Bond−Vector Correlation Functions in Dense Polymer Systems

Multiscale equilibration of highly entangled isotropic model polymer melts

We present a computationally efficient multiscale method for preparing equilibrated, isotropic long-chain model polymer melts. As an application, we generate Kremer-Grest melts of 1000 chains with 200 entanglements and 25 000-2000 beads/chain, which cover the experimentally relevant bending rigidities up to and beyond the limit of the isotropic-nematic transition. In the first step, we employ Monte Carlo simulations of a lattice model to equilibrate the large-scale chain structure above the tube scale while ensuring a spatially homogeneous density distribution. We then use theoretical insight from a constrained mode tube model to introduce the bead degrees of freedom together with random walk conformational statistics all the way down to the Kuhn scale of the chains. This is followed by a sequence of simulations with carefully parameterized force-capped bead-spring models, which slowly introduce the local bead packing while reproducing the larger-scale chain statistics of the target Kremer-Grest system at all levels of force-capping. Finally, we can switch to the full Kremer-Grest model without perturbing the structure. The resulting chain statistics is in excellent agreement with literature results on all length scales accessible in brute-force simulations of shorter chains.

Role of torsional potential in chain conformation, thermodynamics, and glass formation of simulated polybutadiene melts

For polymer chains, the torsional potential is an important intramolecular energy influencing chain flexibility and segmental dynamics. Through molecular dynamics simulations of an atomistic model for melts of cis-trans-1,4-polybutadiene (PBD), we explore the effect of the torsions on conformational properties (bond vector correlations and mean-square internal distances), fundamental thermodynamic quantities (density, compressibility, internal energy, and specific heat), and glass transition temperature T_g. This is achieved by systematically reducing the strength of the torsional potential, starting from the chemically realistic chain (CRC) model with the full potential toward the freely rotating chain (FRC) model without the torsional potential. For the equilibrium liquid, we find that the effect of the torsions on polymer conformations is very weak. Still weaker is the influence on the monomer density ρ and isothermal compressibility κ_T of the polymer liquid, both of which can be considered as independent of the torsional potential. We show that a van der Waals-like model proposed by Long and Lequeux [Eur. Phys. J. E 4, 371 (2001)] allows us to describe very well the temperature (T) dependence of ρ and κ_T. We also find that our data obey the linear relation between 1/k_BTρκ_T and 1/T (with the Boltzmann constant k_B) that has recently been predicted and verified on the experiment by Mirigian and Schweizer [J. Chem. Phys. 140, 194507 (2014)]. For the equilibrium liquid, simulations result in a specific heat, at constant pressure and at constant volume, which increases on cooling. This T dependence is opposite to the one found experimentally for many polymer liquids, including PBD. We suggest that this difference between simulation and experiment may be attributed to quantum effects due to hydrogen atoms and backbone vibrations, which, by construction, are not included in the classical united-atom model employed here. Finally, we also determine T_g from the density-temperature curve monitored in a finite-rate cooling process. While the influence of the torsional potential on ρ(T) is vanishingly small in the equilibrium liquid, the effect of the torsions on T_g is large. We find that T_g decreases by about 150 K when going from the CRC to the FRC model.

Columnar Aggregates of Azobenzene Stars: Exploring Intermolecular Interactions, Structure, and Stability in Atomistic Simulations

We present a simulation study of supramolecular aggregates formed by three-arm azobenzene (Azo) stars with a benzene-1,3,5-tricarboxamide (BTA) core in water. Previous experimental works by other research groups demonstrate that such Azo stars assemble into needle-like structures with light-responsive properties. Disregarding the response to light, we intend to characterize the equilibrium state of this system on the molecular scale. In particular, we aim to develop a thorough understanding of the binding mechanism between the molecules and analyze the structural properties of columnar stacks of Azo stars. Our study employs fully atomistic molecular dynamics (MD) simulations to model pre-assembled aggregates with various sizes and arrangements in water. In our detailed approach, we decompose the binding energies of the aggregates into the contributions due to the different types of non-covalent interactions and the contributions of the functional groups in the Azo stars. Initially, we investigate the origin and strength of the non-covalent interactions within a stacked dimer. Based on these findings, three arrangements of longer columnar stacks are prepared and equilibrated. We confirm that the binding energies of the stacks are mainly composed of π-π interactions between the conjugated parts of the molecules and hydrogen bonds formed between the stacked BTA cores. Our study quantifies the strength of these interactions and shows that the π-π interactions, especially between the Azo moieties, dominate the binding energies. We clarify that hydrogen bonds, which are predominant in BTA stacks, have only secondary energetic contributions in stacks of Azo stars but remain necessary stabilizers. Both types of interactions, π-π stacking and H-bonds, are required to maintain the columnar arrangement of the aggregates.

