Atomistic simulations have been very useful for predicting the viscoelastic properties of polymers but face great difficulties in accessing the dynamics of dense, well entangled longchain melts with relaxation times longer than μs due to the high computational cost required. A plethora of coarse-grained models have been developed to address longer time scales. In this article we present a multiscale simulation strategy that bridges detailed molecular dynamics (MD) simulations to slip-spring based Brownian dynamics/kinetic Monte Carlo (BD/kMC) simulations of long-chain polymer melts. The BD/kMC simulations are based on a mesoscopic Helmholtz energy function incorporating bonded, slip-spring, and nonbonded interaction contributions (Macromolecules 2017, 50, 3004). Bonded contributions are expressed as sums of stretching and bending potentials of mean force derived from detailed MD simulations of shorter-chain melts, while nonbonded interaction contributions in the absence of slipsprings are derived from an equation of state that is consistent with thermodynamic properties predicted by detailed MD and measured experimentally. Monodisperse linear polyethylene melts of chain lengths C 260 to C 2080 are used as a test case. Estimates of the chain self-diffusivity, the longest relaxation time, the stress relaxation modulus, and the zero-shear viscosity from ms-long equilibrium BD/kMC simulations are in excellent agreement with MD results for the shorter-chain melts and with experiment. The BD/kMC scheme is extended to simulate Couette flow using Lees−Edwards periodic boundary conditions over a range of Weissenberg numbers (Wi) from 10 −2 to 10 5 . Predictions for the shear viscosity as a function of shear rate, the first and second normal stress difference coefficients, the startup shear stress, as well as for changes in chain conformation and entangled structure with increasing Wi are in favorable agreement with experimental and atomistic simulation evidence.

We present a reliable simulation strategy for estimating the surface tension, the work of adhesion, and all related macroscopic work functions of fluid/vacuum and fluid/solid interfaces, directly from the atomic-level stresses in the system. Our methodology employs efficient algorithms (developed here and from the literature) for fast and reliable simulations of high molar mass polymer melts and is applied to the well-tested molten polyethylene/graphite interface, as well to the free surface of molten polyethylene, using a united atom model for the polymer. The surface thermodynamic properties are obtained for a broad range of molar masses and temperatures and are compared to experimental data, theoretical models, and earlier simulation studies. The individual components of the stress tensor are isolated, and their profiles along the aperiodic dimension are correlated to the orientational and structural features of the polymer chains near the interfaces. The distributions of end segments in free and capped polymer films are obtained for various temperatures and molar masses. The simulation procedure, the adequacy of the models employed for the stress tensor, and the tail corrections to surface thermodynamic properties as well as subtle issues arising in simulations of polymer/solid interfaces are discussed in detail.

Polymer/matrix nanocomposites (PNCs) are materials with exceptional properties. They offer a plethora of promising applications in key industrial sectors. In most cases, it is preferable to disperse the nanoparticles (NPs)...

A self-consistent field (SCF) theoretic approach, using a general excess Helmholtz energy density functional that includes a square gradient term, is derived for polymer melt surfaces and implemented for linear polyethylene films over a variety of temperatures and chain lengths. The formulation of the SCF plus square gradient approximation (SGA) developed is generic and can be applied with any equation of state (EoS) suitable for the estimation of the excess Helmholtz energy. As a case study, the approach is combined with the Sanchez−Lacombe (SL) EoS to predict reduced density profiles, chain conformational properties, and interfacial free energies, yielding very favorable agreement with atomistic simulation results and noticeable improvement relative to simpler SCF and SGA approaches. The reduced influence parameter invoked in the SGA to achieve accurate density profiles and interfacial free energies is consistent with the definition of Poser and Sanchez, J. Colloid Interface Sci. 1979, 69, 539−548. The new SCF_SL + SGA approach is used to quantify the dominance of chain end segments compared to that of middle segments at free polyethylene surfaces. Schemes are developed to distinguish surface adsorbed from free chains and to decompose the surface density profiles into contributions from trains, loops, and tails; the results for molten polyethylene are compared with the observables of atomistic simulations. Reduced chain shape profiles indicate flattening of the chains in the surface region as compared to the bulk chains. The range of this transitional region is approximately 1.6 radii of gyration (R g ). The inclusion of chain conformational entropy effects, as described by the modified Edwards diffusion equation of the SCF, in addition to the square gradient term in density, provides more accurate predictions of the surface tension, in good match with experimental measurements on a variety of polymer melts and with atomistic simulation findings.

