Mechanical Properties Of 2D Materials Research Articles

Nanomaterials Based Micro/Nanoelectromechanical System (MEMS and NEMS) Devices.

The micro- and nanoelectromechanical system (MEMS and NEMS) devices based on two-dimensional (2D) materials reveal novel functionalities and higher sensitivity compared to their silicon-base counterparts. Unique properties of 2D materials boost the demand for 2D material-based nanoelectromechanical devices and sensing. During the last decades, using suspended 2D membranes integrated with MEMS and NEMS emerged high-performance sensitivities in mass and gas sensors, accelerometers, pressure sensors, and microphones. Actively sensing minute changes in the surrounding environment is provided by means of MEMS/NEMS sensors, such as sensing in passive modes of small changes in momentum, temperature, and strain. In this review, we discuss the materials preparation methods, electronic, optical, and mechanical properties of 2D materials used in NEMS and MEMS devices, fabrication routes besides device operation principles.

Natural overlaying behaviors push the limit of planar cyclic deformation performance in few‐layer MoS2 nanosheets

AbstractAs a typical two‐dimensional (2D) transition metal dichalcogenides (TMDCs) material with nonzero band gap, MoS2 has a wide range of potential applications as building blocks in the field of nanoelectronics. The stability and reliability of the corresponding nanoelectronic devices depend critically on the mechanical performance and cyclic reliability of 2D MoS2. Although an in situ technique has been used to analyze the mechanical properties of 2D materials, the cyclic mechanical behavior, that is, fatigue, remains a major challenge in the practical application of the devices. This study was aimed at analyzing the planar cyclic performance and deformation behavior of three‐layer MoS2 nanosheets (NSs) using an in situ transmission electron microscopy (TEM) variable‐amplitude uniaxial low‐frequency and cyclic loading–unloading tensile acceleration test. We also elucidated the strengthening effect of the natural overlaying affix fragments (other external NSs) or wrinkle folds (internal folds from the NS itself) on cycling performances and service life of MoS2 NSs by delaying the whole process of fatigue crack initiation, propagation, and fracture. The results have been confirmed by molecular dynamics (MDs) simulations. The overlaying enhancement effect effectively ensures the long‐term reliability and stability of nanoelectronic devices made of few‐layer 2D materials.image

A Hybrid‐Density Functional Theory Study of Intrinsic Point Defects in MX2 (M = Mo, W; X = S, Se) Monolayers

Defects can strongly influence the electronic, optical, and mechanical properties of 2D materials, making defect stability under different thermodynamic conditions crucial for material–property engineering. Herein, an account of the structural and electronic characteristics of point defects in monolayer transition metal dichalcogenides MX2 with M = Mo/W and X = S/Se is investigated through density functional theory using the hybrid HSE06 exchange–correlation functional including many‐body dispersion corrections. For the simulation of charged defects, a charge compensation scheme based on the virtual crystal approximation (VCA) is employed. The study relates the stability and the electronic structure of charged vacancy defects in monolayer MoS2 to an explicit calculation of the S monovacancy in MoS2 supported on Au(111), and finds convincing indication that the defect is negatively charged. Moreover, it is shown that the finite‐temperature vibrational contributions to the free energy of defect formation can change the stability transition between adatoms and monovacancies by 300–400 K. Finally, defect vibrational properties are probed by calculating a tip‐enhanced Raman scattering image of a vibrational mode of a MoS2 cluster with and without an S monovacancy.

Mech2d: An Efficient Tool for High-Throughput Calculation of Mechanical Properties for Two-Dimensional Materials.

Two-dimensional (2D) materials have been a research hot topic in the passed decades due to their unique and fascinating properties. Among them, mechanical properties play an important role in their application. However, there lacks an effective tool for high-throughput calculating, analyzing and visualizing the mechanical properties of 2D materials. In this work, we present the mech2d package, a highly automated toolkit for calculating and analyzing the second-order elastic constants (SOECs) tensor and relevant properties of 2D materials by considering their symmetry. In the mech2d, the SOECs can be fitted by both the strain-energy and stress-strain approaches, where the energy or strain can be calculated by a first-principles engine, such as VASP. As a key feature, the mech2d package can automatically submit and collect the tasks from a local or remote machine with robust fault-tolerant ability, making it suitable for high-throughput calculation. The present code has been validated by several common 2D materials, including graphene, black phosphorene, GeSe2 and so on.

