Individual Polymer Chain Dynamics in an Entangled Polymeric Liquid Using a Stochastic Tube Model (original) (raw)
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Physical Review Fluids, 2017
Recent simulation results of a moderately entangled linear polyethylene C 700 H 1402 liquid have confirmed prior simulation and experimental evidence that individual polymer molecules experience periodic rotation and retraction cycles under steady shear flow at high Weissenberg number. With this new insight, theoreticians have begun to grapple with this additional complicating physical phenomenon that needs to be incorporated into rheological models to help explain the new data under conditions of high shear. In this paper, we examine these recent efforts by using NEMD simulations to provide insight into the requisite theoretical variables, and their assigned evolution equations, to evaluate the capability of these new tube-based models to predict accurately the simulated data sets. This analysis has revealed that the primary variables used in tube models to impart a conceptual basis to the theory, namely, the tube orientation tensor and the tube stretch, remain fundamental system properties even far away from equilibrium; however, the theory describing their evolution under flow is not well-suited to quantitative prediction. Furthermore, it is demonstrated that key system properties, such as the entanglement number and disengagement time, should play a more significant role in model development since these quantities can change dramatically under flow, particularly at high Weissenberg number where the chain rotation and retraction cycles dominate the system physics.
Dynamics of linear, entangled polymeric liquids in shear flows
We study predictions in transient and steady shearing flows of a previously proposed self-consistent reptation model, which includes chain stretching, chain-length fluctuations, segment connectivity and constraint release. In an earlier paper it was established that the model is able to capture all trends observed experimentally for viscometric flows allowing focus of the present work on the model. That is, we study in detail the physics and underlying dynamics of the model to explain the macroscopically observed rheological properties in terms of chain behavior and dynamics on the molecular level. More specifically, we discuss the effects of chain tumbling, molecular chain stretching and constraint release and their influence on the macroscopic stress as well as the extinction angle under various flow conditions. In particular, we find that chain tumbling causes the undershoot in extinction angle during inception of shear; chain tumbling is itself suppressed by the presence of molecular stretching; and the anticipated strong correlation between normal stress and molecular stretching is confirmed; following cessation of steady shear, it is observed that chain stretching undershoots, and a mechanism involving constraint release is suggested to explain the phenomenon, and; from stresses following cessation, a previously proposed technique for estimating stretching during steady shear flows-involving a generalized damping function-is shown to be inaccurate. Also investigated is the monomer density along the chain contour which reveals information about the local chain stretching and orientation. Here, it is found that the distribution of monomers along the contour becomes non-uniform when the shear rate exceeds the inverse Rouse relaxation time. Finally, we discuss a possible violation of the stress-optic rule during start up of steady shear flow at high shear rates.
Dynamical structure of entangled polymers simulated under shear flow
The Journal of chemical physics, 2018
The non-linear response of entangled polymers to shear flow is complicated. Its current understanding is framed mainly as a rheological description in terms of the complex viscosity. However, the full picture requires an assessment of the dynamical structure of individual polymer chains which give rise to the macroscopic observables. Here we shed new light on this problem, using a computer simulation based on a blob model, extended to describe shear flow in polymer melts and semi-dilute solutions. We examine the diffusion and the intermediate scattering spectra during a steady shear flow. The relaxation dynamics are found to speed up along the flow direction, but slow down along the shear gradient direction. The third axis, vorticity, shows a slowdown at the short scale of a tube, but reaches a net speedup at the large scale of the chain radius of gyration.
Polymers, 2019
The aim of the present paper is to analyse the differences between tube-based models which are widely used for predicting the linear viscoelasticity of monodisperse linear polymers, in comparison to a large set of experimental data. The following models are examined: Milner–McLeish, Likhtman–McLeish, the Hierarchical model proposed by the group of Larson, the BoB model of Das and Read, and the TMA model proposed by the group of van Ruymbeke. This comparison allows us to highlight and discuss important questions related to the relaxation of entangled polymers, such as the importance of the contour-length fluctuations (CLF) process and how it affects the reptation mechanism, or the contribution of the constraint release (CR) process on the motion of the chains. In particular, it allows us to point out important approximations, inherent in some models, which result in an overestimation of the effect of CLF on the reptation time. On the contrary, by validating the TMA model against expe...
