Reactive Empirical Bond Order Research Articles

A REBO-Potential-Based Model for Graphene Bending by $${{\Gamma}}$$ Γ -Convergence

An atomistic to continuum model for a graphene sheet undergoing bending is presented. Under the assumption that the atomic interactions are governed by a harmonic approximation of the 2nd-generation Brenner REBO (reactive empirical bond-order) potential, involving first, second and third nearest neighbors of any given atom, we determine the variational limit of the energy functionals. It turns out that the $\Gamma$-limit depends on the linearized mean and Gaussian curvatures. If some specific contributions in the atomic interaction are neglected, the variational limit is non-local.

Transversely isotropic elastic properties of carbon nanotubes containing vacancy defects using MD

Molecular dynamics simulations with Adaptive Intermolecular Reactive Empirical Bond Order force fields were conducted to determine the transversely isotropic elastic properties of carbon nanotubes (CNTs) containing vacancies. This is achieved by imposing axial extension, twist, in-plane biaxial tension, and in-plane shear to the defective CNTs. The effects of vacancy concentrations, their position, and the diameter of armchair CNTs were taken into consideration. Current results reveal that vacancy defects affect (i) the axial Young’s and shear moduli of smaller-diameter CNTs more than the larger ones and decrease by 8 and 16% for 1 and 2% vacancy concentrations, respectively; (ii) the plane strain bulk and the in-plane shear moduli of the larger-diameter CNTs more profoundly, reduced by 33 and 45% for 1 and 2% vacancy concentrations, respectively; and (iii) the plane strain bulk and in-plane shear moduli among all the elastic coefficients. It is also revealed that the position of vacancies along the length of CNTs is the main influencing factor which governs the change in the properties of CNTs, especially for vacancy concentration of 1%. The current fundamental study highlights the important role played by vacancy defected CNTs in determining their mechanical behaviors as reinforcements in multifunctional nanocomposites.

Stability and thermal behavior of molybdenum disulfide nanotubes: Nonequilibrium molecular dynamics simulation using REBO potential

This study is an attempt to perform equilibrium molecular dynamics and non-equilibrium molecular dynamics (NEMD) to evaluate the stability and thermal behavior of molybdenum disulfide nanotubes (MoS2NTs) by reactive empirical bond order potential. The stability of nanotubes, cohesive energy, isobaric heat capacity, and enthalpies of fusion in armchair and zigzag structures with different radii were calculated. The observed results illustrate that SWMoS2NTs, which have larger diameters, are more stable with more negative energy than the smaller ones. Moreover, it was found that the melting point is increased with an increase in the nanotube's radius. During the melting process, the structural transformation of nanotubes was investigated using a mean-square displacement and radial distribution function diagrams. Afterwards, using a NEMD simulation, the thermal conductivity of nanotubes with various diameters was calculated at a constant nanotube length. The obtained results show that the thermal conductivity coefficient increases with increasing nanotube diameters when the nanotube length is constant.

Molecular mechanics-based finite element analysis of graphene sheet and carbon nanotubes using the rebo potential

Molecular mechanics-based finite element (FE) models of graphene sheet and single-walled zigzag and armchair carbon nanotubes (CNTs) are developed on the basis of the assumption that the carbon nanostructures, when loaded, behave like frame structures. The behavior of carbon–carbon bonds, which are represented by beam elements, is simulated using the many-body second generation reactive empirical bond order (REBO) potential. By means of the FE models, the tensile behavior of carbon nanostructures is simulated. The FE models are verified against molecular dynamics simulations. The computed results in terms of tensile stress–strain curves and fracture patterns are compared with results obtained using the pairwise modified-Morse potential. Different tensile properties and fracture patterns are predicted using the two potentials. This is mainly attributed to the deviations in the force–bond length curves and to the contribution of bond angle variation which is present in REBO. The present work is the first attempt to implement the REBO potential into a continuum model of carbon nanostructures and paves the way for a more systematic incorporation of atomistic simulation methods into continuum models.

