Zigzag Graphene Sheets Research Articles

Effect of chirality and defects on tensile behavior of carbon nanotubes and graphene: Insights from molecular dynamics

Molecular dynamic simulations based on AIREBO potential function with Nose-Hover thermostat technique have been performed in this study to predict the mechanical properties of pristine as well as defective graphene and carbon nanotubes (CNTs). The effect of structural defects such as point defects (PD) and Stone-Wales (SW) defects on the stress-strain distribution and ultimate strength have been explored under uniaxial tension. The simulations revealed that the defects decrease the strength of graphene sheets and CNTs. Both the strength and failure strain were found to decrease with an increase in the number of defects. The tensile strength was found to be halved on loading the graphene in the armchair direction as compared to loading in the zig-zag direction due to the extension of the carbon‑carbon bond in the armchair loading direction. The fracture strength of the pristine zigzag graphene sheet is higher than for the pristine armchair graphene sheet in case of uniaxial tensile loading. The failure strain of the zigzag graphene sheet is higher than the armchair graphene sheet. PDs have a greater impact on the degradation of strength of nanostructure than the SW defects. The higher the number of defects, the lower is the strength of the nanostructure.

MECHANICAL PROPERTIES, STABILITY, AND BUCKLING OF GRAPHENE SHEETS AND CARBON NANOTUBES (REVIEW)

A review of works devoted to the study of the mechanical properties, stability, and buckling of graphene and carbon nanotubes is presented. Most of these results are obtained by means of molecular dynamics and molecular mechanics, which make it possible to effectively investigate the mechanical properties and stability of nanostructures. The data on the strength of graphene are presented, and bending modes for chair and zigzag graphene sheets are analyzed. The stability and bending modes of natural vibrations of zigzag and chair nanotubes are analyzed.

BN-Doped Graphene and Single-Walled Carbon Nanotubes for the Catalysis of SN2 Reactions: Insights from Density Functional Theory Modeling.

The inner space of carbon nanotubes has already been proven to provide a type of confinement, which can dramatically alter the energetics of chemical reactions when compared to the gas phase. Moreover, BN doping can be used to fine-tune electronic properties, which might influence the enthalpy and activation energy of chemical reactions that take place inside their inner space. The energy profile of the prototype Menshutkin SN2 reaction between ammonia and chloromethane has been analyzed in a variety of carbon-based materials at the DFT (density functional theory) level. Pristine zigzag (9,0) and (12,0) single-walled carbon nanotubes and graphene sheets have been doped with boron and nitrogen at different stoichiometries, namely, BN, BNC, BNC2, and BNC4, that resulted in remarkable variations of their catalytic effects. Graphene has revealed to be the support material, which depends less on doping in terms of enthalpy and energy barrier of the reaction. However, when graphene is rolled up into tubular forms, the influence of doping becomes increasingly stronger as the nanotube radius decreases. In the case of BNC4 doping of (9,0) nanotubes, the activation energy drops 10 kcal/mol when compared to the pristine case, and the reaction became even exothermic by more than 15 kcal/mol.

A Kriging Surrogate Model for Uncertainty Analysis of Graphene Based on a Finite Element Method.

Due to the inevitable presence of random defects, unpredictable grain boundaries in macroscopic samples, stress concentration at clamping points, and unknown load distribution in the investigation of graphene sheets, uncertainties are crucial and challenging issues that require more exploration. The application of the Kriging surrogate model in vibration analysis of graphene sheets is proposed in this study. The Latin hypercube sampling method effectively propagates the uncertainties in geometrical and material properties of the finite element model. The accuracy and convergence of the Kriging surrogate model are confirmed by a comparison with the reported references. The uncertainty analysis for both Zigzag and Armchair graphene sheets are compared and discussed.

Molecular dynamics simulation of shear deformation of multi-layer graphene sheets with Tersoff potential

The failure process of multi-layer graphene sheets with AB stacking order under shear deformation is simulated using molecular dynamics method with Tersoff potential. Shear stress-strain relationships and shear failure modes of zigzag and armchair graphene sheets are obtained, while the effect of the number of graphene layers on the shear properties of zigzag and armchair graphene sheets is investigated. The results indicate that the shear modulus of graphene sheets is inclined to diverge with the increase of the number of graphene layers. Moreover, the ultimate stress and shear failure strain of zigzag and armchair graphene sheets are reduced gradually with the increase of the number of graphene layers.

