Michael C. Böhm

The thermal conductivity and thermal rectification of carbon nanotubes studied using reverse non-equilibrium molecular dynamics simulations

The thermal conductivity of single-walled and multi-walled carbon nanotubes has been investigated as a function of the tube length L, temperature and chiral index using non-equilibrium molecular dynamics simulations. In the ballistic-diffusive regime the thermal conductivity follows a L(alpha) law. The exponent alpha is insensitive to the diameter of the carbon nanotube; alpha approximately 0.77 has been derived for short carbon nanotubes at room temperature. The temperature dependence of the thermal conductivity shows a peak before falling at higher temperatures (>500 K). The phenomenon of thermal rectification in nanotubes has been investigated by gradually changing the atomic mass in the tube-axial direction as well as by loading extra masses on the terminal sites of the tube. A higher thermal conductivity occurs when heat flows from the low-mass to the high-mass region.

Classical Reactive Molecular Dynamics Implementations: State of the Art

Reactive molecular dynamics (RMD) implementations equipped with force field approaches to simulate both the time evolution as well as chemical reactions of a broad class of materials are reviewed herein. We subdivide the RMD approaches developed during the last decade as well as older ones already reviewed in 1995 by Srivastava and Garrison and in 2000 by Brenner into two classes. The methods in the first RMD class rely on the use of a reaction cutoff distance and employ a sudden transition from the educts to the products. Due to their simplicity these methods are well suited to generate equilibrated atomistic or material-specific coarse-grained polymer structures. In connection with generic models they offer useful qualitative insight into polymerization reactions. The methods in the second RMD class are based on empirical reactive force fields and implement a smooth and continuous transition from the educts to the products. In this RMD class, the reactive potentials are based on many-body or bond-order force fields as well as on empirical standard force fields, such as CHARMM, AMBER or MM3 that are modified to become reactive. The aim with the more sophisticated implementations of the second RMD class is the investigation of the reaction kinetics and mechanisms as well as the evaluation of transition state geometries. Pure or hybrid ab initio, density functional, semi-empirical, molecular mechanics, and Monte Carlo methods for which no time evolution of the chemical systems is achieved are excluded from the present review. So are molecular dynamics techniques coupled with quantum chemical methods for the treatment of the reactive regions, such as Car-Parinello molecular dynamics.

Mechanical behavior and interphase structure in a silica–polystyrene nanocomposite under uniaxial deformation

The mechanical behavior of polystyrene and a silica-polystyrene nanocomposite under uniaxial elongation has been studied using a coarse-grained molecular dynamics technique. The Youngs modulus, the Poisson ratio and the stress-strain curve of polystyrene have been computed for a range of temperatures, below and above the glass transition temperature. The predicted temperature dependence of the Youngs modulus of polystyrene is compared to experimental data and predictions from atomistic simulations. The observed mechanical behavior of the nanocomposite is related to the local structure of the polymer matrix around the nanoparticles. Local segmental orientational and structural parameters of the deforming matrix have been calculated as a function of distance from nanoparticles surface. A thorough analysis of these parameters reveals that the segments close to the silica nanoparticles surface are stiffer than those in the bulk. The thickness of the nanoparticle-matrix interphase layer is estimated. The Youngs modulus of the nanocomposite has been obtained for several nanoparticle volume fractions. The addition of nanoparticles results in an enhanced Youngs modulus. A linear relation describes adequately the dependence of Youngs modulus on the nanoparticle volume fraction.

Thermal rectification in mass-graded nanotubes: a model approach in the framework of reverse non-equilibrium molecular dynamics simulations.

The thermal rectification in nanotubes with a mass gradient is studied by reverse non-equilibrium molecular dynamics simulations. We predict a preferred heat flow from light to heavy atoms which differs from the preferential direction in one-dimensional monoatomic systems. This behavior of nanotubes is explained by anharmonicities caused by transverse motions which are stronger at the low-mass end. The present simulations show an enhanced rectification with increasing tube length, diameter and mass gradient. Implications of the present findings for applied topics are mentioned concisely.

Nuclear quantum effects in calculated NMR shieldings of ethylene; a Feynman path integral – ab initio study

Abstract The Feynman path integral Monte-Carlo formalism has been combined with the gauge-including atomic orbital (GIAO) approach to study the absolute magnetic shieldings of C 2 H 4 under consideration of the thermal and quantum degrees of freedom of the nuclei. An ab initio Hamiltonian has been employed for the statistical averaging of NMR parameters. The spatial fluctuations of the atoms around their equilibrium positions lead to a deshielding of both types of nuclei relative to their shieldings at the minimum of the potential energy surface. This behavior is caused by quantum mechanical effects. It is supported by bondlength elongations in thermal equilibrium.

NUCLEAR QUANTUM EFFECTS IN THE ELECTRONIC STRUCTURE OF C2H4 : A COMBINED FEYNMAN PATH INTEGRAL-AB INITIO APPROACH

Abstract A tight-binding equipped Feynman path integral Monte Carlo formalism has been linked to a Hartree–Fock Hamiltonian to derive the electronic properties of C 2 H 4 considering the quantum character of the nuclei. Configurationally averaged electronic quantities are compared with single-configuration results. The potential energy of the vibrational problem is caused by an energetic up-shift of the electron-nuclear interaction of the electronic Hamiltonian under the influence of nuclear quantum fluctuations. Relative to the values optimized by bare electronic Hamiltonians, calculated bond lengths are elongated by nuclear quantum effects. This elongation becomes more pronounced with decreasing atomic masses. Nuclear quantum properties are discussed via the radial distribution function, projected probability distributions and spatial fluctuations.