Influence of reversible cross-link coordination on the mechanical behavior of a linear polymer chain

In this work, we investigate the effect of the coordination of cross-links (i.e., the number of monomers participating in one cross-link) on the mechanical performance of a single polymeric chain. The framework provided by the reactive empirical bond order potential is used to generically describe the ability of certain monomers to form cross-links of different coordination. A systematic investigation of the influence of the coordination of cross-links on the mechanical properties of single polymeric chains is presented by comparing systems that contain cross-links in the classical form between two monomers (dimer) and such where the cross-links are formed by three monomers (trimer). The results show that the mechanical performance crucially depends on the coordination of cross-links. The overall shape of the load-displacement curves as well as mechanical parameters like stiffness, strength and work-to-straighten the molecule are different for the different systems. While the load-displacement curve shows an overall more continuous shape for the system containing trimers compared to the system including dimers only, the mechanical parameters are consistently lower for the first system. On the other hand, in contrast to the dimer case a trimer remains stable upon detachment of one of the monomers and the bonds are more mobile. This will be of importance in the case of fiber bundles, where the loading situation is even more complicated than in the single chain system due to the presence of inter-chain cross-links.

Thermal rectification in partially hydrogenated graphene with grain boundary, a non-equilibrium molecular dynamics study

In the present study, we have tried to investigate thermal conductivity and thermal rectification in the partially hydrogenated graphene sheet with grain boundary through non-equilibrium molecular dynamics simulation method. To this end, the 3-body Tersoff and the Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential were employed. The results revealed that the grain boundary plays an important role in phonon scattering, which flows to the other side of grain boundary. It was observed that temperature drops significantly across a grain boundary that leads to the thermal resistance. It has been also proved that thermal rectification depends on the temperature difference between two ends of the system. Also in such a system, a tuning factor for the tuning of the thermal rectification has been introduced by randomly removing hydrogen atoms of the partially hydrogenated graphene sheet with grain boundary.

Interactions of moving charged particles with triple-walled carbon nanotubes

We study plasmon excitations and channeling trajectories of charged particles in triple-walled carbon nanotubes (TWNTs) based on a semi-classical kinetic model combined with the Molecular Dynamics method. Numerical results show that the outer and inner tubes of a TWNT exert strong influence on the peak structures of the self-energy (or the image potential) and the stopping power curves for the channeling ion, resulting in one or two narrow peaks in the low speed region. In addition, the radial dependencies of the total potential, which includes the image potential due to dynamic polarization of the electron gas in nanotubes and a reactive empirical bond order potential for atomic interactions, are compared for single-walled carbon nanotubes (SWNTs), double-walled carbon nanotubes (DWNTs) and TWNTs. By comparing the ion channeling trajectories in those types of nanotubes, we conclude that the variation of the total energy of ions with their channeling distance along the nanotube axis is related to the types of channeling trajectories, exhibiting smooth helical shapes in TWNTs and a succession of sharp reflections off the wall in SWNTs and DWNTs.

Length and temperature dependence of the mechanical properties of finite-size carbyne

Carbyne is an ideal one-dimensional conductor and the thinnest interconnection in an ultimate nano-device and it requires an understanding of the mechanical properties that affect device performance and reliability. Here, we report the mechanical properties of finite-size carbyne, obtained by a molecular dynamics simulation study based on the adaptive intermolecular reactive empirical bond order potential. To avoid confusion in assigning the effective cross-sectional area of carbyne, the value of the effective cross-sectional area of carbyne (4.148Å2) was deduced via experiment and adopted in our study. Ends-constraints effects on the ultimate stress (maximum force) of the carbyne chains are investigated, revealing that the molecular dynamics simulation results agree very well with the experimental results. The ultimate strength, Young's Modulus and maximum strain of carbyne are rather sensitive to the temperature and all decrease with the temperature. Opposite tendencies of the length dependence of the overall ultimate strength and maximum strain of carbyne at room temperature and very low temperature have been found, and analyses show that this originates in the ends effect of carbyne.

