Hierarchical Modeling of the Dynamics of Polymers with a Nonlinear Molecular Architecture: Calculation of Branch Point Friction and Chain Reptation Time of H-Shaped Polyethylene Melts from Long Molecular Dynamics Simulations

Intrinsic structure and dynamics of monolayer ring polymer melts

We present the general structural and dynamical characteristics of flexible ring polymers in narrowly confined two-dimensional (2D) melt systems using atomistic molecular dynamics simulations. The results are further analyzed via direct comparison with the 2D linear analogue as well as the three-dimensional (3D) ring and linear melt systems. It is observed that dimensional restriction in 2D confined systems results in an increase in the intrinsic chain stiffness of the ring polymer. Fundamentally, this arises from an entropic penalty on polymer chains along with a reduction in the available chain configuration states in phase space and spatial choices for individual segmental walks. This feature in combination with the intermolecular interactions between neighboring ring chains leads to an overall extended interpenetrated chain configuration for the 2D ring melt. In contrast to the generally large differences in structural and dynamical properties between ring and linear polymers in 3D melt systems, relatively similar local-to-global chain structures and dynamics are observed for the 2D ring and linear melts. This is attributed to the general structural similarity (i.e., extended double-stranded chain conformations), the less effective role of the chain ends, and the absence of complex topological constraints between chains (i.e., interchain entanglement and mutual ring threading) in the 2D confined systems compared with the corresponding 3D bulk systems.

Insight into the Structure and Dynamics of Polymers by Neutron Scattering Combined with Atomistic Molecular Dynamics Simulations

Combining neutron scattering and fully atomistic molecular dynamics simulations allows unraveling structural and dynamical features of polymer melts at different length scales, mainly in the intermolecular and monomeric range. Here we present the methodology developed by us and the results of its application during the last years in a variety of polymers. This methodology is based on two pillars: (i) both techniques cover approximately the same length and time scales and (ii) the classical van Hove formalism allows easily calculating the magnitudes measured by neutron scattering from the simulated atomic trajectories. By direct comparison with experimental results, the simulated cell is validated. Thereafter, the information of the simulations can be exploited, calculating magnitudes that are experimentally inaccessible or extending the parameters range beyond the experimental capabilities. We show how detailed microscopic insight on structural features and dynamical processes of various kinds has been gained in polymeric systems with different degrees of complexity, and how intriguing questions as the collective behavior at intermediate length scales have been faced.

Dynamics of asymmetric star polymers under coarse grain simulations

The asymmetric star polymers are studied by coarse grain simulations. Each polymer chain is represented by number of consecutive soft blobs and additional uncrossability constraints are added to prevent chain crossings. In this work two types of asymmetric star polymers with different backbone lengths are structured. Their dynamical properties are discussed by comparisons with corresponding linear chains, the one covers chain length along with the asymmetric arm through the branch point to one of the symmetric arm, or the backbone chain between two symmetric arm ends, or the largest linear possesses the same molecular weight of the entire star. To reveal the influence of the asymmetric arm length on their relaxation decay times, the autocorrelation function of the vectors from each branching point to corresponding asymmetric arm end are calculated, results are compared with the symmetric star having the same backbone chain.

Influence of Branching on the Configurational and Dynamical Properties of Entangled Polymer Melts

We probe the influence of branching on the configurational, packing, and density correlation function properties of polymer melts of linear and star polymers, with emphasis on molecular masses larger than the entanglement molecular mass of linear chains. In particular, we calculate the conformational properties of these polymers, such as the hydrodynamic radius R h , packing length p, pair correlation function g ( r ) , and polymer center of mass self-diffusion coefficient, D, with the use of coarse-grained molecular dynamics simulations. Our simulation results reproduce the phenomenology of simulated linear and branched polymers, and we attempt to understand our observations based on a combination of hydrodynamic and thermodynamic modeling. We introduce a model of "entanglement" phenomenon in high molecular mass polymers that assumes polymers can viewed in a coarse-grained sense as "soft" particles and, correspondingly, we model the emergence of heterogeneous dynamics in polymeric glass-forming liquids to occur in a fashion similar to glass-forming liquids in which the molecules have soft repulsive interactions. Based on this novel perspective of polymer melt dynamics, we propose a functional form for D that can describe our simulation results for both star and linear polymers, covering both the unentangled to entangled polymer melt regimes.

