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.     

Variational principles for multi-walled carbon nanotubes undergoing buckling based on nonlocal elasticity theory

Variational principles are derived for multi-walled carbon nanotubes undergoing buckling using the semi-inverse method. Derivations are based on the continuum modelling of nanotubes taking into account small scale effects via the nonlocal theory of elasticity. Natural and geometric boundary conditions for multi-walled nanotubes are derived which leads to a set of coupled boundary conditions.     

Explicit expressions of mechanical properties for graphene sheets and carbon nanotubes via a molecular-continuum model

Through the equivalence of potential energy and elastic strain energy, a molecular-continuum model combining the concepts of molecular dynamics and continuum mechanics is proposed. Unlike the usual test performed by applying forces, in this model a uniform strain field is employed in the representative volume element of specimens. Through this model, the Young’s moduli, Poisson’s ratios, and shear modulus of graphene sheets and carbon nanotubes (armchair, zigzag, or chiral) can all be written as a simple rational function in which the dependence of radius, chiral angle and thickness can be observed clearly from the explicit closed-form expression. Moreover, according to the proposed molecular-continuum model, an integrated symbolic and numerical computational scheme (ISNC) is established to deal with the general nanoscale elastic solids. Identical results of the closed-form solutions and ISNC verify the correctness of our derivation. Comparison with the results obtained by the other methods or by different potential energy function further justifies the simplicity, validity and efficiency of the proposed model.     

Anomalous increase in the thermopower in a graphene monolayer formed on a tunable graphene bilayer

The conductivity and thermopower of a graphene monolayer formed on a tunable graphene bilayer have been studied within a simple model. It has been shown that kinks of the conductivity and peaks of the thermopower of the graphene monolayer appear near the edges of the band gap of the tunable graphene bilayer.     

Perfect absorption in a monolayer graphene at the near-infrared using a compound waveguide grating by robust critical coupling

We present a perfect graphene absorber with a compound waveguide grating at the near-infrared. The analytical approach is mainly based on the coupled leaky mode theory, which turns the design of the absorber to finding out the required leaky modes supported by the grating structure. Perfect absorption occurs only when the radiative loss of the leaky mode matches the intrinsic absorption loss, which is also named the critical coupling condition.Furthermore, we also demonstrate that the critical coupling of the system can be robustly controlled, and the perfect absorption wavelength can be easily tuned by adjusting the parameters of the compound waveguide grating.     

Wave propagation analysis in nonlinear curved single-walled carbon nanotubes based on nonlocal elasticity theory

Theoretical predictions are presented for wave propagation in nonlinear curved single-walled carbon nanotubes (SWCNTs). Based on the nonlocal theory of elasticity, the computational model is established, combined with the effects of geometrical nonlinearity and imperfection. In order to use the wave analysis method on this topic, a linearization method is employed. Thus, the analytical expresses of the shear frequency and flexural frequency are obtained. The effects of the geometrical nonlinearity, the initial geometrical imperfection, temperature change and magnetic field on the flexural and shear wave frequencies are investigated. Numerical results indicate that the contribution of the higher-order small scale effect on the shear deformation and the rotary inertia can lead to a reduction in the frequencies compared with results reported in the published literature. The theoretical model derived in this study should be useful for characterizing the mechanical properties of carbon nanotubes and applications of nano-devices.     

Computer stability test for aluminum films heated on a graphene sheet

The behavior of single- and double-sided monatomic aluminum films on graphene heated from 300 to 3300 K is studied by the molecular dynamics method. Atoms of single-sided coating are preserved on graphene up to 3300 K, while atoms of double-sided coating leave graphene even at 1800 K; upon a further increase in temperature, this leads to an increase in the horizontal and vertical components of the self-diffusion coefficient. The stresses produced by vertical forces are found to be most significant in metallic films; these stresses almost disappear when temperature reaches 2300 K. The stresses in graphene, the highest of which are concentrated in the zone of formation of the metal film, substantially decrease upon heating.     

