Rheology Of Polymer Melts Research Articles

In situ experimental investigation of fiber orientation kinetics and rheology of polymer composites in shear flow

In this study, we experimentally investigate the fiber orientation kinetics and rheology of fiber-filled polymer melts in shear flow. A novel setup is designed with custom-built bottom and top geometries that are mounted on a conventional rotational rheometer. Shear flow between parallel sliding plates is applied by vertical movement of the top geometry. The axial force measurement data of the rotational rheometer are used to determine the shear stress growth coefficient. The fiber orientation kinetics are measured in situ with this setup using small angle light scattering. We consider a non-Brownian experimental system with short glass fibers for the suspended phase (L/D=8–15) and different polyethylene based materials for the matrix phase. The fiber orientation kinetics are investigated as a function of fiber volume fraction (ϕ=1%, 5%, and 10%) and as a function of the shear rate (γ˙=0.03, 0.55, and 5s−1). Within the studied range, these parameters do not influence the fiber orientation kinetics, and a multiparticle model, based on Jeffery’s equation for single particles, can describe these kinetics. Our results show that, up to the concentrated regime (ϕ≈D/L), fiber-fiber interactions do not influence the fiber orientation in shear flow. Finally, we investigate the shear stress growth coefficient of these composites and demonstrate that a simple rheological model for fiber composites, which assumes a constant, isotropic orientation distribution of the fibers, is able to describe the shear stress growth coefficient of the short fiber composite samples.

Raising Two More Fundamental Questions Regarding the Classical Views on the Rheology of Polymer Melts.

The current paradigm of polymer flow assumes that (i) the effect of the molecular weight of the macromolecules, M, and of the temperature, T, on the expression of the viscosity of polymer melts separate; (ii) the molecular weight for entanglement, Mc, is independent of T; and (iii) the determination of Mc by the break in the log viscosity curve against log M unequivocally differentiates un-entangled melts from entangled melts. We use reliable rheological data on monodispersed polystyrene samples from very low molecular weight (M/Mc = 0.015) to relatively high molecular weight (M/Mc = 34) to test the separation of M and T in the expression of the viscosity; we reveal that an overall illusion of the validity of the separation of T and M is mathematically comprehensible, especially at high temperature and for M > 2Mc, but that, strictly speaking, the separation of M and T is not valid, except for certain periodic values of M equal to Mc, 2Mc, 4Mc, 8Mc, 16Mc, etc. (period doubling) organized around a "pole reference" value MR = 4Mc. We also reveal, for M < Mc, the existence of a lower molecular weight limit, M'c = Mc/8 for the onset of the macromolecular behavior (macro-coil). The discrete and periodic values of M that validate the separation of the effect of M and T on the viscosity generate the fragmentation of the molecular range into three rheological ranges. Likewise, we show that the effect of temperature is also fragmented into three rheological ranges for T > Tg: Tg < T< (Tg + 23°), (Tg + 23°) < T < TLL and T > TLL' where TLL is the liquid-liquid temperature. Our conclusion is that the classical formulation of the viscosity of polymer melts is so overly simplified that it is missing important experimental facts, such as period doubling for the separation of T and M, TLL, M'c, and Mc, resulting in its inability to understand the true nature of entanglements. We present in the discussion of the paper the alternative approach to the viscoelastic behavior, "the duality and cross-duality" of the Dual-conformers, showing how this model formalism was used to test mathematically and invalidate the separation of T and M in the classical formulation of viscosity.

Screw Extrusion Additive Manufacturing of Carbon Fiber Reinforced PA6 Tools

The creation of tools by additive manufacturing is becoming increasingly convenient for CFRP one-off and small batch production. Screw extrusion additive manufacturing of thermoplastic polymers has boosted the development of large format manufacturing solutions. Interlayer adhesion and anisotropic properties of a 3D printed part are indisputably key aspects of tool manufacturing process. In this study, thermal and mechanical properties of large format 40% carbon fiber reinforced polyamide 6 3D printed tools were determined. Moreover, the influence on part performance of two main printing parameters, deposition temperature and extruding pressure, was analyzed with respect to polymer melt rheology. The printed material revealed a highly anisotropic thermal and mechanical behavior associated with the alignment of the high carbon fiber content. The optimal process window was identified in terms of substrate deposition temperature. Along the print direction, no major impact on tensile and flexural mechanical properties was detected, while the injection molding values were exceeded by approximately 10%. The layer adhesion was estimated by measuring the stress at break on transversely Z-oriented specimens. Higher deposition temperatures and pressures, combined with lower viscosity, promote wetting and bond formation between layers, ultimately leading to more consistent performances. The best results in the transverse direction were achieved between 140 and 160 °C, reaching roughly a fifth of the longitudinal values. A significant drop in performance was detected below 120 °C, which was identified as the minimum process temperature. A post-process annealing heat treatment was also investigated, no beneficial outcomes were reported.

