Contour length fluctuations and constraint release in entangled polymers: slip-spring simulations and their implications for binary blend rheology

We study the interaction between constraint release and contour length fluctuations in well entangled polymers, by means of a set of slip-spring simulations in which the rate of constraint release is precisely controlled. In the present simulations, a fraction f = 0.9 of the slip-springs undergo constraint release, while the remaining slip-springs do not, as an idealized model to mimic the constraint release environment of a bidisperse polymer melt. Both populations of slip-springs allow reptation of the chain. Our analysis of the data indicates the time and parameter regions in which contour length fluctuations occur effectively along a thin tube, or along a diluted fat tube. We predict the parameters for which case each is observed and the rate of relaxation due to contour length fluctuations in each region. Finally, we draw the implications of the simulations for bidisperse blend rheology, by revisiting the classic “Viovy diagram” for such melts. We relocate some of the lines on the original diagram, and identify new regimes, based on the physics and quantitative information supplied by the simulation data. In particular, we identify a new region in the diagram in which along-tube motion of the long chains is predominantly along the contour of the thin tube, yet contour length fluctuations occur in the fat tube, resulting in an acceleration of the terminal relaxation. We successfully and quantitatively locate a wide range of literature data on our redrawn diagram

Efficient Determination of Slip-Link Parameters from Broadly Polydisperse Linear Melts

We investigate the ability of a coarse-grained slip-link model and a simple double reptation model to describe the linear rheology of polydisperse linear polymer melts. Our slip-link model is a well-defined mathematical object that can describe the equilibrium dynamics and non-linear rheology of flexible polymer melts with arbitrary polydispersity and architecture with a minimum of inputs: the molecular weight of a Kuhn step, the entanglement activity, and Kuhn step friction. However, this detailed model is computationally expensive, so we also examine predictions of the cheaper double reptation model, which is restricted to only linear rheology near the terminal zone. We report the storage and loss moduli for polydisperse polymer melts and compare with experimental measurements from small amplitude oscillatory shear. We examine three chemistries: polybutadiene, polypropylene and polyethylene. We also use a simple double reptation model to estimate parameters for the slip-link model and examine under which circumstances this simplified model works. The computational implementation of the slip-link model is accelerated with the help of graphics processing units, which allow us to simulate in parallel large ensembles made of up to 50,000 chains. We show that our simulation can predict the dynamic moduli for highly entangled polymer melts over nine decades of frequency. Although the double reptation model performs well only near the terminal zone, it does provide a convenient and inexpensive way to estimate the entanglement parameter for the slip-link model from polydisperse data

Tuning High and Low Temperature Foaming Behavior of Linear and Long-Chain Branched Polypropylene via Partial and Complete Melting

While existing foam studies have identified processing parameters, such as high-pressure drop rate, and engineering measures, such as high melt strength, as key factors for improving foamability, there is a conspicuous absence of studies that directly relate foamability to material properties obtained from fundamental characterization. To bridge this gap, this work presents batch foaming studies on one linear and two long-chain branched polypropylene (PP) resins to investigate how foamability is affected by partial melting (Method 1) and complete melting followed by undercooling (Method 2). At temperatures above the melting point, similar expansion was obtained using both foaming procedures within each resin, while the PP with the highest strain hardening ratio (13) exhibited the highest expansion ratio (45 ± 3). At low temperatures, the foamability of all resins was dramatically improved using Method 2 compared to Method 1, due to access to lower foaming temperatures (<150 °C) near the crystallization onset. Furthermore, Method 2 resulted in a more uniform cellular structure over a wider temperature range (120–170 °C compared to 155–175 °C). Overall, strong extensional hardening and low onset of crystallization were shown to give rise to foamability at high and low temperatures, respectively, suggesting that both characteristics can be appropriately used to tune the foamability of PP in industrial foaming applications

Understanding effect of constraint release environment on end-to-end vector relaxation of linear polymer chains

We propose and verify methods based on the slip-spring (SSp) model [ Macromolecules 2005, 38, 14] for predicting the effect of any monodisperse, binary, or ternary environment of topological constraints on the relaxation of the end-to-end vector of a linear probe chain. For this purpose we first validate the ability of the model to consistently predict both the viscoelastic and dielectric response of monodisperse and binary mixtures of type A polymers, based on published experimental data. We also report the synthesis of new binary and ternary polybutadiene systems, the measurement of their linear viscoelastic response, and the prediction of these data by the SSp model. We next clarify the relaxation mechanisms of probe chains in these constraint release (CR) environments by analyzing a set of “toy” SSp models with simplified constraint release rates, by examining fluctuations of the end-to-end vector. In our analysis, the longest relaxation time of the probe chain is determined by a competition between the longest relaxation times of the effective CR motions of the fat and thin tubes and the motion of the chain itself in the thin tube. This picture is tested by the analysis of four model systems designed to separate and estimate every single contribution involved in the relaxation of the probe’s end-to-end vector in polydisperse systems. We follow the CR picture of Viovy et al. [ Macromolecules 1991, 24, 3587] and refine the effective chain friction in the thin and fat tubes based on Read et al. [ J. Rheol. 2012, 56, 823]. The derived analytical equations form a basis for generalizing the proposed methodology to polydisperse mixtures of linear and branched polymers. The consistency between the SSp model and tube model predictions is a strong indicator of the compatibility between these two distinct mesoscopic frameworks