Atomistic finite element model for axial buckling and vibration analysis of single-layered graphene sheets

In this article, an atomistic model is developed to study the buckling and vibration characteristics of single-layered graphene sheets (SLGSs). By treating SLGSs as space-frame structures, in which the discrete nature of graphene sheets is preserved, they are modeled using three-dimensional elastic beam elements for the bonds. The elastic moduli of the beam elements are determined via a linkage between molecular mechanics and structural mechanics. Based on this model, the critical compressive forces and fundamental natural frequencies of single-layered graphene sheets with different boundary conditions and geometries are obtained and then compared. It is indicated that the compressive buckling force decreases when the graphene sheet aspect ratio increases. At low aspect ratios, the increase of aspect ratios will result in a significant decrease in the critical buckling load. It is also indicated that increasing aspect ratio at a given side length results in the convergence of buckling envelops associated with armchair and zigzag graphene sheets. The influence of boundary conditions will be studied for different geometries. It will be shown that the influence of boundary conditions is not significant for sufficiently large SLGSs.     

Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory

Higher order shear deformation theory (HSDT) is reformulated using the nonlocal differential constitutive relations of Eringen. The equations of motion of the nonlocal theories are derived. The developed equations of motion have been applied to study buckling characteristics of nanoplates such as graphene sheets. Navier's approach has been used to solve the governing equations for all edges simply supported boundary conditions. Analytical solutions for critical buckling loads of the graphene sheets are presented. Nonlocal elasticity theories are employed to bring out the small scale effect on the critical buckling load of graphene sheets. Effects of (i) nonlocal parameter, (ii) length, (iii) thickness of the graphene sheets and (iv) higher order shear deformation theory on the critical buckling load have been investigated. The theoretical development as well as numerical solutions presented herein should serve as reference for nonlocal theories as applied to the stability analysis of nanoplates and nanoshells.     

Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model

In this article, the buckling behavior of nanoscale circular plates under uniform radial compression is studied. Small-scale effect is taken into consideration. Using nonlocal elasticity theory the governing equations are derived for the circular single-layered graphene sheets (SLGS). Explicit expressions for the buckling loads are obtained for clamped and simply supported boundary conditions. It is shown that nonlocal effects play an important role in the buckling of circular nanoplates. The effects of the small scale on the buckling loads considering various parameters such as the radius of the plate and mode numbers are investigated.     

Buckling instability of circular double-layered graphene sheets

In this paper, we study the buckling properties of circular double-layered graphene sheets (DLGSs), using plate theory. The two graphene layers are modeled as two individual sheets whose interactions are determined by the Lennard-Jones potential of the carbon-carbon bond. An analytical solution of coupled governing equations is proposed for predicting the buckling properties of circular DLGSs. Using the present theoretical approach, the influences of boundary conditions, plate sizes, and buckling-mode shapes on the buckling behaviors are investigated in detail. The buckling stability is significantly affected by the buckling-mode shapes. As a result of van der Waals interactions, the buckling stress of circular DLGSs is much larger for the anti-phase mode than for the in-phase mode.     

Elastic instability of bilayer graphene using atomistic finite element

In-plane elastic instability of bilayer graphene sheets is investigated using atomistic finite element approaches. The equivalent homogenised properties of graphene sheet are expressed in terms of the thickness, equilibrium lengths and force-field models used to represent the C–C bonds of the graphene lattice. The covalent bonds are represented as structural beams with stretching, bending, torsional and shear deformation, and the strain energies associated to affine deformation mechanisms. The overall mechanical properties and geometric configurations of the nano-structures represented as truss assemblies are then calculated minimising the total potential energy associated to the loading, thickness and average equilibrium lengths of the bonds. Different boundary conditions and aspect ratios are considered for both bilayer and single-layer graphene sheets. The bilayer graphene sheets are found to be offering remarkably higher buckling strengths as compared to single-layer sheets.     