Rouse Analysis of Nonlinear Rheology of Unentangled Polymer Melts under Fast Shear: Viscoelastic Response to Superposed Oscillatory Strain

Rouse Analysis of Nonlinear Rheology of Unentangled Polymer Melts under Fast Shear: Viscoelastic Response to Superposed Oscillatory Strain

Material Extrusion of Structural Polymer–Aluminum Joints—Examining Shear Strength, Wetting, Polymer Melt Rheology and Aging

Generating polymer–metal structures by means of additive manufacturing offers huge potential for customized, sustainable and lightweight solutions. However, challenges exist, primarily with regard to reliability and reproducibility of the additively generated joints. In this study, the polymers ABS, PETG and PLA, which are common in material extrusion, were joined to grit-blasted aluminum substrates. Temperature dependence of polymer melt rheology, wetting and tensile single-lap-shear strength were examined in order to obtain appropriate thermal processing conditions. Joints with high adhesive strength in the fresh state were aged for up to 100 days in two different moderate environments. For the given conditions, PETG was most suitable for generating structural joints. Contrary to PETG, ABS–aluminum joints in the fresh state as well as PLA–aluminum joints in the aged state did not meet the demands of a structural joint. For the considered polymers and processing conditions, this study implies that the suitability of a polymer and a thermal processing condition to form a polymer–aluminum joint by material extrusion can be evaluated based on the polymer’s rheological properties. Moreover, wetting experiments improved estimation of the resulting tensile single-lap-shear strength.

A new perspective on monomeric friction reduction in fast elongational flows of polystyrene melts and solutions

Primitive chain network (PCN) and non-equilibrium molecular dynamics (NEMD) simulations indicate that the nonuniversality seen in the elongational rheology of linear polymer melts and concentrated solutions is caused by monomeric friction reduction. We present, in the context of tube models with varying tube diameter, a new constitutive equation based on enhanced relaxation of stretch (ERS) and find good agreement with experimental evidence and with predictions of the extended interchain pressure (EIP) model. The stretch evolution equations of the ERS and the EIP model can be converted in a form, which allows expressing them in terms of monomeric friction reduction. Monomeric friction coefficients obtained from the ERS model and those used in PCN and NEMD simulations show at least qualitative agreement. While the reduction of monomeric friction is incorporated in PCN and NEMD simulations by empirical correlations between friction coefficient and segmental orientation or elongational stress fitted to elongational viscosity data, the EIP and ERS models provide analytical and parameter-free relations of monomeric friction reduction as a function of chain stretch.

A constitutive equation for Rouse model modified for variations of spring stiffness, bead friction, and Brownian force intensity under flow