We investigate single and opposing silica plates, either bare of grafted, in contact with vacuum or melt phases, using self-consistent field theory. Solid–polymer and solid–solid nonbonded interactions are described by means of a Hamaker potential, in conjunction with a ramp potential. The cohesive nonbonded interactions are described by the Sanchez-Lacombe or the Helfand free energy densities. We first build our thermodynamic reference by examining single surfaces, either bare or grafted, under various wetting conditions in terms of the corresponding contact angles, the macroscopic wetting functions (i.e., the work of cohesion, adhesion, spreading and immersion), the interfacial free energies and brush thickness. Subsequently, we derive the potential of mean force (PMF) of two approaching bare plates with melt between them, each time varying the wetting conditions. We then determine the PMF between two grafted silica plates separated by a molten polystyrene film. Allowing the grafting density and the molecular weight of grafted chains to vary between the two plates, we test how asymmetries existing in a real system could affect steric stabilization induced by the grafted chains. Additionally, we derive the PMF between two grafted surfaces in vacuum and determine how the equilibrium distance between the two grafted plates is influenced by their grafting density and the molecular weight of grafted chains. Finally, we provide design rules for the steric stabilization of opposing grafted surfaces (or fine nanoparticles) by taking account of the grafting density, the chain length of the grafted and matrix chains, and the asymmetry among the opposing surfaces.

A mesoscopic simulation approach is developed for liquid–gas interfaces of weakly and strongly entangled polymer melts and implemented for linear polyethylene at 450 K. A combined particle and field-theoretic treatment is adopted based on aggressive coarse-graining, each polymer bead representing ∼50 carbon atoms, with effective bonded interactions extracted from atomistic simulations. Nonbonded interactions in the mesoscopic model are dictated by an equation of state (here the Sanchez–Lacombe) in conjunction with a variant of gradient theorythe discrete square gradient theory. The dynamics of free films is examined in the presence and in the absence of topological constraints (modeled by slip-springs) to unveil the impact of the latter on chain self-diffusion, to assess their contribution to the interfacial free energy, and to explore how this contribution can be removed by invoking a compensating potential. The molar mass dependence of surface tensionwhich arises from bonded contributions among beads in the mesoscopic chainsis extracted over a broad range of molar masses (103–106 g/mol), in excellent agreement with experiment. Two approaches for computing the surface tension are adopted, based on stress profiles and based on changes in free energy with interfacial area, leading to consistent results. The predicted density profiles, conformations, and orientational tendencies of the mesoscopic chains are retrieved from the simulations and shown to reproduce very well the corresponding results from atomistic simulations. An annealing scheme is developed with the purpose of accelerating transitions of metastable states into more stable biphasic states such as spherical and cylindrical droplets, free films, and spherical and cylindrical bubbles, which minimize the free energy of the periodic model system. Results for the phase diagram as a function of polymer volume fraction conform to the predictions of atomistic simulations of simpler systems.

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In previous work by the authors, a new methodology was developed for Brownian dynamics/kinetic Monte Carlo (BD/kMC) simulations of polymer melts. In this study, this methodology is extended for dynamical simulations of crosslinked polymer networks in a coarse-grained representation, wherein chains are modeled as sequences of beads, each bead encompassing a few Kuhn segments. In addition, the C++ code embodying these simulations, entitled Engine for Mesoscopic Simulations for Polymer Networks (EMSIPON) is described in detail. A crosslinked network of cis-1,4-polyisoprene is chosen as a test system. From the thermodynamic point of view, the system is fully described by a Helmholtz energy consisting of three explicit contributions: entropic springs, slip springs and non-bonded interactions. Entanglements between subchains in the network are represented by slip springs. The ends of the slip springs undergo thermally activated hops between adjacent beads along the chain backbones, which are tracked by kinetic Monte Carlo simulation. In addition, creation/destruction processes are included for the slip springs at dangling subchain ends. The Helmholtz energy of non-bonded interactions is derived from the Sanchez–Lacombe equation of state. The isothermal compressibility of the polymer network is predicted from equilibrium density fluctuations in very good agreement with the underlying equation of state and with experiment. Moreover, the methodology and the corresponding C++ code are applied to simulate elongational deformations of polymer rubbers. The shear stress relaxation modulus is predicted from equilibrium simulations of several microseconds of physical time in the undeformed state, as well as from stress-strain curves of the crosslinked polymer networks under deformation.