Second-generation Reactive Empirical Bond Order 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.

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.

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.

The atomic scale structure of graphene powder studied by neutron and X-ray diffraction

The structure of graphene obtained by chemical exfoliation of graphiteviathe oxidation/reduction procedure has been determined using wide-angle scattering of neutrons and X-rays combined with computer simulations based on classical molecular dynamics (MD). A comparison of results obtained from wide-angle neutron scattering (WANS) with the D4 neutron diffractometer dedicated for liquids and amorphous materials (Institute Laue–Langevin in Grenoble) and from wide-angle X-ray scattering (WAXS) with the laboratory Rigaku-Denki D/MAX RAPID II diffractometer has shown that both techniques provide data of a good quality that can be used to derive precise and valuable structural information about graphene. To obtain detailed structural information, the paracrystal formalism has been used along with MD simulations. The MD simulations were performed at 300 K with second-generation reactive empirical bond order potential for atoms lying in the same layer and the Lennard–Jones potential for interlayer interactions. The proposed models consist of three-layered systems, 36 Å in diameter, in which mono-vacancy, di-vacancy and Stone–Thrower–Wales types of defects are introduced. The reported results show that the WANS and WAXS methods together with the MD simulations contribute to a detailed description of the graphene materials, including the presence of topological defects, which is important as their structure at the atomic scale dramatically affects their electrical and mechanical properties.

Surface activation of cyclo olefin polymer by oxygen plasma discharge: a molecular dynamics study

Thermoplastic substrates made of cyclo olefin polymer (COP) are treated with oxygen plasma discharges to introduce polar groups at the surface. This is the first step in the process of surface functionalization of COP substrates used in biosensor devices. A molecular dynamics model of basic COP structure is implemented using the second-generation reactive empirical bond order (REBO) potentials for hydrocarbon–oxygen interactions. The model includes covalent bond and Van der Waals interactions. The bombardment of a COP surface with mono-energetic atomic oxygen ions, energy in the range 1-35 eV, is simulated and reported here. The dynamics of the substrate modification reveals that the substrate top layer is de-hydrogenated and subsequently builds up an oxygen–carbon matrix layer, ∼10 Å thick. Analysis of the modified substrates indicates that surface yield is predominantly peroxide groups.

Phonon dispersions in graphene sheet and single-walled carbon nanotubes

In the present research paper, phonons in graphene sheet have been calculated by constructing a dynamical matrix using the force constants derived from the second-generation reactive empirical bond order potential by Brenner and co-workers. Our results are comparable to inelastic X-ray scattering as well as first principle calculations. At Γ point, for graphene, the optical modes (degenerate) lie near 1685 cm − 1. The frequency regimes are easily distinguishable. The low-frequency (ω→ 0) modes are derived from acoustic branches of the sheet. The radial modes can be identified with ω→ 584 cm − 1. High-frequency regime is above 1200 cm − 1 (i.e. ZO mode) and consists of TO and LO modes. The phonons in a nanotube can be derived from zone folding method using phonons of a single layer of the hexagonal sheet. The present work aims to explore the agreement between theory and experiment. A better knowledge of the phonon dispersion of graphene is highly desirable to model and understand the properties of carbon nanotubes. The development and production of carbon nanotubes (CNTs) for possible applications need reliable and quick analytical characterization. Our results may serve as an accurate tool for the spectroscopic determination of the tube radii and chiralities.

Atomic-Scale Quantification of the Chemical Modification of Polystyrene through S, SC, and SH Deposition from Molecular Dynamics Simulations

The chemical modification of amorphous polystyrene (PS) by the deposition of atomic S, SC, and SH with 25, 50, and 100 eV of incident kinetic energy is examined using classical molecular dynamics simulations. The forces are determined using the second-generation reactive empirical bond-order (REBO) potential that has been extended to include sulfur. In all cases, the S atoms or S-containing dimers are deposited randomly on the PS surface with a flux of about 0.4 × 1024 ions/(cm2 s), which is comparable to experimental values. The simulations predict the way in which the depth profiles vary as a function of the identity and kinetic energy of the incident atom or dimer. We also quantify the ways in which the surface is chemically modified and provide a profile of the chemical products formed on the surface, within the substrate, or in the material sputtered from the surface. The simulations predict that the maximum density of deposited atoms throughout the surface substrate, 3.32 × 1018 /cm3, occurs for S deposition with 50 eV of incident energy. We further predict that the highest molecular weight products are formed as a result of S deposition with 100 eV of energy. Additionally, the chemical reactions that occur during the deposition are found to depend on the beam energy for all the incident atoms or dimers considered. Negligible change in the surface roughness is predicted to occur as a result of these deposition processes.

