Double-layered Graphene Sheets Research Articles

Optical force conversion and conveyor belt effect with coupled graphene plasmon waveguide modes.

We propose a double-layer graphene sheets side coupling to a strip of graphene to obtain the optical pulling or pushing force. Combined with coupled mode theory and finite-difference time-domain simulations, it is found that the conveyor belt effect can be realized in conjunction with the lateral optical equilibrium effect upon the radiation loss κe equal to the intrinsic loss κo. The maximum total optical force acting on the strip in the symmetric mode (S-mode) can be up to ∼5.95 in the unit of 1/c and the anti-symmetric (AS-mode) mode reach ∼2.75 1/c. The optical trapping potential Ux and optical trapping force Fx for the S-mode have a value around -22.5 kBT/W and 240 pN/W, while for the AS-mode can up to ∼-56 kBT/W and 520 pN/W, respectively. Our work opens a new avenue for optical manipulation with potential applications in optoelectronic devices and lab-on-a-chip platforms.

Chaotic vibrations of double-layer graphene sheet system

Nonlinear vibrations of double-layer nanoplate system are studied by numerical simulation. The governing equations are derived on a base of the nonlocal elasticity theory, von Kármán nonlinear theory, and Kirchhoff’s hypotheses. Both layers are assumed to be with the same material properties, while interaction between them is taken by the Winkler model. Discretization of the system of governing differential equations is performed by the Bubnov-Galerkin method with the two-mode approximation model, and the obtained system of ordinary differential equations is analysed by the Runge–Kutta method. The study of a linearized system allows the construction of regions of instability. The application of nonlinear dynamics methods made it possible to determine the nature of oscillations when stability is lost, and when small-scale effects are manifested.

Nanoresonator vibrational behaviour analysis of single- and double-layer graphene with atomic vacancy and pinhole defects

Nanosensors and actuators are frequently made of graphene. Any defect in the graphene's manufacturing has an impact on its sensing performance and on its dynamic behaviour. Using a molecular dynamics technique, the influence of pinhole defects and atomic defects on the performance parameters of single-layer graphene sheets (SLGSs) and double-layer graphene sheets (DLGSs) with various boundary conditions and lengths is explored. In contrast to the perfect nanostructure of a graphene sheet, defects are described as holes formed by atomic vacancies. As the number of defects increases, the simulation results show that the presence of defects has the greatest impact on the resonance frequency of SLGSs and DLGSs. The influence of pinhole defect (PD) and atomic vacancy defect (AVD) on armchair, zigzag, and chiral SLGSs and DLGSs was investigated in this article using molecular dynamics simulation. The influence of both types of defects is largest when it is adjacent to the fixed support for all three different types of graphene sheets, i.e. armchair, zigzag, and chiral. The structure of the graphene sheet has been created using ANSYS APDL software. In the structure of the graphene sheet, atomic and pinhole defects have been generated. SLG and DLG sheets are modelled using a space frame structure that is identical to a three-dimensional beam. Dynamic analysis of single-layer and double-layer graphene sheets performed with different lengths using the atomistic finite element method. The interlayer separation in the form of Van der Waals interaction is modelled using characteristic spring element (Combin14). The upper and lower sheets of DLGSs are described as elastic beams connected by a spring element. With atomic vacancy defect for the bridged boundary condition, the highest frequency of 2.86 × 108 Hz was found for zigzag DLG (20 0) and with same boundary condition for pinhole defect 2.79 × 108 Hz frequency achieved. In a single-layer graphene sheet with an atomic vacancy and cantilever boundary condition, the maximum efficiency was 4.13 × 103 Hz for SLG (20 0), while in a pinhole defect, it produced 2.73 × 107 Hz. Moreover, the elastic parameters of beam components are calculated using the mechanical properties of covalent bonds between carbon atoms in the hexagonal lattice. The model has been tested against previous research. The focus of this research is to develop a mechanism for determining how defects affect graphene frequency band in application as nano resonators.

The nonlocal elasticity theory for geometrically nonlinear vibrations of double-layer nanoplate systems in magnetic field

The geometrically nonlinear vibrations of simply supported double-layer graphene sheet systems under in-plane magnetic field are considered in the presented manuscript. The interaction between layers is taken into account due to van der Waals forces. The investigation is based on the nonlocal elasticity theory, Kirchhoff plate theory and von Kármán theory. The effect of the magnetic field is due to the Lorentz force based on Maxwell’s equations. The governing equations are used in mixed form by introducing the stress Airy function. The analytical presentation of the nonlinear frequency ratio for in-phase vibration and anti-phase vibration modes is presented. It is shown that the nonlocal parameter in the compatibility equation can significantly change the vibration characteristics.

