Single-layer Graphene Sheets Research Articles

Impact behavior of single-layered graphene sheets based on analytical model and molecular dynamics simulation

A dynamic analysis of impact of striker on single-layered graphene sheets (SLGSs) is investigated by using analytical spring-mass model and the molecular dynamics (MD) and finite element simulations.An analytical model is conducted to obtain the maximum dynamic deflections of a square and rectangular SLGSs with various values of side-length and striker parameter. The accuracy and stability of the present methods are verified by MD simulations and explicit finite element analysis.Effect of (i) chirality, (ii) graphene side-length, (iii) striker mass and (iv) striker velocity on the maximum dynamic deflections of graphene are investigated.The results show that chirality does not have a significant effect in impact behavior of SLGSs.It is found that the present spring-mass model have an excellent capability to predict the maximum dynamic deflections of SLGSs due to impact loading before fracture is occurred.

Exact solution for free vibration of coupled double viscoelastic graphene sheets by viscoPasternak medium

Based on nonlocal theory, this article discusses vibration of CDVGS11Coupled double viscoelastic graphene sheets. systems. The properties of each single layer graphene sheet (SLGS) are assumed to be orthotropic and viscoelastic. The two SLGSs are simply supported and coupled by an enclosing viscoelastic medium which is simulated as a Visco-Pasternak layer. This model is aimed at representing dynamic interactions in nanocomposite materials with dissipation effect. By considering the Kirchhoff plate theory and Kelvin–Voigt model, the governing equation is derived using Hamilton's principle. The equation is solved analytically to obtain the complex natural frequency. The parametric study is thoroughly performed, concentrating on the series effects of viscoelastic damping structure, aspect ratio, visco-Pasternak medium, and mode number. In this system, in-phase (IPV) and out-of-phase (OPV) vibrations are investigated. The numerical results of this article show a perfect correspondence with those of the previous researches.

Thermal vibration of a circular single-layered graphene sheet with simply supported or clamped boundary

The thermal vibration of a Circular Single-Layered Graphene Sheet (CSLGS) is studied by using a circular thin plate model with quantum effects taken into account when the law of energy equipartition is unreliable. The relation between the temperature and the Root of Mean Squared (RMS) amplitude of vibration at any point of the CSLGS with simply supported or clamped boundary is derived first from the circular thin plate model via Bessel functions and modified Bessel functions of the first kind. The RMS amplitude of the CSLGS is constant at any point with the same radius for either quantum case or classical case. The study shows that the RMS amplitude of the CSLGS predicted from the quantum theory is lower than that predicted from the law of energy equipartition. The quantum effect is more important for the thermal vibration in the case of higher order modes, smaller diameter and lower temperature. The relative difference of the maximal RMS amplitude of thermal vibration of the CSLGS decreases monotonically with an increase of temperature.

Scalable and high-yield production of exfoliated graphene sheets in water and its application to an all-solid-state supercapacitor

One of the most critical issues in graphite exfoliation is realizing efficient, low-cost, eco-friendly, and scalable production of graphene for energy storage applications. The most promising strategies for exfoliating graphite to single-layer graphene sheets in scalable quantities with nearly non-oxidized content is the exfoliation of graphite by using an environmentally friendly solution. Herein, we demonstrate a universal exfoliation principle that uses imidazole, which has an anionic nature and π-conjugated heterocyclic coplanar structure, as the exfoliant for the successful production of large quantities of graphene suspensions in water. The exfoliant interacts with both surfaces of the exfoliated graphene sheets and the aqueous solution, significantly improving graphene dispersion (1mg/mL) in water. Exfoliation in aqueous solutions produced graphene in high yield (>90%, ⩽3 layers), with a large lateral size (μm) and high quality (ID/IG ratio≈0.1). The electrical conductivity of the graphene paper is 131.7S/cm, which is superior to the values reported from exfoliated graphene prepared using solution processes. An all-solid-state supercapacitor with a new design fabricated using the atomically thin and flat conductive exfoliated graphene sheets delivered an ultrahigh area capacitance (∼71.9mF/cm2). Therefore, imidazole -assisted exfoliation has great potential for scalable preparation of graphene suspensions for supercapacitor applications.

