Uncertainty Quantification Guided Parameter Selection in a Fully Coupled Molecular Dynamics-Finite Element Model of the Mechanical Behavior of Polymers.

The objective of investigating macroscopic polymer properties with a low computing cost and a high resolution has led to the development of efficient hybrid simulation tools. Systems generated from such simulation tools can fail in service if the effect of uncertainty of model inputs on its outputs is not accounted for. This work focuses on quantifying the effect of parametric uncertainty in our coarse-grained molecular dynamics-finite element coupling approach using uncertainty quantification. We consider uniaxial deformation simulations of a polystyrene sample at T = 100 K in our study. Parametric uncertainty is assumed to originate from parameters in the molecular dynamics model with a nonperiodic boundary (the force constant between polymer beads and anchor points, the number of anchor points, and the size of the surrounding dissipative particle dynamics domain) and a parameter to blend the energies of particles and continuum (weighting factor). Key issues that arise in uncertainty quantification are discussed on the basis of the quantities of interest including mass density, end-to-end distance, and radial distribution function. This work reveals the influence of key input parameters on the properties of polymer structure and facilitates the determination of those parameters in the application of this hybrid molecular dynamics-finite element approach.

Predicting the Mobility Increase of Coarse-Grained Polymer Models from Excess Entropy Differences.

We cast the acceleration of the dynamics of coarse-grained polymer models, or, conversely, the decrease in monomer friction in terms of excess entropy differences between different coarse-grained resolutions. From a simple bead-spring model of unentangled polymers in a melt, we systematically derive two coarse-grained models of different resolutions, for which exact excess entropies are obtained through a carefully carried out two-step thermodynamic integration. We found that the excess entropy differences between the coarser and finer models correlated well with the logarithm of the ratio of dynamical properties quantifying the acceleration upon changing the model resolution. Moreover, we have considered how well the two-body approximation to the excess entropy is correlated and also the scaling of the excess entropy in the analysis. Our results indicate that the acceleration brought about by coarse-graining can be understood in terms of excess entropy differences for unentangled polymers also. The correlations presented in this work may open new possibilities to a posteriori correct the coarse-graining dynamics by a simple route.

Investigation of interphase effects in silica-polystyrene nanocomposites based on a hybrid molecular-dynamics-finite-element simulation framework.

A recently developed hybrid method is employed to study the mechanical behavior of silica-polystyrene nanocomposites (NCs) under uniaxial elongation. The hybrid method couples a particle domain to a continuum domain. The region of physical interest, i.e., the interphase around a nanoparticle (NP), is treated at molecular resolution, while the surrounding elastic continuum is handled with a finite-element approach. In the present paper we analyze the polymer behavior in the neighborhood of one or two nanoparticle(s) at molecular resolution. The coarse-grained hybrid method allows us to simulate a large polymer matrix region surrounding the nanoparticles. We consider NCs with dilute concentration of NPs embedded in an atactic polystyrene matrix formed by 300 chains with 200 monomer beads. The overall orientation of polymer segments relative to the deformation direction is determined in the neighborhood of the nanoparticle to investigate the polymer response to this perturbation. Calculations of strainlike quantities give insight into the deformation behavior of a system with two NPs and show that the applied strain and the nanoparticle distance have significant influence on the deformation behavior. Finally, we investigate to what extent a continuum-based description may account for the specific effects occurring in the interphase between the polymer matrix and the NPs.

Atomic and global mechanical properties of systems described by the Stillinger-Weber potential.