Analytical Investigation and Systematic Design Approach for High-Sensitivity Guided Mode Resonance Sensors With Graphene-Enabled Tunability

The high quality factor of guided mode resonance (GMR) structures and their sensitivity to the adjacent media’s refractive index (RI) make them excellent candidates for sensing applications. In this study, we derive analytical sensitivity equations for the GMR structures for the first time, which can be utilized to better understand and optimize their behavior. The simulated structures (based on the finite element method) show excellent agreement with the analytical sensitivities for both the transverse electric and magnetic (TE and TM) modes. The effects of waveguide height, working wavelength, and material RIs on the obtained sensitivities were surveyed, which helped achieve a design approach based on the analytical equations. The substrate RI should be as low as possible for any application. For analytes, the RI of the waveguide thin film should be low, whereas this trend is different for gas sensors; there is an optimum RI for the waveguide in the TE mode, and in the TM mode, the waveguide should have a higher possible RI. Moreover, the TM-mode gas sensors exhibit optimum sensitivity for a specified waveguide height. The design approach was used for a gas sensor operating at methane resonance wavelength (1653.7 nm), which can be tuned using a double-layer graphene sheet. A linear tunability of up to 5 nm was achieved using 1 eV chemical potential adjustment, whereas the device sensitivity remains between 291.9 to 295.5 nm/RIU. Moreover, higher sensitivities up to 950 nm/RIU can be obtained for analyte sensors at 1550 nm.

Buckling analysis of single and double-layer annular graphene sheets in thermal environment

Buckling analysis of single and double-layer annular graphene sheets in thermal environment

A continuum PNP model of double species ion transport between graphene

In this paper, we employ Poisson–Nernst–Planck equations in conjunction with the Navier–Stokes equations and the mean-field theory to investigate the charge transport of double species monovalent ions in double-layered graphene sheets, driven by an external electric field. Unlike most classical models, we develop a simple mechanical model by incorporating the microscopic effects of the physical systems so that the ionic interactions between ions and the host material, and the steric repulsions among ions are considered. Taking Li+-PF6−1 monovalent ions as an example, we find that the transport pattern for the present double species ionic systems and that for the pure lithium ions are dramatically different. Due to the mutual attractive ionic forces between ions and their counter-ions, such double species systems turn out to be more stable than that of the single species systems. In addition, the storage patterns of the former systems are richer, which depend heavily on initial ionic states, however less on the strength of applied electric fields and external temperatures when the graphene separation is not too large. The fluid flows, the electric conductivities and the stability of such double species systems are subsequently scrutinized. The current study could form a theoretical basis to help designing high-performance lithium batteries and explaining ion transport in biological channels.

FREE AND FORCED VIBRATIONS OF DOUBLE-LAYERED VISCOELASTIC ORTHOTROPIC GRAPHENE SHEETS WITH A HIGH-ORDER SURFACE STRESS EFFECT

Transverse vibrations of a double-layered viscoelastic orthotropic graphene sheet system are investigated. The two sheets in the system are coupled by the visco-Pasternak medium. General governing equations for free and forced vibrations of the double-layered graphene sheet system with a high-order surface stress effect are formulated. Theoretical solutions for the damped vibrational frequency, damping ratio, and relative deflection of the two sheets with simply supported boundary conditions are obtained. The effects of the high-order surface stress on the damped frequency and damping ratio of the system for in-phase and out-of-phase free vibrations are discussed. The impacts of the high-order surface stress, structural damping, medium damping, Winkler modulus, and shear modulus of the medium on the relative deflection of the two sheets for forced vibrations are investigated. It is demonstrated that the high-order surface stress effects on the vibrational properties of the system are more significant than those of the conventional surface stress.

Free and Forced Vibrations of Double-Layered Viscoelastic Orthotropic Graphene Sheets with a High-Order Surface Stress Effect

Free and Forced Vibrations of Double-Layered Viscoelastic Orthotropic Graphene Sheets with a High-Order Surface Stress Effect

Mechanical analysis of eccentric defected bilayer graphene sheets considering the van der Waals force

In this article, we have tried to simulate nonlinear bending analysis of a double-layered graphene sheet which contains a geometrical imperfection based on an eccentric hole. The first-order shear deformation theory is considered to obtain the governing equations. Also, the nonlinear von Kármán strain field has been assumed in order to obtain large deformations. Whereas the double-layered graphene sheet has been considered, the effect of van der Waals forces has been taken into account in the analysis. In order to implement the nanoscale impact, the nonlocal elasticity theory has been employed. The solution methodology, which is here based on the semi-analytical polynomial method solving technique presented previously by the authors, has been applied and again its efficiency has been demonstrated due to its highly accurate results. Due to the fact that this research has been done for the first time and there is no validation available, the results of the local single layer sheet are compared with ABAQUS software. The effects of some other parameters on the results have been studied such as the value of eccentricity, van der Waals interaction, and nonlocal parameter.