Thermal transport behaviors of suspended graphene sheets with different sizes

We experimentally investigated the thermal transport behaviors of suspended single-layer graphene (SLG) and graphene sheets with different sizes. The length of graphene sheet suspended on a groove of SiO2/Si substrate is equal to the groove width (508 μm). Laser cutting technology is used to tailor SLG to obtain graphene sheets with different widths. A one-dimensional steady-state method is applied to measure the thermal conductivity, k, of graphene sheet and SLG at different conditions. k of the graphene sheets with different widths is much higher than that of SLG and increases with the decrease of graphene sheet width, and the increase in k appears significant when the width decreases greatly. We proposed that the Umklapp scattering may become dominant in phonon transport with the increasing of graphene sheet width, resulting in the thermal conductivity decrease. Another anomalous behavior is that k increases firstly and then decreases with an increase in temperature, and has a peak value at around 50 °C. The competition effects of boundary scattering, point defect scattering, grain-boundary phonon scattering, and Umklapp scattering in phonon transport may contribute to this phenomenon. A maximum k value of 2450.55 W m−1 K−1 is obtained under the condition of 50 °C when the SLG is cut for the fourth times. The electrical conductivity of graphene sheets with different widths at room temperature is in the range of 0.7584–2.7002 × 106 Ω−1 m−1. The graphene sheet with small width exhibits better thermal and electronic properties that make them attractive for the fabrication of nanoscale electronics and promising for the application in thermal management.

Wrinkling in Graphene Subjected to Gradient Tension

In the present study, the initiation and evolution mechanisms of wrinkles in a square single layer graphene sheet (SLGS) under gradient tensile displacements are investigated based on molecular dynamics (MD) simulations. The mechanism of wrinkling process is elucidated by studying the atomic out-of-plane displacements development of the key atoms in SLGS. It reveals that the loading and boundary conditions play dominant roles in the wrinkling deformation of graphene. The dependences of the wrinkling amplitude, wavelength, out-of-plane displacement, direction angle and wrinkling area ratio on the applied gradient tensile displacements are obtained. The effects of temperature, size of graphene and loading grads on graphene wrinkling are investigated.

Relaxation Properties of Single Layer Graphene on SiO2 Substrate.

The relaxation properties of single layer graphene sheet on the SiO2 substrate are investigated through molecular dynamics simulation technique in this article. The graphene sheet models with different aspect ratios on SiO2 substrate are established and sufficiently relaxed at different thermodynamic temperatures. Subsequently, the morphology, equilibrium position and undulation of graphene on SiO2 substrate are discussed. It is observed that after sufficient relaxation processes, all the graphene sheets are adsorbed on SiO2 substrates and have some certain degree of undulations both on the edge and in the inner surface rather than perfect planar structures. Further observation from the simulation results shows that with different initial distances between the graphene sheet and SiO2 substrate, the graphene sheet would eventually stabilize to an identical equilibrium level at the same temperature. In addition, the final average distance between the graphene sheet and the substrate is a constant of 3.44 A at 0.01 K, in close proximity to the value of parameter r in Lennard-Jones potential function, and the higher the temperature is, the larger the final distance becomes. The results also indicate that for the same size of the graphene sheet, the increasing of temperature significantly aggravates the undulation of graphene sheet. With the increase of aspect ratios, the undulation of the graphene sheet is also aggravated, even the graphene sheet would crimp to a certain extent.

Nonlocal mass-nanosensor model based on the damped vibration of single-layer graphene sheet influenced by in-plane magnetic field

Nano-materials such as graphene sheets have a great opportunity to be applied in development of a new generation of nanomechanical sensors and devices due to their unique physical properties. Based on the nonlocal continuum theory and vibration analysis, the single-layered graphene sheet with attached nanoparticles affected by in-plane magnetic field is proposed as a new type of the mass-nanosensor. The nonlocal Kirchhoff-Love plate theory is adopted to describe mechanical behavior of single-layered graphene sheet as an orthotropic nanoplate. The equation of motion of a simply supported orthotropic nanoplate is derived, where the influence of Lorentz magnetic force is introduced through classical Maxwell׳s equations. Complex natural frequencies, damped frequency shifts and relative shift of damping ratio for nanoplate with attached nanoparticles are obtained in the explicit form. The influences of the nonlocal and magnetic field parameter, different mass weights and positions of attached nanoparticles and damping coefficients on the relative damped frequency shift and relative shift of damping ratio are examined. The presented results can be useful in the analysis and design of nanosensors applied in the presence of strong magnetic field. Our results show that magnetic field could be successfully used to improve sensibility performances of nanomechanical sensors.