Analytical expressions for the stress and elasticity tensors of materials, in which the interactions are described by the Stillinger-Weber potential, are derived in the context of the stress fluctuation formalism. The derived formulas can be used both in Monte Carlo and molecular dynamics simulations. As an example of possible applications, they are employed to calculate the influence of the temperature and system size on the mechanical properties of crystalline cubic boron nitride. The system has been studied by molecular dynamics simulations. The computed mechanical properties are in good agreement with available experimental data and first principle calculations. In the studied crystalline cubic boron nitride system, the employed formalism is of higher accuracy than the 'small-strain' non-equilibrium method. The dominant contributions to the elastic constants stem from the Born and stress fluctuation terms. An increase in the system size reduces the statistical uncertainties in the computation of the mechanical properties. A rise of the temperature leads to a slight increase in the observed uncertainties. The derived expressions for the stress and elasticity tensors are further decomposed into sums of atomic level stress and atomic level elasticity tensors. The developed factorization enables us (i) to quantify the contribution of the various chemical groups, in the case under consideration of the different atoms, to the observed mechanical properties and (ii) to determine the elastic constants with reduced computational uncertainties. The reason is that the exact values of some terms of the proposed factorization can be determined theoretically beforehand. Thus, they can be substituted in the derived formulas leading to an enhanced convergence.

Interfacial thermal transport and structural preferences in carbon nanotube-polyamide-6,6 nanocomposites: how important are chemical functionalization effects?

We employ reverse nonequilibrium molecular dynamics simulations to investigate the interfacial heat transfer in composites formed by an ungrafted or a grafted carbon nanotube which is surrounded by oligomeric polyamide-6,6 chains. The structural properties of the polymer matrix and the grafted chains are also studied. The influence of the grafting density, the length of the grafted chains as well as their chemical composition on the interfacial thermal conductivity (λi) are in the focus of our computational study. For the considered grafted polyethylene and polyamide chains we do not find a sizeable difference in the observed λi values. In contrast to this insensitivity, we predict a rather strong influence on λi by the grafting density and the length of the grafted chains. This dependence is an outcome of modifications in the structural properties of the polymer matrix as well as the grafted chains. Functionalization of the nanotube has a sizeable influence on the interfacial thermal conductivity. Its enhancement is caused by the chemical bonds between the nanotube and grafted chain atoms which reduce the number of Kapitza resistances hindering the heat transfer in polymer samples. The phonon density of states profiles confined to the bonded nanotube and the grafted chain atoms are used to emphasize the phonon support of the thermal conductivity in nanocomposites with grafted tubes. Strategies to tailor nanotube containing composites with higher thermal conductivities than that realized in the bare polymer are shortly touched.

Robustness of a new molecular dynamics-finite element coupling approach for soft matter systems analyzed by uncertainty quantification.

Key parameters of a recently developed coarse-grained molecular dynamics-finite element coupling approach have been analyzed in the framework of uncertainty quantification (UQ). We have employed a polystyrene sample for the case study. The new hybrid approach contains several parameters which cannot be determined on the basis of simple physical arguments. Among others, this includes the so-called anchor points as information transmitters between the particle-based molecular dynamics (MD) domain and the surrounding finite element continuum, the force constant between polymer beads and anchor points, the number of anchor points, and the relative sizes of the MD core domain and the surrounding dissipative particle dynamics domain. Polymer properties such as density, radius of gyration, end-to-end distance, and radial distribution functions are calculated as a function of the above model parameters. The influence of these input parameters on the resulting polymer properties is studied by UQ. Our analysis shows that the hybrid method is highly robust. The variation of polymer properties of interest as a function of the input parameters is weak.

The glass transition in cured epoxy thermosets: A comparative molecular dynamics study in coarse-grained and atomistic resolution.

We investigate the volumetric glass transition temperature Tg in epoxy thermosets by means of molecular dynamics simulations. The epoxy thermosets consist of the resin bisphenol A diglycidyl ether and the hardener diethylenetriamine. A structure based coarse-grained (CG) force field has been derived using iterative Boltzmann inversion in order to facilitate simulations of larger length scales. We observe that Tg increases clearly with the degree of cross-linking for all-atomistic (AA) and CG simulations. The transition Tg in CG simulations of uncured mixtures is much lower than in AA-simulations due to the soft nature of the CG potentials, but increases all the more with the formation of rigid cross-links. Additional simulations of the CG mixtures in contact with a surface show the existence of an interphase region of about 3 nm thickness in which the network properties deviate significantly from the bulk. In accordance to experimental studies, we observe that Tg is reduced in this interphase region and gradually increases to its bulk value with distance from the surface. The present study shows that the glass transition is a local phenomenon that depends on the network structure in the immediate environment.