Molecular dynamics simulation of shear deformation of multi-layer graphene sheets with Tersoff potential

The failure process of multi-layer graphene sheets with AB stacking order under shear deformation is simulated using molecular dynamics method with Tersoff potential. Shear stress-strain relationships and shear failure modes of zigzag and armchair graphene sheets are obtained, while the effect of the number of graphene layers on the shear properties of zigzag and armchair graphene sheets is investigated. The results indicate that the shear modulus of graphene sheets is inclined to diverge with the increase of the number of graphene layers. Moreover, the ultimate stress and shear failure strain of zigzag and armchair graphene sheets are reduced gradually with the increase of the number of graphene layers.

A computational investigation of length-scale effects in the fracture behaviour of a graphene sheet using the atomistic J-integral

The overarching objective of this paper is to investigate the validity of application of continuum-based linear elastic fracture mechanics (LEFM) methodology, which is often employed by researchers to model fracture processes at the “discrete” atomic scale. The potential sources of error in the application of LEFM at the nanoscale are: (a) Length-scale effects, (b) non-local effects due to long range inter-atomic forces, and (c) entropic effects due to random thermal motion of atoms. The material selected for this study is monolayer graphene, primarily because extensive data, both experimental and analytical, already exist for this material in the literature for model validation. Further, an atomistic J-integral is implemented as a nano-scale fracture metric to investigate flaw-tolerance at the nanoscale reported by many researchers, and to develop a methodology to predict the initiation fracture toughness of the material. For this purpose, a bond-order based potential (ReaxFF) available in LAMMPS molecular dynamics (MD) software is utilized to accurately pinpoint bond separation. Predictions obtained using the atomistic J are compared with LEFM predictions for the case of a single (zig-zag) graphene sheet with a center-crack under tensile loading at room temperature, and show significant deviation from LEFM for crack lengths below a certain threshold.

An ordinary state-based peridynamic model for the fracture of zigzag graphene sheets.

This study develops an ordinary state-based peridynamic coarse-graining (OSPD-CG) model for the investigation of fracture in single-layer graphene sheets (SLGS), in which the peridynamic (PD) parameters are derived through combining the PD model and molecular dynamics (MD) simulations from the fully atomistic system via energy conservation. The fracture failure of pre-cracked SLGS under uniaxial tension is studied using the proposed PD model. And the PD simulation results agree well with those from MD simulations, including the stress-strain relations, the crack propagation patterns and the average crack propagation velocities. The interaction effect between cracks located at the centre and the edge on the crack propagation of the pre-cracked SLGS is discussed in detail. This work shows that the proposed PD model is much more efficient than the MD simulations and, thus, indicates that the PD-based method is applicable to study larger nanoscale systems.

Effect of Double-Atom Vacancy Defects on the Elastic Properties of Single-Layered Graphene Sheets

A molecular structural mechanics approach is used to study the effect of double-atom vacancy defects (DAVD) on the elastic properties of zigzag and armchair single-layered graphene sheets (SLGS). To this end, the space frame structure is also adopted to model the interatomic forces of the C–C bonds. The numerical simulation results obtained via the finite element method strongly suggest that double-atom vacancy defects reduce the elastic module of SLGS, which effect weakens with graphene size. Finally, the elastic modulus and Poisson’s ratio of SLGS are found to decrease with the number of DAVDs.

Compressive Buckling of Rippled Graphene via Molecular Dynamics Simulations

This paper studies the compressive buckling of near-square rippled monolayer graphene sheets in thermal environments by using molecular dynamics simulations. Armchair and zigzag graphene sheets are both considered and the four edges of a graphene sheet are either simply supported or clamped. Compressive force instead of the commonly used compressive strain is gradually applied to the edges of the graphene sheet until the graphene sheet is crushed. It is found that ripples in the graphene are formed owing to thermal fluctuations even before the compressive force is applied. The amplitude of ripples is reduced when the compressive force is applied to the graphene. The buckling mode of the graphene may show local or global mode shape features, depending on the chirality, the support conditions and the size of the graphene. Most buckling modes of the graphene sheets are very different from the global (1,1) mode of a uniaxially loaded and simply supported or clamped square plate as predicted by continuum mechanics models. A clamped graphene can take significantly more compressive force after the occurrence of initial buckling and before the graphene is completely crushed. A zigzag graphene has a larger initial buckling force than its armchair counterpart. Raising the environmental temperature may either increase or decrease the initial buckling force of the graphene depending on the support conditions and the chirality of the graphene.

