Adhesion mechanics of graphene membranes

The interaction of graphene with neighboring materials and structures plays an important role in its behavior, both scientifically and technologically. The interactions are complicated due to the interplay between surface forces and possibly nonlinear elastic behavior. Here we review recent experimental and theoretical advances in the understanding of graphene adhesion. We organize our discussion into experimental and theoretical efforts directed toward: graphene conformation to a substrate, determination of adhesion energy, and applications where graphene adhesion plays an important role. We conclude with a brief prospectus outlining open issues.     

Estimation of the Electron–Phonon Coupling Constants for Graphene and Metallic and Nonmetallic Substrates

Two modes of graphene–substrate interaction have been considered: a weak van der Waals bond and a strong covalent bond. The Lennard–Jones potential and Harrison bond-orbital method are used in the former and latter cases, respectively. Analytical expressions for the electron–phonon interaction constants, which contain only two parameters (binding energy E _B for graphene and a substrate and distance d between them) have been obtained. The constants have been calculated for metallic, semiconductor, and dielectric substrates.

     

Multiphonon Raman spectroscopy properties and Raman mapping of 2D van der Waals solids: graphene and beyond

Strong in‐plane bonding (covalent) and weak van der Waals (vdW) interplanar interactions characterize a number of layered solids, as epitomized by graphite. The advent of graphene (Gr), individual atomic two‐dimensional (2D) layers, isolated from mineral graphite via micromechanical exfoliation enabled the ability to pick, place and stack of arbitrary compositions. Moreover, this discovery implicated an access to other 2D vdW solids beyond graphene and artificially stacking atomic layers forming heterostructures/superlattices. Raman spectroscopy (RS) is a fast reliable non‐destructive analytical tool and an integral part for lattice dynamical structural characterization of crystalline solids at nanoscale, revealing not only the collective atomic/molecular motions but also localized vibrations/modes and specifically used to determine the number of graphene layers and of other 2D vdW solids. We present Raman spectroscopy in first‐, second‐ and higher‐order vibrational modes involving 3 and 4 phonons (overtones and combination) and mapping of graphene (mono‐, bi‐, tri‐ and few‐) layers, semiconducting transition metal dichalcogenides (TMDs) [molybdenum disulfide (MoS₂) and tungsten disulfide (WS₂)] and wide bandgap hexagonal boron nitride (h‐BN) dispersed monolayers, revealing various molecular vibrations and structural quality/disorder. First‐ and higher‐order phonon modes are observed and analyzed in terms of Raman intensity (spatial inhomogeneity or thickness variation), band position (intrinsic mechanical strain) and intensity ratio (structural disorder) as a function of graphene layer (n). An empirical relation for G band position with n is corroborated. All of the higher order modes are observed to upshift almost linearly with n, betraying the underlying interlayer vdW interactions. These findings exemplify the evolution of structural parameters in layered materials in changing from 3‐ to 2‐ or low‐dimensional regime. The results are presented in view of applications of graphene by itself and in combination that help better understanding of physical and electronic properties for nano‐/optoelectronics. Copyright © 2015 John Wiley & Sons, Ltd.     

Guided modes in graphene waveguides with magnetic-electric barrier

An analysis of guided modes in graphene waveguides in the presence of magnetic-electric barrier is presented. The graphene waveguide is controlled by the gate voltages and the magnetic field by depositing two parallel ferromagnets on a dielectric layer. Both in the classical motion and Klein tunneling cases, the fundamental modes exist with the applied magnetic field. The electron wave propagation can be modulated in two different ways by changing the magnetic intensity or the incident energy. We hope that these characteristics can provide potential applications in the graphene-based waveguide devices.     

Nanoscale continuum calculation of basal dislocation core structures in graphite

In this work, we calculate the core structures of basal dislocations in graphite in a nanoscale continuum framework. The model consists of a stack of buffered Kirchhoff plates where the plates represent the covalent interactions within individual graphene sheets and the buffer layers represent the secondary interactions between them. In the mid-plane of the buffer layers, cohesive surfaces are introduced to account for the nonlinear deformations due to basal dislocations. The cohesive surface separation is governed by using an empirical 4-8 Lennard–Jones potential. Meanwhile, their relative shear sliding is governed by using a newly proposed empirical periodic stacking-fault potential. With these potentials, the core structures of full dislocations and partials are calculated and examined. It is shown that the full dislocations automatically split into partials that repel each other. The core sizes of individual partials, measured between peak stresses, are about 5?nm wide for the edge component and slightly narrower for the screw component. Since these sizes are about 10 times the lattice constant, they lend credence to our continuum model of basal dislocation cores in graphite. It is also shown that when the dislocations are densely packed on the same glide plane, i.e. in a pile-up, with spacing one to two times the core size, the split partials retain their individual identity with well-defined and well-separated stress peaks. Meanwhile, the membrane normal stresses in the graphene sheets rise considerably at the pile-up tips which, in turn, may provoke further deformation and damage modes such as kinking and delamination.     