Reptation and constraint release dynamics in bidisperse polymer melts.

Bidisperse melts of linear, entangled polymer chains were studied using dissipative particle dynamics. The entanglement constraints were mimicked with our newly developed slip-spring approach. The compositions cover blends with short matrix chains, slightly above the molecular entanglement weight as well as blends were both chain lengths exhibit distinct entangled dynamics at various weight fractions. The Struglinsky-Graessley parameter Gr, which is the ratio between the relaxation time of the long chains due to pure reptation and the relaxation time of the tube caused by constraint release, ranges between values high above and below unity. We compare our slip-spring model with simulations that use conventional generic polymer models where bond crossings are prevented by excluded-volume interactions and find fairly good agreement in terms of the mean squared displacement. However, the slip-spring approach requires only a fraction of the computational time, making large scale systems feasible. The dynamical interference of the two different chain lengths is discussed in terms of reptation and constraint release dynamics. For bidisperse melt compositions with Gr < 1.0 the relaxation time of the long chain component is not affected by constraint release. However, for compositions where constraint release is supposed to contribute significantly to the relaxation mechanism (Gr > 1.0), we find strong evidence that the long chains reptate inside a dilated tube whose diameter increases with an exponent of 1/2 towards lower weight fraction of the long chains. Furthermore we observe a linear relation between the relaxation time and weight fraction. Therefore, based on the relaxation times, our results support the validity of the tube dilation model as proposed by Doi et al. [Macromolecules 20, 1900-1906 (1987)].

Ice and water droplets on graphite: a comparison of quantum and classical simulations.

Ice and water droplets on graphite have been studied by quantum path integral and classical molecular dynamics simulations. The point-charge q-TIP4P/F potential was used to model the interaction between flexible water molecules, while the water-graphite interaction was described by a Lennard-Jones potential previously used to reproduce the macroscopic contact angle of water droplets on graphite. Several energetic and structural properties of water droplets with sizes between 10(2) and 10(3) molecules were analyzed in a temperature interval of 50-350 K. The vibrational density of states of crystalline and amorphous ice drops was correlated to the one of ice Ih to assess the influence of the droplet interface and molecular disorder on the vibrational properties. The average distance of covalent OH bonds is found 0.01 Å larger in the quantum limit than in the classical one. The OO distances are elongated by 0.03 Å in the quantum simulations at 50 K. Bond distance fluctuations are large as a consequence of the zero-point vibrations. The analysis of the H-bond network shows that the liquid droplet is more structured in the classical limit than in the quantum case. The average kinetic and potential energy of the ice and water droplets on graphite has been compared with the values of ice Ih and liquid water as a function of temperature. The droplet kinetic energy shows a temperature dependence similar to the one of liquid water, without apparent discontinuity at temperatures where the droplet is solid. However, the droplet potential energy becomes significantly larger than the one of ice or water at the same temperature. In the quantum limit, the ice droplet is more expanded than in a classical description. Liquid droplets display identical density profiles and liquid-vapor interfaces in the quantum and classical limits. The value of the contact angle is not influenced by quantum effects. Contact angles of droplets decrease as the size of the water droplet increases which implies a positive sign of the line tension of the droplet.

Molecular dynamics approach to locally resolve elastic constants in nanocomposites and thin films: mechanical description of solid-soft matter interphases via Young's modulus, Poisson's ratio and shear modulus.

A molecular dynamics approach based on a small-deformation mechanical response has been extended from the evaluation of locally resolved Poisson's ratios, νj, in nanocomposites to the calculation of local Young's moduli, Ej, (with j labelling a subvolume of the studied sample). On the basis of the νj and Ej, the local values of the shear modulus, Gj, can be derived as well. The capability of the developed method to derive locally resolved elastic constants of complex (nanocomposite) systems has been tested for an atomistic model of silica and atactic polystyrene. When measuring the interphase dimension of the composite in terms of local Ej, νj and Gj elements, a surface influence exceeding three times the polymer bulk radius of gyration (Rg ≈ 1 nm in the studied 20 mer composite) is predicted while for the majority of static quantities (e.g., polymer mass density, polymer orientation relative to the nanoparticle surface, radius of gyration, end-to-end distance) interphase dimensions only slightly larger than the polymer Rg are found. Calculated local values of mechanical descriptors can be adopted as input parameters in the micromechanical modelling of multicomponent nanocomposites.