Thermal Vibrations of Single-Layered Graphene Sheets by Molecular Dynamics

Dynamics problems in the thermal vibration of single-layered graphene sheets (SLGSs) are investigated using molecular dynamics (MD) method based on the Brenner's second-generation reactive empirical bond order (REBO) potential. The in plane stiffness and Poisson ratio of SLGSs are calculated by stretching SLGSs. The effective thickness of SLGSs is obtained by MD simulations for the thermal vibration of SLGSs through the natural frequency. The natural frequencies for SLGSs of different sizes with initial stress in different temperatures are calculated through MD. The thin plate theory can predict the MD results very well in a certain range of strain. For the nonlinear relation between stress and strain when the strain is very large, the deviation between the MD results and plate theory becomes larger when the strain increases. The difference between the plate theory and the MD results becomes more and more obvious, when the size of graphene sheet is very small.

The Local Defect Effect on Molecular Local Density State in Carbon Diamond Structures

The effect of local molecular structural cavity defect on the atom frequencies of bonded atoms is investigated in this study. The molecular dynamic (MD) simulation method is used to simulate the variation of atom frequency near by the cavity defect in a carbon diamond structure. The potential energy model, i.e. the second-generation reactive empirical bond order (REBO) potential function, is employed to derive the dynamic interaction between bonded atoms. The effect of local defect on the vibration amplitude and the density of state (DOS) is studied. The simulated results indicate that the local defect may affect the dynamic behavior of atoms near the local cavity defect significantly.

Mechanisms of Ion-Beam Modification of Terthiophene Oligomers from Atomistic Simulations

Ion-beam deposition on organic surfaces is a common approach to induce surface modification. Here, the difference in argon and polyatomic thiophene hyperthermal deposition on terthiophene oligomers is explored in classical molecular dynamics simulations. The forces on the atoms are determined using the second-generation reactive empirical bond order potential for hydrocarbons that is modified to include sulfur. Details of the potential fit and parametrization are provided. The simulations predict that the thiophene induces fracture of the terthiophene rings while largely retaining the chemical structure of terthiophene. Conversely, argon is predicted to alter the number of carbons within the terthiophene during modification.

A deformation–fluctuation hybrid method for fast evaluation of elastic constants with many-body potentials

A universal, fast deformation–fluctuation hybrid approach with the merits of both the direct and fluctuation methods for evaluation of elastic constants is proposed. Deformation is shown to provide an inherent connection between the latter two methods. Based on this finding, the hybrid method utilizes group perturbation of atoms by means of six homogeneous deformations for fast evaluation of the Born term in the stress fluctuation method. The hybrid method is tested with three typical and widely used many-body potentials, i.e., for crystalline silicon with a Stillinger–Weber potential, for crystalline copper with second nearest-neighbor modified embedded-atom method and for diamond with a second-generation reactive empirical bond order potential. The calculated elastic constants agree well with either the theoretical or experimental results for all three cases. The hybrid method is especially valuable for complicated many-body potentials for which the analytical second derivative of the energy is challenging or impractical to obtain.

The effects of vacancy defects and nitrogen doping on the thermal conductivity of armchair (10, 10) single-wall carbon nanotubes

The influence of vacancy defects and nitrogen doping on the thermal conductivity of typical armchair (10, 10) single-walled carbon nanotubes is investigated using molecular dynamics (MD) simulation. The second-generation reactive empirical bond order potential and Tersoff potential are used to describe the interatomic interactions and the thermal conductivities are calculated using the Müller-Plathe approach (also called non-equilibrium MD simulation). Vacancy defects decrease the thermal conductivity whereas the substitution of nitrogen at vacancy sites improves the thermal conductivity. Quantum correction of the calculated results produces a thermal conductance temperature dependence that is in qualitative agreement with experimental data.