We derived a constitutive equation for the Rouse model (the most frequently utilized bead-spring model) with its spring constant κ, bead friction coefficient ζ, and the (squared) Brownian force intensity B being allowed to change under flow. Specifically, we modified the Langevin equation of the original Rouse model by introducing time (t)-dependent κ, ζ, and B (of arbitrary t dependence), which corresponded to the decoupling and preaveraging approximations often made in bead-spring models. From this modified Langevin equation, we calculated time evolution of second-moment averages of the Rouse eigenmode amplitudes and further converted this evolution into a constitutive equation. It turned out that the equation has a functional form, σ(t)=∫−∞tdt′{κ(t)/κ(t′)}M(t,t′)C−1(t,t′), where σ(t) and C−1(t,t′) are the stress and Finger strain tensors, and M(t,t′) is the memory function depending on κ(t′), ζ(t′), and B(t′) defined under flow. This equation, serving as a basis for analysis of nonlinear rheological behavior of unentangled melts, reproduces previous theoretical results under specific conditions, the Lodge–Wu constitutive equation for the case of t-independent κ, ζ, and B [A. S. Lodge and Y. Wu, “Constitutive equations for polymer solutions derived from the bead/spring model of Rouse and Zimm,” Rheol. Acta 10, 539 (1971)], the finite extensible nonlinear elastic (FENE)-Peterlin mean-Rouse formulation for the case of t-dependent changes of the only κ reported by Wedgewood and co-workers [L. E. Wedgewood et al., “A finitely extensible bead-spring chain model for dilute polymer solutions,” J. Non-Newtonian Fluid Mech. 40, 119 (1991)], and analytical expression of steady state properties for arbitrary κ(t), ζ(t), and B(t) reported by ourselves [H. Watanabe et al., “Revisiting nonlinear flow behavior of Rouse chain: Roles of FENE, friction reduction, and Brownian force intensity variation,” Macromolecules 54, 3700 (2021)]. It is to be added that a constitutive equation reported by Narimissa and Wagner [E. Narimissa and M. H. Wagner, “Modeling nonlinear rheology of unentangled polymer melts based on a single integral constitutive equation,” J. Rheol. 64, 129 (2020)] has a significantly different functional form and cannot be derived from the Rouse model with any simple modification of the Rouse–Langevin equation.

On finding the zero‐shear‐rate viscosity of polymer melts

AbstractA significant fraction of the experimental works on the rheology of polymer melts include an attempt to find the zero‐shear‐rate viscosity η0. This is done for good reasons, because η0 is a limiting property that depends only on thermodynamic variables and, importantly, the molecular and supermolecular structure of the melt. As with all limiting properties, η0 is impossible to measure directly. Fortunately with many melts, it can be estimated from viscosity measurements at very low shear rates or frequencies, but still remains one of those properties that becomes in the limit very prone to error. The common approach is to use a set of frequency‐ or shear‐rate‐dependent data and extrapolate to find η0. As with any extrapolation, the major question is the function used for the extrapolation. This question is addressed in some detail in this article. The question of which function to use was discarded in favor of using a large sample of 20 equations of many functional forms. This sample of randomly chosen equations was used to generate a set of η0 values, and the statistics of this distribution were examined, in the usual fashion, by description with an analytical probability density function that gives a high probability of being a likely generator of the data. In addition, a weighted average was proposed, where the weighting factor takes into account the quality of the fit. For testing these ideas, the room temperature melts of poly(vinyl isobutyl ether), poly(isobutylene), and poly(dimethyl siloxane) were used. The η0 of the latter was reachable; for the other resins, a falling ball technique was attempted.

Pre-plasticization of thermal binder facilitates processing and granule growth during melt granulation of gabapentin using co-rotating twin screw extruder

Plasticization, a common method of reducing the polymer melt viscosity in plastics extrusion, was investigated to improve the processability of a pharmaceutical formulation during twin-screw melt granulation. The thermolabile drug gabapentin was used as a model compound given previous work showed the benefit of preparing 80% drug loading gabapentin granules with hydroxypropyl cellulose as thermal binder. The plasticizer triethyl citrate was selected based on physicochemical compatibility with both the thermal binder and gabapentin by assessing polymer melt rheology and drug stability, respectively. Gabapentin was melt granulated at 80% drug loading with pre-plasticized binder using a co-rotating twin-screw extruder. The chemical stability and tabletability of the pre-plasticized granules were assessed to evaluate granule tabletability, drug stability, and process robustness. The granulation of gabapentin was facilitated by pre-plasticization, showing both increased granule growth and the ability to optimize processing conditions by lowering processing temperature. Pre-plasticization of thermal binder was therefore shown to be beneficial during melt granulation as a method of optimizing processing conditions while maintaining granule robustness.

A revisitation of generalized Newtonian fluids

Creating an entry vortex growth simulation to show viscous and elastic fluid behaviors has always been a major challenge for the computational rheology of well-characterized polymer melts with extension thickening. For one thing, it is difficult to ensure stable convergence and reliable solutions via the viscoelastic constitutive equations at a relatively high Deborah number. From a revisitation of the generalized Newtonian fluids (GNFs), deriving the weighted viscosity is natural with the coexistence of shear and extensional flow; it is called the eXtended GNF (GNF-X) model. Herein, 3D contraction flow simulations incorporating the GNF-X weighted viscosity were significantly carried out over a wide range of Deborah numbers. Numerical results regarding changes in vortex sizes exhibit the same trend of experimental observations, while the predictive accuracy is enhanced for a quantitative comparison. More importantly, the vortex formation, in terms of the weighted viscosity and the extensional flow, is demonstrated with supporting evidence.

