Theory on Capillary Filling of Polymer Melts in Nanopores.

A unified theory for the imbibition dynamics of entangled polymer melting into nanopores is presented. Experiments demonstrate the validity of t1/2 dependence but contradict the predictions of the classical Lucas-Washburn equation because of the prefactor. A reversal in dynamics of capillary filling is reported with increasing polymer molecular weight. Polymer imbibition under nanometer confinement can be discussed by two mechanisms: one is the standard hydrodynamic flow, resulting in a parabolic flow profile. When the inner wall has a strong attraction to the polymer, a layer of immobile chains is created, resulting in an increase of the effective viscosity and to slower imbibition. The other is the reptation model proposed by Johner et al., leading to a plug flow profile and to the reduction in the effective viscosity (faster imbibition). The reversal in dynamics of polymer imbibition can be explained by the competition between these two mechanisms.

A practical tutorial to set up NMR diffusometry equipment: application to liquid crystals.

NMR diffusometry is nowadays a well-established and powerful technique to investigate molecular translation in fluid materials. Standard NMR diffusometry approaches are based on pulsed field gradients generated by specific hardware and specially designed NMR probes. Here, we present an alternative set-up that exploits the static gradient present in the fringe field of any commercial superconducting magnet. This stray field diffusometry technique can be particularly useful to study diffusional processes in fast-relaxing and slow-diffusing systems, such as thermotropic liquid crystals, ionic liquids and polymer melts.

Predicting High-Density Polyethylene Melt Rheology Using a Multimode Tube Model Derived Using Non-Equilibrium Thermodynamics.

Based on the Generalized bracket, or Beris-Edwards, formalism of non-equilibrium thermodynamics, we recently proposed a new differential constitutive model for the rheological study of entangled polymer melts and solutions. It amended the shortcomings of a previous model that was too strict regarding the values of the convective constraint release parameter for the model not to violate the second law of thermodynamics, and it has been shown capable of predicting a transient stress undershoot (following the overshoot) at high shear rates. In this study, we wish to further examine this model's capability to predict the rheological response of industrial polymer systems by extending it to its multiple-mode version. The comparison with industrial rheological data (High-Density Polyethylene resins), which was based on comparison with experimental data available in (a) Small Amplitude Oscillatory shear, (b) start-up shear, and (c) start-up uniaxial elongation, was noted to be good.

Temperature Dependence of Conformational Relaxation of Poly(ethylene oxide) Melts.

The time-temperature superposition (TTS) principle, employed extensively for the analysis of polymer dynamics, is based on the assumption that the different normal modes of polymer chains would experience identical temperature dependence. We aim to test the critical assumption for TTS principle by investigating poly(ethylene oxide) (PEO) melts, which have been considered excellent solid polyelectrolytes. In this work, we perform all-atom molecular dynamics simulations up to 300 ns at a range of temperatures for PEO melts. We find from our simulations that the conformations of strands of PEO chains in melts show ideal chain statistics when the strand consists of at least 10 monomers. At the temperature range of T= 400 to 300 K, the mean-square displacements (⟨Δr2(t)⟩) of the centers of mass of chains enter the Fickian regime, i.e., ⟨Δr2(t)⟩∼t1. On the other hand, ⟨Δr2(t)⟩ of the monomers of the chains scales as ⟨Δr2(t)⟩∼t1/2 at intermediate time scales as expected for the Rouse model. We investigate various relaxation modes of the polymer chains and their relaxation times (τn), by calculating for each strand of n monomers. Interestingly, different normal modes of the PEO chains experience identical temperature dependence, thus indicating that the TTS principle would hold for the given temperature range.

An Experimental Investigation of Viscoelastic Flow in a Contraction Channel.

In order to assess the predictive capability of the S-MDCPP model, which may describe the viscoelastic behavior of the low-density polyethylene melts, a planar contraction flow benchmark problem is calculated in this investigation. A pressure-stabilized iterative fractional step algorithm based on the finite increment calculus (FIC) method is adopted to overcome oscillations of the pressure field due to the incompressibility of fluids. The discrete elastic viscous stress splitting (DEVSS) technique in combination with the streamline upwind Petrov-Galerkin (SUPG) method are employed to calculate the viscoelastic flow. The equal low-order finite elements interpolation approximations for velocity-pressure-stress variables can be applied to calculate the viscoelastic contraction flows for LDPE melts. The predicted velocities agree well with the experimental results of particle imagine velocity (PIV) method, and the pattern of principal stress difference calculated by the S-MDCPP model has good agreement with the results measured by the flow induced birefringence (FIB) device. Numerical and experimental results show that the S-MDCPP model is capable of accurately capturing the rheological behaviors of branched polymers in complex flow.