Interfacial Degradation and Pattern Evolution of Exfoliated Graphene by Cyclic Mechanical Loading

AbstractThe interfacial interactions between 2D materials and polymer substrates receive increasing interest due to the surge of flexible electronics, multifunctional coatings, and nanocomposites. Although the strain effect on electrical, optical, and mechanical properties of 2D materials is extensively investigated, understanding the interfacial mechanics of 2D material‐polymer systems by dynamic loading is still a challenge. Here, the interfacial degradation and pattern evolution of mechanically exfoliated single‐ and few‐layer graphene on polydimethylsiloxane (PDMS) substrates by cyclic mechanical loading, are reported. It is found that the tensile strain leads to interfacial slippage between graphene and PDMS, whereas the compressive strain can be transferred to graphene with a transfer efficiency above 80%. Through cyclic loading, the graphene surface is seriously deformed by formation of multiple instability patterns including wrinkles and cracks. The morphological characteristic and evolution mechanism of the wrinkles and cracks are analyzed and discussed in detail. The interfacial adhesion energy is evaluated by wrinkle profiles and it decreases from ≈23 to ≈2 mJ m−2 as the cycle number increases. This work can promote better understanding of the interfacial effect of 2D materials on polymer substrates and controllable fabrication of various wrinkled or crumpled surfaces of 2D functional materials by cyclic mechanical loading.

Structural Spectrum of 2D Materials in Solution: Toward Establishing 2D Assemblies’ Digital Factory

AbstractThe numerous hierarchical architectures of 2D assemblies endow them with a new dimension to realize novel properties. From theoretical perspective, freedoms stem from in‐plane and out‐plane mechanical properties of 2D materials separately, which makes 2D materials embrace more than one “persistence length” giving rise to the diverse morphologies. However, the understanding of 3D architecture formation in 2D assemblies is still in its infancy. In fact, there is even no theoretical classification or reference to help clarify structural difference among numerous experimental obtained 2D assemblies. Based on the theoretical model composed by 2D sheets and Lennard‐Jones liquids, solution concentration dependence of 2D materials conformation is systematically studied, and a ln K behavior is uncovered that can realize the theoretical conformation prediction of 2D materials. More importantly, the digital production line (solution processing procedure) is set up toward establishing the 2D assemblies’ digital factory. The obtained structures may provide a reference to 2D assemblies, which benefits the understanding of the structural difference among different experiments and even help to guide the experimental design of 2D assemblies with targeted architectures and properties.

Mechanical properties characterization of 2D materials via pressure bulge testing

Pressure bulge testing is one of the standard techniques for characterizing the mechanical properties of thin films, whereas it is far less often used to characterize the mechanical properties of 2D materials. In the present work, the effectiveness of bulge testing on determining the mechanical properties of 2D materials is systematically investigated using numerical analysis. After assuming 2D materials as continuum thin films, we start by simulating the relationship between the pressure difference across the suspended film and the film deflection, and then fit the results with analytical models to extract the elastic modulus of the film. It should be noted that the clamped, pre-stretched film widely assumed in the existing analytical model is not appropriate for atomically thin materials; instead, freestanding 2D materials are actually slack in bulge testing due to the delamination of their adhesive boundary condition. Therefore, the initially unstressed flat films, pre-stretched films and slack films are investigated in the present work, and the Poisson’s ratio effect is considered to investigate the effectiveness of bulge testing for most 2D materials. It is found that bulge testing can be an effective approach to characterize the mechanical properties of 2D materials.