Estimation of critical dislocation distances

In this article, graphene is investigated with respect to its electronic properties when introduced into field effect devices (FED). With the exception of manual graphene deposition, conventional top-down CMOS-compatible processes are applied. Few and monolayer graphene sheets are characterized by scanning electron microscopy, atomic force microscopy and Raman spectroscopy. The electrical properties of monolayer graphene sandwiched between two silicon dioxide films are studied. Carrier mobilities in graphene pseudo-MOS structures are compared to those obtained from double-gated Graphene-FEDs and silicon metal-oxide-semiconductor field-effect-transistors (MOSFETs).     

单层石墨烯片的非线性板模型

基于实验得到的非线性本构关系和板理论,本文建立了包含三次及五次非线性项的单层石墨烯片的板动力学模型.针对四边简支矩形板,使用Ritz法研究了在板中点作用集中力时的静力弯曲,以及边界均匀受力时的静力屈曲问题.结果显示,基于非线性本构关系的板模型能很好的描述单层石墨烯片的力学行为,而且模型中的五次非线性项对结构的弯曲变形有显著影响.     

Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics

This paper presents an investigation on the buckling characteristics of nanoscale rectangular plates under bi-axial compression considering non-uniformity in the thickness. Based on the nonlocal continuum mechanics, governing differential equations are derived. Numerical solutions for the buckling loads are obtained using the Galerkin method. The present study shows that the buckling behaviors of single-layered graphene sheets (SLGSs) are strongly sensitive to the nonlocal and non-uniform parameters. The influence of percentage change of thickness on the stability of SLGSs is more significant in the strip-type nonoplates (nanoribbons) than in the square-type nanoplates.     

硅晶体表面石墨烯褶皱形貌的分子动力学模拟研究

本文利用分子动力学的方法和模拟退火技术从原子尺度分析研究了Si (100), Si (111)和Si (211)表面单原子层石墨烯的褶皱形貌及其演化特点. 研究表明, 分别置于Si晶体的三种不同原子表面的石墨烯都展现出原子尺度的褶皱形貌. 石墨烯与Si晶体表面原子的晶格失配是引起石墨烯褶皱的主要原因. 研究发现, Si晶体表面石墨烯的褶皱形貌强烈的依赖于退火温度. 石墨烯的褶皱形貌还将直接影响其在Si晶体表面的吸附稳定性. 这些研究结果有助于人们认识基于Si晶体衬底的石墨烯的结构形貌及其稳定性, 为石墨烯的进一步应用提供理论参考.     

Calculation of electron spectra and some problems in the thermodynamics of graphene layers

The expressions for the energy spectra of monolayer, bilayer, and multilayer graphene, as well as epitaxial graphene, are derived using the quantum Green’s functions method. Analytic expressions are obtained for the densities of states of these systems. It is shown that a bandgap can appear the spectrum of an epitaxial graphene bilayer. A number of problems in the thermodynamics of electrons in free and epitaxial graphene layers are considered as applications. Analytic expressions are obtained for the chemical potential and heat capacity in the limiting cases of low and high temperatures. Quantum oscillations of heat capacity in graphene are analyzed taking into account the Coulomb interaction. The Berry phase of epitaxial graphene is investigated.     

Anisotropic quantum transport in monolayer graphene in the presence of Rashba spin–orbit coupling

We have studied spin-dependent electron tunneling through the Rashba barrier in a monolayer graphene lattices. The transfer matrix method, have been employed to obtain the spin dependent transport properties of the chiral particles. It is shown that graphene sheets in the presence of Rashba spin–orbit barrier will act as an electron spin-inverter.     