DNA as a Model for Probing Polymer Entanglements: Circular Polymers and Non-Classical Dynamics

Double-stranded DNA offers a robust platform for investigating fundamental questions regarding the dynamics of entangled polymer solutions. The exceptional monodispersity and multiple naturally occurring topologies of DNA, as well as a wide range of tunable lengths and concentrations that encompass the entanglement regime, enable direct testing of molecular-level entanglement theories and corresponding scaling laws. DNA is also amenable to a wide range of techniques from passive to nonlinear measurements and from single-molecule to bulk macroscopic experiments. Over the past two decades, researchers have developed methods to directly visualize and manipulate single entangled DNA molecules in steady-state and stressed conditions using fluorescence microscopy, particle tracking and optical tweezers. Developments in microfluidics, microrheology and bulk rheology have also enabled characterization of the viscoelastic response of entangled DNA from molecular levels to macroscopic scales and over timescales that span from linear to nonlinear regimes. Experiments using DNA have uniquely elucidated the debated entanglement properties of circular polymers and blends of linear and circular polymers. Experiments have also revealed important lengthscale and timescale dependent entanglement dynamics not predicted by classical tube models, both validating and refuting new proposed extensions and alternatives to tube theory and motivating further theoretical work to describe the rich dynamics exhibited in entangled polymer systems.

Microscopic Dynamics and Topology of Polymer Rings Immersed in a Host Matrix of Longer Linear Polymers: Results from a Detailed Molecular Dynamics Simulation Study and Comparison with Experimental Data

We have performed molecular dynamics (MD) simulations of melt systems consisting of a small number of long ring poly(ethylene oxide) (PEO) probes immersed in a host matrix of linear PEO chains and have studied their microscopic dynamics and topology as a function of the molecular length of the host linear chains. Consistent with a recent neutron spin echo spectroscopy study (Goossen et al., Phys. Rev. Lett. 2015, 115, 148302), we have observed that the segmental dynamics of the probe ring molecules is controlled by the length of the host linear chains. In matrices of short, unentangled linear chains, the ring probes exhibit a Rouse-like dynamics, and the spectra of their dynamic structure factor resemble those in their own melt. In striking contrast, in matrices of long, entangled linear chains, their dynamics is drastically altered. The corresponding dynamic structure factor spectra exhibit a steep initial decay up to times on the order of the entanglement time τe of linear PEO at the same temperature but then they become practically time-independent approaching plateau values. The plateau values are different for different wavevectors; they also depend on the length of the host linear chains. Our results are supported by a geometric analysis of topological interactions, which reveals significant threading of all ring molecules by the linear chains. In most cases, each ring is simultaneously threaded by several linear chains. As a result, its dynamics at times longer than a few τe should be completely dictated by the release of the topological restrictions imposed by these threadings (interpenetrations). Our topological analysis did not indicate any effect of the few ring probes on the statistical properties of the network of primitive paths of the host linear chains.

Influence of molecular architecture on the entanglement network: topological analysis of linear, long- and short-chain branched polyethylene melts via Monte Carlo simulations

We present detailed results on the effect of chain branching on the topological properties of entangled polymer melts via an advanced connectivity-altering Monte Carlo (MC) algorithm. Eleven representative model linear, short-chain branched (SCB), and long-chain branched (LCB) polyethylene (PE) melts were employed, based on the total chain length and/or the longest linear chain dimension. Directly analyzing the entanglement [or the primitive path (PP)] network of the system via the Z-code, we quantified several important topological measures: (a) the PP contour length Lpp, (b) the number of entanglements Zes per chain, (c) the end-to-end length of an entanglement strand des, (d) the number of carbon atoms per entanglement strand Nes, and (e) the probability distribution for each of these quantities. The results show that the SCB polymer melts have significantly more compact overall chain conformations compared to the linear polymers, exhibiting, relative to the corresponding linear analogues, (a) ∼20% smaller values of 〈Lpp〉 (the statistical average of Lpp), (b) ∼30% smaller values of 〈Zes〉, (c) ∼20% larger values of 〈des〉, and (d) ∼50% larger values of 〈Nes〉. In contrast, despite the intrinsically smaller overall chain dimensions than those of the linear analogues, the LCB (H-shaped and A3AA3 multiarm) PE melts exhibit relatively (a) 7-8% larger values of 〈Lpp〉, (b) 6-11% larger values of 〈Zes〉 for the H-shaped melt and ∼2% smaller values of 〈Zes〉 for the A3AA3 multiarm, (c) 2-5% smaller values of 〈des〉, and (d) 7-11% smaller values of 〈Nes〉. Several interesting features were also found in the results of the probability distribution functions P for each topological measure.