Effectiveness of the analytical models used in standard techniques for mechanical property characterization of 2D materials

Two dimensional (2D) materials are usually assumed to be continuum thin films to study their mechanical behavior. Freestanding indentation testing and pressure bulge testing are two standard techniques for characterizing the mechanical properties of thin films. Compared with the former, the latter is far less often used to characterize the elastic moduli of 2D materials, even though there is no solid evidence to show that the former is more effective than the latter. In the present work, the effectiveness of the analytical models adopted in both approaches on determining the elastic moduli of 2D materials are investigated using numerical analysis, which can be evaluated based upon the accuracy of the determined elastic moduli, and the effects of Poisson’s ratio and the applied loading range are also considered. To account for the effect of the adhesive boundary condition of freestanding 2D materials in the testing, the numerical simulations of the initially unstressed samples, pre-stretched samples and slack samples are all analyzed in the present work. It is found that the bulge testing model is actually more effective than the indentation model on determining the mechanical properties of 2D materials.

Atomistic insights into the mechanical anisotropy and fragility of monolayer fullerene networks using quantum mechanical calculations and machine-learning molecular dynamics simulations

In this work, we comprehensively study the mechanical properties of the newly synthesized monolayer quasi-hexagonal-phase fullerene (qHPF) membrane [Hou et al., 2022] under uniaxial tension by using quantum mechanical density-functional-theory (DFT) calculations and molecular dynamics (MD) simulations with a machine-learned neuroevolution potential (NEP). The elastic properties and fracture behaviors of monolayer qHPF are found to be strongly anisotropic due to the different properties between the inter-fullerene C–C single bonds and [2 + 2] cycloaddition bonds. Moreover, the tensile strength and fracture strain of monolayer qHPF are much smaller than those of any other existing two-dimensional (2D) carbon crystals. The very small tensile strength or fracture strain is ascribed to the inhomogeneous deformation of the stretched monolayer qHPF, which originates from the stiffness difference between the soft inter-fullerene bonds and the rigid intra-fullerene bonds. Compared with DFT calculations at the ground state, the NEP-based extensive MD simulations predict a much smaller tensile strength and fracture strain for monolayer qHPF due to their consideration of the effects of temperature and membrane size. Our work not only reveals the underlying mechanism of the fracture behaviors of monolayer fullerene networks from an atomistic perspective, but also shows the effectiveness and accuracy of the NEP approach in determining the mechanical properties of 2D materials in the realistic situations.

Deep‐Learning‐Based Microscopic Imagery Classification, Segmentation, and Detection for the Identification of 2D Semiconductors

Abstract2D materials and their heterostructures are prominent for fabricating next‐generation optical and photonic devices. The optical, electrical, and mechanical properties of 2D materials largely depend on atomic layer numbers. Although machine learning techniques are implemented to identify large‐area thickness distribution using microscopic images, the existing work mainly focuses on rough identification of thicknesses with in‐house datasets which limits fair and comprehensive comparisons of new machine learning approaches. Here, first a microscopic dataset is collected and released for three fundamental image processing tasks including multilabel classification, segmentation, and detection. Then three deep‐learning architectures DenseNet, U‐Net, and Mask‐region convolutional neural network (RCNN) are benchmarked on three tasks and their robustness is evaluated on the augmented 2D microscopic images with different optical contrast variations. Deep learning models are trained and evaluated to identify mono‐, bi‐, tri‐, multilayer and bulk flakes using microscopic images of MoS2 fabricated on the SiO2/Si substrate by chemical vapor deposition. The relation between model performances and statistics of datasets is studied based on the international commission on illumination (CIE) 1931 color space and red, green, blue (RGB) histograms of optical contrast differences. Finally, the robust pretrained models are integrated into a graphic user interface for the on‐site use of full field‐of‐view images captured by bright‐field microscopes.