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.

Ab Initio Modeling Of Friction Reducing Agents Shows Quantum Mechanical Interactions Can Have Macroscopic Manifestation.

Two of the most commonly encountered friction-reducing agents used in plastic sheet production are the amides known as erucamide and behenamide, which despite being almost identical chemically, lead to markedly different values of the friction coefficient. To understand the origin of this contrasting behavior, in this work we model brushes made of these two types of linear-chain molecules using quantum mechanical numerical simulations under the density functional theory at the B97D/6-31G(d,p) level of theory. Four chains of erucamide and behenamide were linked to a 2 × 10 zigzag graphene sheet and optimized both in vacuum and in continuous solvent using the SMD implicit solvation model. We find that erucamide chains tend to remain closer together through π-π stacking interactions arising from the double bonds located at C13-C14, a feature behenamide lacks, and thus a more spread configuration is obtained with the latter. It is argued that this arrangement of the erucamide chains is responsible for the lower friction coefficient of erucamide brushes, compared with behenamide brushes, which is a macroscopic consequence of cooperative quantum mechanical interactions. While only quantum level interactions are modeled here, we show that behenamide chains are more spread out in the brush than erucamide chains as a consequence of those interactions. The spread-out configuration allows more solvent particles to penetrate the brush, leading in turn to more friction, in agreement with macroscopic measurements and mesoscale simulations of the friction coefficient reported in the literature.

Self healing nature of bilayer graphene

The phenomenon of self healing of cracks in bilayer graphene sheet has been studied using molecular dynamics simulations. The bilayer graphene sheet was subjected to uniaxial tensile load resulting in initiation and propagation of cracks on exceeding the ultimate tensile strength. Subsequently, all forces acting on the sheet were removed and sheet was relaxed. The cracks formed in the graphene sheet healed without any external aid within 0.4 ps The phenomenon of self healing of the cracks in graphene sheet was found to be independent of the length of the crack, but occurred for critical crack opening distance less than 5 Å for AA stacked sheet and 13 Å for AB stacked bilayer graphene sheet. Self healing was observed for both AB (mixed stacking of armchair and zigzag graphene sheet) and AA (both sheets of similar orientation i.e. either armchair-armchair or zigzag-zigzag) stacking of bilayer graphene sheet.

Shear buckling of rippled graphene by molecular dynamics simulation

This paper presents a study on the shear buckling of rippled single-layered graphene sheets in thermal environments by using molecular dynamics simulation. A zigzag or armchair graphene sheet is simply supported or clamped on its four edges and incremental in-plane shear forces instead of the commonly used shear strains are applied to the edges until initial buckling and final crushing of the graphene sheet are achieved. It is observed that the shear buckling modes of square and rectangular graphene sheets obtained from the molecular dynamics simulations are different from the ones of thin square and rectangular plates as predicted by continuum mechanics models. The shear buckling capacity of a rectangular zigzag graphene sheet is higher than its armchair counterpart. The environmental temperature, when it varies from 300 to 900K, has insignificant impact on the shear buckling forces of the simply supported and clamped square graphene sheets.

MOLECULAR DYNAMICS ANALYSIS FOR FRACTURE BEHAVIOR OF GRAPHENE SHEETS WITH V-SHAPED NOTCHES UNDER TENSION

Molecular dynamics (MD) simulations are performed to study the fracture behavior of armchair and zigzag graphene sheets with V-shaped notches subjected to tensile loading. The effects of temperature and notches depth on the fracture characteristics of the graphene sheets are examined. The results show that the cracks propagate from the notch tip along the direction perpendicular to the loading axis for armchair sheets. This is different from the zigzag graphene propagating along the direction of 45° from the loading axis. In addition, the fracture energy of zigzag graphene sheets is larger than armchair one at the same temperature condition.