Excess entropy scaling for the segmental and global dynamics of polyethylene melts.

The range of validity of the Rosenfeld and Dzugutov excess entropy scaling laws is analyzed for unentangled linear polyethylene chains. We consider two segmental dynamical quantities, i.e. the bond and the torsional relaxation times, and two global ones, i.e. the chain diffusion coefficient and the viscosity. The excess entropy is approximated by either a series expansion of the entropy in terms of the pair correlation function or by an equation of state for polymers developed in the context of the self associating fluid theory. For the whole range of temperatures and chain lengths considered, the two estimates of the excess entropy are linearly correlated. The scaled bond and torsional relaxation times fall into a master curve irrespective of the chain length and the employed scaling scheme. Both quantities depend non-linearly on the excess entropy. For a fixed chain length, the reduced diffusion coefficient and viscosity scale linearly with the excess entropy. An empirical reduction to a chain length-independent master curve is accessible for both dynamic quantities. The Dzugutov scheme predicts an increased value of the scaled diffusion coefficient with increasing chain length which contrasts physical expectations. The origin of this trend can be traced back to the density dependence of the scaling factors. This finding has not been observed previously for Lennard-Jones chain systems (Macromolecules, 2013, 46, 8710-8723). Thus, it limits the applicability of the Dzugutov approach to polymers. In connection with diffusion coefficients and viscosities, the Rosenfeld scaling law appears to be of higher quality than the Dzugutov approach. An empirical excess entropy scaling is also proposed which leads to a chain length-independent correlation. It is expected to be valid for polymers in the Rouse regime.

Influence of longitudinal isotope substitution on the thermal conductivity of carbon nanotubes: results of nonequilibrium molecular dynamics and local density functional calculations.

We report reverse nonequilibrium molecular dynamics calculations of the thermal conductivity of isotope substituted (10,10) carbon nanotubes (CNTs) at 300 K. (12)C and (14)C isotopes both at 50% content were arranged either randomly, in bands running parallel to the main axis of the CNTs or in bands perpendicular to this axis. It is found that the systems with randomly distributed isotopes yield significantly reduced thermal conductivity. In contrast, the systems where the isotopes are organized in patterns parallel to the CNTs axis feature no reduction in thermal conductivity when compared with the pure (14)C system. Moreover, a reduction of approximately 30% is observed in the system with the bands of isotopes running perpendicular to the CNT axis. The computation of phonon dispersion curves in the local density approximation and classical densities of vibrational states reveal that the phonon structure of carbon nanotubes is conserved in the isotope substituted systems with the ordered patterns, yielding high thermal conductivities in spite of the mass heterogeneity. In order to complement our conclusions on the (12)C-(14)C mixtures, we computed the thermal conductivity of systems where the (14)C isotope was turned into pseudo-atoms of 20 and 40 atomic mass units.

Transversal thermal transport in single-walled carbon nanotube bundles: influence of axial stretching and intertube bonding.

Using reverse nonequilibrium molecular dynamics simulations the influence of intermolecular bridges on the thermal conductivity (λ) in carbon nanotube (CNT) bundles has been investigated. The chosen cross linkers (CH2, O, CO) strengthen the transversal energy transport relative to the one in CNT bundles without bridges. The results showed that λ does not increase linearly with the linker density. The efficiency of the heat transport is determined by the number of linkers in the direction of the heat flux, the type of the linker, and their spatial ordering. The influence of a forced axial stress on the transversal λ has been also studied. The observed λ reduction with increasing axial stretching in a neat CNT bundle can be (over)compensated by cross linkers. The present computational data emphasize the contribution of phonons to the transversal heat transport in CNT bundles with intertube bonds.

