Reactive Empirical Bond Order Potential Research Articles

Refined multiscale model based on the second generation interatomic potential for the mechanics of graphene sheets

Computationally efficient multiscale model based on the refined constitutive law, including second generation reactive empirical bond order potential with dihedral energy term, is employed to investigate the static response of the graphene sheets under transverse and in-plane compressive loads including material nonlinearity through atomic interactions and Green-Lagrange geometric nonlinearity through the strain displacement relations. The bending modulus of the graphene sheet predicted without considering the dihedral energy term in the constitutive law is almost half than those of predicted through first principle calculations. The inclusion of the dihedral energy term predicts bending modulus close to those of through first principle calculations. The atomistic and continuum deformations are coupled through the Cauchy–Born rule. In the present study, the effect of the dihedral energy term on the linear and nonlinear bending and postbuckling response of the graphene sheets under transverse and in-plane compressive loads is investigated in detail. The governing finite element equations for the graphene sheet are derived through the principle of minimum potential energy. The spatial approximation of the graphene sheet at the continuum scale is attained through the finite element method.

Thermal transport in MoS2 from molecular dynamics using different empirical potentials

Thermal properties of molybdenum disulfide (MoS$_2$) have recently attracted attention related to fundamentals of heat propagation in strongly anisotropic materials, and in the context of potential applications to optoelectronics and thermoelectrics. Multiple empirical potentials have been developed for classical molecular dynamics (MD) simulations of this material, but it has been unclear which provides the most realistic results. Here, we calculate lattice thermal conductivity of single- and multi-layer pristine MoS$_2$ by employing three different thermal transport MD methods: equilibrium, nonequilibrium, and homogeneous nonequilibrium ones. These methods allow us to verify the consistency of our results and also facilitate comparisons with previous works, where different schemes have been adopted. Our results using variants of the Stillinger-Weber potential are at odds with some previous ones and we analyze the possible origins of the discrepancies in detail. We show that, among the potentials considered here, the reactive empirical bond order (REBO) potential gives the most reasonable predictions of thermal transport properties as compared to experimental data. With the REBO potential, we further find that isotope scattering has only a small effect on thermal conduction in MoS$_2$ and the in-plane thermal conductivity decreases with increasing layer number and saturates beyond about three layers. We identify the REBO potential as a transferable empirical potential for MD simulations of MoS$_2$ which can be used to study thermal transport properties in more complicated situations such as in systems containing defects or engineered nanoscale features. This work establishes a firm foundation for understanding heat transport properties of MoS$_2$ using MD simulations.

The Application of the Methodology of Fast Automatic Differentiation to Calculate the Gradient of the Potential REBO (LAMMPS)

In this paper, we consider the problem of finding the energy minimum of the aggregate of atoms of a fragment of a planar crystal lattice. To calculate the energy, the Brennor or REBO (reactive empirical bond order) method is used. The REBO potential is calculated using the LAMMPS package (Large-scale Atomic / Molecular Massively Parallel Simulator). As optimization methods, both the gradientless methods and the methods using the first derivatives of the functional are used. To calculate the derivatives, the combined differentiation method, implemented in the LAMMPS package, is used, using sequentially forward and reverse methods of fast automatic differentiation.

Molecular Dynamics Simulations of Si ion Substituted Graphene by Bombardment

Molecular dynamics simulations with Tersoff-Ziegler-Biersack-Littmark (Tersoff-ZBL) potential and adaptive intermolecular reactive empirical bond order (AIREBO) potential are performed to study the substitutional process of silicon ions by bombardment. The silicon ions bombardment of graphene is simulated at energies 100 eV, 100 eV, 68 eV and 67 eV, respectively. All silicon atoms are substitute for the relevant carbon atoms at these energies. And a perfect region of SiC structure in graphene sheet is observed, this approach can viewed as a new preparation of graphene-based SiC electronics in theory.

Molecular Dynamics Simulations of Hydrocarbon Film Growth from Acetylene Monomers and Radicals: Effect of Substrate Temperature

In an attempt to rationalize the mechanisms occurring during plasma polymerization of acetylene, classical molecular dynamics computer simulations investigating the deposition and reaction of a mixed gas of acetylene molecules and radicals on the Ag(111) substrate were performed for a wide range of substrate temperatures. Prior to that, this article establishes a methodology for film deposition and identifies the appropriate potentials for hydrocarbons by comparison with electronic calculations using density functional theory. On the basis of this preliminary study, simulations of film growth are carried out at different temperatures using the reactive empirical bond order potential. Our results show that the rates of formation of new C–C and C–H bonds are higher at the beginning of the film growth when the substrate is still exposed than when it is covered with polymeric chains, and these initial reaction rates are proportional to temperature. The analysis of the hybridization of carbon atoms in the film...

Mathematical Treatise to Model Dihedral Energy in the Multiscale Modeling of Two-Dimensional Nanomaterials

An approximate mathematical treatise is proposed to improve the accuracy of multiscale models for nonlinear mechanics of two-dimensional (2D) nanomaterials by taking into account the contribution of dihedral energy term in the nonlinear constitutive model for the generalized deformation (three nonzero components of each strain and curvature tensors) of the corresponding continuum. Twelve dihedral angles per unit cell of graphene sheet are expressed as functions of strain and curvature tensor components. The proposed model is employed to study the bending modulus of graphene sheets under finite curvature. The atomic interactions are modeled using first- and second-generation reactive empirical bond order (REBO) potentials with the modifications in the former to include dihedral energy term for accurate prediction of bending stiffness coefficients. The constitutive law is obtained by coupling the atomistic and continuum deformations through Cauchy–Born rule. The present model will facilitate the investigations on the nonlinear mechanics of graphene sheets and carbon nanotubes (CNTs) with greater accuracy as compared to those reported in the literature without considering dihedral energy term in multiscale modeling.

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.

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.

Correcting for Tip Geometry Effects in Molecular Simulations of Single-Asperity Contact

Molecular simulation is a powerful tool for studying the nanotribology of single-asperity contacts, but computational limits require that compromises be made when choosing tip sizes. To assess and correct for the finite size effects, complementary finite element (FE) and molecular statics (MS) simulations examining the effects of tip size (height and radius) on contact stiffness and stress were performed. MS simulations of contact between paraboloidal tips and a flat, rigid diamond substrate using the 2B-SiCH reactive empirical bond-order potential were used to generate force–displacement curves and stress maps. Tips of various radii and heights, truncated by a rigid boundary, were formed from carbon- and silicon-containing materials so that they possessed differing elastic properties. Results were compared to FE simulations with matching geometries and elastic properties. FE analysis showed that the rigid boundary at the back of the tip influences the contact stiffness strongly, deviating from the Hertz model for small tip heights and radii. By examining the relationships between force, tip height, tip radii, and elastic properties obtained with FE simulations, a map interpolation method is presented that accounts for the effect of tip size and enables the extraction of Young’s modulus from MS force–displacement data. Furthermore, the FE results show that the effect of the finite size of the tip on contact stress is less pronounced than its effect on stiffness. The MS simulations also demonstrate that stress propagation within the tip is significantly impacted by the structure of the tip.

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.

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).