Unraveling mechanics of armchair and zigzag graphene nanoribbons

The unraveling process of armchair and zigzag graphene nanoribbons (GNRs) was studied with molecular dynamics simulations using the Adaptive Intermolecular Reactive Empirical Bond Order Potential for carbon–carbon bond. Simulations were performed at 300°K, with GNR length and width varying from 2.5 nm to 15 nm in 2.5 nm increments. In these simulations, the unraveling of the GNRs was started from two positions; the corner or the middle of the top side. Force–displacement relationship was analyzed for the terminal atom of the unraveling chains. For armchair GNRs (AGNRs) that were unraveled from the corner, the force required for the onset of the unraveling is in the range of 4.279–5.045 eV/Å, and the observed failure force in the carbon chain is in the range of 5.553–5.963 eV/Å. Unraveling will not happen when AGNRs are unraveled from the middle, and zigzag GNRs (ZGNRs) are unraveled either from corner or middle. For the latter cases, the bond between the terminal atom and GNR sheet breaks under the stretching force, and only one carbon atom can be pulled out from the GNR sheet. The size effect of width and length on the unraveling process was also studied. Simulations show that size has a trivial effect on unraveling. Comparison between unraveling of AGNRs and ZGNRs indicates that AGNRs are perfect structure to produce Monatomic Carbon Chains, while ZGNRs are more stable and are good candidate for graphene nanodevices that are free from unraveling disintegration.

Atomic simulation of thermal fluctuation (ripples) in constrained single-layer MoS2 membranes

Molecular dynamics simulations based on reactive empirical bond order potentials are performed to investigate the attributes of the thermally agitated ripples in single-layer molybdenum disulfide (SLMoS2) membranes, including the vibrational mode and the height fluctuation. The effects of aspect ratio, type and shape of boundary conditions, and chirality, on the attributes of the ripples are mainly concerned. The aspect ratio has a major influence on the vibrational mode of the ripples for rectangular SLMoS2 membranes. Most of the effect of chirality is concentrated on the height fluctuation for the slender SLMoS2 nanoribbons due to inducing different number of ripples. The types of boundary conditions is shown to have minor influence on the vibrational mode and height fluctuation for the rectangular SLMoS2 membranes. Only high-order resonant mode is thermally agitated in SLMoS2 nanosheets with circular boundary conditions. The height fluctuation in most of SLMoS2 membranes increases with increasing the temperature, which is consistent with the elastic theory of membrane. The work can be useful for the application of strain engineering in SLMoS2 nanodevices.

Molecular Modeling and Adsorption Properties of Ordered Silica-Templated CMK Mesoporous Carbons.

Realistic molecular models of silica-templated CMK-1, CMK-3, and CMK-5 carbon materials have been developed by using carbon rods and carbon pipes that were obtained by adsorbing carbon in a model MCM-41 pore. The interactions between the carbon atoms with the silica matrix were described using the PN-Traz potential, and the interaction between the carbon atoms was calculated by the reactive empirical bond order (REBO) potential. Carbon rods and pipes with different thicknesses were obtained by changing the silica-carbon interaction strength, the temperature, and the chemical potential of carbon vapor adsorption. These equilibrium structures were further used to obtain the atomic models of CMK-1, CMK-3, and CMK-5 materials using the same symmetry as found in TEM pictures. These models are further refined and made more realistic by adding interconnections between the carbon rods and carbon pipes. We calculated the geometric pore size distribution of the different models of CMK-5 and found that the presence of interconnections results in some new features in the pore size distribution. Argon adsorption properties were investigated using GCMC simulations to characterize these materials at 77 K. We found that the presence of interconnection results greatly improves the agreement with available experimental data by shifting the capillary condensation to lower pressures. Adding interconnections also induces smoother adsorption/condensation isotherms, and desorption/evaporation curves show a sharp jump. These features reflex the complexity of the nanovoids in CMKs in terms of their pore morphology and topology.