Scaling Characteristics of Rotational Dynamics and Rheology of Linear Polymer Melts in Shear Flow

Rheological properties of polymer melts under weak flow reflect the orientational anisotropy of the chains, which is established experimentally as the validity of the stress-optical rule (SOR). In ...

Molecular Dynamics Reveals a Dramatic Drop of the Friction Coefficient in Fast Flows of Polymer Melts

We here revisit existing results of Kremer–Grest molecular dynamics simulations of polymer melts that provide values of the friction coefficient ζ of the Kremer–Grest bead for the coarse-grained Fraenkel chain model, both at equilibrium, and in very fast uniaxial extensional flows. The Fraenkel chain model is chosen because it can guarantee chain inextensibility in the flow-induced fully aligned conformation. Since the value of ζaligned for the fully aligned conformation is found to be much smaller than the equilibrium value ζeq, a controversial issue of the nonlinear rheology of polymer melts is here resolved. Indeed, this finding confirms previous evidence emerging from the rheology of several polymers, where seemingly the friction coefficient decreases with increasing flow-induced molecular coalignment. Often, however, such evidence was indirect, and the friction coefficient reduction has not been accepted by a large fraction of the scientific community.

Modeling nonlinear rheology of unentangled polymer melts based on a single integral constitutive equation

The experimental data of Matsumiya et al. [Macromolecules 51, 9710–9729 (2018)] for start-up and the steady-state elongational flow of monodisperse unentangled polystyrene PS27k and poly(p-tert-butylstyrene) PtBS53k melts are analyzed based on the relaxation spectrum of the Rouse model and a single integral constitutive equation. As shown by Lodge and Wu [Rheol. Acta 10, 539–553 (1971)], the stress tensor of the Rouse model is equivalent to the rubberlike-liquid constitutive equation, and the relaxation modes of Rouse chains can be represented by an ensemble of virtual viscoelastic “strands” with relaxation times and creation rates. Instead of the affine deformation hypothesis, we assume that due to the flow, strands are oriented and stretched. The use of a history integral avoids preaveraging of orientation and stretch. Stretch is limited by a finite conformational stretch parameter. We find good agreement between model predictions and experimental data for start-up and the steady-state elongational flow of melts PS27k and PtBS53k and qualitative agreement with stress-relaxation after the stop of elongation. Extension-thickening and extension-thinning observed are caused by finite chain stretch in combination with strand orientation. The model predicts a scaling exponent for high Weissenberg number elongational flows of ηE∝Wi−1/2 in agreement with experimental evidence. The same scaling exponent was observed and predicted earlier for high Weissenberg number shear flows [R. Colby et al., Rheol. Acta, 46, 569–575 (2007)], and we show that the steady-shear data of unentangled polystyrene melts are in nearly quantitative agreement with model prediction assuming only the orientation of strands in the shear flow with no stretch.

On the universality in the extensional rheology of monodisperse polymer melts and oligomer dilutions thereof

The startup and steady extensional viscosities were measured on two narrow molar mass distributed (NMMD) poly(methyl methacrylates) (PMMA) diluted in 57% 2.1 kg/mole oligomer methyl methacrylates. The oligomer is short enough to be random configured and un-entangled though it is still a Kuhn chain. The weight-based average molecular weights of the PMMAs are 86 kg/mole and 270 kg/mole with polydispersites of 1.08 and 1.09 respectively. The extensional viscosities were in theoretical agreement with a constant ‘interchain pressure’ model, representing the maximal level of strain hardening in a Kuhn fluid. This has been observed for similar (styrene) oligomer diluted NMMD polystyrenes before, when the styrene oligomers were Kuhn chains. The original ‘interchain pressure’ model by Marrucci and Ianniruberto (Macromolecules 37(10):3934–3942, 2004), represents the minimal level of strain hardening in a Kuhn fluid. It has been shown previously to predict the extensional viscosities of NMMD polystyrene melts, and it is also in agreement with the extensional viscosities of the 86 kg/mole NMMD PMMA melt as well.