Multiscale nonlinear frequency response analysis of single-layered graphene sheet under impulse and harmonic excitation using the atomistic finite element method

The atomistic finite element method (AFEM) is a multiscale technique where a sequential mode is used to transfer information between two length scales to model and simulate nanostructures at the continuum level. This method is used in this paper to investigate the nonlinear frequency response of a single-layered graphene sheet (SLGS) for impulse and harmonic excitation. The multi-body interatomic Tersoff–Brenner (TB) potential is used to represent the energy between two adjacent carbon atoms. Based on the TB potential, the equivalent geometric and elastic properties of carbon–carbon bonds are derived which are consistent with the material constitutive relations. These properties are used further to derive the nonlinear material model (stress–strain curve) of carbon–carbon bonds based on the force–deflection curve using the multi-body interatomic Tersoff–Brenner potential. A square SLGS is considered and its nonlinear vibration characteristics under an impulse and harmonic excitation for bridged, cantilever and clamped boundary conditions are investigated using the derived nonlinear material model (NMM). Before using the proposed nonlinear material model, the derived equivalent geometric and elastic properties of carbon–carbon bond are validated using molecular dynamics simulation results. The geometric (large deformation) and material nonlinearities are included in the nonlinear frequency response analysis. The investigated results of the nonlinear frequency response analysis are compared with those of the linear frequency response analysis, and the effect of the nonlinear behavior of carbon–carbon bonds on the frequency response of SLGS is studied.

Nonlocal continuum model for vibration of single-layered graphene sheets based on the element-free kp-Ritz method

In this paper, an implementation of the kp-Ritz method with the nonlocal continuum model as an element-free computational framework has been performed to investigate the free vibration behavior of a single-layered graphene sheet (SLGS). The nonlocal continuum model, which combines the Eringen nonlocal constitutive equation with the classical plate theory, has the ability to take the small scale effect into account. The study has shown that the element-free kp-Ritz method is an efficient approach for solving nonlocal continuum model for the SLGS vibration. The accuracy of the kp-Ritz method has been validated through comparison with the MD computation. The values of nonlocal parameter used in the study have been derived by matching the frequency of nonlocal continuum model with that of the MD model for different sizes and boundary conditions. The simulated results have illustrated that the value of nonlocal parameter depends on the sizes and boundary conditions of SLGS.

Transient analysis of single-layered graphene sheet using the kp-Ritz method and nonlocal elasticity theory

In this paper, an investigation on the transient analysis of single-layered graphene sheets (SLGSs) is performed using the element-free kp-Ritz method. The classical plate theory is used to describe the dynamic behavior of SLGSs. Nonlocal elasticity theory, in which nonlocal parameter is introduced, is incorporated to reflect the small effect. Newmark’s method is employed to solve the discretized dynamic equations. Several numerical examples are presented to examine the effect of boundary conditions, aspect ratio, side length load distribution type and load variation type on the transient behavior of SLGSs. The present work can serve as the foundation for further investigation of the transient response of multi-layered graphene sheets.

High-quality, single-layered epitaxial graphene fabricated on 6H-SiC (0001) by flash annealing in Pb atmosphere and mechanism

High-quality epitaxial graphene is produced on silicon carbide by flash annealing of 6H-SiC in a lead (Pb) atmosphere at ∼1400 °C for 30 s. Nearly three top bilayers of SiC are decomposed due to fast heating and cooling, and sublimation of Si atoms from SiC is retarded by the Pb atmosphere. The synergetic effects promote the growth of continuous single-layered graphene sheets on the SiC terraces, and a model is established to elucidate the effects and growth mechanism.