Methane Behavior in Carbon Nanotube as a Function of Pore Filling and Temperature Studied by Molecular Dynamics Simulations

We report structural and dynamic properties of methane inside the (15,15) carbon nanotube (CNT) obtained from molecular dynamics simulations of flexible methane molecules, and intramolecular interactions are introduced by the reactive empirical bond order potential. The calculations are performed for a wide range of temperatures and loadings that correspond to states from the dense gas phase to the liquid state. The properties of flexible and rigid models of methane molecules are compared. The diffusivity of molecular translations along the CNT and rotations increase with temperature, and they decrease with pressure. Temperature dependences of the diffusion coefficients for flexible molecules are predicted by the Arrhenius equation. Internal motions of the CH4 atoms diminish the activation energies of the translational diffusion and increase the energies of the rotational diffusion, especially for higher pressures. The results mean that the possibility of changes of molecular bond lengths and valence angl...

Relationship between local buckling and atomic elastic stiffness in multi-walled carbon nanotubes under compression and bending deformations

This paper discusses unified criteria for the local buckling of multi-walled carbon nanotubes in both compression and bending deformations from a standpoint of atomic simulations. Defective and non-defective five-walled carbon nanotubes are subjected to compression and bending deformation by the molecular dynamics method using the adaptive intermolecular reactive empirical bond order potential. The atomic elastic stiffness of each atom, Bijα, is then evaluated during the deformations to discuss the onset of local buckling. The Bijα corresponds to the second-order derivatives of the atomic energy, i.e., the gradient of the local stress–strain surfaces in six-dimensional strain space. If Bijα has a negative eigenvalue, a local unstable path will exist in the direction of the strain. Under compression, the smallest eigenvalues, λ(1)α, of the Bijα for all atoms changes to a negative value long before buckling occurs, while the second-smallest eigenvalues, λ(2)α, of the Bijα of some atoms change to a negative value just prior to buckling. Under bending deformation, the change in the positivity of λ(2)α corresponds to a rippling deformation on the side of compressive bending stresses. A variation in the location of defects in the carbon nanotubes affects the peak stresses under compression and the peak moments under a bending deformation. However, for all models, local buckling occurs from the dense region of atoms whose λ(2)α<0 in some outer layers. This suggests that the atomic elastic stiffness is capable of acting as an evaluation criterion for local buckling in multi-walled carbon nanotubes.

Based on the molecular dynamics characteristic research of heat conduction of graphyne nanoribbons with vacancy defects

As a kind of nano-material, graphyne nanoribbon has some physical properties and its properties should be studied for its better usage. In the process of preparing graphyne nanoribbons, it is possible that vacancy defects exist in the lattice structure, which will affect the physical properties of the graphyne nanoribbons. The flotation of graphyne is closer to the actual situation in engineering than the complete graphyne nanoribbons, and the diversity of vacancy defects can lead to various thermal conductivities, so it is very important to simulate the effects of various vacancy defects on thermal conductivity. In order to better predicte and control heat transfer characteristics of graphyne nanoribbons, this paper focuses on the effects of vacancy defects on the heat transfer characteristics of graphyne nanoribbons. According to the different cutting directions of graphyne nanoribbons, two different types of graphyne nanoribbons are obtained, i.e., armchair type and zigzag type. We compare the effects of vacancy defects on the thermal conductivity of two different chiral graphynes nanoribbons to improve the persuasiveness of the conclusion. In this paper, non-equilibrium molecular dynamics method is adopted, by applying periodic boundary conditions in the length direction of the nanoribbons, the interaction between the carbon-carbon atoms is described based on a potential function of adaptive intermolecular reactive empirical bond order (AIREBO). At 300 K, the effects of single vacancy defect in the acetylene chain, single vacancy defect in the benzene ring or double vacancy defects in the acetylene chain on the thermal conductivities of single-layer graphyne nanoribbons are simulated. Fourier's law is used to calculate the thermal conductivities of graphyne nanoribbons. The simulation results show that for the thermal conductivity of graphyne nanoribbons in a-few-dozen nanometer range:1) as a result of the phonon scattering and enhanced phonon Umklapp process, the graphyne nanoribbons with vacancy defects will cause the thermal conductivity to decrease and becomes lower than that of the complete graphyne nanoribbons; 2) due to the difference in phonon density-of-states matching degree, the vacancy defect in the benzene ring of graphyne nanoribbons has a greater effect on the thermal conductivity than that of vacancy defect in the acetylene chain of graphyne nanoribbons, the vacancy defects have a strong influence on the thermal conductivity of in the acetylene chain of graphyne nanoribbons; 3) because of the influence of size effect, the thermal conductivity of graphyne nanoribbon increases with length increasing. In this paper, the research of the thermal conductivity of graphyne nanoribbon provides the reference for controlling their thermal conductivity on a certain scale.

