Reactive Empirical Bond Order Potential Research Articles

Molecular Dynamics Simulations of Effects of Geometric Parameters and Temperature on Mechanical Properties of Single-Walled Carbon Nanotubes

Carbon nanotubes (CNTs) are considered an advanced form of carbon. They have superior characteristics in terms of mechanical and thermal properties compared to other available fibers and can be used in various applications, such as supercapacitors, sensors, and artificial muscles. The properties of single-walled carbon nanotubes (SWNTs) are significantly affected by geometric parameters such as chirality and aspect ratio, and testing conditions such as temperature and strain rate. In this study, the effects of geometric parameters and temperature on the mechanical properties of SWNTs were studied by molecular dynamics (MD) simulations using the Large-scaled Atomic/Molecular Massively Parallel Simulator (LAMMPS). Based on the second-generation reactive empirical bond order (REBO) potential, SWNTs of different diameters were tested in tension and compression under different strain rates and temperatures to understand their effects on the mechanical behavior of SWNTs. It was observed that the Young’s modulus and the tensile strength decreases with increasing SWNT tube diameter. As the chiral angle increases, the tensile strength increases, while the Young’s modulus decreases. The simulations were repeated at different temperatures of 300 K, 900 K, 1500 K, 2100 K and different strain rates of 1 × 10−3/ps, 0.75 × 10−3/ps, 0.5 × 10−3/ps, and 0.25 × 10−3/ps to investigate the effects of temperature and strain rate, respectively. The results show that the ultimate tensile strength of SWNTs increases with increasing strain rate. It is also seen that when SWNTs were stretched at higher temperatures, they failed at lower stresses and strains. The compressive behavior results indicate that SWNTs tend to buckle under lower stresses and strains than those under tensile stress. The simulation results were validated by and consistent with previous studies. The presented approach can be applied to investigate the properties of other advanced materials.

Comparison of Interatomic Potentials for Modeling Defects in Graphene Using Molecular Dynamics

Comparison of Interatomic Potentials for Modeling Defects in Graphene Using Molecular Dynamics

Investigation of fullerene cluster growth mechanisms by carbon atom addition using classical molecular dynamics.

The mechanisms of carbon sticking reactions to C36 and C-C80 fullerenes were investigated with molecular dynamics simulations (MD) using the Second-generation Reactive Empirical Bond Order (SREBO) and Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potentials that were specifically optimized for carbon-carbon interactions. Results showed the existence of three possible sticking configurations where the projectile atom can stick either to one, two or three atoms of the target fullerene. They also showed that although the two potentials give similar magnitudes for the sticking cross-sections, they yield fairly different results as far as sticking mechanisms and configurations at thermal collision-energies, i.e., in the range 0.05-0.5eV, are concerned. While AIREBO, that takes into account the long-range Lennard-Jones interaction, essentially results in a surface-sticking configuration with a single atom of the target fullerene, SREBO potential yields both surface- and two neighbors-sticking (2N-sticking) configurations. The fullerene structure is preserved in the last configuration while it can be recovered by a 2000K annealing in the former configuration. Results obtained with SREBO eventually showed larger sticking probabilities for C36 as compared with C80. In spite of this, the sticking cross-sections obtained for C80 are similar to or even larger than those obtained for C36 due to the larger size of C80 that compensates for its smaller sticking probabilities.

Molecular dynamics simulation of free transverse vibration behavior of single-walled coiled carbon nanotubes

Coiled carbon nanotubes (CCNTs) belong to one of the prominent classes of carbon nanostructures with unique mechanical properties and vibrational behavior due to their helical geometries. In this paper, the free transverse vibration behavior of single-walled CCNTs is investigated by molecular dynamics (MD) simulations and the adaptive intermolecular reactive empirical bond-order (AIREBO) potential under different boundary conditions (B.Cs.). The beating phenomenon is observed in CCNTs due to the presence of longitudinal, transverse, and torsional coupled vibrations and the proximity of their corresponding frequency. Generally, the frequency of the CCNTs decreases by increasing the length () or the number of pitches ( Moreover, the pitch angle plays a more decisive role compared to other geometric parameters. At constant length () of CCNTs, the frequency increases by enhancing the pitch angle Furthermore, the fundamental frequency range of the studied CCNTs is obtained less than 331.9 GHz for lengths greater than 2 nm under different boundary conditions. This indicates that CCNTs have a higher vibration sensitivity than straight CNTs. Therefore, CCNTs can be a proper alternative to straight CNTs in sensors. The results of this study can be used in the design and analysis of nanoelectromechanical systems (NEMs) with CCNTs elements as well as to calibrate continuum mechanics methods.