Molecular dynamics simulations of single-layer and rotated double-layer graphene sheets under a high velocity impact by fullerene

Molecular dynamics (MD) simulations are employed in this paper to study the behavior of single-layer and rotated double-layer graphene sheets under a high velocity impact. The AIREBO force field is used for MD simulations. Stress wave propagation is investigated, and cone-wave and axial-wave velocities are determined. The coefficient of restitution for the double-layer graphene sheet is calculated at different impact incident angles and velocities. Impact and rebound kinetic energy of projectile under the impact simulation of different rotation angles double-layer graphene sheet is monitored. High cone-wave and axial-wave velocities show that single-layer and double-layer graphene sheets have potential applications in impact protection materials.

Nonlinear Vibration and Stability Analysis of Thermally Postbuckled Double-Layered Graphene Sheet under 1:1 and 3:1 Internal Resonance

In the present research, vibration behavior is presented for a thermally postbuckled double layered graphene sheet (DLGS). The DLGS is modeled as a nonlocal orthotropic plate and contains small-scale effects. The formulations are based on Kirchhoff’s plate theory and nonlinearity of von Karman type is considered in strain–displacement relations. The thermal effects, van der Waals forces between layers and chirality are also included, and some of the material properties are assumed to be temperature-dependent. A coupled system of equations is derived and a new semi-analytical solution is obtained using multiple time-scale methods. The effects of variation of small-scale parameter on the natural frequencies, deflections and response curve of DLGS are analyzed, and the numerical results are obtained from the nonlocal plate model; also, molecular dynamics (MD) simulations are used to investigate different vibration behaviors of DLGS and calibration of the small-scale coefficient. Numerical results are compared with those of similar researches. Effects of various parameters on the postbuckled vibration of DLGS in thermal environments such as scale parameter, environmental damping, length and thermal load are presented. The stability and occurrence of internal resonance between vibration modes around a stable buckled configuration are investigated.

Buckling and Vibration Analysis of a Double-layer Graphene Sheet Coupled with a Piezoelectric Nanoplate

In this article, the vibration and buckling of a double-layer Graphene sheet (DLGS) coupled with a piezoelectric nanoplate through an elastic medium (Pasternak and Winkler models) are under consideration. DLGS are subjected to biaxial in-plane forces and van der Waals force existing between each layer. Polyvinylidene fluoride (PVDF) piezoelectric nanoplate is subjected to an external electric potential. For the sake of this study, sinusoidal shear deformation theory of orthotropic plate expanded with Eringen’s nonlocal theory is selected The results indicate that nondimensional frequency and nondimensional critical buckling load rise, when the ratio of width to thickness increases. Furthermore, incrementing the effect of elastic medium parameter results in increasing the stiffness of the system and, consequently, rising nondimensional frequency and critical buckling load.

Flexural Wave Propagation of Double-Layered Graphene Sheets Based on the Hamiltonian System

Double-layered graphene sheets (DLGSs) as a new type of nanocomponents, with special mechanical, electrical and chemical properties, have the potential of being applied in the nanoelectro-mechanical systems (NEMS) and nanoopto-mechanical systems (NOMS). In DLGSs structure, the two graphene sheets are connected by van der Waals (vdW) interaction. Thus, it can exhibit two vibration modes during the propagation of the flexural wave, i.e., in-phase mode and anti-phase mode. Based on the Kirchhoff plate theory and the nonlocal elasticity theory, Hamiltonian equations of the DLGSs are established by introducing the symplectic dual variables. By solving the Hamiltonian equation, the dispersion relation of the flexural wave propagation of the DLGSs is obtained. The numerical calculation indicates that the bending frequency, phase velocity and group velocity of the in-phase mode and anti-phase mode for the DLGSs are closely related to the nonlocal parameters, the foundation moduli and the vdW forces. The research results will provide theoretical basis for the dynamic design of DLGSs in micro-nanofunctional devices.

Nonlinear Forced Vibration of Thermally Postbuckled Double-Layered Triangular Graphene Sheet with Clamped Boundary Conditions

In the present research, vibration behavior is presented for a thermally postbuckled double-layered triangular graphene sheet (DLTGS). The DLTGS is modeled as a nonlocal orthotropic plate and contains small-scale effects. The formulations are based on the Kirchhoff’s plate theory, and a nonlinearity of von Karman-type is considered in strain–displacement relations. The thermal effects and van der Waals forces between layers are also included and some of the material properties are assumed to be temperature-dependent. A semi-analytical solution is obtained using the multiple time scales method. The effects of variation of small-scale parameter to the natural frequencies, deflections and response curve of DLTGS are analyzed, and the numerical results are obtained from the nonlocal plate model. Numerical results are compared with those of similar researches. Effects of various parameters on the postbuckled vibration of DLTGS in thermal environments such as scale parameter and thermal load are presented. The stability and occurrence of the internal resonance between vibration modes around a stable buckled configuration is investigated.