Recovering the reptation dynamics of polymer melts in dissipative particle dynamics simulations via slip-springs.

We report a multi-chain approach for dissipative particle dynamics where the uncrossability constraints of polymer chains are mimicked by temporary cross-links, so-called slip-springs. The conformational statistics of the chains are not affected by the introduction of slip-springs. Dynamical properties such as mean square displacements, diffusion coefficient, and longest relaxation time are in good agreement with the results of reptation theory. According to our analysis, the present formalism is 500 times faster and requires 7 times fewer beads than conventional generic polymer models employing Newtonian dynamics and excluded-volume potentials.

Molecular dynamics method to locally resolve Poisson's ratio: Mechanical description of the solid-soft-matter interphase.

A method based on "small-deformation mechanical response" has been developed to locally resolve the Poisson's ratio via molecular dynamics simulations. The approach can be used for simple and composite materials to characterize systems with two or more continuous phases in the framework of periodic boundary conditions. The proposed technique represents a simple method to obtain a local mechanical description of complex systems. A polystyrene bulk, a silica bulk, and a polystyrene-silica heterogeneous composite material have been characterized under imposed strain. The results show the effects of local material inhomogeneities which are present in the glassy material and in the composite system. The Poisson's ratio spatial profiles for silica, the polystyrene bulk, and in the interphase region between the soft polymer bulk and the hard surface have also been calculated. The obtained local mechanical description can be employed in micromechanical models developed to predict the overall mechanical properties of multicomponent materials.

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 Young's 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 Young's 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 nanoparticle's surface. A thorough analysis of these parameters reveals that the segments close to the silica nanoparticle's surface are stiffer than those in the bulk. The thickness of the nanoparticle-matrix interphase layer is estimated. The Young's modulus of the nanocomposite has been obtained for several nanoparticle volume fractions. The addition of nanoparticles results in an enhanced Young's modulus. A linear relation describes adequately the dependence of Young's modulus on the nanoparticle volume fraction.

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.

Thermal conductivity of carbon nanotube-polyamide-6,6 nanocomposites: reverse non-equilibrium molecular dynamics simulations.

The thermal conductivity of composites of carbon nanotubes and polyamide-6,6 has been investigated using reverse non-equilibrium molecular dynamics simulations in a full atomistic resolution. It is found, in line with experiments, that the composites have thermal conductivities, which are only moderately larger than that of pure polyamide. The composite conductivities are orders of magnitude less than what would be expected from naïve additivity arguments. This means that the intrinsic thermal conductivities of isolated nanotubes, which exceed the best-conducting metals, cannot be harnessed for heat transport, when the nanotubes are embedded in a polymer matrix. The main reason is the high interfacial thermal resistance between the nanotubes and the polymer, which was calculated in addition to the total composite thermal conductivity as well as that of the subsystem. It hinders heat to be transferred from the slow-conducting polymer into the fast-conducting nanotubes and back into the polymer. This interpretation is in line with the majority of recent simulation works. An alternative explanation, namely, the damping of the long-wavelength phonons in nanotubes by the polymer matrix is not supported by the present calculations. These modes provide most of the polymers heat conduction. An additional minor effect is caused by the anisotropic structure of the polymer phase induced by the nearby nanotube surfaces. The thermal conductivity of the polymer matrix increases slightly in the direction parallel to the nanotubes, whereas it decreases perpendicular to it.

Thermal conductivity reduction through isotope substitution in nanomaterials: predictions from an analytical classical model and nonequilibrium molecular dynamics simulations.

We introduce an analytical model to rapidly determine the thermal conductivity reduction due to mass disorder in nanomaterials. Although this simplified classical model depends only on the masses of the different atoms, it adequately describes the changes in thermal transport as the concentrations of these atoms vary. Its predictions compare satisfactorily with nonequilibrium molecular dynamics simulations of the thermal conductivity of (14)C-(12)C carbon nanotubes as well as with previous simulations of other materials. We present it as a simple tool to quantitatively estimate the thermal conductivity decrease that is induced by isotope substitution in various materials.

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.