Tunable Fano resonances in the ballistic transmission and tunneling lifetime in a biased bilayer graphene nanostructure

Dynamics of the Dirac fermions, in particular the transmission coefficient and the resonant tunneling lifetime are studied across a bilayer graphene electrostatic double barrier structure modulated by an in plane homogeneous electric field. Asymmetric Fano type resonances are noted for the first time in the transmission spectrum of the bilayer graphene nanostructures and are found to be highly sensitive to the direction of incidence of the charge carriers and the applied homogeneous electric field. The effect of the external field on the extended and the evanescent modes is also analysed. Resonant tunneling lifetime is found to be highly anisotropic in nature. The chiral carriers are either accelerated or decelerated by the electric field depending on the energy of the quasi-bound states, the angle of incidence and the magnitude of the applied field. Effects of the external field on the localization of the chiral carriers are also discussed.     

Quantized electrons and holes in tellurium surfaces

A calculation has been made for surface phonons at the (001) surface of some fcc and bcc transition metals. A model consisting of first and second neighbor central interactions together with angle bending forces is used. The general harmonic approximation is used. A least mean square fit of the bulk phonon spectrum determines the parameters characterizing the interactions. Specific results have been obtained for surface phonons of Pt, Pd, Cu and Ag as well as Fe and W. The effect of varying the force constant near the surface is also reported showing the possibility for the existence of soft surface modes which may account for superstructures.     

石墨烯-纳米探针相互作用有限元准静态计算

纳米尺度探针是研究纳米薄膜材料的重要工具.针对纳米探针和石墨烯相互作用有限元模型静态计算中难以收敛的困难,应用动态显式算法通过间歇式探针进给方式进行能量耗散,得出静态计算结果.模型中界面作用力由界面黏结能和原子间作用势导出并植入Abaqus软件中界面作用子程序,实现对石墨烯、探针,基体系统内相互作用的仿真计算.通过对比计算结果和实验数据,对实验结果给出了一致性解释.     

Nonlinear dynamics of bi-layered graphene sheet,double-walled carbon nanotube and nanotube bundle

Due to strong van der Waals (vdW) interactions, the graphene sheets and nanotubes stick to each other and form clusters of these corresponding nanostructures, viz. bi-layered graphene sheet (BLGS), double-walled carbon nanotube (DWCNT) and nanotube bundle (NB) or ropes. This research work is concerned with the study of nonlinear dynamics of BLGS, DWCNT and NB due to nonlinear interlayer vdW forces using multiscale atomistic finite element method. The energy between two adjacent carbon atoms is represented by the multibody interatomic Tersoff–Brenner potential, whereas the nonlinear interlayer vdW forces are represented by Lennard-Jones 6–12 potential function. The equivalent nonlinear material model of carbon–carbon bond is used to model it based on its force–deflection relation. Newmark’s algorithm is used to solve the nonlinear matrix equation governing the motion of the BLGS, DWCNT and NB. An impulse and harmonic excitations are used to excite these nanostructures under cantilevered, bridged and clamped boundary conditions. The frequency responses of these nanostructures are computed, and the dominant resonant frequencies are identified. Along with the forced vibration of these structures, the eigenvalue extraction problem of armchair and zigzag NB is also considered. The natural frequencies and corresponding mode shapes are extracted for the different length and boundary conditions of the nanotube bundle.     

Guided modes in asymmetric graphene waveguides

An asymmetric quantum well in graphene can act as a slab waveguide for electron waves in a manner analogous to the electromagnetic waves in dielectrics. Guided modes and the probability current density are analyzed in the graphene electron waveguide induced by asymmetric electrostatic potential. The modes in an asymmetric graphene waveguide include guided modes, “cover modes”, “substrate modes” and “radiation modes”. The conditions for a guided mode are quantified. It is found that the fundamental mode is absent when both the Klein tunneling and classical motion are present. The confinement of electrons for lower order mode is stronger than for higher order mode. We hope that these characteristics in asymmetric graphene waveguide can provide potential applications in graphene-based waveguide devices.     

Computation of elastic moduli of graphene monolayer in nonsymmetric formulation using energy-based approach

In the paper, elastic moduli of finite-sized graphene monolayers are computed in a nonsymmetric formulation using the lattice statics approach. The motion of atoms due to their interaction is not considered, lattice stability is not studied. The presence of covalent binding is assumed to preserve material structure and all atoms are assigned displacements that correspond to a homogeneous deformation gradient tensor. As a result, the deformation kinematics of graphene is strictly controlled and the material response is defined using a variant of the interatomic interaction potential of the Mie family. The dimensionless parameters of the potential are identified using the coincidence criterion of the experimentally determined Poisson ratio of graphene with an estimated value. The obtained potential parameters are used to determine the elastic properties of a graphene monolayer in a nonsymmetric formulation for low strains and low temperatures. It is shown that the graphene monolayer under homogeneous deformation goes to a nonequilibrium state. In order to provide the potential energy minimum of the specimen in the deformed state, it is necessary to assign displacements to a part of graphene atoms that form one of its “triangular” sublattices relative to atoms of another sublattice, with each sublattice being deformed homogeneously.     