Mechanical Behaviour of Graphene Reinforced Aluminum Nano composites

In this paper, molecular dynamics (MD) simulations are performed on graphene-aluminum (GS-Al) nanocomposite. The mechanical properties of the nanocomposite are investigated by the application of uni-axial load on one end of the representative volume element (RVE) and fixing the other end. The interactions between the atoms of Al are modelled using Embedded Atom Method (EAM) potentials, whereas Adaptive Intermolecular Reactive Empirical Bond-Order (AIREBO) potential is used for the interactions among carbon atoms and these pair potentials are coupled with the Lennard-Jones (LJ) potential. The result shows that the incorporation of Gn into the Al matrix can increase the Young's modulus of the nanocomposite substantially. The nanocomposite containing 6.7 vol.%of GS exhibits Young’s modulus of 143.8 GPa and 116.8 GPa along longitudinal and transverse directions, respectively that are 82.8% and 46.5% higher than pure Al. Results from the molecular dynamics simulations are also compared with analytical results obtained from semi-empirical Halphin-Tsai (H-T) model and the Rule of Mixtures (ROM).

Pristine Study of Axial Tensile Strain Energy Curve for Single-Walled Carbon Nanotube using Molecular Dynamics Simulation

Although the discovery of carbon nanotube was dated back in 1952 by Radushkevich and Lukyanovich, it has attracted attention of the industrial and scientific communities only when Iijima succeeded in synthesizing the first Multi-Walled Carbon Nanotubes (MWCNTs) in 1991. The unique properties of carbon nanotubes, in particular mechanical, have sparked designing, fabrication and commercialization of robust carbon nanotube based materials. The robustness of any material, i.e., the mechanical properties, is in factgreatly affected by the presence of defects. In this paper, one of the mechanical properties for the zigzag type Single Walled Carbon Nanotubes (SWCNTs) is studied. The strain energy curve under axial tensile loads is determined by using the Molecular Dynamics (MD) simulation. The interaction force between atoms is modeled by using the second-generation of Reactive Empirical Bond-Order (REBO) potential coupled with the Lennard-Jones potential. The validation with Young’s modulus is presented and discussed. The effect of the size of the tube diameter of SWCNT on the strain energy curve is also discussed.

Gold nanoparticles promote amorphous carbon to be ammonia gas sensor

As gold-nanoparticles–embedded in amorphous carbon films the sp3 carbon orbits near the interface will be partially transferred to sp2. The Raman spectrum measurements as well as the molecular-dynamics simulations used the second reactive empirical bond order (REBO) potential simulating the interatomic force between carbon atoms both confirm the orbital transformations. The amorphous carbon films are initially inert to gases, while the films embedded with gold nanoparticles exhibit the increase of resistance in ammonia atmosphere. Namely, gold-nanoparticles–embedded amorphous carbon films become the candidate for ammonia gas sensor materials.

The Effect of VMoS3 Point Defect on the Elastic Properties of Monolayer MoS2 with REBO Potentials

