Vibration analysis of defective graphene sheets using nonlocal elasticity theory

Many papers have studied the free vibration of graphene sheets. However, all this papers assumed their atomic structure free of any defects. Nonetheless, they actually contain some defects including single vacancy, double vacancy and Stone-Wales defects. This paper, therefore, investigates the free vibration of defective graphene sheets, rather than pristine graphene sheets, via nonlocal elasticity theory. Governing equations are derived using nonlocal elasticity and the first-order shear deformation theory (FSDT). The influence of structural defects on the vibration of graphene sheets is considered by applying the mechanical properties of defective graphene sheets. Afterwards, these equations solved using generalized differential quadrature method (GDQ). The small-scale effect is applied in the governing equations of motion by nonlocal parameter. The effects of different defect types are inspected for graphene sheets with clamped or simply-supported boundary conditions on all sides. It is shown that the natural frequencies of graphene sheets decrease by introducing defects to the atomic structure. Furthermore, it is found that the number of missing atoms, shapes and distributions of structural defects play a significant role in the vibrational behavior of graphene. The effect of vacancy defect reconstruction is also discussed in this paper.     

Comparison of Goos–Hänchen shifts of the reflected beam from graphene on dielectrics and metals

The Goos–Hänchen shifts of the reflected beam from graphene-on-dielectric (or metal) in the optical wavelength are investigated by using the stationary-phase method. For the graphene-on-dielectric substrates, it is found that the pseudo-Brewster angle and Goos–Hänchen shift are influenced greatly by the introduced graphene sheets for TM polarization. By changing number of graphene sheets, the lateral shifts can be large positive or negative near the pseudo-Brewster angle. For TE polarization, the lateral shift is still small; however it can also be positive or negative by changing the number of graphene sheets. For the graphene-on-metal substrates, graphene sheets exert a great impact on the reflectance while has little effect on the lateral shifts of both polarizations. Finally, the role of the graphene sheets on the lateral shifts for the different visible wavelengths is discussed.     

Young’s modulus and the Poisson’s ratio of planar and nanotubular supracrystalline structures

A method has been proposed for calculating the two-dimensional Young??s modulus and the Poisson??s ratio for planar and nanotubular structures through the components of the two-dimensional elastic rigidity tensor obtained by numerical methods. The method has been tested for graphene and two-dimensional supracrystalline sheets.     

掺杂石墨烯吸附特性的第一性原理研究

利用第一性原理方法研究了一氧化碳分子在本征和硼、氮、铝、磷掺杂的有限尺寸石墨烯上的吸附机理.结果表明,石墨烯作为一氧化碳传感器时的性能依赖于掺杂元素.本征、硼和氮掺杂石墨烯吸附一氧化碳时的吸附能较低,为物理吸附.铝、磷掺杂石墨烯的吸附能显著提高,比本征、硼和氮掺杂时高出约一个数量级,且铝和磷原子从石墨烯中突出,使其发生局部弯曲.铝掺杂石墨烯增强了石墨烯与一氧化碳分子之间的相互作用,可以提高石墨烯的气敏性和吸附能力,是一氧化碳传感器的最佳候选材料之一.     

First-principles study of lithium intercalated bilayer graphene

Lithium intercalated bilayer graphene has been investigated using first-principles density functional theory calculations. Results show that there exist AB and AA stacking sequences for bilayer graphene in which the latter is more favorable for the Li storage and the former will evolve into the latter with the intercalation of Li ions. The relationship between the interlayer distance of two graphene sheets and the intercalated capacity of Li ions is discussed. It is found that structural defect is identified to store Li ions more favorably than pristine bilayer graphene and an isolated C atom vacancy in bilayer graphene can capture three Li ions between two graphene sheets.     

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.     

