Generalized two-variable plate theory for multi-layered graphene sheets with arbitrary boundary conditions

In the present study, the free vibration, mechanical buckling and thermal buckling analyses of multi-layered graphene sheets (MLGSs) are investigated. Eringen’s nonlocal elasticity equations are incorporated in new two-variable plate theories accounting for small-scale effects. The MLGSs are taken to be perfectly bonded to the surrounding medium. The governing differential equations of this model are solved analytically under various boundary conditions and taking into account the effect of van der Waals forces between adjacent layers. New functions for the displacements are proposed here to satisfy the different boundary conditions. Comparison of the results with those being in the open literature is made. This comparison illustrates that the present scheme yields very accurate results. Furthermore, the influences of nonlocal coefficient, moduli of the surrounding elastic medium and aspect ratio on the frequencies and buckling of the embedded MLGSs are examined.     

Vibration characteristics of embedded multi-layered graphene sheets with different boundary conditions via nonlocal elasticity

A nonlocal elastic plate model accounting for the small scale effects is developed to investigate the vibrational behavior of multi-layered graphene sheets under various boundary conditions. Based upon the constitutive equations of nonlocal elasticity, derived are the Reissner–Mindlin-type field equations which include the interaction of van der Waals forces between adjacent and non-adjacent layers and the reaction from the surrounding media. The set of coupled governing equations of motion for the multi-layered graphene sheets are then numerically solved by the generalized differential quadrature method. The present analysis provides the possibility of considering different combinations of layerwise boundary conditions in a multi-layered graphene sheet. Based on exact solution, explicit expressions for the nonlocal frequencies of a double-layered graphene sheet with all edges simply supported are also obtained. The results from the present numerical solution, where possible, are indicated to be in excellent agreement with the existing data from the literature.     

Influence of initial shear stress on the vibration behavior of single-layered graphene sheets embedded in an elastic medium based on Reddy's higher-order shear deformation plate theory

In this article, the small-scale effect on the vibration behavior of orthotropic single-layered graphene sheets is studied based on the nonlocal Reddy's plate theory embedded in elastic medium considering initial shear stress. Elastic theory of the graphene sheets is reformulated using the nonlocal differential constitutive relations of Eringen. To simulate the interaction between the graphene sheet and surrounding elastic medium we used both Winkler-type and Pasternak-type foundation models. The effects of initial shear stress and surrounding elastic medium and boundary conditions on the vibration analysis of orthotropic single-layered graphene sheets are studied considering five different boundary conditions. Numerical approach of the obtained equation is derived by differential quadrature method. Effects of shear stress, nonlocal parameter, size of the graphene sheets, stiffness of surrounding elastic medium, and boundary conditions on vibration frequency rate are investigated. The results reveal that as the stiffness of the surrounding elastic medium increases, the nonlocal effect decreases. Further, the nonlocal effect increases as the size of the graphene sheet is decreased. It is also found that the frequency ratios decrease with an increase in vibration modes.     

Nanoscale vibration analysis of embedded multi-layered graphene sheets under various boundary conditions

The present article deals with the vibrational analysis of multi-layered graphene sheets with different boundary conditions amongst sheets. An elastic multiple-plate model is utilized in which the nested plates are coupled with each other through the van der Waals interlayer force. The interaction of van der Waals forces between adjacent and non-adjacent layers and the reaction from the surrounding media are included in the Reissner–Mindlin-type field equations on which the theoretical formulation is based. The set of coupled equations of motion for the multi-layered graphene sheets is then solved by the generalized differential quadrature method. The numerical analysis presented herein provides the possibility of considering various combinations of layerwise boundary conditions in a multi-layered graphene sheet. Based on exact solution, explicit formulas for the frequencies of a double-layered graphene sheet with all edges simply supported are also obtained. The results of the present numerical solution are shown to be in excellent agreement with those of exact solution for simply supported graphene sheets.     

Nanoscale modeling of an embedded multi-shell fullerene and its application to vibrational analysis

In this paper, nanoscale modeling of a multi-shell fullerene embedded in an elastic medium and its application to vibrational analysis is investigated. The spherical layers of the multi-shell fullerene are concentrically nested, with carbon-carbon van der Waals interactions between them. Also, the whole multi-shell fullerene is influenced by polymer-carbon van der Waals forces from the surrounding elastic medium. The elasticity generated by the carbon-carbon bonds is assumed to be distributed isotropically over the fullerene surfaces. Following derivation of explicit equations for the motion of the multi-shell fullerene, vibrational behavior of a double-shell fullerene is analyzed and resonant frequencies and the associated mode shapes are determined.     