Structural defects in monolayer molybdenum disulfide (MoS2) have significant influence on the electric, optical, thermal, chemical, and mechanical properties of the material. Among all the types of structural defects of the chemical vapor phase-grown monolayer MoS2, the VMoS3 point defect (a vacancy complex of Mo and three nearby S atoms) is another type of defect preferentially generated by the extended electron irradiation. Here, using the classical molecular dynamics simulation with reactive empirical bond-order (REBO) potential, we first investigate the effect of VMoS3 point defects on the elastic properties of monolayer MoS2 sheets. Under the constrained uniaxial tensile test, the elastic properties of monolayer MoS2 sheets containing VMoS3 vacancies with defect fraction varying from 0.01 to 0.1 are obtained based on the plane anisotropic constitutive relations of the material. It is found that the increase of VMoS3 vacancy concentration leads to the noticeable decrease in the elastic modulus but has a slight effect on Poisson’s ratio. The maximum decrease of the elastic modulus is up to 25 %. Increasing the ambient temperature from 10 K to 500 K has trivial influences on the elastic modulus and Poisson’s ratio for the monolayer MoS2 without defect and with 5 % VMoS3 vacancies. However, an anomalous parabolic relationship between the elastic modulus and the temperature is found in the monolayer MoS2 containing 0.1 % VMoS3 vacancy, bringing a crucial and fundamental issue to the application of monolayer MoS2 with defects.

Bending response of single layer MoS2

Using molecular mechanics (or dynamics) simulations, three different approaches, including the targeted molecular mechanics, four-point bending and nanotube methods, are employed to investigate the bending response of single layer MoS2 (SLMoS2), among which four-point bending is the most accurate approach to determine the bending stiffness according to the continuum theory. It is found that when the bending curvature radius is large enough (e.g. >4 nm), three approaches will give the same bending stiffness of SLMoS2 and the bending behavior is isotropic for SLMoS2, whereas the nanotube method with small tubes (e.g. <4 nm) cannot give the correct bending stiffness. Compared with the reported result from the MoS2 nanotube calculated by density functional theory, the revised Stillinger–Weber (SW) and reactive empirical bond-order (REBO) potentials can give the reasonable bending stiffness of SLMoS2 (8.7–13.4 eV) as well as the effective deformed conformation. In addition, since the Mo–S bond deformation of SLMoS2 under bending is similar to that under in-plane tension/compression, the continuum bending theory can quite accurately predict the bending stiffness of SLMoS2 if a reasonable thickness of SLMoS2 is given. For SLMoS2, the reasonable thickness should be larger than the distance between its two S atomic planes and lower than the distance between two Mo atomic planes of bulk MoS2 crystal, e.g. 0.375–0.445 nm.

Geometry and Self-stress of Single-Wall Carbon Nanotubes and Graphene via a Discrete Model Based on a 2nd-Generation REBO Potential

The main purpose of this paper is to evaluate the self-stress state of single-walled Carbon NanoTubes (CNTs) and Flat Graphene Strips (FGSs) in their natural equilibrium state, that is, the state prior to the application of external loads. We model CNTs as discrete elastic structures, whose shape and volume changes are governed by a Reactive Empirical Bond-Order (REBO) interatomic potential of second generation. The kinematical variables we consider are bond lengths, bond angles, and dihedral angles; to changes of each of these variables we associate a work-conjugate nanostress. To determine the self-stress state in a given CNT, we formulate the load-free equilibrium problem as a minimum problem for the interatomic potential, whose solution yields the equilibrium nanostresses; next, by exploiting the nonlinear constitutive dependence we derive for nanostresses in terms of a list of kinematical variables, we determine the equilibrium values of the latter; finally, from the equilibrium values of the kinematical variables we deduce the natural geometry and, in particular, the natural radius. Our theoretical framework accommodates CNTs of whatever chirality. In the achiral case, the stationarity conditions implied by energy minimization are relatively easy to derive and solve numerically, because we can count on maximal intrinsic symmetries and hence the number of independent unknowns is reduced to a minimum; for chiral CNTs, we prefer to solve the minimum problem directly. The natural-radius predictions we achieve within our discrete-mechanics framework are in good agreement with the results of calculations based on Density Functional Theory (DFT) and Tight Binding (TB) theory; the same is true for our predictions of the self-energy, that is, the energy associated with self-stress (called cohesive energy in the literature); we surmise that our discrete mechanical model may serve as a source of benchmarks for Molecular-Dynamics (MD) simulation algorithms. We find that self-stress depends on changes in both bond and dihedral angles in achiral CNTs and, in addition, on changes in bond length in chiral CNTs. Our analysis applies also to FGSs, whose self-stress and self-energy we evaluate; we find that in FGSs self-stress is associated exclusively with changes in bond angle.