Comparing equilibration schemes of high-molecular-weight polymer melts with topological indicators.

Recent theoretical studies have demonstrated that the behaviour of molecular knots is a sensitive indicator of polymer structure. Here, we use knots to verify the ability of two state-of-the-art algorithms-configuration assembly and hierarchical backmapping-to equilibrate high-molecular-weight (MW) polymer melts. Specifically, we consider melts with MWs equivalent to several tens of entanglement lengths and various chain flexibilities, generated with both strategies. We compare their unknotting probability, unknotting length, knot spectra, and knot length distributions. The excellent agreement between the two independent methods with respect to knotting properties provides an additional strong validation of their ability to equilibrate dense high-MW polymeric liquids. By demonstrating this consistency of knotting behaviour, our study opens the way for studying topological properties of polymer melts beyond time and length scales accessible to brute-force molecular dynamics simulations.

Rheological Measurements and Structural Analysis of Polymeric Materials.

Rheological measurements of polymer melts are widely used for quality control and the optimization of processing. Another interesting field of rheology is to provide information about molecular parameters of polymers and the structure build-up in heterogeneous polymeric systems. This paper gives an overview of the influence of molar mass, molar mass distribution and long-chain branching on various rheological characteristics and describes the analytical power following from established relations. With respect to applications, we discuss how rheological measurements can be used to gain insight into the thermal stability of a material. A special impact lies in the demonstration, how long-chain branching can be analyzed using rheological means like the zero-shear viscosity as a function of molar mass and strain hardening occurring in elongation. For contributions to branching analysis, the thermorheological behavior and activation energies are particularly discussed. The use of elastic quantities in the case of mechanical pretreatment effects is briefly addressed. The influence of fillers on recoverable properties in the linear range of deformation is analyzed and the role of their specific surface area for interactions described. It is shown how the fundamental results can be applied to study the state of nanoparticle dispersions obtained under special conditions. Furthermore, it is demonstrated that the findings on polymer/filler systems are the base of structure analyses in heterogeneous polymeric materials like polyvinylchloride (PVC) and acrylonitrile-butadiene-styrene copolymers (ABS).

Electric Field Enhances Shear Resistance of Polymer Melts via Orientational Polarization in Microstructures.

In this paper, we studied the alteration of viscoelastic properties of a neat poly(methyl methacrylate) (PMMA), induced by an applied external electric field. The rheological properties of PMMA are measured using a rotational rheometer at elevated temperatures. The electric field effect on the shear resistance of the polymer was studied by examining rheological responses under difference experimental scenarios. We find that the external electric field can remarkably enhance shear resistance and prevent flow of PMMA melt, enabling it to behave more predictably at high temperatures. Dynamic rheological analysis illustrates that the external electric field speeds up the recovery of mechanical properties of the PMMA melt after large deformations, whereas the PMMA melt exhibits thixotropic behaviors. The recovery velocity is influenced by the strength of the electric field, specifically, and is found to be proportional to the electric field strength. Our experimental characterization may provide new evidence on the tuning mechanical properties of polymer melts via controlling segmental polarization.

Collective Motions and Mechanical Response of a Bulk of Single-Chain Nano-Particles Synthesized by Click-Chemistry.

We investigate the effect of intra-molecular cross-links on the properties of polymer bulks. To do this, we apply a combination of thermal, rheological, diffraction, and neutron spin echo experiments covering the inter-molecular as well as the intermediate length scales to melts of single-chain nano-particles (SCNPs) obtained through 'click' chemistry. The comparison with the results obtained in a bulk of the corresponding linear precursor chains (prior to intra-molecular reaction) and in a bulk of SCNPs obtained through azide photodecomposition process shows that internal cross-links do not influence the average inter-molecular distances in the melt, but have a profound impact at intermediate length scales. This manifests in the structure, through the emergence of heterogeneities at nanometric scale, and also in the dynamics, leading to a more complex relaxation behavior including processes that allow relaxation of the internal domains. The influence of the nature of the internal bonds is reflected in the structural relaxation that is slowed down if bulky cross-linking agents are used. We also found that any residual amount of cross-links is critical for the rheological behavior, which can vary from an almost entanglement-free polymer bulk to a gel. The presence of such inter-molecular cross-links additionally hinders the decay of density fluctuations at intermediate length scales.

Simple, Accurate and User-Friendly Differential Constitutive Model for the Rheology of Entangled Polymer Melts and Solutions from Nonequilibrium Thermodynamics.