Effect of CNT’s volume fraction on the mechanical properties of CNT reinforced Al/Cu alloy nanocomposite using molecular dynamics simulation

Aluminum is one of most widely available elements on planet earth. After oxygen and silicon, aluminum is the third available element in the crust of the earth with a contribution of about 8%. It has a unique set of properties for which it has been used heavily in different aspects of life but yet its mechanical properties such as strength and hardness may be enhanced by the addition of other elements to form an alloy or a composite. Carbon nanotubes (CNTs) have attracted a great attention as reinforcements in metal matrix composites due to their extraordinary characteristics such as strength, stiffness, and low density. Aluminum/Copper (Al/Cu) alloy enhanced with CNTs of different volume fractions is the topic of this work which was not addressed previously in the literature. Embedded atom method (EAM) potential was used to model the interaction between aluminum and copper while the Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential was used to model the CNT. The interactions between Al/Cu alloy and CNT was modeled using the pairwise Morse potential. Mechanical properties of Al/Cu alloy with alloying percentage of 10% reinforced with single walled carbon nanotube of different volume fractions are studied under tensile loading using molecular dynamics (MD) simulation. The open-source code LAMMPS is used to conduct the MD simulations. An armchair CNT with a chirality of (6,6) is considered for the study. The modulus of elasticity and the ultimate tensile strength of the Al/Cu-CNT nanocomposite are both observed to increase as the volume fraction of the CNT increases. The modulus of elasticity increased by almost 75% as the volume fraction of the CNT increased from 1% to 10%. The failure strains are almost the same in all cases. The results showed a maximum practical threshold of 10% CNT volume fraction to the Al/Cu alloy.

Mechanical properties of pristine and nanocrystalline graphene up to ultra-high temperatures

Despite being the basic building block of most carbon materials used in high and ultra-high temperature applications, the mechanical properties of graphene at such temperatures remain totally unknown. Here we compute these properties using tensile molecular dynamics simulations at temperatures ranging from room temperature to 5000 K (i. e. about the melting temperature) for pristine and nanocrystalline graphene. Mechanical simulations at such temperatures are made possible via the use of the screened environment dependent reactive empirical bond order potential [Perriot et al. Phys. Rev. B 88, 064101 (2013)]. We show that even at the highest temperature, both graphene and nanocrystalline graphene retain high stiffness, strength and fracture strain. Analyses of tensile curves and trajectories (including an analysis of in-plane non-affine atomic displacements) show that both pristine and nanocrystalline graphene show brittle rupture, whatever the temperature, even though some early sign of ductility can be detected for the nanocrystalline graphene at 5000 K. This rules out the possibility of a ductile fracture in graphene at any temperature below the melting point. Finally, the simulations also highlight the importance of bond rotation (Stone-Wales) based defects in the fracture initiation mechanism for pristine graphene. Especially at intermediate temperature (3000 K) crack nucleation in pristine graphene is shown to take place exactly at the moment and place of the first Stone-Wales defect formation.

Defect structure classification of neutron-irradiated graphite using supervised machine learning

Molecular dynamics simulations were performed to predict the behavior of graphite atoms under neutron irradiation using large-scale atomic/molecular massively parallel simulator (LAMMPS) package with adaptive intermolecular reactive empirical bond order (AIREBOM) potential. Defect structures of graphite were compared with results from previous studies by means of density functional theory (DFT) calculations. The quantitative relation between primary knock-on atom (PKA) energy and irradiation damage on graphite was calculated.and the effect of PKA direction on the amount of defects is estimated by counting displaced atoms. Defects are classified into four groups: structural defects, energy defects, vacancies, and near-defect structures, where a structural defect is further subdivided into six types by decision tree method which is one of the supervised machine learning techniques.

Multi-objective parametrization of interatomic potentials for large deformation pathways and fracture of two-dimensional materials

This investigation presents a generally applicable framework for parameterizing interatomic potentials to accurately capture large deformation pathways. It incorporates a multi-objective genetic algorithm, training and screening property sets, and correlation and principal component analyses. The framework enables iterative definition of properties in the training and screening sets, guided by correlation relationships between properties, aiming to achieve optimal parametrizations for properties of interest. Specifically, the performance of increasingly complex potentials, Buckingham, Stillinger-Weber, Tersoff, and modified reactive empirical bond-order potentials are compared. Using MoSe2 as a case study, we demonstrate good reproducibility of training/screening properties and superior transferability. For MoSe2, the best performance is achieved using the Tersoff potential, which is ascribed to its apparent higher flexibility embedded in its functional form. These results should facilitate the selection and parametrization of interatomic potentials for exploring mechanical and phononic properties of a large library of two-dimensional and bulk materials.

