Nonlocal vibration analysis of nanomechanical systems resonators using circular double-layer graphene sheets

Double-layer graphene sheets (DLGSs) have potential applications as nanoelectromechanical systems (NEMS) resonators due to their specific carrier spectrum of electrons. In this study, analysis of the vibration modes of NEMS resonators using simply supported circular DLGSs has been undertaken based on nonlocal thin plate theory. Considering the properties of DLGSs, the vibration mode of circular DLGSs can be divided into an in-phase mode (IPM) and an anti-phase mode (APM). The range of resonance frequencies in the IPM is much larger than in the APM because of the influence of van der Waals forces. Nonlocal effects significantly influence the resonance frequency of circular DLGSs in higher vibration modes and at lower aspect ratios.     

Atomistic evaluation of the stress concentration factor of graphene sheets having circular holes

Stress concentration factor concept has been developed for single-layered graphene sheets (SLGSs) with circular holes through an atomistic point of view by the application of molecular structural mechanics (MSM) approach. In this approach the response of SLGSs against unidirectional tensile loading is matched to the response of a frame-like macro structure containing beam elements by making an equivalence between strain energies of beam elements in MSM and potential energies of chemical bonds of SLGSs. Both chirality and size effects are considered and the atomistic evaluation of stress concentration factor is performed for different sizes of circular holes. Also, molecular dynamics simulations are implemented to verify the existence and location of the predicted stress concentration. The results reveal that size effects and the diameters of circular holes have a significant influence on the stress concentration factor of SLGSs and armchair SLGSs show a larger value of stress concentration than zigzag ones.     

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.     

Computational studies of the purine-functionalized graphene sheets

We performed a computational work to investigate the properties of functionalized graphene sheets (S) by adenine (A) and guanine (G) purine nucleobases. To achieve the purpose of this work, we examined the functionalization of armchair and zigzag tips of the S model by each of the A and G purines. The results indicated that the optimized properties for the investigated hybrid structures are different depending on the tip of functionalization and the used purine nucleobase. Moreover, the atomic level properties of the investigated structures were investigated by evaluating quadrupole coupling constants (C_Q) for the atoms of the optimized structures. The remarkable trend of the C_Q parameters is that the changes of atomic properties are many more significant for the functionalization of the zigzag-tip by the G nucleobase, which is in agreement with the results of the optimized properties.     

Free vibrations and buckling of graphene sheets

The molecular mechanics method is used to determine both eigenfrequencies and modes of vibrations and the critical compressing loads and buckling modes of graphene sheets. To simulate interatomic interactions in graphene, the DREIDING field of potential forces is used. This field includes four types of potential energies of covalent atomic interactions such as central forces, the variations in the angle between the neighboring bonds, the dihedral angle that is responsible for the torsion of the covalent bond, and the inversion angle (the angle corresponding to the retiring of the atom from the plane relative to three neighboring atoms).     

Buckling instability in liquid crystalline physical gels

In a nematic gel we observe a low-energy buckling deformation arising from soft and semisoft elastic modes. We prepare the self-assembled gel by dissolving a coil-side-group liquid-crystalline polymer-coil copolymer in a nematic liquid crystal. The gel has long network strands and a precisely tailored structure, making it ideal for studying nematic rubber elasticity. Under polarized optical microscopy we observe a striped texture that forms when gels uniformly aligned at 35 degrees C are cooled to room temperature. We model the instability using the molecular theory of nematic rubber elasticity, and the theory correctly captures the change in pitch length with sample thickness and polymer concentration. This buckling instability is a clear example of a low-energy deformation that arises in materials where polymer network strains are coupled to the director orientation.     

A cosmological model for corrugated graphene sheets

Defects play a key role in the electronic structure of graphene layers flat or curved. Topological defects in which an hexagon is replaced by an n-sided polygon generate long range interactions that make them different from vacancies or other potential defects. In this work we review previous models for topological defects in graphene. A formalism is proposed to study the electronic and transport properties of graphene sheets with corrugations as the one recently synthesized. The formalism is based on coupling the Dirac equation that models the low energy electronic excitations of clean flat graphene samples to a curved space. A cosmic string analogy allows to treat an arbitrary number of topological defects located at arbitrary positions on the graphene plane. The usual defects that will always be present in any graphene sample as pentagon–heptagon pairs and Stone-Wales defects are studied as an example. The local density of states around the defects acquires characteristic modulations that could be observed in scanning tunnel and transmission electron microscopy.     