In a recent reformulation of the Marrucci-Ianniruberto constitutive equation for the rheology of entangled polymer melts in the context of nonequilibrium thermodynamics, rather large values of the convective constraint release parameter ßccr had to be used in order for the model not to violate the second law of thermodynamics. In this work, we present an appropriate modification of the model, which avoids the splitting of the evolution equation for the conformation tensor into an orientation and a stretching part. Then, thermodynamic admissibility simply dictates that ßccr ≥ 0, thus allowing for more realistic values of ßccr to be chosen. Moreover, and in view of recent experimental evidence for a transient stress undershoot (following the overshoot) at high shear rates, whose origin may be traced back to molecular tumbling, we have incorporated additional terms into the model accounting, at least in an approximate way, for non-affine deformation through a slip parameter ξ. Use of the new model to describe available experimental data for the transient and steady-state shear and elongational rheology of entangled polystyrene melts and concentrated solutions shows close agreement. Overall, the modified model proposed here combines simplicity with accuracy, which renders it an excellent choice for managing complex viscoelastic fluid flows in large-scale numerical calculations.

Recoverable Extensional Flow of Polymer Melts and Its Relevance for Processing.

While the uniaxial elongational viscosity is widely investigated, and its relevance for processing is described in the literature, much less has been published on the recoverable extensional flow of polymer melts. This paper presents a short overview of the dependencies of the recoverable elongation on the molecular structure of a polymer, and on some experimental parameters. Its main focus lies on the discussion of processing operations and applications that are largely affected by the elastic components of elongational flow. The recoverable portions of stretched films are considered, and the exploitation of the shrinkage of films, due to the recovery of frozen recoverable deformations, and its role for applications are addressed. The analysis of measurements of velocity fields in the entry region of a slit die and results on the determination of the recoverable elongation from uniaxial experiments, according to the literature, lead to the conclusion of dominant elastic extensions. Considering these facts, the assumptions for Cogswell's widely used method of determining elongational viscosities under processing conditions from entrance flow are not realistic. As examples of a direct application of extrudate swell from short dies for processing, pelletizing and fused deposition modelling within additive manufacturing are addressed. The special features of extrudate swell from short dies, and uniaxial recoverable elongation for a polymer filled with rigid particles in comparison to an immiscible polymer blend, are presented and discussed.

Comparative Analysis of Different Tube Models for Linear Rheology of Monodisperse Linear Entangled Polymers.

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 experimental data, we show that this effect is underestimated in TMA. Therefore, in order to obtain accurate predictions, a novel modification to the TMA model is proposed. Our current work is a continuation of earlier research (Shchetnikava et al., 2014), where a similar analysis is performed on well-defined star polymers.

Individual Molecular Dynamics of an Entangled Polyethylene Melt Undergoing Steady Shear Flow: Steady-State and Transient Dynamics.

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 ( γ ˙ < τ d - 1 ), orientation of the reptation tube network dictates the rheological response. Within the second regime ( τ d - 1 < γ ˙ < τ 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 ( τ R - 1 < γ ˙ < τ 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 ( γ ˙ > τ 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, η + , with the dynamic responses of key variables of the tube model, including the tube segmental orientation, S , and tube stretch, λ , revealed that the stress overshoot and undershoot in steady shear flow of entangled liquids are essentially originated and dynamically controlled by the S x y component of the tube orientation tensor, rather than the tube stretch, over a wide range of flow strengths.

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.

In-plane and out-of-plane rotational motion of individual chain molecules in steady shear flow of polymer melts and solutions.

Recent nonequilibrium molecular dynamics (NEMD) simulations of mildly entangled C400H802 and moderately entangled C700H1402 linear polyethylene melts undergoing steady shear flow have revealed that several inconsistencies between theory and experiment could be rectified by consideration of the rotational motion of individual polymer chains that occurs at moderate to high flow strengths. In this study, we investigated the configurational dynamics of the individual molecular chains that allow these once-entangled, long-chain molecules to execute retraction/extension semi-periodic cycles in response to the imposed shear via NEMD simulations. Brownian dynamics simulations were also performed to extract dynamical and configurational information about the similar cycles of polymer chain behavior that occur in dilute solutions of macromolecular chain liquids dissolved in low molecular weight solvents. Results revealed that the configurational motions of the individual chains in both melt and solution were essentially the same and governed by a single timescale that scaled exponentially with the magnitude of the shear rate. This configurational motion contained both in-plane and out-of-plane components with respect to the flow-gradient plane, with the out-of-plane component playing a much larger role during the retraction phase of the cycle than during the extension phase. This was determined to be caused by the enhancement of the retraction motion by the out-of-plane entropic Brownian forces; however, these entropic forces were detrimental to the in-plane hydrodynamic diffusive forces during the extension phase of the cycle and were thus suppressed. Consequently, the configuration of a rotating chain was significantly more compact during the retraction stage than during the extension stage, wherein the latter phase most molecules were more preferentially distributed in the flow-gradient plane.