Anisotropic Mechanics of 2D Materials

Anisotropic mechanics of van der Waals (vdWs) materials offers opportunity to peel off individual atomic layers, initiating a 2D revolution in the fields of materials science, physics, and chemistry. The elasticity, bending, and fracture strength of most of their 2D derivatives are also orientation‐dependent, which not only determines the reliability of devices based on 2D materials but also offers a vast playground for atomic manufacturing with tunable functions. Therefore, a comprehensive understanding of the anisotropic mechanical properties of 2D materials is imminent. In this review, the anisotropic mechanical properties of 2D materials are summarized in attempt to capture the current progress in this field, as well as the route toward their applications. Following a brief discussion of the anisotropic lattice structures of 2D materials, unique experimental methodologies that have been developed to characterize their anisotropic mechanics are discussed. Then, the review pivots on recent processes in anisotropic elastic, fracture, friction, and bending properties of 2D materials. Unique applications of these anisotropic properties, such as mechanical fabrication of atomic precision, as well as anisotropic strain‐induced piezoelectric and band modulation, are further highlighted. Finally, besides emphasizing the need for breakthrough in anisotropic mechanics, prospects for the developments of this field are suggested.

RF Sputtered Nb-Doped MoS2 Thin Film for Effective Detection of NO2 Gas Molecules: Theoretical and Experimental Studies.

Doping plays a significant role in affecting the physical and chemical properties of two-dimensional (2D) dichalcogenide materials. Controllable doping is one of the major factors in the modification of the electronic and mechanical properties of 2D materials. MoS2 2D materials have gained significant attention in gas sensing owing to their high surface-to-volume ratio. However, low response and recovery time hinder their application in practical gas sensors. Herein, we report the enhanced gas response and recovery of Nb-doped MoS2 gas sensor synthesized through physical vapor deposition (PVD) toward NO2 at different temperatures. The electronic states of MoS2 and Nb-doped MOS2 monolayers grown by PVD were analyzed based on their work functions. Doping with Nb increases the work function of MoS2 and its electronic properties. The Nb-doped MoS2 showed an ultrafast response and recovery time of trec = 30/85 s toward 5 ppm of NO2 at their optimal operating temperature (100 °C). The experimental results complement the electron difference density functional theory calculation, showing both physisorption and chemisorption of NO2 gas molecules on niobium substitution doping in MoS2.

Efficient prediction of temperature-dependent elastic and mechanical properties of 2D materials

An efficient automated toolkit for predicting the mechanical properties of materials can accelerate new materials design and discovery; this process often involves screening large configurational space in high-throughput calculations. Herein, we present the ElasTool toolkit for these applications. In particular, we use the ElasTool to study diversity of 2D materials and heterostructures including their temperature-dependent mechanical properties, and developed a machine learning algorithm for exploring predicted properties.

First-principles study of stability and electronic properties of single-element 2D materials

We have estimated stability of single-element 2D materials (C2, N2, Si2, P2, Ge2, As2, Sn2, Sb2, Pb2, and Bi2) by ab initio calculations. The calculations of structural and mechanical properties of 2D materials were performed using the VASP software package. The results of calculations of stiffness tensors, Young's modulus, and Poisson's ratios show that all studied single-element 2D materials are mechanically stable. Dynamic stability was investigated by calculating the phonon dispersion of the materials using the finite displacement method. Only Pb2 has imaginary modes in the phonon dispersion curves and therefore it has dynamic unstable structure at low temperatures. The analysis of the band structures indicates the presence of insulators (N2), semiconductors (P2, As2, Bi2, Sb2), semimetals, and metals among the studied group of single-element 2D materials.

Two-Dimensional Nanofluidic Membranes toward Harvesting Salinity Gradient Power.