A review on silicene — New candidate for electronics

Silicene-the silicon-based counterpart of graphene-has a two dimensional structure that is responsible for the variety of potentially useful chemical and physical properties. The existence of silicene has been achieved recently owing to experiments involving epitaxial growth of silicon as stripes on Ag(001), ribbons on Ag(110), and sheets on Ag(111). The nano-ribbons observed on Ag(110) were found-by both high definition experimental scanning tunneling microscopy images and density functional theory calculations-to consist of an arched honeycomb structure. Angle resolved photo-emission experiments on these silicene nano-ribbons on Ag(110), along the direction of the ribbons, showed a band structure which is analogous to the Dirac cones of graphene. Unlike silicon surfaces, which are highly reactive to oxygen, the silicene nano-ribbons were found to be resistant to oxygen reactivity.On the theoretical side, recent extensive efforts have been deployed to understand the properties of standalone silicene sheets and nano-ribbons using both tight-binding and density functional theory calculations. Unlike graphene it is demonstrated that silicene sheets are stable only if a small buckling (0.44 Å) is present. The electronic properties of silicene nano-ribbons and silicene sheets were found to resemble those of graphene.Although this is a fairly new avenue, the already obtained outcome from these important first steps in understanding silicene showed promising features that could give a new future to silicon in the electronics industry, thus opening a promising route toward wide-range applications. In this review, we plan to introduce silicene by presenting the available experimental and theoretical studies performed to date, and suggest future directions to be explored to make the synthesis of silicene a viable one.     

Quasi-particle spectrum and density of electronic states in AA- and AB-stacked bilayer graphene

The present work deals with the analysis of the quasi-particle spectrum and the density of states of monolayer and bilayer (AB- and AA-stacked) graphene. The tight binding Hamiltonian containing nearest-neighbor and next-nearest neighbor hopping and onsite Coulomb interaction within two triangular sub-lattice approach for monolayer graphene, along-with the interlayer coupling parameter for bilayer graphene has been employed. The expressions of quasi-particle energies and the density of states (DOS) are obtained within mean-field Green’s function equations of motion approach. It is found that next-nearest-neighbour intralayer hopping introduce asymmetry in the electronic states above and below the zero point energy in monolayer and bilayer (AA- and AB-stacked) graphene. The behavior of electronic states in monolayer and bilayer graphene is different and highly influenced by interlayer coupling and Coulomb interaction. It has been pointed out that the interlayer coupling splits the quasi-particle peak in density of states while the Coulomb interaction suppresses the bilayer splitting and generates a gap at Fermi level in both AA- and AB-stacked bilayer graphene. The theoretically obtained quasi-particle energies and density of states in monolayer and bilayer (AA- and AB-stacked) graphene has been viewed in terms of recent ARPES and STM data on these systems.     

Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler–Pasternak elastic substrate medium

In the present work, thermal buckling of single-layered graphene sheets lying on an elastic medium is analyzed. For this purpose, the sinusoidal shear deformation plate theory in tandem with the nonlocal continuum theory, which takes the small scale effects into account, is employed. The non-linear stability equations, which contain the reaction of Winkler–Pasternak elastic substrate medium, are derived and then solved analytically for a plate with various boundary conditions and based on various plate theories. Closed form solutions are formulated for three types of thermal loadings as uniform, linear and nonlinear temperature rise through the thickness of the plate. A number of examples are presented to illustrate the numerical results concerned with the buckling temperature response of nanoplates resting on two-parameter elastic foundations. The influences played by transversal shear deformation, plate aspect ratio, side-to-thickness ratio, nonlocal parameter, and elastic foundation parameters are all investigated.     

Universal optical conductance of graphite

We find experimentally that the optical sheet conductance of graphite per graphene layer is very close to (pi/2)e2/h, which is the theoretically expected value of dynamical conductance of isolated monolayer graphene. Our calculations within the Slonczewski-Weiss-McClure model explain well why the interplane hopping leaves the conductance of graphene sheets in graphite almost unchanged for photon energies between 0.1 and 0.6 eV, even though it significantly affects the band structure on the same energy scale. The f-sum rule analysis shows that the large increase of the Drude spectral weight as a function of temperature is at the expense of the removed low-energy optical spectral weight of transitions between hole and electron bands.     