Magnetic Proximity Effect in Graphene/CrBr3 van der Waals Heterostructures

2D van der Waals heterostructures serve as a promising platform to exploit various physical phenomena in a diverse range of novel spintronic device applications. Efficient spin injection is the prerequisite for these devices. The recent discovery of magnetic 2D materials leads to the possibility of fully 2D van der Waals spintronics devices by implementing spin injection through the magnetic proximity effect (MPE). Here, the investigation of MPE in 2D graphene/CrBr₃ van der Waals heterostructures is reported, which is probed by the Zeeman spin Hall effect through non-local measurements. Quantitative estimation of the Zeeman splitting field demonstrates a significant MPE field even in a low magnetic field. Furthermore, the observed anomalous longitudinal resistance changes at the Dirac point R_XX,D with increasing magnetic field near ν = 0 may be attributed to the MPE-induced new ground state phases. This MPE revealed in the graphene/CrBr₃ van der Waals heterostructures therefore provides a solid physics basis and key functionality for next-generation 2D spin logic and memory devices.     

Ultrastrong adhesion of graphene membranes

As mechanical structures enter the nanoscale regime, the influence of van der Waals forces increases. Graphene is attractive for nanomechanical systems because its Young's modulus and strength are both intrinsically high, but the mechanical behaviour of graphene is also strongly influenced by the van der Waals force. For example, this force clamps graphene samples to substrates, and also holds together the individual graphene sheets in multilayer samples. Here we use a pressurized blister test to directly measure the adhesion energy of graphene sheets with a silicon oxide substrate. We find an adhesion energy of 0.45±0.02 J m(-2) for monolayer graphene and 0.31±0.03 J m(-2) for samples containing two to five graphene sheets. These values are larger than the adhesion energies measured in typical micromechanical structures and are comparable to solid-liquid adhesion energies. We attribute this to the extreme flexibility of graphene, which allows it to conform to the topography of even the smoothest substrates, thus making its interaction with the substrate more liquid-like than solid-like.     

Investigation of the vibrational characteristics of double-walled carbon nanotubes/double-layered graphene sheets using the finite element method

This article concerns the investigation of the vibrational behavior of double-walled carbon nanotubes/double-layered graphene sheets junctions using the finite element method. The bonds and atoms are modeled by beam and mass elements, respectively. Moreover, the van der Waals interactions are simulated by spring elements. The effects of the length of the nanotube and the dimensions of the nanosheet on the natural frequencies of the junctions are examined. It is shown that when the boundary conditions are applied on the nanotube, the geometrical parameters of nanotubes have a significant effect on the vibrational behavior of the junctions.     

Dirac Semimetal Heterostructures: 3D Cd3As2 on 2D Graphene

Dirac semimetal is an emerging class of quantum matters, ranging from 2D category, such as, graphene and surface states of topological insulator to 3D category, for instance, Cd₃As₂ and Na₃Bi. As 3D Dirac semimetals typically possess Fermi‐arc surface states, the 2D–3D Dirac van der Waals heterostructures should be promising for future electronics. Here, graphene–Cd₃As₂ heterostructures are fabricated through direct layer‐by‐layer stacking. The electronic coupling results in a notable interlayer charge transfer, which enables us to modulate the Fermi level of graphene through Cd₃As₂. A planar graphene p–n–p junction is achieved by selective modification, which demonstrates quantized conductance plateaus. Moreover, compared with the bare graphene device, the graphene–Cd₃As₂ hybrid device presents large nonlocal signals near the Dirac point due to the charge transfer from the spin‐polarized surface states in the adjacent Cd₃As₂. The results enrich the family of van der Waals heterostructure and should inspire more studies on the application of Dirac/Weyl semimetals in spintronics.     

An analytical approach to determination of bending modulus of a multi-layered graphene sheet

In this paper, the bending modulus of a multi-layered graphene sheet is investigated using a geometrically based analytical approach. For this purpose, a bending potential energy is derived, based on the van der Waals interactions of atoms belonging to the two neighboring sheets of a double-layered graphene sheet. The inter-atomic spacing between the adjacent layers is determined along the line of action of the applied bending moments. The bending potential of the double-layered sheet is calculated by summing up the potentials at discrete hexagons over the length and width of the sheet. A multi-layered graphene sheet is considered as consisting of many stacking double-layers. It is observed that the bending modulus of a multi-layered graphene sheet does not depend on the length of the sheet and is a property for the multi-layered sheet.     