Hyperelastic tension of graphene

In this paper, we investigate the hyperelastic tensile behaviour of single layer graphene sheets (SLGSs). A one-term incompressible Ogden-type hyperelastic model is chosen to describe the mechanical response of C-C bonds. By establishing equality between the Ogden strain-energy and the variation of the Tersoff-Brenner interatomic potential, three different geometries of SLGSs are studied under tensile loading. We compute the Young's modulus, the finite-deformation Poisson's ratio, ultimate strains, total reactions, and the variation of the potential energy per carbon atom for large strains. Numerical simulations are compared with results obtained by molecular mechanics and molecular dynamics simulations, finite elements, continuum mechanics theory, and experiments. Our predictions are validated, revealing the potential predictive capabilities of the present hyperelastic framework for the analysis of graphene in the context of infinitesimal and large deformations. The good agreement found between our calculations and the published data suggests that graphene may be described as a hyperelastic material.

Graphene-Based Resonant Sensors for Detection of Ultra-Fine Nanoparticles: Molecular Dynamics and Nonlocal Elasticity Investigations

Application of single layered graphene sheets (SLGSs) as resonant sensors in detection of ultra-fine nanoparticles (NPs) is investigated via molecular dynamics (MD) and nonlocal elasticity approaches. To take into consideration the effect of geometric nonlinearity, nonlocality and atomic interactions between SLGSs and NPs, a nonlinear nonlocal plate model carrying an attached mass-spring system is introduced and a combination of pseudo-spectral (PS) and integral quadrature (IQ) methods is proposed to numerically determine the frequency shifts caused by the attached metal NPs. In MD simulations, interactions between carbon–carbon, metal–metal and metal–carbon atoms are described by adaptive intermolecular reactive empirical bond order (AIREBO) potential, embedded atom method (EAM), and Lennard–Jones (L–J) potential, respectively. Nonlocal small-scale parameter is calibrated by matching frequency shifts obtained by nonlocal and MD simulation approaches with same vibration amplitude. The influence of nonlinearity, nonlocality and distribution of attached NPs on frequency shifts and sensitivity of the SLGS sensors are discussed in detail.

Study on wrinkling in graphene under gradient shear by molecular dynamics simulation.

The formation and development mechanisms of wrinkles in a rectangular single layer graphene sheet (SLGS) subjected to in-plane gradient shear displacements are investigated through molecular dynamics (MD) simulations. The growth and propagation process of the SLGS wrinkling is elucidated by the developing atomic out-of-plane displacements of the key atoms. It reveals that the shape of SLGSandloading condition have a significant effect on the SLGS wrinkling deformation. The dependences of the wrinkling amplitude, wavelength, and out-of-plane displacements on the applied gradient shear displacements are obtained with MD simulations. The effects of aspect ratio, temperature, and loading grads on wrinkling in graphene are also studied.

Non-metal catalytic synthesis of graphene from a polythiophene monolayer on silicon dioxide

Direct synthesis of graphene without metal catalysts on a dielectric substrate is a major goal in graphene-based electronics and is an increasingly popular nanotechnology alternative to metal oxide semiconductor technology. However, current methods for the synthesis of these graphenes have many limitations, including the use of metal catalyst. Herein, we report a facile approach to the direct synthesis of graphene sheets based on the self-assembled monolayers (SAMs) technique. The new method for metal catalyst-free direct synthesis of a graphene sheet is through a solution-processable, inexpensive, easy, and reproducible cross-linked polythiophene self-assembled monolayer (SAM) that is formed via the [4+2] π cycloaddition reaction of π-electron conjugated thiophene layer self-assembled on the dielectric silicon dioxide substrate. The bifunctional molecules were carefully designed to create an SAM via silanization of alkoxy silane groups on the SiO2 substrate, and at the other end, a thin cross-linked polythiophene layer via a [4+2] π-electron cycloaddition reaction of π-electron conjugated thiophene SAM. By heating the cross-linked polythiophene SAM up to 1000°C under a high vacuum, single-layered or few-layered graphene sheets were successfully prepared on the dielectric silicon oxide substrate.

Shear buckling of rippled graphene by molecular dynamics simulation

This paper presents a study on the shear buckling of rippled single-layered graphene sheets in thermal environments by using molecular dynamics simulation. A zigzag or armchair graphene sheet is simply supported or clamped on its four edges and incremental in-plane shear forces instead of the commonly used shear strains are applied to the edges until initial buckling and final crushing of the graphene sheet are achieved. It is observed that the shear buckling modes of square and rectangular graphene sheets obtained from the molecular dynamics simulations are different from the ones of thin square and rectangular plates as predicted by continuum mechanics models. The shear buckling capacity of a rectangular zigzag graphene sheet is higher than its armchair counterpart. The environmental temperature, when it varies from 300 to 900K, has insignificant impact on the shear buckling forces of the simply supported and clamped square graphene sheets.