Molecular Dynamics Simulation on Collision Frictional Properties of a Molybdenum Disulfide (MoS2) Film in Microgravity Environment

In this paper, a collision friction model for a double-layer MoS2 film is proposed considering the microgravity induced collision in space environment. A modified REBO (Reactive Empirical Bond Order) potential is used to describe interactions among the atoms in the MoS2 film. The collision friction process of the MoS2 film is simulated by vibrations in the y and z directions, and the dependence of average friction force is analyzed. The influence of a single vibration in the y direction on the friction forces can be ignored, while the vibration in the z direction shows great influence. The effects of vibration frequency and amplitude on frictional behaviors of the MoS2 film are investigated. The average friction forces during the collision friction process correlate with the frequency of the vibration in the z direction, and the relationship shows four stages. As the frequency increases, average friction forces show low values in the first stage, and they are increased as the frequency in the second stage. In the third stage, the average friction forces are decreased, and they come to a stable level in the fourth stage. Increasing the vibration amplitude at different frequencies leads to an increase in average friction force, due to that the increased amplitude results in a high indentation depth. The puckering phenomenon occurs at a specific frequency, which is a reason that the average friction force is increased during this collision friction process.

Effects of Orientation and Temperature on the Tensile Strength of Pristine and Defective Bi-Layer Graphene Sheet – A Molecular Dynamics Study

Molecular dynamics simulations with adaptive intermolecular reactive empirical bond order (AIREBO) potential were carried out to study the effect of temperature and orientation on the tensile strength of pristine and defective bilayer graphene (BLG) sheet. Results obtained reveal that the fall in tensile strength of pristine AA stacked BLG due to the presence of vacancy is significant at room temperature (300 K) but decreases at higher temperature (1073 K). Interestingly, this phenomenon reverses in case of AB stacked BLG, wherein the percentage fall in strength at higher temperature due to defect is more than that at room temperature. In order to understand these discrepancies in the results obtained, three case studies were conducted, and the results obtained suggested that when defects are present in armchair direction, this phenomenon occurs. The study also reveals that in case of AB stacked BLG, zigzag direction is more defect tolerant at room and high temperatures. Interestingly, variation of tensile strength due to the orientation is in good agreement with projections from potential energy concepts and theoretical calculations. We envisage that the study will provide useful information to the device engineers for the optimisation of the mechanical properties and convenient structural adaptation of bilayer graphene while working at wide range of temperatures.

Comparing different multibody reactive potentials for the elastic properties and nonlinear mechanics of the carbon nanostructures

A multiscale model in conjunction with the finite element method is employed to investigate the accuracy of the different reactive empirical bond order potentials involving material and geometric nonlinearities. The four different sets of empirical parameters for the Tersoff-Brenner potential are considered in the present study and among these four sets of empirical parameters, one set is newly proposed herein and three are taken from the available reference sources. The atomistic-continuum coupling is established using kinematics of quadratic type Cauchy-Born rule for establishing the energy density of the unit cell. The finite element method is used to solve the governing equations at the continuum scale. The revised set of empirical parameters is found better for predicting the elastic properties and bond length than the formerly proposed three sets of empirical parameters when compared to those reported using quantum mechanics calculations. The results of the newly proposed potential are compared with DFT based continuum models for a wide range of numerical problems. The proposed potential parameters are tested for a variety of problems such as the energy of the carbon nanotubes with different radii, torsion of the carbon nanotubes, free vibrations of the graphene sheets and carbon nanotubes and numerical simulations of the nanoindentation experiments for circular graphene sheets.