Probing the electronic structure and optical response of a graphene quantum disk supported on monolayer graphene

In this paper, we show that a graphene quantum disk (GQD) can be generated on monolayer graphene via structural modification using the electron beam. The electronic structure and local optical responses of the GQD, supported on monolayer graphene, were probed with electron energy-loss spectrum imaging on an aberration-corrected scanning transmission electron microscope. We observe that for small GQD, ~1.3 nm in diameter, the electronic structure and optical response are governed by the dominating edge states, and are distinctly different from either monolayer graphene or double-layer graphene. Highly localized plasmon modes are generated at the GQD due to the confinement from the edge of the GQD in all directions. The highly localized optical response from GQDs could find use in designing nanoscale optoelectronic and plasmonic devices based on monolayer graphene.     

Size-dependent geometrically nonlinear free vibration analysis of fractional viscoelastic nanobeams based on the nonlocal elasticity theory

In recent decades, mathematical modeling and engineering applications of fractional-order calculus have been extensively utilized to provide efficient simulation tools in the field of solid mechanics. In this paper, a nonlinear fractional nonlocal Euler–Bernoulli beam model is established using the concept of fractional derivative and nonlocal elasticity theory to investigate the size-dependent geometrically nonlinear free vibration of fractional viscoelastic nanobeams. The non-classical fractional integro-differential Euler–Bernoulli beam model contains the nonlocal parameter, viscoelasticity coefficient and order of the fractional derivative to interpret the size effect, viscoelastic material and fractional behavior in the nanoscale fractional viscoelastic structures, respectively. In the solution procedure, the Galerkin method is employed to reduce the fractional integro-partial differential governing equation to a fractional ordinary differential equation in the time domain. Afterwards, the predictor–corrector method is used to solve the nonlinear fractional time-dependent equation. Finally, the influences of nonlocal parameter, order of fractional derivative and viscoelasticity coefficient on the nonlinear time response of fractional viscoelastic nanobeams are discussed in detail. Moreover, comparisons are made between the time responses of linear and nonlinear models.     

Temperature effects on the magnetoplasmon spectrum of a weakly modulated graphene monolayer

In this work, we determine the effects of temperature on the magnetoplasmon spectrum of an electrically modulated graphene monolayer as well as a two-dimensional electron gas (2DEG). The intra-Landau band magnetoplasmon spectrum within the self-consistent field approach is investigated for both the aforementioned systems. Results obtained not only exhibit Shubnikov-de Haas (SdH) oscillations but also commensurability oscillations (Weiss oscillations). These oscillations are periodic as a function of inverse magnetic field. We find that both the magnetic oscillations, SdH and Weiss, have a greater amplitude and are more robust against temperature in graphene compared to a conventional 2DEG. Furthermore, there is a π phase shift between the magnetoplasmon oscillations in the two systems which can be attributed to Dirac electrons in graphene acquiring a Berry's phase as they traverse a closed path in a magnetic field.     

Electron scattering in the monolayer graphene with a band-asymmetric annular potential well

Electron scattering in the monolayer graphene has been considered within the framework of our model of short-range defects proposed earlier. Electronic properties are determined by the Dirac equation for the two-component spinor wave function. Perturbation is modeled by the annular well with a band-asymmetric potential. Band-asymmetry of the potential stems from the local structure defect and leads to the mass (gap) perturbation in the Dirac equation. Transitions between the K and K’ critical points in the Brillouin zone are neglected, which is valid provided that the short-range perturbation has a finite radius. Exact explicit formulas for the scattering matrix have been derived. Results are presented in terms of the scattering phases and in the geometrical form of a relation between some 2-vectors. The characteristic equation for the bound and resonance states has been obtained in the form of an orthogonality condition. An approximate calculation of observables in terms of the scattering theory results is outlined.     