Localization of chain dynamics in entangled polymer melts

The dynamics of polymer melts in both the unentangled and entangled regimes is described by a Langevin equation for the correlated motion of a group of chains, interacting through both intra- and inter-molecular potentials. Entanglements are represented by an intermolecular monomer-monomer confining potential that has no effect on short chains, while interpolymer interactions, responsible for correlated motion and subdiffusive center-of-mass dynamics, are represented by an intermolecular center-of-mass potential derived from the Ornstein-Zernike equation. This potential ensures that the liquid of phantom chains reproduces the compressibility and free energy of the real samples. For polyethylene melts the calculated dynamic structure factor is found to be in quantitative agreement with neutron spin echo experiments of polyethylene melts with chain lengths that span both the unentangled and the entangled regimes. The theory shows a progressive localization of the cooperative chain dynamics at the crossover from the unentangled to the entangled regime, in the spirit of the reptation model.

Combined molecular algorithms for the generation, equilibration and topological analysis of entangled polymers: methodology and performance

We review the methodology, algorithmic implementation and performance characteristics of a hierarchical modeling scheme for the generation, equilibration and topological analysis of polymer systems at various levels of molecular description: from atomistic polyethylene samples to random packings of freely-jointed chains of tangent hard spheres of uniform size. Our analysis focuses on hitherto less discussed algorithmic details of the implementation of both, the Monte Carlo (MC) procedure for the system generation and equilibration, and a postprocessing step, where we identify the underlying topological structure of the simulated systems in the form of primitive paths. In order to demonstrate our arguments, we study how molecular length and packing density (volume fraction) affect the performance of the MC scheme built around chain-connectivity altering moves. In parallel, we quantify the effect of finite system size, of polydispersity, and of the definition of the number of entanglements (and related entanglement molecular weight) on the results about the primitive path network. Along these lines we approve main concepts which had been previously proposed in the literature.

Cooperative dynamics in homopolymer melts: a comparison of theoretical predictions with neutron spin echo experiments

We present a comparison between theoretical predictions of the generalized Langevin equation for cooperative dynamics (CDGLE) and neutron spin echo data of dynamic structure factors for polyethylene melts. Experiments cover an extended range of length and time scales, providing a compelling test for the theoretical approach. Samples investigated include chains with increasing molecular weights undergoing dynamics across the unentangled to entangled transition. Measured center-of-mass (com) mean-square displacements display a crossover from subdiffusive to diffusive dynamics. The generalized Langevin equation for cooperative dynamics relates this anomalous diffusion to the presence of the interpolymer potential, which correlates the dynamics of a group of slowly diffusing molecules in a dynamically heterogeneous liquid. Theoretical predictions of the subdiffusive behavior, of its crossover to free diffusion, and of the number of macromolecules undergoing cooperative motion are in quantitative agreement with experiments.

