Dielectric Relaxation as an Independent Examination of Relaxation Mechanisms in Entangled Polymers Using the Discrete Slip-Link Model

Experiments and Modeling of Flow-Enhanced Nucleation in LLDPE

A computational and experimental framework for quantifying flow-enhanced nucleation (FEN) in polymers is presented and demonstrated for an industrial-grade linear low-density polyethylene (LLDPE). Experimentally, kinetic measurements of isothermal crystallization were performed by using fast-scanning calorimetry (FSC) for melts that were presheared at various strain rates. The effect of shear on the average conformation tensor of the melt was modeled with the discrete slip-link model (DSM). The conformation tensor was then related to the acceleration in nucleation kinetics by using an expression previously validated with nonequilibrium molecular dynamics (NEMD). The expression is based on the nematic order tensor of Kuhn segments, which can be obtained from the conformation tensor of entanglement strands. The single adjustable parameter of the model was determined by fitting to the experimental FSC data. This expression accurately describes FEN for the LLDPE, representing a significant advancement toward the development of a fully integrated processing model for crystallizable polymers.

Thermodynamically consistent incorporation of entanglement spatial fluctuations in the slip-link model

We evaluate the thermodynamic consistency of the anisotropic mobile slip-link model for entangled flexible polymers. The level of description is that of a single chain, whose interactions with other chains are coarse grained to discrete entanglements. The dynamics of the model consist of the motion of entanglements through space and of the chain through the entanglements, as well as the creation and destruction of entanglements, which are implemented in a mean-field way. Entanglements are modeled as discrete slip links, whose spatial positions are confined by quadratic potentials. The confinement potentials move with the macroscopic velocity field, hence the entanglements fluctuate around purely affine motion. We allow for anisotropy of these fluctuations, described by a set of shape tensors. By casting the model in the form of the general equation for the nonequilibrium reversible-irreversible coupling from nonequilibrium thermodynamics, we show that (i) since the confinement potentials contribute to the chain free energy, they must also contribute to the stress tensor, (ii) these stress contributions are of two kinds: one related to the virtual springs connecting the slip links to the centers of the confinement potentials and the other related to the shape tensors, and (iii) these two kinds of stress contributions cancel each other if the confinement potentials become anisotropic in flow, according to a lower-convected evolution of the confinement strength or, equivalently, an upper-convected evolution of the shape tensors of the entanglement spatial fluctuations. In previous publications, we have shown that this cancellation is necessary for the model to obey the stress-optical rule and the Green-Kubo relation, and simultaneously to agree with plateau modulus predictions of multichain models and simulations.

Slip-spring simulations of different constraint release environments for linear polymer chains

The constraint release (CR) mechanism has important effects on polymer relaxation and the chains will show different relaxation behaviour in conditions of monodisperse, bidisperse and other topological environments. By comparing relaxation data of linear polyisoprene (PI) chains dissolved in very long matrix and monodisperse melts, Matsumiya et al. showed that CR mechanism accelerates both dielectric and viscoelastic relaxation (Matsumiya et al. 2013 Macromolecules 46, 6067. (doi:10.1021/ma400606n)). In this work, the experimental data reported by Matsumiya et al. are reproduced using the single slip-spring (SSp) model and the CR accelerating effects on both dielectric and viscoelastic relaxation are validated by simulations. This effect on viscoelastic relaxation is more pronounced. The coincidence for end-to-end relaxation and the viscoelastic relaxation has also been checked using probe version SSp model. A variant of SSp with each entanglement assigning a characteristic lifetime is also proposed to simulate various CR environment flexibly. Using this lifetime version SSp model, the correct relaxation function can be obtained with equal numbers of entanglement destructions by CR and reptation/contour length fluctuation (CLF) for monodisperse melts. Good agreement with published experiment data is also obtained for bidisperse melts, which validates the ability to correctly describe the CR environment of the lifetime version model.