Impact and vibration response of multi-layered graphene sheets under different striker based on the analytical model and molecular dynamics

An impact behavior of striker on double-layered (DLGS) and multi-layered (MLGS) graphene sheet is investigated based on three degrees of freedom spring-mass model and the molecular dynamics (MD) simulations. The van der Waals (vdW) interaction between two layers of a DLGS is incorporated in the analytical model. An analytical model is able to predict the time history of deflection and vibration of the graphene sheets (GSs) and MD simulation cooperates various values of a dimension, chirality, boundary condition, number of layered and also striker parameters such as mass, velocity, and geometry. The analytical method is verified by MD simulations. The results from the spring-mass model demonstrated good agreement with MD simulation for a square and rectangular DLGS. The analytical model also accounts the relative motion between two layered of GS that is due to the local indentation in upper GS as can be seen in MD simulation. The maximum deflection and vibration after impact by the sphere, cone, sharp cone, and block strikers are investigated by MD simulations.

Thermal Effect on Vibration Responses of Double-Layered Graphene Sheet–Based Nanomechanical Resonators Based on Galerkin Strip Transfer Function Method

Thermal effect on mass detection sensitivity of double-layered graphene sheet (DLGS) resonators based on their nonlocal vibration is investigated. A rectangular DLGS with a nanoparticle anywhere at the upper sheet is modeled as two nanoplates connected by van der Waals force. Based on the nonlocal Kirchhoff theory of plates which incorporates size effects into the classical theory, Galerkin strip transfer function method (GSTFM), which is a semi-analytical method, is developed to solve the characteristic equations and in settling the semi-analytical solutions of the frequency shift of the mass-plate vibrating system. It can give exact closed-form solutions along the strip longitudinal direction. Obtained results from the semi-analytical solutions are in good agreement with the available data in literature. Parametric studies on the natural frequency shift including the temperature changes, the nonlocal parameter and the location of the attached nanoparticle are discussed. The obtained results show that an increase of the temperature difference yields to reduction of fundamental frequency, and the DLGS-based nanomechanical resonator became more sensitive at a negative temperature change. Those conclusions are helpful to the design and application of GS-based resonator as nanomass sensor.

A continuum study of layer analysis for single species ion transport inside double-layered graphene sheets with various separations

We investigate the formation of thin ionic layers driven by electro-osmotic forces, that are commonly found in micro- and nano-channels. Recently, multi-layers have been reported in the literature. However, the relation between classical Debye layers and multi-layers, which is a practically and fundamentally important question, was previously unexplained. Here, we fill this gap by using a continuum approach to investigate the flow of lithium ions inside double-layered graphene sheets. Fluid flow, charge conductivity and thermal stability will be investigated. We show that the separation and strength of forces between the sheets, the external electric field and thermal effects determine the topology of the ionic layers between the graphene sheets.

NEMS Resonators for Detection of Chemical Warfare Agents Based on Graphene Sheet

Graphene sheets are the basis of nanoelectromechanical (NEMS) mass resonators that are in recent years experimentally used for detection of specific gas molecules in air. The aim of this paper is to theoretically investigate the possibility of application of graphene sheets in detection of Chemical Warfare Agents (CWA’s). By application of the nonlocal theory of elasticity and classical plate theory, equations that describe natural vibrations of the simply supported single-layer graphene sheet (SLGS) and double-layer graphene sheet (DLGS) were derived. In order to detect attached CWA molecule, the frequency shift method was applied. The results indicate that the proposed methodology could be successfully implemented in order to detect an attached CWA molecule. However, only specific mode shapes could be employed for such detection.

Computing Buckling Characteristics of Double-Layered Graphene Film Embedded in an Elastic Foundation

Given the unique and extremely valuable properties, research has significantly focussed on graphene sheets (GSs). To premeditate the small-scale effect, the present work applies the nonlocal theory to study the buckling behavior of a double-layered GS (DLGS) embedded in an elastic foundation. To derive the equation, classical plate theory is adopted. For the elastic foundation, Pasternak-type model is used. In terms of buckling response, a meshless method is utilized to compute simulation results. Accordingly, we examine the effects of aspect ratio, geometry, boundary conditions and nonlocal parameters on the buckling responses of DLGSs.