等离激元增强的石墨烯光吸收

石墨烯中等离激元具有特殊的光电性质,其和入射光的强烈耦合可以引起光吸收的增强.本文基于时域有限差分法和多体自洽场理论研究了等离激元对处于光学谐振腔中的石墨烯光吸收的影响.由于石墨烯中等离激元与入射光动量和能量不匹配而不能直接相互作用,因此石墨烯上施加了金属光栅结构.研究发现光栅结构能够对入射光进行动量补偿并且能够引起其下石墨烯中的电场强度产生很大程度增强,从而导致在该石墨烯结构中太赫兹等离激元和入射光发生强烈耦合而产生太赫兹等离极化激元,同时引起石墨烯光吸收的增强.希望本文能够加深对石墨烯光电特性的理解以及可以为基于石墨烯的太赫兹光电装置提供一定的理论依据.     

Probing the interaction of ionic liquids with graphene using surface‐enhanced Raman spectroscopy

We report an in situ measurement of the interaction of an imidazolium‐based room temperature ionic liquid with both pure silver and a graphene‐over‐silver electrode under an applied electrochemical potential. At a negative applied potential, overall signal intensity increased indicating enhanced ionic liquid concentration at both silver and graphene electrodes. Vibrational modes associated with the imidazolium ring exhibited greater intensity enhancements and larger peak shifts compared with the anion indicating that the cation adsorbs with the ring and alkyl chain parallel to the electrode surface for both silver and graphene. In contrast to the silver, the surface enhanced Raman spectra of the ionic liquid near graphene showed shifts in the cation peaks even at no applied potential because of the strong π–π interaction between the ionic liquid and the graphene. Furthermore, the intensity of the graphene peak decreased in the presence of ionic liquid possibly due to the interaction between the ionic liquid and graphene. These results illustrate the effectiveness of surface‐enhanced Raman spectroscopy to investigate electrolyte interactions with graphene at the liquid/electrode interface. Copyright © 2015 John Wiley & Sons, Ltd.     

Surface vibrations on face centered cubic metal surfaces: the (111) surfaces

We have studied the dynamics of atom motion at face centered metal (111) surfaces. The interactions between atoms are modelled with central forces and angle bending forces. Results for frequencies and polarizations of surface modes are presented for the following metals: Ag, Al, Au, Cu, Ni, Pd and Pt. In addition, the results obtained for phonon spectral densities are presented for nickel.     

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.     

Diamond-like C2H nanolayer, diamane: Simulation of the structure and properties

We consider a new C₂H nanostructure based on bilayer graphene transformed under the covalent bond of hydrogen atoms adsorbed on its external surface, as well as compounds of carbon atoms located opposite each other in neighboring layers. They constitute a “film” of the 〈111〉 diamond with a thickness of less than 1 nm, which is called diamane. The energy characteristics and electron spectra of diamane, graphene, and diamond are calculated using the density functional theory and are compared with each other. The effective Young’s moduli and destruction thresholds of diamane and graphene membranes are determined by the molecular dynamics method. It is shown that C₂H diamane is more stable than CH graphane, its dielectric “gap” is narrower than the band gap of bulk diamond (by 0.8 eV) and graphane (by 0.3 eV), and is harder and more brittle than the latter.     

Rippled graphene in an in-plane magnetic field: effects of a random vector potential

We report measurements of the effects of a random vector potential generated by applying an in-plane magnetic field to a graphene flake. Magnetic flux through the ripples cause orbital effects: Phase-coherent weak localization is suppressed, while quasirandom Lorentz forces lead to anisotropic magnetoresistance. Distinct signatures of these two effects enable the ripple size to be characterized.     

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.     

Interplay between out-of-plane magnetic plasmon and lattice resonance for modified resonance lineshape and near-field enhancement in double nanoparticles array

Two-dimensional double nanoparticle （DNP） arrays are demonstrated theoretically, supporting the interaction between out-of-plane magnetic plasmons and in-plane lattice resonances, which can be achieved by tuning the nanoparticle height or the array period due to the height-dependent magnetic resonance and the periodicity-dependent lattice resonance. The interplay between the two plasmon modes can lead to a remarkable change in resonance lineshape and an improvement on magnetic field enhancement. Simultaneous electric field and magnetic field enhancement can be obtained in the gap region between neighboring particles at two resonance frequencies as the interplay occurs, which presents “open” cavities as electromagnetic field hot spots for potential applications on detection and sensing. The results not only offer an attractive way to tune the optical responses of plasmonic nanostructure, but also provide further insight into the plasmon interactions in periodic nanostructure or metamaterials comprising multiple elements.