The salinity gradient between seawater and river water has been identified as a promising, clean, renewable, and sustainable energy source that can be converted into electricity using ion-selective membranes in a reverse electrodialysis (RED) configuration. However, the major hindrance to current salinity gradient power (SGP) conversion is its poor energy efficiency due to the use of low-performance membrane processes, which affords power for neither miniaturized devices nor industrial-level applications. Nanofluidics, which combines strong confinement and surface charge effects at the nanoscale, contributes to novel transport properties, including excellent ion selectivity and high ion throughput; thus, nanofluidics may lead to technological breakthroughs and act as an emerging platform for harnessing SGP. Recently, two-dimensional (2D) materials have provided impressive energy extraction performance and further insight into fundamental transport mechanisms and theoretical feasibility. To reach the commercialization benchmark and real-world applications, an array of nanopores and channels that can be scaled up to industrial sizes is in high demand; additionally, it remains challenging to develop macroscale nanofluidic membranes that meet the "selectivity versus throughput" dual requirement. In the first section, we start with our understanding of the underlying mechanism of ion-channel interactions and transport characteristics in nanofluidic channel systems from the microscale to the macroscale. We review our recent efforts in this field by constructing a heterojunction with asymmetric ion transport behavior that generates rectification of the ion flux and creates an osmotic diode, which is composed of two nanofluidic layers with opposite polar charges and different chemical compositions. Another efficient way to improve the performance of the system is introducing charged functional materials intercalated into laminar 2D nanosheets. The intercalated nanofluidic material can be explained by two classical models to account for the synergistic effects that (i) improve the stability and mechanical properties of 2D materials with a fixed interlayer spacing and (ii) provide space charge for modulating ion diffusion; both of these effects contribute to its considerable energy conversion performance. Further, layer-by-layer membranes are superior to traditional membranes consisting of a simple stack because they retain their repulsion effect toward co-ions, largely strengthening the efficiency of ion separation and conversion. In particular, we highlight our views on the role of the 2D phase structure (e.g., semiconductor 2H phase and metallic 1T phase) in which the two phases differ from each other in physical and chemical properties, including ionic conductance, surface charge, and wetting, thereby presenting a state-of-the-art avenue for controlling ion transport. In view of the nature of 2D materials, we also report improved osmotic energy harvesting by exploiting the photoinduced heat gradient and electrons that increase ion mobility and surface charge, respectively. Finally, we point out specific research topics in which a combined project can certainly come into the limelight. For example, we discuss the combination of SGP with desalination systems and water splitting. We expect that this Account will stimulate further efforts toward functionalized 2D nanoporous materials and facilitate interdisciplinary efforts in chemistry, material engineering, environmental science, and nanotechnology.

In-situ investigation of the elastic behavior of two-dimensional MoS2 on flexible substrate by nanoindentation

Mechanical properties are a crucial factor for the application of two-dimensional (2D) materials in flexible electronic and optoelectronic devices. Until now, mechanical properties of 2D materials have been primarily investigated from the load–deformation relationship of freely suspended 2D nanofilms by in-situ atomic force microscope probe nanoindentation measurements. Herein, we acquired the mechanical behavior of monolayer and few-layer molybdenum disulfide (MoS2) via applying a point load on 2D MoS2 on a soft poly-dimethylsiloxane (PDMS) substrate. The primary objective of this work is to study the elastic behavior of 2D MoS2 based on the indentation deformation of the 2D MoS2/PDMS substrate. Nanoindentation behavior of 2D MoS2 mounted on PDMS substrate is also simulated by finite element method. Combining nanoindentation experiments with theoretical simulations, we can understand the mechanical behavior of 2D materials on flexible substrates perfectly well. This work provides a new method to characterize the mechanical response of atomically ultrathin 2D nanofilms with substrate-binding effect, which is essential to promote flexible devices based on functional 2D materials.

Experimental nanomechanics of 2D materials for strain engineering

The past 2 decades have witnessed the explosion of research on two-dimensional (2D) materials, where notable efforts have been made in the synthesis and design of a wide spectrum of applications. To understand their mechanical properties and responses triggered by deformation, the prerequisites for reliable applications under realistic service conditions, novel experimental methods have to be developed due to the limitations of traditional bulk mechanical testing for atomically-thin structures. Besides, the nearly-ideal 2D crystalline structures of many 2D materials endow them the great capability of deformation, showing promising potentials in “strain engineering” and “interface engineering” applications. This review summaries several representative approaches in experimental nanomechanics and corresponding progresses in the characterization of structural and mechanical properties of 2D materials, with the aim to provide insights into the instrumental design for nanomechanical tests. In addition, examples of strain-tuned material behaviors and changes in their performance are also discussed to demonstrate the significance of the nanomechanical approach for functional device design and applications.