Molecular Dynamics Simulations for Resolving Scaling Laws of Polyethylene Melts.

Long-timescale molecular dynamics simulations were performed to estimate the actual physical nature of a united-atom model of polyethylene (PE). Several scaling laws for representative polymer properties are compared to theoretical predictions. Internal structure results indicate a clear departure from theoretical predictions that assume ideal chain statics. Chain motion deviates from predictions that assume ideal motion of short chains. With regard to linear viscoelasticity, the presence or absence of entanglements strongly affects the duration of the theoretical behavior. Overall, the results indicate that Gaussian statics and dynamics are not necessarily established for real atomistic models of PE. Moreover, the actual physical nature should be carefully considered when using atomistic models for applications that expect typical polymer behaviors.

Monte Carlo studies of two-dimensional polymer-solvent systems.

The static properties of two-dimensional athermal polymer solutions were studied by performing Monte Carlo lattice simulations using the cooperative motion algorithm (CMA) and taking into account the presence of explicit solvent molecules. The simulations were performed for a wide range of polymer chain lengths N (16-1024) and concentrations φ (0.0156-1). The results obtained for short chains (N < 256) were in good agreement with those given by previous simulations. For the longest chains (512 or 1024 beads), some unexpected behavior was observed in the dilute and semidilute regimes. A pronounced change in the concentration dependence of chain size and shape was observed below a certain critical concentration (0.6 for the longest chains under consideration, consisting of 1024 beads). Longer chains became more extended below this concentration. The behavior of the single-chain structure factor confirmed these changes in the fractal dimension of the chain as a function of the concentration. The observed phenomena are related to the excluded volume of solvent molecules, which causes the chain statistics to be modified in the vicinity of other chains; this effect is important in strictly 2D systems. Graphical abstract Extended long chains at moderate density with solvent molecules inside coils.

Molecular structure of bottlebrush polymers in melts.

Bottlebrushes are fascinating macromolecules that display an intriguing combination of molecular and particulate features having vital implications in both living and synthetic systems, such as cartilage and ultrasoft elastomers. However, the progress in practical applications is impeded by the lack of knowledge about the hierarchic organization of both individual bottlebrushes and their assemblies. We delineate fundamental correlations between molecular architecture, mesoscopic conformation, and macroscopic properties of polymer melts. Numerical simulations corroborate theoretical predictions for the effect of grafting density and side-chain length on the dimensions and rigidity of bottlebrushes, which effectively behave as a melt of flexible filaments. These findings provide quantitative guidelines for the design of novel materials that allow architectural tuning of their properties in a broad range without changing chemical composition.

Evaluation of Thermally Induced Degradation of Branched Polypropylene by Using Rheology and Different Constitutive Equations.

In this work, virgin as well as thermally degraded branched polypropylenes were investigated by using rotational and Sentmanat extensional rheometers, gel permeation chromatography and different constitutive equations. Based on the obtained experimental data and theoretical analysis, it has been found that even if both chain scission and branching takes place during thermal degradation of the tested polypropylene, the melt strength (quantified via the level of extensional strain hardening) can increase at short degradation times. It was found that constitutive equations such as Generalized Newtonian law, modified White-Metzner model, Yao and Extended Yao models have the capability to describe and interpret the measured steady-state rheological data of the virgin as well as thermally degraded branched polypropylenes. Specific attention has been paid to understanding molecular changes during thermal degradation of branched polypropylene by using physical parameters of utilized constitutive equations.

Electrophoresis of a charge-inverted macroion complex: Molecular-dynamics study.

We have performed molecular-dynamics simulations to study the effect of an external electric field on a macroion in the solution of multivalent Z : 1 salt. To obtain plausible hydrodynamics of the medium, we explicitly make the simulation of many neutral particles along with ions. In a weak electric field, the macroion drifts together with the strongly adsorbed multivalent counterions along the electric field, in the direction proving inversion of the charge sign. The reversed mobility of the macroion is insensitive to the external field, and increases with salt ionic strength. The reversed mobility takes a maximal value at intermediate counterion valence. The motion of the macroion complex does not induce any flow of the neutral solvent away from the macroion, which reveals screening of hydrodynamic interactions at short distances in electrolyte solutions. A very large electric field, comparable to the macroion unscreened field, disrupts charge inversion by stripping the adsorbed counterions off the macroion.