Nonperiodic stochastic boundary conditions for molecular dynamics simulations of materials embedded into a continuum mechanics domain

A scheme is described for performing molecular dynamics simulations on polymers under nonperiodic, stochastic boundary conditions. It has been designed to allow later the embedding of a particle domain treated by molecular dynamics into a continuum environment treated by finite elements. It combines, in the boundary region, harmonically restrained particles to confine the system with dissipative particle dynamics to dissipate energy and to thermostat the simulation. The equilibrium position of the tethered particles, the so-called anchor points, are well suited for transmitting deformations, forces and force derivatives between the particle and continuum domains. In the present work the particle scheme is tested by comparing results for coarse-grained polystyrene melts under nonperiodic and regular periodic boundary conditions. Excellent agreement is found for thermodynamic, structural, and dynamic properties.

Finite-temperature properties of the muonium substituted ethyl radical CH2MuCH2: nuclear degrees of freedom and hyperfine splitting constants

The finite-temperature (T) properties of the muonium substituted ethyl radical CH2MuCH2 have been theoretically studied by Feynman path integral quantum Monte Carlo (PIMC) simulations. To derive the ensemble averaged expectation values we have combined the PIMC formalism with an efficient tight-binding (TB) Hamiltonian and a density functional operator of the B3LYP type in the EPRIII basis. The TB operator has been used to calculate the potential energy surface (PES) of the ethyl radical in the doublet ground state, the harmonic and anharmonic vibrational wave numbers as well as several probability density functions of the nuclei. The harmonic linear response approximation, which makes use of the Feynman centroid density, has been adopted to evaluate the anharmonic wave numbers. The large anharmonicities in the nuclear potential lead to bond lengths in thermal equilibrium which exceed the vibrationless parameters at the PES minimum. This enhancement is particularly strong for the C–Mu bond. It is responsible for the suppression of the intramolecular rotation for temperatures below room temperature. In C2 H5 the rotation is allowed down to 10u2009K. The dissimilar rotational dynamics for H2MuCH2 and C2 H5 has been studied with the help of TB-based probability density functions. The nuclear configurations of CH2MuCH2 and C2 H5, which are populated in thermal equilibrium, have been used to evaluate the isotropic and anisotropic hyperfine splitting (hfs) constants under explicit consideration of the nuclear vibrations and the internal rotation. The hfs constants have been determined with the help of the B3LYP-EPRIII Hamiltonian. The hindered low-temperature rotation in the Mu isomer is responsible for roto-vibrational corrections to the isotropic hfs constants which are smaller than the corrections in C2 H5. The shortcomings of single-configuration approaches for the evaluation of isotropic hfs constants have been demonstrated for both radicals. The ensemble corrections to the isotropic hfs parameters are correlated with fluctuations in the atomic spin densities. Differences in the absolute values of the isotropic hfs parameters in CH2MuCH2 and C2 H5 can be traced back to differences in the nuclear degrees of freedom. The ensemble shift for each isotropic hfs parameter can be explained by characteristic nuclear motions. For this discussion we make use of the distribution functions of the isotropic hfs constants. Roto-vibrational corrections to the anisotropic hfs constants are rather small. PIMC simulations have been performed between 25 and 1000u2009K, i.e. in a T interval that is large enough to consider nuclear effects beyond zero-point motions. The TB and B3LYP-EPRIII based physical quantities of CH2MuCH2 and C2 H5 have been compared with experimental findings whenever possible.

Nuclear quantum effects in calculated NMR shieldings of benzene; a Feynman path integral study

The Feynman path integral Monte Carlo approach has been coupled to the gauge including atomic orbital formalism in order to analyse the absolute magnetic shieldings of the benzene nuclei under the conditions of thermal equilibrium. The Hamiltonian employed in the derivation of ensemble averaged NMR quantities is of the Hartree-Fock type. The basis set used is of 6–31G quality. The spatial delocalization of the atoms leads to a deshielding of both types of benzene nuclei relative to the shieldings experienced at the minimum of the potential energy surface. This deshielding has to be traced back to bond length elongations in thermal equilibrium. The influence of the nuclear fluctuations on the NMR parameters of benzene is quantum driven up to temperatures of 400 K; classical fluctuations are of minor importance in this low-temperature window.

Feynman path integral–ab initio investigation of the excited state properties of C2H4

Abstract A tight binding based Feynman path integral Monte-Carlo approach has been combined with an ab initio configuration interaction scheme to study the excited singlet states of C 2 H 4 under consideration of the nuclear degrees of freedom. Transition energies and oscillator strengths, which have been averaged over manifolds of nuclear configurations, are compared with single-point values calculated at the minimum of the potential energy. The quantum fluctuations of the nuclei cause a reduction of the transition energies and a complete redistribution in the transition intensities. Transitions, which are dipole allowed in the rigid D 2h geometry of ethylene, lose intensity under the influence of the nuclear fluctuations; vice versa for transitions that are dipole forbidden under D 2h symmetry.