Impact of chosen force fields and applied load on thin film lubrication

The rapid development of molecular dynamics (MD) simulations, as well as classical and reactive atomic potentials, has enabled tribologists to gain new insights into lubrication performance at the fundamental level. However, the impact of adopted potentials on the rheological properties and tribological performance of hydrocarbons has not been researched adequately. This extensive study analyzed the effects of surface structure, applied load, and force field (FF) on the thin film lubrication of hexadecane. The lubricant film became more solid-like as the applied load increased. In particular, with increasing applied load, there was an increase in the velocity slip, shear viscosity, and friction. The degree of ordering structure also changed with the applied load but rather insignificantly. It was also significantly dependent on the surface structure. The chosen FFs significantly influenced the lubrication performance, rheological properties, and molecular structure. The adaptive intermolecular reactive empirical bond order (AIREBO) potential resulted in more significant liquid-like behaviors, and the smallest velocity slip, degree of ordering structure, and shear stress were compared using the optimized potential for liquid simulations of united atoms (OPLS-UAs), condensed-phase optimized molecular potential for atomic simulation studies (COMPASS), and ReaxFF. Generally, classical potentials, such as OPLS-UA and COMPASS, exhibit more solid-like behavior than reactive potentials do. Furthermore, owing to the solid-like behavior, the lubricant temperatures obtained from OPLS-UA and COMPASS were much lower than those obtained from AIREBO and ReaxFF. The increase in shear stress, as well as the decrease in velocity slip with an increase in the surface potential parameter ζ, remained conserved for all chosen FFs, thus indicating that the proposed surface potential parameter ζ for the COMPASS FF can be verified for a wide range of atomic models.

Flexural modes of graphene resonators derived from the reactive empirical bond-order potential

Flexural modes play an important role in mechanical, thermal, and electronic properties of two-dimensional materials. Graphene nanoelectromechanical systems have been found in wide applications and have attracted huge attention recently, where the molecular dynamics (MD) simulation has been an essential route for the investigation of the mechanical responses of the system. In this paper, based on the expressions and parameters of the reactive empirical bond-order potential for the carbon-carbon atomic interactions implemented in Large-scale Atomic/Molecular Massively Parallel Simulator, the linearized part of the force for each atom along the $z$ direction has been obtained, yielding the stiffness matrix of the graphene lattice. By diagonalizing the stiffness matrix, the flexural modes and their corresponding frequencies can be obtained. The results have been validated with MD simulations in circular and square graphene resonators with different sizes. Since the stiffness matrix for graphene resonators with arbitrary shapes can be obtained readily from our results, we expect broad applications where eigenfrequencies and flexural modes are needed in the analysis for the nanoscale resonators.

Influence of vacancy defects on vibration analysis of graphene sheets applying isogeometric method: Molecular and continuum approaches

The main objective of this research paper is to consider vibration analysis of vacancy defected graphene sheet as a nonisotropic structure via molecular dynamic and continuum approaches. The influence of structural defects on the vibration of graphene sheets is considered by applying the mechanical properties of defected graphene sheets. Molecular dynamic simulations have been performed to estimate the mechanical properties of graphene as a nonisotropic structure with single- and double- vacancy defects using open source well-known software i.e., large-scale atomic/molecular massively parallel simulator (LAMMPS). The interactions between the carbon atoms are modelled using Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential. An isogeometric analysis (IGA) based upon non-uniform rational B-spline (NURBS) is employed for approximation of single-layered graphene sheets deflection field and the governing equations are derived using nonlocal elasticity theory. The dependence of small-scale effects, chirality and different defect types on vibrational characteristic of graphene sheets is investigated in this comprehensive research work. In addition, numerical results are validated and compared with those achieved using other analysis, where an excellent agreement is found. The interesting results indicate that increasing the number of missing atoms can lead to decrease the natural frequencies of graphene sheets. It is seen that the degree of the detrimental effects differ with defect type. The Young\'s and shear modulus of the graphene with SV defects are much smaller than graphene with DV defects. It is also observed that Single Vacancy (SV) clusters cause more reduction in the natural frequencies of SLGS than Double Vacancy (DV) clusters. The effectiveness and the accuracy of the present IGA approach have been demonstrated and it is shown that the IGA is efficient, robust and accurate in terms of nanoplate problems.

Molecular dynamics investigation on the nano-mechanical behaviour of C60 fullerene and its crystallized structure.

C60 fullerene has been utilized in various applications, including low friction and wear coatings, due to its unique molecular structure. In this work, molecular dynamics simulations were conducted to assess the nano-mechanical behaviour of a single C60 fullerene and its crystallized structure. A single C60 model and a model of a face-centred cubic structured C60 crystal with a one-unit-cell thickness were prepared for compression and unloading simulations based on the adaptive intermolecular reactive empirical bond-order potential for carbon. Force-displacement curves and molecule-averaged virial stresses were obtained during the simulation. The models applied during the compression and unloading processes were visualized to confirm the deformation behaviour. Both the single and crystal C60 models showed a perfectly reversible deformation before the point of force decrease that occurred during compression. In particular, the face-centred cubic structure of the crystal C60 model was severely altered during compression before the individual C60 molecules experienced permanent deformation. The maximum values of the normal virial stress in the compression direction before the permanent deformation of the molecules were almost same for both the single and crystallized models.