4–10 V capacitors with graphene-based electrodes and ionic liquid electrolyte

Atomically thin graphene is a promising capacitor electrode material, but the cell voltages achieved so far with various electrolytes are too low for a typical capacitor's application. In this paper it is demonstrated that in a dicyanamide-based ionic liquid electrolyte a graphene electrode passivates at 10 V and at the same time the conductivity of the single-layer graphene sheet increases more than 5 times. The protective self-healing nanolayer formed is a new carbon–nitrogen material with dielectric constant value up to 9.8. In the cell voltage range from 4 to 10 V, capacitors with large surface area reduced graphene oxide electrodes outperform any commercial capacitor technology by better energy density.

Defect density engineering for better graphene performance

Graphenes are emerging electrode materials used in many technologies such as electronics, sensors, as well as energy conversion and storage. The pristine graphenes, due to the elimination of density of states (DOS) at/near the Dirac point (Fermi level), have limited activities for charge transfer and storage. Fortunately, introduction of structural defects and disorders in graphenes can increase the DOS near the Fermi level by forming mid-gap and/or defect states, similar to that in silicon and other semiconducting materials. This improvement significantly promoted the application of pristine graphenes in electrochemical sensing and energy devices. In addition, defects related electronic structure variations in graphenes provides novel opportunity in studying the electrochemical structure-property relationship [1]. However, the delicate control over the defect-related electronic structures and precise correlation between the electrochemical activity and defect density remain challenging. Researchers led by Prof. Dongping Zhan and Prof. Bin Ren in Xiamen University have made significant advance in this field. In their recent work published in J. Am. Chem. Soc. [2], the authors demonstrated that the density of vacancy defects in a graphene sheet can be precisely controlled through Ar irradiation. They prepared patterns of different defect densities on a single-layer graphene sheet, and simultaneously mapped the defect density and the heterogeneous electron transfer (ET) rate of hydroxymethylferrocene (FcMeOH) oxidation over the same patterned graphene sheet (Figure 1), using Raman spectroscopy and the so-called scanning electrochemical microscopy. This new approach allowed them to quantitatively correlate the defect density in graphenes with the electrochemical activity for the heterogeneous ET reactions. The experimental results showed that the ET activity of graphene can be improved by increasing the density of vacancy defects. In addition, they obtained an optimal ET rate of FcMeOH oxidation over a graphene sheet with a moderate defect density. At such an optimal state, a balance between the increase of Fermi DOS and the decrease of sheet conductivity due to increasing the defect density was achieved, so that the whole graphene sheet not only becomes electrochemically activated, but also maintains structural integrity. According to their density functional theory calculations, the vacancy defect can induce mid-gap states in graphene. Because multiple electronic levels and states are involved in the heterogeneous ET between a solid electrode and redox molecules, the corresponding ET rates become proportional to the electronic overlap integral between the electrode and the redox molecules [1]. The introduction of mid-gap states should be able to enlarge the overlap between the DOS distribution of graphene and the redox molecules. The work by Zhan and coworkers represents an elegant example in tailoring the structure and property of graphene through defect density engineering.

Single Layer Graphene Sheet-based Nanoelectromechanical Resonator as Mass Detection

Mass detection of molecules using single layer graphene sheet is investigated in the present paper. A nanoelectromechanical system resonator device is proposed which is modeled as single layer graphene coupled to electronic transport through such device via two metallic leads. The conductance of such device is deduced by solving eigenvalue differential equation. The influence of both photon energy of an induced ac-field and magnetic field are taken into consideration. The present results show that both the resonant frequency shift and the quality factor are very sensitive to the mass of certain molecule. Also, the photon energy of the induced ac-field enhances the sensitivity of these parameters. The present research is very important for detecting the mass of both chemical molecules and bio-molecules. This can be achieved experimentally by measuring the quantum conductance of the present device, which is related to the resonant frequency shift and the quality factor.