Two-dimensional Janus Ti3C2FxO2-x MXene with tunable electronic and mechanical properties

In two-dimensional (2D) Janus materials, the asymmetric surface termination structure can significantly enhance material functionality. Here we explore the combined influence of surface termination composition and disorder on the electronic and mechanical properties of Janus Ti3C2Fxn O2-x (x = 0.5, 1, or 1.5, n = 1–3). Increasing compositions of surface O atoms induce weak C-p-Ti-d coupling due to a relatively strong interaction between the surface Ti and O atoms; while the presence of F in the mixed surface termination considerably enhances the C-p-Ti-d coupling strength compared with a purely F-terminated structure. Asymmetric disordered surface functionalization influences electronic structure, creating controllable mechanical properties. Mixed surface termination leads to a significant enhancement in the elastic constant. Janus Ti3C2F1O configuration is found to possess superior flexibility, with 31% critical strain, especially useful in practical large-magnitude-strain engineering. Our results provide a strategy to tune the electronic and mechanical properties of 2D materials.

Two-Dimensional Janus Ti <sub>3</sub>C <sub>2</sub>F <sub>x</sub>O <sub>2-X</sub> MXene with Tunable Electronic and Mechanical Properties

In two-dimensional (2D) Janus materials, the asymmetric surface termination structure can significantly enhance material functionality. Here we explore the combined influence of surface termination composition and disorder on the electronic and mechanical properties of Janus Ti3C2F n x O2-x (x = 0.5, 1, or 1.5, n = 1–3). Increasing compositions of surface O atoms induce weak C-p-Ti-d coupling due to a relatively strong interaction between the surface Ti and O atoms; while the presence of F in the mixed surface termination considerably enhances the C-p-Ti-d coupling strength compared with a purely F-terminated structure. Asymmetric disordered surface functionalization influences electronic structure, creating controllable mechanical properties. Mixed surface termination leads to a significant enhancement in the elastic constant. Janus Ti3C2F1O configuration is found to possess superior flexibility, with 31% critical strain, especially useful in practical large-magnitude-strain engineering. Our results provide a strategy to tune the electronic and mechanical properties of 2D materials.

REVIEW OF THE APPLICATION OF ATOMIC FORCE MICROSCOPY IN TESTING THE MECHANICAL PROPERTIES OF TWO-DIMENSIONAL MATERIALS

Graphene and other two-dimensional (2D) materials possess various excellent properties and hold great promises for next generation of electronic devices and other applications. The mechanical properties are of fundamental importance in the research and application of 2D materials. Despite the fact that 2D materials have been extensively investigated in the past two decades, efforts on the mechanical properties are strikingly lacking and vastly needed. Atomic force microscopy (AFM) is one of the most widely used tools for the mechanical characterizations of low-dimensional materials. Particularly, the AFM-based nano-indentation technique has been extensively employed to explore the mechanical properties of 2D materials. In this review, we first introduce the basic backgrounds of 2D materials and atomic force microscopy. The mechanism and theoretical background of AFM-based nano-indentation are then demonstrated. In the second part, we review the research work by employing nano-indentation on studying the in-plane mechanical properties of 2D materials. The measurement errors of AFM-based nano-indentation and their origins are also discussed. Nano-indentation is perfectly suitable for the in-plane/intralayer mechanical measurement but also greatly limited in probing the out-of-plane/interlayer elasticity, due to the extreme anisotropy of 2D materials. Therefore, in the third part, we introduce an unconventional AFM-based technique - Angstrom-indentation which allows for sub-nm deformation on 2D materials. With such a shallow indentation depth comparable to the interlayer spacing of 2D materials, Angstrom-indentation is capable of measuring and tuning the interlayer van der Waals interactions in 2D materials. The interlayer elasticities of graphene and graphene oxide measured by Angstrom-indentation are discussed as examples in the third part. In the final part, we give a quick overview of a new type of 2D material - van der Waals heterostructure and its novel mechanical properties. We also discuss the potential application of A-indentation in the investigation of the mechanical properties of van der Waals heterostructures.