Individual molecule dynamics have been shown to influence significantly the bulk rheological and microstructural properties of short-chain, unentangled, linear polyethylene liquids undergoing high strain-rate flows. The objective of this work was to extend this analysis to a linear polyethylene composed of macromolecules of a much greater length and entanglement density; i.e., a liquid consisting of C400H802 molecules, with approximately ten kinks per chain at equilibrium, as calculated by the Z1 code of Kröger [Comput. Phys. Commun. 168, 209–232 (2005)]. To achieve this, we performed nonequilibrium molecular dynamics (NEMD) simulations of a model system using the well-established potential model of Siepmann et al. [Nature 365, 330–332 (1993)] for a wide range of Weissenberg numbers (Wi) under steady shear flow. A recent study by Baig et al. [Macromolecules 43, 6886–6902 (2010)] examined this same system using NEMD simulations, but focused on the bulk rheological and microstructural properties as calculated from ensemble averages of the chains comprising the macromolecular liquids. In so doing, some key features of the system dynamics were not fully elucidated, which this article aims to highlight. Specifically, it was found that this polyethylene liquid displays multiple timescales associated with not only the decorrelation of the end-to-end vector (commonly related to the Rouse time or disengagement time, depending on the entanglement density of the liquid), but also ones associated with the retraction and rotation cycles of the individual molecules. Furthermore, when accounting for these individual chain dynamics, the “longest” relaxation time of the system was higher by a factor of 1.7, independent of shear rate, when calculated self-consistently due to the coupling of relaxation modes. Brownian dynamics (BD) simulations were also performed on an analogous free-draining bead-rod chain model to compare the rotation and retraction dynamics of a single chain in dilute solution with individual molecular motions in the melt. These BD simulations revealed that the dynamics of the free-draining chain are qualitatively and quantitatively similar to those of the individual chains comprising the polyethylene melt at strain rates in excess of Wi ≈ 50, implying a possible breakdown of reptation theory in the high shear limit. An examination of the bulk-average properties revealed the effects of the chain rotation and retraction cycles upon commonly modeled microstructural properties, such as the distribution function of the chain end-to-end vector and the entanglement number density.

The startup and steady shear flow properties of an entangled, monodisperse polyethylene liquid (C₁₀₀₀H₂₀₀₂) were investigated via virtual experimentation using nonequilibrium molecular dynamics. The simulations revealed a multifaceted dynamical response of the liquid to the imposed flow field in which entanglement loss leading to individual molecular rotation plays a dominant role in dictating the bulk rheological response at intermediate and high shear rates. Under steady shear conditions, four regimes of flow behavior were evident. In the linear viscoelastic regime ( $\dot{\gamma }<{\tau }_d^{-1}$ ), orientation of the reptation tube network dictates the rheological response. Within the second regime ( ${\tau }_d^{-1}<\dot{\gamma }<{\tau }_R^{-1}$ ), the tube segments begin to stretch mildly and the molecular entanglement network begins to relax as flow strength increases; however, the dominant relaxation mechanism in this region remains the orientation of the tube segments. In the third regime ( ${\tau }_R^{-1}<\dot{\gamma }<{\tau }_e^{-1}$ ), molecular disentangling accelerates and tube stretching dominates the response. Additionally, the rotation of molecules become a significant source of the overall dynamic response. In the fourth regime ( $\dot{\gamma }>{\tau }_e^{-1}$ ), the entanglement network deteriorates such that some molecules become almost completely unraveled, and molecular tumbling becomes the dominant relaxation mechanism. The comparison of transient shear viscosity, ${\eta }^{+}$ , with the dynamic responses of key variables of the tube model, including the tube segmental orientation, $S$ , and tube stretch, $\lambda$ , revealed that the stress overshoot and undershoot in steady shear flow of entangled liquids are essentially originated and dynamically controlled by the $S_{xy}$ component of the tube orientation tensor, rather than the tube stretch, over a wide range of flow strengths.

The rheological properties and dynamical responses of a monodisperse polyethylene (PE) liquid, C700H1402, were examined using equilibrium molecular dynamics and nonequilibrium molecular dynamics simulations of the atomistically detailed molecules. Equilibrium structural and dynamical properties of the PE liquid, such as the disengagement time (τd), Rouse time (τR), entanglement time, (τe), reptation tube diameter, number of entanglements, and the distribution of the chain end-to-end vector, each followed very closely the predictions of the Doi and Edwards theory. Under steady shear conditions, the rheological and dynamical responses exhibited starkly different behavior as functions of shear rate, which could be categorized within four distinct shear rate regions; namely, γ̇<τd−1, τd−1<γ̇<τR−1, τR−1<γ̇<τe−1, and γ̇>τe−1. In the first region, the topological properties of the liquid remained relatively unperturbed from quiescent conditions and the rheological characteristic functions remained constant throughout. Little in the way of chain orientation or stretching occurred, and reptation theory described very well the system properties. Within the second range, chain orientation became the dominant dynamical system response with only a slight degree of chain stretching being evident. Rheological characteristic functions displayed shear-thinning behavior, and a plateau in the shear stress profile was observed. In the third range, significant chain stretching became apparent which led to a dramatic reduction in the number of entanglements, thereby enabling a rotational motion of the individual chain molecules in response to the vorticity of the shear field. A new timescale became evident that was associated with the period of the rotation/retraction cycles of the individual molecules. In the fourth region, the rotational motion of the chains became the sole relaxation mode of the system as the number of entanglements was gradually reduced to a level too low to support the conventional reptation theory. Furthermore, the individual molecular motions shared the same characteristics as those of similar chains in dilute and semidilute solution. Comparisons of the corresponding structural and dynamical properties of the C700H1402 liquid with those of the mildly entangled PE liquid C400H802 revealed how the properties of the liquids scaled with chain length.

Manufacturing of plastics is typically performed via flow processing of a molten polymeric fluid. Until recently, conventional knowledge has maintained that the deformation of the constituent molecules under flow is homogeneous and obeys Gaussian statistics. In this study via virtual experimentation, an entangled polyethylene melt subjected to planar elongational flow displays an unanticipated microphase separation into a heterogeneous liquid composed of regions of either highly stretched or tightly coiled macromolecules, thus providing a natural realization of a biphasic coil-stretch transition.

Recent simulation results of a moderately entangled linear polyethylene ${\mathrm{C}}_{700}{\mathrm{H}}_{1402}$ 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 insight, theoreticians have begun to grapple with this additional complicating physical phenomenon that needs to be incorporated into rheological models to help explain the data under conditions of high shear. In this paper we examine these recent efforts by using nonequilibrium molecular dynamics simulations to provide insight into the requisite theoretical variables and their assigned evolution equations to evaluate the capability of these tube-based models to predict accurately the simulated data sets. This analysis reveals 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.