Molecular dynamics study of the material property changes induced by accumulated point defects in graphite

Molecular dynamics simulations were performed on pristine graphite using an adaptive intermolecular reactive empirical bond-order (AIREBO) potential, which introduced various concentrations of point defects and different sizes in defect clusters. Induced by the accumulation of mono-vacancy and self-interstitial atoms (SIA), the changes to the geometry, density, Young’s modulus, fracture strength, and coefficient of thermal expansion (CTE) of graphite were simulated over a range of defect concentrations and cluster sizes. We found that accumulated Frenkel pairs lead to clearly-observed changes to the geometric and elastic properties in graphite crystal, but a relatively negligible effect on CTE. As expected, changing size of defect clusters with a given concentration relates to the variation of material properties. The property changes simulated in the present work are qualitatively consistent with the experimental observations. The results are expected to provide some insights into the link between cascade-induced point defects and experimentally irradiation-assisted material property changes.

Mechanical and fracture behavior of water submerged graphene

In this article, molecular dynamics (MD)-based simulations were performed to study the structural stability, tensile strength, and fracture behavior of graphene submerged in water. MD-based atomistic simulations were performed in conjunction with adaptive intermolecular reactive empirical bond order and TIP3P potentials for capturing the interatomic interaction in graphene and water molecules, respectively, whereas nonbonded interactions between the two were estimated with the help of Lennard-Jones potential. It was predicted from the simulations that water has a significant effect on the structural stability and the fracture behavior of graphene. The structural stability of water submerged graphene decreases as compared to dry graphene, whereas the fracture behavior of water submerged graphene shows dependency on the chirality and the passivation of crack edge atoms with hydrogen. It was also predicted from the simulations that hydrogen passivation helps in reducing the reactivity of crack edge atoms with the water molecules. Results presented in this article will help in exploring the full potential of graphene for water submerged applications.

Exploring the Effect of Dihedral Energy on the Nonlinear Mechanics of the Carbon Nanotubes Using a Multiscale Modeling

Abstract A hierarchical multiscale finite element model is employed to investigate the effect of dihedral energy term on the numerical simulation of two-dimensional materials. The numerical examples of the carbon nanotubes and graphene sheets are studied employing a refined constitutive model in conjunction with a multiscale finite element method. The constitutive law refined with the greater accuracy on the bending modulus using second generation reactive empirical bond order potential with dihedral energy term is employed to investigate the linear and nonlinear response of the carbon nanotubes incorporating material and Green–Lagrange geometric nonlinearities. The inclusion of the dihedral energy term predicts bending modulus close to those of through first principle calculations. The deformations at the nanoscale and macroscopic scales are related through the Cauchy–Born rule. The effect of the dihedral energy term on the response of the carbon nanotubes is studied in detail. The governing equation of motion for the carbon nanotubes is formulated through Hamilton’s energy principle. The spatial approximation of the carbon nanotubes at the continuum scale is attained through the finite element method. The membrane locking in the circumferential strain is eliminated through the membrane consistent interpolation functions obtained through the least-square method.

Nanomechanical properties of single- and double-layer graphene spirals: a molecular dynamics simulation

This paper relates to a computational investigation of nanomechanical properties of graphene spirals. The molecular dynamics simulation method was used to investigate the mechanical properties including the stress–strain and force–strain diagrams under tensile tests as well as the fracture characteristics of the single- and double-layer graphene spirals. The adaptive intermolecular reactive empirical bond order potential was employed to model the covalent bonds and van der Waals interactions between the carbon atoms. Also, in the last section of the paper, the mechanical behavior of the spirals is scrutinized with respect to nitrogen and boron doping with various percentages and the Young’s moduli of the graphene spirals are presented as the functions of size and doping ratios according to the stress–strain diagrams. The results reveal three major deformation phases namely, elastic due to the van der Waals interactions, elastic due to the covalent bonds, and inelastic regimes. According to the results, the graphene spirals have superelastic characteristics in the range of 2000–3000% strains and very high strength values depending on the nanostructure size.

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.