Molecular simulation of the effect of temperature and architecture on polyethylene barrier properties

We present a multiscale approach for calculating the low-concentration solubility, diffusivity, and selectivity of small molecules through polymer matrixes. The proposed modeling scheme consists of two main stages; first, thoroughly equilibrated and representative poly(ethylene) (PE) atomistic melt configurations were obtained through the application of a Monte Carlo (MC) scheme based on advanced chain-connectivity altering moves (linear architectures) or the combination of localized MC moves followed by molecular dynamics. In the second phase, transition-state theory (TST), as proposed by Gusev and Suter [Gusev, A. A.; Suter, U. W. J. Chem. Phys. 1993, 99, 2228], was invoked in a coarser level of description to calculate the barrier properties of the studied macromolecules to small gas molecules at infinite dilution. The multiscale methodology was successfully applied on PE melts characterized by various molecular weights (MW) (from C78 up to C1000) and polydispersity indices at a wide range of temperature conditions. The effect of molecular architecture on the barrier properties was examined through the comparison between linear and short-chain branched structures bearing the same total number of carbon atoms. Simulation results were found to be in very good agreement with available experimental data. Additionally, the new scheme has been further validated by comparing the qualitative behavior of solubility, diffusivity, and selectivity with previously reported trends in the literature based on both experimental and simulation studies. The present study concludes that density plays a dominant role that determines the behavior of the polymer as a barrier material, especially in terms of diffusivity. Additionally, it is evidenced that short-chain branching has a small effect on the barrier properties of PE when the comparison is performed on purely amorphous samples. The hierarchical method presented here not only is faster when compared against conventional molecular dynamics simulations, but in some cases, like the vicinity of the glass transition temperature or for long polymer chain melts, it opens the way to the calculation of the barrier properties at realistic simulation times.

Water and Polymer Dynamics in Chemically Cross-Linked Hydrogels of Poly(vinyl alcohol): A Molecular Dynamics Simulation Study

A topologically extended model of a chemically cross-linked hydrogel of poly(vinyl alcohol) (PVA) at high hydration degree has been developed for a molecular dynamics simulation with atomic detail at 323 K. The analysis of the 5 ns trajectory discloses structural and dynamic aspects of polymer solvation and elucidates the water hydrogen bonding and diffusion in the network. The features of local polymer dynamics indicate that PVA mobility is not affected by structural constraints of chemical junctions at the investigated cross-linking density, with a prevailing dumping effect due to water interaction. Simulation results are validated by a favorable comparison with findings of an incoherent quasi-elastic neutron scattering study of the same hydrogel system.

Flexible ring polymers in an obstacle environment: Molecular theory of linear viscoelasticity

We formulate a coarse-grained mean-field approach to study the dynamics of the flexible ring polymer in any given obstacle (gel or melt) environment. The similarity of the static structure of the ring polymer with that of the ideal randomly branched polymer is exploited in formulating the dynamical model using aspects of the pom-pom model for branched polymers. The topological constraints are handled via the tube model framework. Based on our formulation we obtain expressions for diffusion coefficient D, relaxation times tau, and dynamic structure factor g(k,t). Further, based on the framework we develop a molecular theory of linear viscoelasticity for ring polymers in a given obstacle environment and derive the expression for the relaxation modulus G(t). The predictions of the theoretical model are in agreement with previously proposed scaling arguments and in qualitative agreement with the available experimental results for the melt of rings.

Molecular Dynamics Simulation of Structure, Thermodynamic, and Dynamic Properties of Poly(dimethylsilamethylene), Poly(dimethylsilatrimethylene) and Their Alternating Copolymer

Molecular dynamics is used for the simulation of silicon-containing polymers with promising membrane material properties. An atomistic force field is developed for the description of bond bending, torsional angle variation, and nonbonded intra- and intermolecular interactions. Detailed ab initio quantum mechanics calculations on corresponding monomers that appeared recently in the literature are used for the parametrization of the bonded and nonbonded local intramolecular force field. For the intermolecular and nonbonded nonlocal intramolecular interactions, parameters are obtained from accurate force fields proposed in the literature for similar compounds. The force field is used subsequently for the calculation of thermodynamic, structure, and dynamic properties of two homopolymers, namely, poly(dimethylsilamethylene) and poly(dimethylsilatrimethylene), and their alternating copolymer. A wide range of temperatures and pressures is examined. Polymer systems of different molecular weights are simulated. Experimental data available for these polymers are very limited. In all cases, simulation results are in good agreement with these data. Furthermore, simulation results agree very well with empirical macroscopic correlations used widely for rubbery polymers for the properties under consideration.