Analytical expressions for electrostatics of graphene structures

This study focuses on electrostatics of various graphene structures as graphene monolayer, graphene nanoribbons, as well as multi-layer graphene or graphene flakes. An atomistic moment method based on classical electrostatics is utilized in order to evaluate the charge distribution in each nanostructure. Assuming a freestanding graphene structure in an infinite or in a semi-infinite space limited by a grounded infinite plane, the effect of the length, width, number of layers and position of the nanostructure on its electrostatic charge distributions and total charge and capacitance is examined through a parametric analysis. The results of the present show good agreement with corresponding available data in the literature, obtained from different theoretical approaches. Performing nonlinear regression analysis on the numerical results, where it is possible, simple analytical expressions are proposed for the total charge and charge distribution prediction based on structure geometry.     

Curcumin-assisted ultrasound exfoliation of graphite to graphene in ethanol

In this paper, we demonstrated a simple and cost-effective method to produce graphene from graphite in ethanol using ultrasound assisted with curcumin. The influence of curcumin concentration, starting graphite amount, sonication power, and sonication time on the graphene concentration was studied schematically. The π-π interaction between curcumin and graphene, being confirmed by FTIR spectrum, facilitate the exfoliation of the graphite into graphene. The concentration of the graphene in the ethanol reached up to 1.44 mg mL⁻¹ and the exfoliated suspension was relatively stable. The content of monolayer, bilayer, and multilayer in the exfoliated graphene suspension were 21%, 37%, and 42%, respectively. The as-prepared graphene sheets were free-defect. This novel approach may not only enable to exfoliate the graphite into graphene but also to make the graphene-curcumin hybrid which might find applications in pharmaceutical industry.     

Direct observation of nanocrystallite buckling in carbon fibers under bending load

Single carbon fibers are deformed in bending by forming loops with varying radius. Position-resolved x-ray diffraction patterns from the bent fibers are collected from the tension to the compression region with a synchrotron radiation nanobeam of 100 nm size from a waveguide structure. A strain redistribution with a shift of the neutral axis is observed. A significant increase of the misorientation of the graphene sheets in the compression region shows that intense buckling of the nanosized carbon crystallites is the physical origin of different tensile and compressive properties.     

Self-assembly between graphene sheets and cationic poly(methyl methacrylate) (PMMA) particles: preparation and characterization of PMMA/graphene composites

In this study, we presented a simple approach to prepare poly(methyl methacrylate) (PMMA)/graphene composites based on the self-assembly between graphene oxide (GO) sheets and cationic PMMA emulsion particles. Briefly, cationic PMMA emulsion particles were first synthesized by a soap-free emulsion polymerization process, in which methacryloyloxyethyl trimethyl ammonium chloride was used as the emulsifier, and then blended with the aqueous solution of GO. Through electrostatic attraction, the exfoliated GO sheets were tightly adhered on the PMMA particles. The GO sheets could be reduced in situ into graphene sheets by a chemical method, without the aggregation. The structure of the prepared composites and the influences of GO and graphene sheets on the properties of PMMA were investigated. Both GO and graphene sheets can increase the glass transition temperature and storage modulus of PMMA. Moreover, graphene sheets provided a more significant reinforcement effect.     

Crystal structure of cold compressed graphite

Through a systematic structural search we found an allotrope of carbon with Cmmm symmetry which we predict to be more stable than graphite for pressures above 10 GPa. This material, which we refer to as Z-carbon, is formed by pure sp(3) bonds and it provides an explanation to several features in experimental x-ray diffraction and Raman spectra of graphite under pressure. The transition from graphite to Z-carbon can occur through simple sliding and buckling of graphene sheets. Our calculations predict that Z-carbon is a transparent wide band-gap semiconductor with a hardness comparable to diamond.