Mechanical Properties of Single Crystal Diamond Estimated by Molecular Dynamics Simulation with the Second-Generation REBO Potential

ABSTRACTWe investigated the effects of tensile direction and periodic boundary condition (PBC) on the mechanical properties of single crystal diamond (SCD) under tensile loading, using MD simulations with the second-generation reactive empirical bond order (REBO) potential. We found that when the Poisson’s ratio is assumed to be constant under the canonical (NVT) ensemble and the PBC is applied to all directions of X, Y, and Z, each qualitative relation between a mechanical property such as tensile strength or Young’s modulus and the tensile direction is in agreement with both the results calculated by the first principle and by the cleavage energy method. In addition, we found that when the PBC is applied only to the Y direction under the NVT ensemble, each qualitative relation between a mechanical property and the tensile directions is in agreement with the MD results using the Tersoff potential.Our results indicate that the second-generation REBO potential is also useful for MD simulations on the tension of diamond.

Theoretical study of the vibrational edge modes in graphene nanoribbons

We investigate the phonon normal modes in hydrogen-terminated graphene nanoribbons (GNRs) using the second-generation reactive empirical bond order (REBOII) potential and density-functional theory calculations. We show that specific modes, absent in pristine graphene and localized at the GNR edges, are intrinsic signatures of the vibrational density of states of the GNRs. Three particular modes are described in details: a transverse phonon mode related to armchair GNRs, a hydrogen out-of-plane mode present in both armchair and zigzag GNRs, and the Raman radial-breathing-like mode. The good agreement between the frequencies of selected edge modes obtained using REBOII and first-principles methods shows the reliability of this empirical potential for the calculation and the assignment of phonon modes in carbon nanostructures where carbon atoms present a $s{p}^{2}$ hybridization.

Elastic constants of silicon materials calculated as a function of temperature using a parametrization of the second-generation reactive empirical bond-order potential

A parametrization for silicon is presented that is based on the second-generation reactive empirical bond-order (REBO) formalism [Brenner, Shenderova, Harrison, Stuart, Ni, and Sinnott J. Phys.: Condens. Matter 14, 783 (2002)]. Because it shares the same analytic form as Brenner's second-generation REBO, this new potential is a step toward a single potential that can model many atom systems that contain C, Si, and H, where bond breaking and bond making are important. The widespread use of Brenner's REBO potential, its ability to model both zero-Kelvin elastic constants of diamond and the temperature dependence of the elastic constants, and the existence of parameters for many atom types were the motivating factors for obtaining this parametrization for Si. While Si-C-H classical bond-order potentials do exist, they are based on Brenner's original formalism. This new parametrization is validated by examining the structure and stability of a large number of crystalline silicon structures, by examining the relaxation energies of point defects, the energies of silicon surfaces, the effects of adatoms on surface energies, and the structures of both liquid silicon and amorphous silicon. Finally, the elastic constants of diamond-cubic and amorphous silicon between 0 and $1100\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ are calculated with this new parametrization and compared to values calculated using a previously published potential.

Examining the effects of wall numbers on buckling behavior and mechanical properties of multiwalled carbon nanotubes via molecular dynamics simulations

Molecular dynamics simulations are performed on multiwalled carbon nanotubes (MWCNTs) under axial compression to investigate the effects of the number of walls and their van der Waals (vdW) interaction on the buckling behaviors and mechanical properties (Young’s modulus and Poisson’s ratio). The Brenner second-generation reactive empirical bond order and Lennard–Jones 12-6 potential have been adopted to describe the short-range bonding and long-range vdW atomic interaction within the carbon nanotubes, respectively. In the presence of vdW interaction, the buckling strain and Young’s modulus of MWCNTs increase as the number of tubes is increased while keeping the outermost tube diameter constant, whereas Poisson’s ratio was observed to decrease. On the other hand, when the MWCNTs are formed by progressively adding outer tubes while keeping the innermost tube diameter constant, Young’s modulus and buckling strain were observed to decrease, whereas Poisson’s ratio increases. The buckling load increases with increasing the number of walls due to the larger cross-sectional areas. Individual tubes of MWCNTs with a relatively large difference between the diameters of the inner and outer tubes buckle one at a time as opposed to simultaneously for MWCNTs with a relatively small difference in diameters.