Slip-Spring and Kink Dynamics Models for Fast Extensional Flow of Entangled Polymeric Fluids

We combine a slip-spring model with an 'entangled kink dynamics' (EKD) model for strong uniaxial extensional flows (with Rouse Weissenberg number W i R ≫ 1 ) of long ( M w > 1   Mkg / mol for polystyrene) entangled polymers in solutions and melts. The slip-spring model captures the dynamics up to the formation of a 'kinked' or folded state, while the kink dynamics simulation tracks the dynamics from that point forward to complete extension. We show that a single-chain slip-spring model using affine motion of the slip-spring anchor points produces unrealistically high tension near the center of the chain once the Hencky strain exceeds around unity or so, exceeding the maximum tension that a chain entangled with a second chain is able to support. This unrealistic tension is alleviated by pairing the slip links on one chain with those on a second chain, and allowing some of the large tension on one of the two to be transferred to the second chain, producing non-affine motion of each. This explicit pairing of entanglements mimics the entanglement pairing also used in the EKD model, and allows the slip spring simulations to be carried out to strains high enough for the EKD model to become valid. We show that results nearly equivalent to those from paired chains are obtained in a single-chain slip-spring simulation by simply specifying that the tension in a slip spring cannot exceed the theoretical maximum value of ζ ' ϵ ˙ L 2 / 8 where ζ ' , ϵ ˙ and L are the friction per unit length, strain rate and contour length of the chain, respectively. The effects of constraint release (CR) and regeneration of entanglements is also studied and found to have little effect on the chain statistics up to the formation of the kinked state. The resulting hybrid model provides a fast, simple, simulation method to study the response of high molecular weight ( M w > 1   Mkg / mol ) polymers in fast flows ( W i R ≫ 1 ), where conventional simulation techniques are less applicable due to computational cost.

Primitive chain network simulations of probe rheology

Probe rheology experiments, in which the dynamics of a small amount of probe chains dissolved in immobile matrix chains is discussed, have been performed for the development of molecular theories for entangled polymer dynamics. Although probe chain dynamics in probe rheology is considered hypothetically as single chain dynamics in fixed tube-shaped confinement, it has not been fully elucidated. For instance, the end-to-end relaxation of probe chains is slower than that for monodisperse melts, unlike the conventional molecular theories. In this study, the viscoelastic and dielectric relaxations of probe chains were calculated by primitive chain network simulations. The simulations semi-quantitatively reproduced the dielectric relaxation, which reflects the effect of constraint release on the end-to-end relaxation. Fair agreement was also obtained for the viscoelastic relaxation time. However, the viscoelastic relaxation intensity was underestimated, possibly due to some flaws in the model for the inter-chain cross-correlations between probe and matrix chains.

Entangled Polymer Dynamics in Equilibrium and Flow Modeled Through Slip Links

The idea that the dynamics of concentrated, high–molecular weight polymers are largely governed by entanglements is now widely accepted and typically understood through the tube model. Here we review alternative approaches, slip-link models, that share some similarities to and offer some advantages over tube models. Although slip links were proposed at the same time as tubes, only recently have detailed, quantitative mathematical models arisen based on this picture. In this review, we focus on these models, with most discussion limited to mathematically well-defined objects that conform to state-of-the-art beyond-equilibrium thermodynamics. These models are connected to each other through successive coarse graining, using nonequilibrium thermodynamics along the way, and with a minimal parameter set. In particular, the most detailed level of description has four parameters, three of which can be determined directly from atomistic simulations. Once the remaining parameter is determined for any system, all parameters for all members of the hierarchy are determined. We show how, using this hierarchy of slip-link models combined with atomistic simulations, we can make predictions about the nonlinear rheology of monodisperse homopolymer melts, polydisperse melts, or blends of different architectures. Mathematical details are given elsewhere, so these are limited here, and physical ideas are emphasized. We conclude with an outlook on remaining challenges that might be tackled successfully using this approach, including complex flow fields and polymer blends.