Nonlinear rheology of highly entangled polymer liquids: Step shear damping function
Journal of Rheology, 2001
Orientation angle and stress-relaxation dynamics of entangled polystyrene (PS)/diethyl phthalate solutions were investigated in steady and step shear flows. Concentrated (19 vol %) solutions of 0.995, 1.81, and 3.84 million molecular weight (MW) PS and a semidilute (6.4 vol %) solution of 20.6 million MW PS were used to study the effects of entanglement loss on dynamics. A phase-modulated flow birefringence apparatus was developed to facilitate measurements of time-dependent changes in optical equivalents of shear stress (n 12 Ϸ C) and first normal stress differences (n 1 ϭ n 11 Ϫ n 22 Ϸ CN 1 ) in a planar-Couette shear-flow geometry. Flow birefringence results were supplemented with cone-and-plate mechanical rheometry measurements to extend the range of shear rates over which entangled polymer dynamics are studied. In slow ( d0 Ϫ1 Ͼ ␥ ) steady shear-flow experiments using the ultrahigh MW polymer sample (20.6 ϫ 10 6 MW PS), steady-state n 12 and n 1 results manifest unusual powerlaw dependencies on shear rate [n 12,ss ϳ ␥ 0.4 and n 1,ss ϳ ␥ 0.8 ]. At shear rates in the range d0 Ϫ1 Ͻ ␥ Ͻ R Ϫ1 , steady-state orientation angles SS are found to be nearly independent of shear rate for all but the most weakly entangled materials investigated. For solutions containing the highest MW PS, an approximate plateau orientation angle p in the range 20 -24°is observed; p values ranging from 14 to 16°are found for the other materials. In the start-up of fast steady shear flow (␥ Ն R Ϫ1 ), transient undershoots in orientation angle are also reported. The molecular origins of these observations were examined with the help of a tube model theory that accommodates changes in polymer entanglement density during flow.
Nonlinear shear of entangled polymers from nonequilibrium molecular dynamics
Journal of Polymer Science Part B: Polymer Physics, 2019
This study aims to use molecular dynamics (MD) simulations of Kremer-Grest (KG) chains to inform future developments of models of entangled polymer dynamics. We perform nonequilibrium MD simulations, under shear flow, for wellentangled KG chains. We study chains of 512 and 1000 KG beads, corresponding to 8 and 15 entanglements, respectively. We compute the linear rheological properties from equilibrium simulations of the stress autocorrelation and obtain from these data the tube model parameters. Under nonlinear shear flow, we compute the shear viscosity, the first and second normal stress differences, and chain contour length. For chains of 512 monomers, we obtain agreement with the results of Cao and Likhtman (ACS Macro. Lett. 2015, 4, 1376). We also compare our nonlinear results with the Graham, Likhtman and Milner-McLeish (GLaMM) model. We identify some systematic disagreement that becomes larger for the longer chains. We made a comparison of the transient shear stress maximum from our simulations, two nonlinear models and experiments on a wide range of melts and solutions, including polystyrene (PS), polybutadiene, and styrene-butadiene rubber. This comparison establishes that the PS melt data show markedly different behavior to all other melts and solutions and KG simulations reproduce the PS data more closely than either the GLaMM or Xie and Schweizer models. We discuss the performance of these models against the data and simulations. Finally, by imposing a rapid reversing flow, we produce a method to extract the recoverable strain from MD simulations, valid for sufficiently entangled monodisperse polymers. We explore how the resulting data can probe the melt state just before the reversing flow.
Nonquiescent Relaxation in Entangled Polymer Liquids after Step Shear
Physical Review Letters, 2006
Large step shear experiments revealed through particle tracking velocimetry that entangled polymeric liquids display either internal macroscopic movements upon shear cessation or rupturelike behavior during shear. Visible inhomogeneous motions were detected in five samples with the number of entanglements per chain ranging from 20 to 130 at amplitudes of step strain as low as 135%.
Yieldlike constitutive transition in shear flow of entangled polymeric fluids
Physical review letters, 2003
We describe an unexpected constitutive transition in entangled polymer solutions. At and beyond a critical stress, the initial spatially homogeneous and well-entangled sample transforms from its entangled (coiled) state into a fully disentangled (stretched) state over a period during which the resulting shear rate increases in a spatially inhomogeneous fashion. In the mode of controlled shear rate, the sample exhibits a stress plateau over three decades. Flow birefringence and normal stress observations unravel additional features of these flow phenomena.
The Journal of Chemical Physics, 2010
The topological state of entangled polymers has been analyzed recently in terms of primitive paths which allowed obtaining reliable predictions of the static ͑statistical͒ properties of the underlying entanglement network for a number of polymer melts. Through a systematic methodology that first maps atomistic molecular dynamics ͑MD͒ trajectories onto time trajectories of primitive chains and then documents primitive chain motion in terms of a curvilinear diffusion in a tubelike region around the coarse-grained chain contour, we are extending these static approaches here even further by computing the most fundamental function of the reptation theory, namely, the probability ͑s , t͒ that a segment s of the primitive chain remains inside the initial tube after time t, accounting directly for contour length fluctuations and constraint release. The effective diameter of the tube is independently evaluated by observing tube constraints either on atomistic displacements or on the displacement of primitive chain segments orthogonal to the initial primitive path. Having computed the tube diameter, the tube itself around each primitive path is constructed by visiting each entanglement strand along the primitive path one after the other and approximating it by the space of a small cylinder having the same axis as the entanglement strand itself and a diameter equal to the estimated effective tube diameter. Reptation of the primitive chain longitudinally inside the effective constraining tube as well as local transverse fluctuations of the chain driven mainly from constraint release and regeneration mechanisms are evident in the simulation results; the latter causes parts of the chains to venture outside their average tube surface for certain periods of time.