Study of the polarizability of fullerenes with a monopole–dipole interaction model

Static dielectric properties of some fullerenes and fullerene-based molecules are studied using a Gaussian renormalized monopole–dipole interaction model. Many kinds of molecules have been constructed on the computer: fullerenes with icosahedral shape, Stone–Wales rounded fullerenes, and carbon onions constructed with these two types of fullerenes. The geometry optimization has been performed with the second-generation reactive empirical bond order potential energy [D.W. Brenner, J. Phys. Condens. Matter 14 (2002) 783]. As expected, the molecular polarizability of spherical and icosahedral fullerenes is found to vary linearly with the cube of their mean radius. The contribution of internal layers in multi-shell onions is very small due to a strong screening. The presence of defects in spherical fullerenes decreases the atomic density and the screening effects between atoms, which yields a slight increase of the dielectric response. Some examples of peanut-shape fullerenes, which have been observed experimentally, are also considered.

Application of Molecular Dynamics Simulations for Structural Studies of Carbon Nanotubes

Molecular dynamics studies based on the Brenner-Tersoff second-generation reactive empirical bond order potential and the Lennard-Jones carbon-carbon potential for intra- and inter-layer interactions have been performed for carbon nanotubes. These potentials reproduce reasonably the carbon-carbon distances and inter-layer spacing. The structure factors and the reduced radial distribution functions computed from the cartesian coordinates, resulting from energy minimisation and molecular dynamics simulations at 2 K and 300 K have been obtained for two models of two- and five-wall carbon nanotubes containing defects in the form of five and seven membered carbon rings. The results of computations have been compared with experimental data obtained from neutron and X-ray diffraction. The energy relaxation and the molecular dynamics simulations at 2 K and 300 K with appropriate values of the Debye-Waller factor lead practically to the same results which are in a good agreement with the experimental data indicating that molecular dynamics reproduce all structure features of the investigated carbon nanotubes together with thermal oscillations. Possible applications of this approach for other carbon nanotubes and related materials have been also discussed.

Effect of strain rate on the buckling behavior of single- and double-walled carbon nanotubes

Molecular dynamics simulations are performed on single- (SWCNTs) and double-walled carbon nanotubes (DWCNTs) to investigate the effects of strain rate on their buckling behavior. The Brenner’s second-generation reactive empirical bond order and Lennard-Jones 12-6 potentials are used to describe the short range bonding and long range van der Waals atomic (vdW) interaction within the carbon nanotubes, respectively. The sensitivity of the buckling behavior with respect to the strain rate is investigated by prescribing different axial velocities to the ends of the SWCNTs and DWCNTs in the compression simulations. In addition, the effects of vdW interaction between the walls of the DWCNTs on their buckling behavior are also examined. The simulation results show that higher strain rates lead to higher buckling loads and buckling strains for both SWCNTs and DWCNTs. A distinguishing characteristic between SWCNTs and DWCNTs is that the former experiences an abrupt drop in axial load whereas the axial load in latter decreases over a finite, albeit small, range of strain after buckling initiates. The buckling capability of DWCNT is enhanced in the presence of vdW interaction. DWCNTs can sustain a higher strain before buckling than SWCNTs of similar diameter under otherwise identical conditions.

A reactive empirical bond order (REBO) potential for hydrocarbon–oxygen interactions

The expansion of the second-generation reactive empirical bond order (REBO) potential forhydrocarbons, as parametrized by Brenner and co-workers, to include oxygen ispresented. This involves the explicit inclusion of C–O, H–O, and O–O interactionsto the existing C–C, C–H, and H–H interactions in the REBO potential. Thedetails of the expansion, including all parameters, are given. The new, expandedpotential is then applied to the study of the structure and chemical stabilityof several molecules and polymer chains, and to modelling chemical reactionsamong a series of molecules, within classical molecular dynamics simulations.