Equilibration of High Molecular-Weight Polymer Melts: A Hierarchical Strategy

A strategy is developed for generating equilibrated high molecular-weight polymer melts described with microscopic detail by sequentially backmapping coarse-grained (CG) configurations. The microscopic test model is generic but retains features like hard excluded volume interactions and realistic melt densities. The microscopic representation is mapped onto a model of soft spheres with fluctuating size, where each sphere represents a microscopic subchain with $N_{\rm b}$ monomers. By varying $N_{\rm b}$ a hierarchy of CG representations at different resolutions is obtained. Within this hierarchy, CG configurations equilibrated with Monte Carlo at low resolution are sequentially fine-grained into CG melts described with higher resolution. A Molecular Dynamics scheme is employed to slowly introduce the microscopic details into the latter. All backmapping steps involve only local polymer relaxation thus the computational efficiency of the scheme is independent of molecular weight, being just proportional to system size. To demonstrate the robustness of the approach, microscopic configurations containing up to $n=1000$ chains with polymerization degrees $N=2000$ are generated and equilibration is confirmed by monitoring key structural and conformational properties. The extension to much longer chains or branched polymers is straightforward

One size fits all: equilibrating chemically different polymer liquids through universal long-wavelength description

Mesoscale behavior of polymers is frequently described by universal laws. This physical property motivates us to propose a new modeling concept, grouping polymers into classes with a common long-wavelength representation. In the same class samples of different materials can be generated from this representation, encoded in a single library system. We focus on homopolymer melts, grouped according to the invariant degree of polymerization. They are described with a bead-spring model, varying chain stiffness and density to mimic chemical diversity. In a renormalization group-like fashion library samples provide a universal blob-based description, hierarchically backmapped to create configurations of other class-members. Thus large systems with experimentally-relevant invariant degree of polymerizations (so far accessible only on very coarse-grained level) can be microscopically described. Equilibration is verified comparing conformations and melt structure with smaller scale conventional simulations

Hierarchical modeling of polystyrene melts: From soft blobs to atomistic resolution

We demonstrate that hierarchical backmapping strategies incorporating generic blob-based models can equilibrate melts of high-molecular-weight polymers, described with chemically specific, atomistic, models. The central idea behind these strategies, is first to represent polymers by chains of large soft blobs (spheres) and efficiently equilibrate the melt on mesoscopic scale. Then, the degrees of freedom of more detailed models are reinserted step by step. The procedure terminates when the atomistic description is reached. Reinsertions are feasible computationally because the fine-grained melt must be re-equilibrated only locally. To develop the method, we choose a polymer with sufficient complexity. We consider polystyrene (PS), characterized by stereochemistry and bulky side groups. Our backmapping strategy bridges mesoscopic and atomistic scales by incorporating a blob-based, a moderately CG, and a united-atom model of PS. We demonstrate that the generic blob-based model can be parameterized to reproduce the mesoscale properties of a specific polymer -- here PS. The moderately CG model captures stereochemistry. To perform backmapping we improve and adjust several fine-graining techniques. We prove equilibration of backmapped PS melts by comparing their structural and conformational properties with reference data from smaller systems, equilibrated with less efficient methods.Comment: 18 page

Can Soft Models Describe Polymer Knots?

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Self-Assembly in Thin Films of Mixtures of Block Copolymers and Homopolymers Interacting by Hydrogen Bonds

We report on the self-assembling behavior in thin films of mixtures of polystyrene-block-poly(ethylene oxide) copolymers (PS-b-PEO), having PEO cylindrical microdomains, with poly(acrylic acid) homopolymers (PAA). We study the effect of adding PAA of different molecular weights, specifically interacting with the PEO block by hydrogen bonding, on the thin film characteristics: morphology, microdomain orientation and spacing. It is found that the addition of PAA induces an orientation of the cylindrical microdomains perpendicularly to the film surface. The lattice spacing increases with the amount of PAA added until a transition toward lamellar morphology is observed. This transition occurs at lower PAA content for PAA of small molecular weight. The experiments also reveal that the PAA homopolymer is localized in the center of the PEO microdomains. The trends observed in the experiments were validated by self-consistent field theory calculations using a newly and specifically developed model

Nematic Ordering, Conjugation, and Density of States of Soluble Polymeric Semiconductors

We develop a generic coarse-grained model for describing liquid crystalline ordering of polymeric semiconductors on mesoscopic scales, using poly­(3-hexylthiophene) (P3HT) as a test system. The bonded interactions are obtained by Boltzmann-inverting the distributions of coarse-grained degrees of freedom resulting from a canonical sampling of an atomistic chain in Θ-solvent conditions. The nonbonded interactions are given by soft anisotropic potentials, representing the combined effects of anisotropic π<i>–</i>π interactions and entropic repulsion of side chains. We demonstrate that the model can describe uniaxial and biaxial nematic mesophases, reproduces the experimentally observed effect of molecular weight on phase behavior, and predicts Frank elastic constants typical for polymeric liquid crystals. We investigate charge transport properties of the biaxial nematic phase by analyzing the length distribution of conjugated segments and the internal energetic landscape for hole transport. Results show how conjugation defects tend to localize near chain ends and how long-range orientational correlations lead to a spatially correlated, non-Gaussian density of states