Scanning probe microscopy study of exfoliated oxidized graphene sheets

Exfoliated oxidized graphene (OG) sheets, suspended in an aqueous solution, were deposited on freshly cleaved HOPG and studied by ambient AFM and UHV STM. The AFM images revealed oxidized graphene sheets with a lateral dimension of 5–10 μm. The oxidized graphene sheets exhibited different thicknesses and were found to conformally coat the HOPG substrate. Wrinkles and folds induced by the deposition process were clearly observed. Phase imaging and lateral force microscopy showed distinct contrast between the oxidized graphene and the underlying HOPG substrate. The UHV STM studies of oxidized graphene revealed atomic scale periodicity showing a (0.273 ± 0.008) nm × (0.406 ± 0.013) nm unit cell over distances spanning few nanometers. This periodicity is identified with oxygen atoms bound to the oxidized graphene sheet. I(V) data were taken from oxidized graphene sheets and compared to similar data obtained from bulk HOPG. The dI/dV data from oxidized graphene reveals a reduction in the local density of states for bias voltages in the range of ±0.1 V.     

Density functional theory study on the adsorption of alkali metal ions with pristine and defected graphene sheet

The graphene-based materials along with the adsorption of alkali metal ions are suitable for energy conversion and storage applications. Hence in the present work, we have investigated the structural and electronic properties of pristine and defected graphene sheet upon the adsorption of alkali metal ions (Li⁺, Na⁺, and K⁺) using density functional theory (DFT) calculations. The presence of vacancies or vacancy defects enhances the adsorption of alkali ions than the pristine sheet. From the obtained results, it is found that the adsorption energy of Li⁺ on the vacancies defected graphene sheet is higher (3.05?eV) than the pristine (2.41?eV) and Stone–Wales (2.50?eV) defected sheets. Moreover, the pore radius of the pristine and defected graphene sheets are less affected by metal ions adsorption. The increase in energy gap upon the adsorption of metal ions is found to be high in the vacancy defected graphene than that of other sheets. The metal ions adsorption in the defective vacancy sheets has high charge transfer from metal ions to the graphene sheet. The bonding characteristic between the metal ions and graphene sheet are analysed using QTAIM analysis. The influence of alkali ions on the electronic properties of the graphene sheet is examined from the Total Density of States (TDOS) and Partial Density of States (PDOS).     

拉伸作用对单层石墨片电子能隙的影响

基于紧束缚方法,在考虑最近邻相互作用的情况下,研究了拉伸锯齿型边和扶手型边单层石墨的能带结构,得到了两种类型单层石墨片的π电子能带及带隙与拉力的解析关系式.通过数值计算能够发现：拉力不但使单层石墨产生带隙,而且带隙随着拉力的增大而变宽,并且锯齿型比扶手型的带隙更易变宽. 关键词： 单层石墨片 拉伸形变 电子能隙     

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.     

Comparative study on graphene growth mechanism using Ni films,Ni/Mo sheets,and Pt substrates

We demonstrate a comparative study on graphene growth mechanism using various catalytic metal substrates such as Ni thin films, Ni-deposited Mo (Ni/Mo) sheets, and Pt sheets during chemical vapor deposition (CVD). Depending on the substrates, two kinds of graphene growth mechanisms that involve either precipitation or surface adsorption of carbon have been reported. We synthesized graphene, focusing especially on the initial growth stage during CVD, by varying synthesis parameters such as synthesis time, amount of feedstock, and cooling rate after synthesis. We concluded that precipitation-driven synthesis is dominant in the case of Ni substrates whereas adsorption-driven growth is dominant in the Ni/Mo system. In the case of the Pt substrate, which is generally believed to grow by carbon precipitation, graphene growth by adsorption was found to be dominant. We believe that our results will contribute to a clearer understanding of the graphene synthesis mechanism, and development of manufacturing routes for controllable synthesis of high-quality graphenes.     

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.     

Computational study of the formation of aluminum-graphene nanocrystallites

The molecular dynamics method is used to study the formation of the Al/graphene nanocomposite in the structural grains of different size under the action of internal stresses. The behavior of graphene sheets inside an individual structural grain as well as in the process of two Al grains containing graphene are joined is investigated. The motion of graphene films, starting from the middle of the aluminum matrix, ends with their location at the crystallite boundaries. Graphene moves in the Al matrix along closely packed planes. In this case, graphene sheets acquire curvature. An intergrowth of graphene sheets is also observed. A contact between two Al-C nanocrystallites through a graphene interlayer is created. The self-diffusion coefficients of atoms and the partial potential energies increased with decreasing nanocrystallite size. The angular distribution of the nearest geometric neighbors and the distribution of distances to the nearest neighbors are determined using the construction of Voronoi polyhedra.     