Multiscale approach to equilibrating model polymer melts

We present an effective and simple multiscale method for equilibrating Kremer Grest model polymer melts of varying stiffness. In our approach, we progressively equilibrate the melt structure above the tube scale, inside the tube and finally at the monomeric scale. We make use of models designed to be computationally effective at each scale. Density fluctuations in the melt structure above the tube scale are minimized through a Monte Carlo simulated annealing of a lattice polymer model. Subsequently the melt structure below the tube scale is equilibrated via the Rouse dynamics of a force-capped Kremer-Grest model that allows chains to partially interpenetrate. Finally the Kremer-Grest force field is introduced to freeze the topological state and enforce correct monomer packing. We generate 15 melts of 500 chains of 10.000 beads for varying chain stiffness as well as a number of melts with 1.000 chains of 15.000 monomers. To validate the equilibration process we study the time evolution of bulk, collective, and single-chain observables at the monomeric, mesoscopic, and macroscopic length scales. Extension of the present method to longer, branched, or polydisperse chains, and/or larger system sizes is straightforward.

Conformations of a Long Polymer in a Melt of Shorter Chains: Generalizations of the Flory Theorem

Large-scale simulations of the swelling of a long N-mer in a melt of chemically identical P-mers are used to investigate a discrepancy between theory and experiments. Classical theory predicts an increase of probe chain size R ∼ P^-0.18 with decreasing degree of polymerization P of melt chains in the range of 1 < P < N^1/2. However, both experiment and simulation data are more consistent with an apparently slower swelling R ∼ P^-0.1 over a wider range of melt degrees of polymerization. This anomaly is explained by taking into account the recently discovered long-range bond correlations in polymer melts and corrections to excluded volume. We generalize the Flory theorem and demonstrate that it is in excellent agreement with experiments and simulations.

Rouse Mode Analysis of Chain Relaxation in Homopolymer Melts

We use molecular dynamics simulations of the Kremer–Grest (KG) bead–spring model of polymer chains of length between 10 and 500, and a closely related analogue that allows for chain crossing, to clearly delineate the effects of entanglements on the length-scale-dependent chain relaxation in polymer melts. We analyze the resulting trajectories using the Rouse modes of the chains and find that entanglements strongly affect these modes. The relaxation rates of the chains show two limiting effective monomeric frictions, with the local modes experiencing much lower effective friction than the longer modes. The monomeric relaxation rates of longer modes vary approximately inversely with chain length due to kinetic confinement effects. The time-dependent relaxation of Rouse modes has a stretched exponential character with a minimum of stretching exponent in the vicinity of the entanglement chain length. None of these trends are found in models that allow for chain crossing. These facts, in combination, argue for the confined motion of chains for time scales between the entanglement time and their ultimate free diffusion.

Mode-coupling approach to polymer diffusion in an unentangled melt. I. The effect of density fluctuations

We quantitatively assess the effect of density fluctuation modes on the dynamics of a tagged polymer in an unentangled melt. To this end, we develop a density-based mode-coupling theory (dMCT) using the Mori-Zwanzig approach and projecting the fluctuating force onto pair-density fluctuation modes. The effect of dynamical density fluctuations on the center-of-mass (c.m.) dynamics is also analyzed based on a perturbative approach and we show that dMCT and perturbation techniques yield identical results. The c.m. velocity autocorrelation function (c.m. VAF) exhibits a slow power law relaxation in the time range between the monomer time t_{1} and the Rouse relaxation time t_{N}. We obtain an analytical expression for the c.m. VAF in terms of molecular parameters. In particular, the c.m. VAF scales as -N^{-1}t^{-5/4} (where N is the number of monomer units per chain) in the relevant time regime. The results are qualitatively accounted for by the dynamical correlation hole effect. The predicted -t^{-5/4} dependence of the c.m. VAF is supported by data of non-momentum-conserving computer simulations. However, the comparison shows that the theory significantly underestimates the amplitude of the effect. This issue is discussed and an alternative approach is addressed in the second part of this series [Farago et al., Phys. Rev. E 85, 051807 (2012), the following paper].

Surface induced self-organization of comb-like macromolecules

We present a review of the theoretical and experimental evidence for the peculiar properties of comb copolymers, demonstrating the uniqueness of these materials among other polymer architectures. These special properties include an increase in stiffness upon increasing side-chain length, the spontaneous curvature of adsorbed combs, rod-globule transition, and specific intramolecular self-assembly. We also propose a theory of chemically heterogeneous surface nanopattern formation in ultrathin films of comblike macromolecules containing two different types (A and B) of incompatible side chains (so-called binary combs). Side chains of the binary combs are strongly adsorbed on a surface and segregated with respect to the backbone. The thickness of surface domains formed by the B side chains is controlled by the interaction with the substrate. We predict the stability of direct and inverse disc-, torus- and stripelike nanostructures. Phase diagrams of the film are constructed.