Synthesis of graphene from naphthalene molecules on the surface of a Langmuir monolayer

This paper considers some approaches to the technology of the synthesis of a graphene monolayer at a phase interface. A surfactant monolayer on an aqueous subphase is proposed as the substrate for graphene synthesis. A monolayer is formed by the Langmuir–Blodgett method. Simple polyaromatic molecules, in particular, naphthalene, are considered as the basic substance for the synthesis of graphene. Arachidic acid is used as the basic surfactant molecule. To confirm the possibility of synthesizing graphene by the mentioned method, both experimental and theoretical studies are performed. In the course of experiemnts, it is shown that naphthalene molecules are pressed into the space above arachidic acid molecules upon the compression of monolayer of arachidic acid–naphthalene mixtures (such an assumption is made due to the characteristic value of the surface areas attributed to different phases of the monolayer and also to its characteristic parameters). The formation of a layer of naphthalene molecules on the surface of a monolayer is modeled by the molecular dynamics method (Amber potential). Different variants of the initial distribution of molecules are considered.     

Modeling and active vibration suppression of a single-walled carbon nanotube subjected to a moving harmonic load based on a nonlocal elasticity theory

This paper investigates active vibration suppression of a single-walled carbon nanotube (SWCNT) under the action of a moving harmonic load using Eringen’s nonlocal elasticity theory. The SWCNT is modeled according to the nonlocal Euler–Bernoulli beam theory. A Dirac-delta function is used to describe the position of the moving load along the SWCNT. Next, a linear classical optimal control algorithm with displacement-velocity feedback is used to suppress vibration in the SWCNT with control forces acting as actuators. The effects of a small-scale parameter, slenderness ratio, moving load velocity, and the excitation frequency of a moving load on the dynamic deflection of the SWCNT are examined. Finally, the ability of the control algorithm to suppress the response of the SWCNT under the effects of a moving load with a number of controlled modes and control forces is surveyed.     

High-sensitive refractive index sensing and excellent slow light based on tunable triple plasmon-induced transparency in monolayer graphene based metamaterial

A patterned monolayer graphene metamaterial structure consisting of six graphene blocks and two graphene strips is proposed to generate triple plasmon-induced transparency(PIT).TriplePIT can be effectively modulated by Fermi levels of graphene.The theoretically calculated results by coupled mode theory show a high matching degree with the numerically simulated results by finite-difference time-domain.Intriguingly,the high-sensitive refractive index sensing and excellent slow-light performance ca...     

Valley polarized electronic transport through a line defect in graphene: An analytical approach based on tight-binding model

We develop a tight-binding theory to study the electronic transport through an extended line defect in monolayer graphene. After establishing an analytical expression of the transmission probability, we clarify the following issues concerning the valley polarization in the electronic transport process. Firstly, we find that the valley polarization is robust in the total linear dispersion region. More interestingly, we find that the lattice deformation around the line defect play an important role in tuning the incident angle for complete transmission. Finally, we indicate that next nearest neighbor interaction only causes a small suppression to the valley polarization.     

Effect of edge vacancies on localized states in a semi-infinite zigzag graphene sheet

The effect of vacancies on the robustness of zero-energy edge electronic states in zigzag-type graphene layer is studied at different concentrations and distributions of defects. All calculations are performed by using the Green’s function method and the tight-binding approximation. It is found that the arrangement of defects plays a crucial role in the destruction of the edge states. We have specified a critical distance between edge vacancies when their mutual influence becomes significant and affects markedly the density of electronic states at graphene edge.     

Effect of a single localized impurity on the local density of States in monolayer and bilayer graphene

We use the T-matrix approximation to analyze the effect of a localized impurity on the local density of states in monolayer and bilayer graphene. For monolayer graphene the Friedel oscillations generated by intranodal scattering obey an inverse-square law, while the internodal ones obey an inverse law. In the Fourier transform this translates into a filled circle of high intensity in the center of the Brillouin zone, and empty circular contours around its corners. For bilayer graphene both types of oscillations obey an inverse law.     

Plasma waves in a superlattice based on graphene

The law of plasma wave dispersion in an electron gas in a superlattice based on graphene on a striped substrate is studied numerically. Calculations are performed based on the quantum theory of plasma waves in the approximation of random phases with allowance for umklapp processes. The estimated plasmon frequencies for the graphene-based superlattices on striped substrates now under theoretical study is ω ≤ 10¹⁴ s^?1.