Multiscale modeling of graphene- and nanotube-based reinforced polymer nanocomposites

A combination of molecular dynamics, molecular structural mechanics, and finite element method is employed to compute the elastic constants of a polymeric nanocomposite embedded with graphene sheets, and carbon nanotubes. The model is first applied to study the effect of inclusion of graphene sheets on the Young modulus of the composite. To explore the significance of the nanofiller geometry, the elastic constants of nanotube-based and graphene-based polymer composites are computed under identical conditions. The reinforcement role of these nanofillers is also investigated in transverse directions. Moreover, the dependence of the nanocomposite?s axial Young modulus on the presence of ripples on the surface of the embedded graphene sheets, due to thermal fluctuations, is examined via MD simulations. Finally, we have also studied the effect of sliding motion of graphene layers on the elastic constants of the nanocomposite.     

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.     

Strong suppression of weak localization in graphene

Low-field magnetoresistance is ubiquitous in low-dimensional metallic systems with high resistivity and well understood as arising due to quantum interference on self-intersecting diffusive trajectories. We have found that in graphene this weak-localization magnetoresistance is strongly suppressed and, in some cases, completely absent. The unexpected observation is attributed to mesoscopic corrugations of graphene sheets which can cause a dephasing effect similar to that of a random magnetic field.     

Synthesis of graphene oxide sheets decorated by silver nanoparticles in organic phase and their catalytic activity

The graphene oxide(GO) sheets decorated by Ag nanoparticles were prepared using a liquid–liquid two-phase method at the room temperature. The synthesized samples existed in the organic phase and were characterized by X-ray diffraction, transmission electron microscopy, UV–vis spectroscopy and Raman spectra. The results demonstrate that these silver-nanoparticles with diameter of about 10 nm assembled on graphene oxide sheets are flexible and can form stable suspensions in organic phase. Raman signals of graphene oxide sheets are increased by the attached silver nanoparticles, displaying higher surface-enhanced Raman scattering activity. Furthermore, Ag/GO are found to serve as effective catalysts to activate the reduction of 4-nitrophenol (4NP) in the presence of NaBH₄.     

Geometric stability and adsorption property of hydroxyl group on graphene sheets

The stable geometrics and adsorption behaviors of hydroxyl (OH) groups on graphene sheets are investigated using the first-principles calculations. The single hydroxyl adatom has small adsorption energy and diffusion barrier on pristine graphene. The binding strength of the hydroxyl group increases with the coverage, and the aggregations of the hydroxyl groups reduce the structural bucking of graphene sheet. On the graphene with single vacancy (SV-graphene), the large trapping zones mean the adsorbed OH would be easily trapped at the vacancy site. The hydroxyl groups prefer to aggregate on graphene surfaces and form the water molecule, leaving the epoxy group on pristine graphene or oxygen dopant in SV-graphene, which is used to constitute the structural model of oxidized graphene. These results would provide us a useful reference to understand the atomic structure and adsorption property of functional groups on graphene sheets.     

STM observation of the quantum interference effect in finite-sized graphite

Superperiodic patterns were observed by STM on two kinds of finite-sized graphene sheets. One is nanographene sheets inclined from a highly oriented pyrolitic graphite (HOPG) substrate and the other is a several-layer-thick graphene sheets with dislocation-network structures against a HOPG substrate. As for the former, the in-plane periodicity increased gradually in the direction of inclination, and it is easily changed by attachment of a nanographite flake on the nanographene sheets. The oscillation pattern can be explained by the interference of electron waves confined in the inclined nanographene sheets. As for the latter, patterns and their corrugation amplitudes depended on the bias voltage and on the terrace height from the HOPG substrate. The interference effect by the perturbed and unperturbed waves in the overlayer is responsible for the patterns whose local density of states varies in space.