Vibration analysis of orthotropic graphene sheets embedded in Pasternak elastic medium using nonlocal elasticity theory and differential quadrature method

In this paper, the small scale effect on the vibration analysis of orthotropic single layered graphene sheets embedded in elastic medium is studied. Elastic theory of the graphene sheets is reformulated using the nonlocal differential constitutive relations of Eringen. Both Winkler-type and Pasternak-type foundation models are employed to simulate the interaction between the graphene sheet and surrounding elastic medium. Using the principle of virtual work the governing differential equations are derived. Differential quadrature method is employed to solve the governing differential equations for various boundary conditions. Nonlocal theories are employed to bring out the small scale effect of the nonlocal parameter on the natural frequencies of the orthotropic graphene sheets embedded in elastic medium. Further, effects of (i) nonlocal parameter, (ii) size of the graphene sheets, (iii) stiffness of surrounding elastic medium and (iv) boundary conditions on non-dimensional vibration frequencies are investigated.     

Number‐Resolved Single‐Photon Detection with Ultralow Noise van der Waals Hybrid

Van der Waals hybrids of graphene and transition metal dichalcogenides exhibit an extremely large response to optical excitation, yet counting of photons with single‐photon resolution is not achieved. Here, a dual‐gated bilayer graphene (BLG) and molybdenum disulphide (MoS₂) hybrid are demonstrated, where opening a band gap in the BLG allows extremely low channel (receiver) noise and large optical gain (≈10¹⁰) simultaneously. The resulting device is capable of unambiguous determination of the Poissonian emission statistics of an optical source with single‐photon resolution at an operating temperature of 80 K, dark count rate 0.07 Hz, and linear dynamic range of ≈40 dB. Single‐shot number‐resolved single‐photon detection with van der Waals heterostructures may impact multiple technologies, including the linear optical quantum computation.     

Numerical investigation of elastic mechanical properties of graphene structures

The computation of the elastic mechanical properties of graphene sheets, nanoribbons and graphite flakes using spring based finite element models is the aim of this paper. Interatomic bonded interactions as well as van der Waals forces between carbon atoms are simulated via the use of appropriate spring elements expressing corresponding potential energies provided by molecular theory. Each layer is idealized as a spring-like structure with carbon atoms represented by nodes while interatomic forces are simulated by translational and torsional springs with linear behavior. The non-bonded van der Waals interactions among atoms which are responsible for keeping the graphene layers together are simulated with the Lennard-Jones potential using appropriate spring elements. Numerical results concerning the Young’s modulus, shear modulus and Poisson’s ratio for graphene structures are derived in terms of their chilarity, width, length and number of layers. The numerical results from finite element simulations show good agreement with existing numerical values in the open literature.     

Vibration analysis of multi-walled carbon nanotubes using a spring–mass based finite element model

We report a study of the vibrational characteristics of multi-walled carbon nanotubes modeled exclusively using springs and lumped masses. Based on the atomic microstructure of the nanotube, three-dimensional nanoscale spring elements are utilized to simulate the dynamic behavior of each layer of the multi-walled carbon nanotubes. Appropriate spring elements are also developed to model the interlayer interactions and describe the van der Waals potentials between carbon atoms on different layers. Direct application of the physical variables of molecular mechanics theory to the springs is used to simulate the relative translations and rotations between atoms as well as the masses of the carbon atoms. The stiffness and mass matrices of the problem are used to construct the dynamic equilibrium equation. The natural modes of vibration and the corresponding natural frequencies are derived by solving the eigenvalue problem for different support conditions. The present method suggests novel basic modes of vibration, beyond those reported in the literature pertaining to multi-walled carbon nanotubes. The effects on the basic modes and natural frequencies created by van der Waals interactions and geometric parameters such as number of layers and aspect ratio are investigated in the context of elastic support conditions. Comparisons with other theoretical studies reveal very good correlations in terms of fundamental modes and frequencies.     

Magnetically Controlled Growth‐Factor‐Immobilized Multilayer Cell Sheets for Complex Tissue Regeneration

The scaffold‐free cell‐sheet technique plays a significant role in stem‐cell‐based regeneration. Furthermore, growth factors are known to direct stem cell differentiation and enhance tissue regeneration. However, the absence of an effective means to incorporate growth factors into the cell sheets hinders further optimization of the regeneration efficiency. Here, a novel design of magnetically controlled “growth‐factor‐immobilized cell sheets” is reported. A new Fe₃O₄ magnetic nanoparticle (MNP) coated with nanoscale graphene oxide (nGO@Fe₃O₄) is developed to label stem cells and deliver growth factors. First, the nGO@Fe₃O₄ MNPs can be easily swallowed by dental‐pulp stem cells (DPSCs) and have no influence on cell viability. Thus, the MNP‐labeled cells can be organized via magnetic force to form multilayered cell sheets in different patterns. Second, compared to traditional Fe₃O₄ nanoparticles, the graphene oxide coating provides plenty of carboxyl groups to bind and deliver growth factors. Therefore, with these nGO@Fe₃O₄ MNPs, bone‐morphogenetic‐protein‐2 (BMP2) is successfully incorporated into the DPSCs sheets to induce more bone formation. Furthermore, an integrated osteochondral complex is also constructed using a combination of DPSCs/TGFβ3 and DPSCs/BMP2. All these results demonstrate that the new cell‐sheet tissue‐engineering approach exhibits promising potential for future use in regenerative medicine.     