Combined CI-MD approach in formulation of engineering moduli of single layer graphene sheet

An evolutionary approach of multi-gene genetic programming (GP) is used to study the effects of aspect ratio, temperature, number of atomic planes and vacancy defects on the engineering moduli viz. tensile and shear modulus of single layer graphene sheet. MD simulation based on REBO potential is used to obtain the engineering moduli. This data is then fed into the paradigm of a GP cluster comprising of genetic programming, which was specifically designed to formulate the explicit relationship of engineering moduli of graphene sheets loaded in armchair and zigzag directions with respect to aspect ratio, temperature, number of atomic planes and vacancy defects. We find that our MGGP model is able to model the engineering moduli of armchair and zigzag oriented graphene sheets well in agreement with that of experimental results. We also conducted sensitivity and parametric analysis to find out specific influence and variation of each of the input system parameters on the engineering moduli of armchair and zigzag graphene sheets. It was found that the number of defects has the most dominating influence on the engineering moduli of graphene sheets.

Localized states of a semi-infinite zigzag graphene sheet with impurity lines

The localized states of a semi-infinite zigzag graphene sheet are studied using a tight-binding model that allows for the inclusion of either one or two lines of impurities. These impurity lines of atoms are placed in rows labeled as n (n = 1, 2, 3, …), where n = 1 is the free edge. The localized defect modes associated with these impurities are studied analytically and numerically within a tridiagonal matrix formalism. For one impurity line, the modes are analyzed according to the position of that line on the sheet, whereas the modes for two impurities are studied also according to their separation and their positions relative to the edge. When an impurity line is located at the edge (n = 1), it is found that the edge states are modified. When the impurities are positioned away from an edge (n > 1), additional localized modes are found to occur that may be relatively flat in their dispersion.

Tension buckling of graphene: A new phenotype

We report here a new phenotype of buckling of a monolayer free hanging graphene subjected to uniform distributed tension force on all atoms by molecular dynamics simulations. We find that buckling occurs when tension force is applied and is sufficiently large for both armchair and zigzag monolayer graphene sheets. The maximum amplitude oscillates around 3.60nm for the free hanging zigzag graphene, but is decreased for the free hanging armchair graphene; whereas the associated applied tension force is decreased for both armchair and zigzag graphene sheets when the temperature is increased.

Equivalent Mechanical Properties of Graphene Predicted by an Improved Molecular Structural Mechanics Model

Based on molecular mechanics and the stick-spiral model, this paper first presents the analytical analysis of the effective in-plane mechanical properties of both zigzag and armchair monolayer graphene sheets. We find that the equivalent in-plane elastic constants of monolayer graphene sheets are the same in the two principal directions of graphene. The effective in-plane mechanical properties of graphene are then evaluated numerically using an improved molecular structural mechanics (MSM) model, in which the flexible connections are used to characterize the bond angle variations of graphene. Furthermore, the effective bending rigidity of the beam representing a C-C bond in this improved MSM model is determined from the energy equivalence over the basic cell of graphene and the force constants given by molecular mechanics. A rigidly connected frame model with the bending stiffness of the equivalent beams for C-C bonds different from the existing structural mechanics model is also used to evaluate the mechanical properties of graphene. The flexibly connected frame model gives very good results of Youngs modulus and Poisson ratio of monolayer graphene sheet. The new rigidly connected frame model presented here also gives improved results than the existing rigidly connected frame model of graphene.

Prediction of the nonlocal scaling parameter for graphene sheet

Abstract A nonlocal model considering the nonlocal stress as the weighted average stress, which incorporates information about small size scale, is presented. With this model, the explicit expression of the nonlocal scaling parameter is derived and the implication of the nonlocal scaling parameter is revealed. Moreover, exact closed form solutions for the nonlocal scaling parameter for zigzag and armchair graphene sheets are obtained and verified by molecular dynamics simulations. Nonlocal scaling parameter is not a constant but a scale-related variable dependent on the size of the structures and independent of the value of the loads.