Quantum friction controlled by plasmons between graphene sheets

We theoretically study quantum friction between two infinite graphene sheets, which is controlled by plasmons excited at the interfaces of graphenes and dielectrics. In near-field regime, quantum friction can be enhanced due to the coupling of plasmons between two graphene sheets. Dependences of friction coefficient on distance, chemical potential of graphene, temperature of environment, and dielectric constant of substrate have been investigated in detail. Friction coefficient can be increased by increasing temperature or dielectric constants of substrates, and can be reduced by increasing distance or chemical potential.     

石墨烯弛豫性能的分子动力学模拟

分别采用REBO势和AIREBO势对单层和多层石墨烯的弛豫性能进行了分子动力学模拟,模拟了石墨烯在弛豫过程中的动态平衡演化过程.模拟结果表明,理想的自由状态下,单层石墨烯薄膜并非完美的平面结构,表面不完全平整,在薄膜边缘处出现明显的波纹状褶皱,而在薄膜内部褶皱并不明显,多层石墨烯边缘处的起伏幅度要比单层石墨烯的稍小.     

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.     

Folding and cracking of graphene oxide sheets upon deposition

Graphene Oxide (GO) sheets, suspended in an aqueous solution, were deposited on freshly cleaved highly oriented pyrolytic graphite (HOPG) and studied using Raman spectroscopy, atomic force microscopy (AFM) and scanning tunneling microscopy (STM). AFM phase imaging shows a distinct contrast between GO and the underlying HOPG substrate. Raman spectroscopy clearly showed the presence of GO sheets on the top of HOPG substrate. The AFM and STM images also reveal wrinkling, folding, and tearing of individual GO sheets after depositing onto an HOPG substrate. We have also observed a distinct cracking of a GO sheet after folding. We attribute this new cracking phenomenon to a weakening of C–C bonds during the oxidation of a graphene sheet.     

Dynamic cavitations in incompressible hyperelastic pre-strained circular sheets

A class of dynamic cavitations is examined for an isotropic incompressible hyperelastic circular sheet under a pre-strained state caused by an initially applied finite radial tension.The solutions that describe the radially symmetric motion of the pre-strained sheet are obtained.The conditions of cavitated bifurcation that describe cavity formation and motion with time at the axial line of the pre-strained sheet are proposed,that is to say,a circular cavity will form if the suddenly applied radial tensile l...     

Buckling of hybrid nanocomposites with embedded graphene and carbon nanotubes

With the aid of atomistic multiscale modelling and analytical approaches, buckling strength has been determined for carbon nanofibres/epoxy composite systems. Various nanofibres configurations considered are single walled carbon nano tube (SWCNT) and single layer graphene sheet (SLGS) and SLGS/SWCNT hybrid systems. Computationally, both eigen-value and non-linear large deformation-based methods have been employed to calculate the buckling strength. The non-linear computational model generated here takes into account of complex features such as debonding between polymer and filler (delamination under compression), nonlinearity in the polymer, strain-based damage criteria for the matrix, contact between fillers and interlocking of distorted filler surfaces with polymer. The effect of bridging nanofibres with an interlinking compound on the buckling strength of nano-composites has also been presented here. Computed enhancement in buckling strength of the polymer system due to nano reinforcement is found to be in the range of experimental and molecular dynamics based results available in open literature. The findings of this work indicate that carbon based nanofillers enhance the buckling strength of host polymers through various local failure mechanisms.     

Nonlocal plate model for free vibrations of single-layered graphene sheets

Vibration analysis of single-layered graphene sheets (SLGSs) is investigated using nonlocal continuum plate model. To this end, Eringens's nonlocal elasticity equations are incorporated into the classical Mindlin plate theory for vibrations of rectangular nanoplates. In contrast to the classical model, the nonlocal model developed in this study has the capability to evaluate the natural frequencies of the graphene sheets with considering the size-effects on the vibrational characteristics of them. Solutions for frequencies of the free vibration of simply-supported and clamped SLGSs are computed using generalized differential quadrature (GDQ) method. Then, molecular dynamics (MD) simulations for the free vibration of various SLGSs with different values of side length and chirality are employed, the results of which are matched with the nonlocal model ones to derive the appropriate values of the nonlocal parameter relevant to each boundary condition. It is found that the value of the nonlocal parameter is independent of the magnitude of the geometrical variables of the system.     

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.