Enhanced Peltier Effect in Wrinkled Graphene Constriction by Nano‐Bubble Engineering

Inspired by the promising applications in thermopower generation from waste heat and active on‐chip cooling, the thermoelectric and electrothermal properties of graphene have been extensively pursued by seeking ingeniously designed structures with thermoelectric conversion capability. The graphene wrinkle is a ubiquitous structure formed inevitably during the synthesis of large‐scale graphene films but the corresponding properties for thermoelectric and electrothermal applications are rarely investigated. Here, the electrothermal Peltier effect from the graphene wrinkle fabricated on a germanium substrate is reported. Peltier cooling and heating across the wrinkle are visualized unambiguously with polarities consistent with p‐type doping and in accordance with the wrinkle spatial distribution. By direct patterning of the nano‐bubble structure, the current density across the wrinkle can be boosted by current crowding to enhance the Peltier effect. The observed Peltier effect can be attributed to the nonequilibrium charge transport by interlayer tunneling across the van der Waals barrier of the graphene wrinkle. The graphene wrinkle in combination with nano‐bubble engineering constitutes an innovative and agile platform to design graphene and other more general two‐dimensional (2D) thermoelectrics and opens the possibility for realizing active on‐chip cooling for 2D nanoelectronics with van der Waals junctions.     

Conductivity Maximum in 3D Graphene Foams

In conventional foams, electrical properties often play a secondary role. However, this scenario becomes different for 3D graphene foams (GrFs). In fact, one of the motivations for synthesizing 3D GrFs is to inherit the remarkable electrical properties of individual graphene sheets. Despite immense experimental efforts to study and improve the electrical properties of 3D GrFs, lack of theoretical studies and understanding limits further progress. The causes to this embarrassing situation are identified as the multiple freedoms introduced by graphene sheets and multiscale nature of this problem. In this article, combined with transport modeling and coarse‐grained molecular dynamic (MD) simulations, a theoretical framework is established to systematically study the electrical conducting properties of 3D GrFs with or without deformation. In particular, through large‐scale and massive calculations, a general relation between contact area and conductance for two van der Waals bonded graphene sheets is demonstrated, in terms of which the conductivity maximum phenomenon in GrFs is first theoretically proposed and its competition mechanism is explained. Moreover, the theoretical prediction is consistent with previous experimental observations.     

Vibration frequency of graphene based composites: A multiscale approach

This paper presents a multiscale approach for vibration frequency analysis of graphene/polymer composites. The graphene is modelled at the atomistic scale, and the matrix deformation is analysed by the continuum finite element method. Inter-connectivity between graphene and polymer matrix are assumed to be bonded by van der Waals interactions at the interface. The impact of geometrical configuration (armchair and zigzag), boundary conditions and length on the overall stiffness of the graphene reinforced plastics (GRP) is studied. The natural frequency and vibrational mode shapes of GRP studied have displayed dependence on the length and also the boundary conditions. The exceptional vibrational behaviour and large stiffness displayed by GRP makes them a potential replacement for conventional composite fibres such as carbon and glass fibres.     

A High‐On/Off‐Ratio Floating‐Gate Memristor Array on a Flexible Substrate via CVD‐Grown Large‐Area 2D Layer Stacking

Memristors such as phase‐change memory and resistive memory have been proposed to emulate the synaptic activities in neuromorphic systems. However, the low reliability of these types of memories is their biggest challenge for commercialization. Here, a highly reliable memristor array using floating‐gate memory operated by two terminals (source and drain) using van der Waals layered materials is demonstrated. Centimeter‐scale samples (1.5 cm × 1.5 cm) of MoS₂ as a channel and graphene as a trap layer grown by chemical vapor deposition (CVD) are used for array fabrication with Al₂O₃ as the tunneling barrier. With regard to the memory characteristics, 93% of the devices exhibit an on/off ratio of over 10³ with an average ratio of 10⁴. The high on/off ratio and reliable endurance in the devices allow stable 6‐level memory applications. The devices also exhibit excellent memory durability over 8000 cycles with a negligible shift in the threshold voltage and on‐current, which is a significant improvement over other types of memristors. In addition, the devices can be strained up to 1% by fabricating on a flexible substrate. This demonstration opens a practical route for next‐generation electronics with CVD‐grown van der Waals layered materials.