinkle structure or kirigami structures, and (v) heterogeneous strain-induced emerging functionalities in exciton and phase engineering. Overall, heterogeneous deformation offers unique advantages for 2D materials research by enabling spatial tunability of 2D materials' interactions with photons, electrons, and molecules in a programmable and controlled manner.

Effect of anomalous elasticity on bubbles in van der Waals heterostructures

It is shown that the anomalous elasticity of membranes affects the profile and thermodynamics of a bubble in van der Waals heterostructures. Our theory generalizes the nonlinear plate theory as well as the membrane theory of the pressurised blister test to incorporate the power-law scale dependence of the bending rigidity and Young's modulus of a two-dimensional crystalline membrane. This scale dependence, caused by long-range interaction of relevant thermal fluctuations (flexural phonons), is responsible for the nonlinear Hooke law observed recently in graphene. It is shown that this anomalous elasticity affects the dependence of the maximal height of the bubble as a function of its radius and temperature. We determine the characteristic temperature above which the anomalous elasticity is important. It is suggested that, for graphene-based van der Waals heterostructures, the predicted anomalous regime is experimentally accessible at room temperature.

Bending of Multilayer van der Waals Materials

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 (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_{graphene}>E_{hBN}>E_{MoS_{2}}), but the bending rigidity follows an opposite trend, D_{graphene}<D_{hBN}<D_{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.

Programmable graphene nanobubbles with three-fold symmetric pseudo-magnetic fields

Graphene nanobubbles (GNBs) have attracted much attention due to the ability to generate large pseudo-magnetic fields unattainable by ordinary laboratory magnets. However, GNBs are always randomly produced by the reported protocols, therefore, their size and location are difficult to manipulate, which restricts their potential applications. Here, using the functional atomic force microscopy (AFM), we demonstrate the ability to form programmable GNBs. The precision of AFM facilitates the location definition of GNBs, and their size and shape are tuned by the stimulus bias of AFM tip. With tuning the tip voltage, the bubble contour can gradually transit from parabolic to Gaussian profile. Moreover, the unique three-fold symmetric pseudo-magnetic field pattern with monotonous regularity, which is only theoretically predicted previously, is directly observed in the GNB with an approximately parabolic profile. Our study may provide an opportunity to study high magnetic field regimes with the designed periodicity in two dimensional materials.