Effect of Finite Extensibility on Nonlinear Extensional Rheology of Polymer Melts

We recently showed that two systems have the same nonlinear flow dynamics if they have (1) the same number of entanglements, Z, (2) the same number of Kuhn segments between entanglements, Ne, and (3) a single monomeric friction reduction between all species. Because differences in polymer chemistry result in different values of (1)–(3), these results show that the likelihood of two melts having the same nonlinear behavior is improbable. This work determines the dependence of the nonlinear extensional flow behavior on Ne for three polymer melts: polystyrene, poly(methyl methacrylate), and poly(tert-butylstyrene). We show that polymer melts with the same Z have almost identical scaled linear viscoelasticity. Extensional rheology at constant strain rate shows strain hardening depends strongly on the value of Ne. More specifically, our data suggest a power-law dependence of steady state stress on the Weissenberg number which increases with increasing Ne.

Effect of Molecular Structure Change on the Melt Rheological Properties of a Polyamide (Nylon 6).

Tailoring the polymer melt rheology and the chain relaxation dynamics permits easy handling of polymer processing and enables broader range of applications. Novel strategy to control the polymer melt rheology and the chain relaxation dynamics was devised. A simple process for molecular structural change in a polyamide (nylon 6) to easily generate a long-chain branching in a controllable manner without forming a network structure led to unusually large enhancements in the relaxation dynamics. The zero shear viscosity of the polyamide has increased more than 200 folds of linear chains viscosity, whereas the molar mass change was ca. 1.6 times. Storage modulus and the loss modulus at low frequency increased more than 104 and 103 times to those of neat polyamide without forming a network structure. The rheological properties of the polymer (nylon 6) melts can be finely tailored by this simple process to cover a broad range of applications.

A novel hyperbolic slit contraction with constant strain rate for elongational rheology of polymer melts

We present an online rheometer for measuring the elongational viscosity of polymer melts and filled compounds that builds upon a recently presented design, which we modified to feature a novel hyperbolic two-part contraction between two slit sections. Our rheometer allows constant monitoring of both shear and elongational viscosity during extrusion. The hyperbolic slit contraction was designed to enable constant elongation rates along the die that are higher at the same flow rate than those of our previous model. Further, it allows pressure transducers to be incorporated directly into the flow channels, which prevents material from accumulating in pressure holes. We compare the results obtained with our new rheometer to those of other methods, including Cogswell analysis of High Pressure Capillary Rheometer (HPCR) data, measurement with a wedge-shaped slit die and measurement using a Sentmanat Extensional Rheometer (SER). Additionally, we report on the differences in elongational and shear flow behaviors of a linear low-density polyethylene, various polypropylene grades (e.g., for pipe, thermoforming and tape applications) and glass-fiber-reinforced polypropylenes. Elongational rheology is valuable in online quality control, since it is very sensitive, for instance, to differences in macromolecular structure or fiber-length distribution.

Review of the hierarchical multi‐mode molecular stress function model for broadly distributed linear and LCB polymer melts

We developed a novel Hierarchical Multi‐mode Molecular Stress Function (HMMSF) model for linear and long‐chain branched (LCB) polymer melts implementing the basic ideas of (1) hierarchical relaxation, (2) dynamic dilution, (3) interchain tube pressure, and (4) convective constraint release. With a minimum number of nonlinear free parameters and remarkable quantitative predictions of the rheology of polymer melts, this model is an outstanding option for the simulation of different processing operations in the polymer industry. The excellent predictions of this model were demonstrated in uniaxial, equibiaxial, and planar extensional deformations for linear and LCB melts, as well as in shear flow for a LCB polymer, with a minimum number of adjustable free nonlinear material parameters, that is, one in the case of extensional flows, and two in shear flow. In this contribution, we review the development of the HMMSF model and present a reduced number of well‐defined constitutive relations comprising the rheology of both linear and LCB melts. We also extend the comparison of model and data to cover the shear flow of a linear polymer melt. POLYM. ENG. SCI., 59:573–583, 2019. © 2018 Society of Plastics Engineers

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.

Determination of polymer melts flow-activation energy a function of wide range shear rate

The majority of the processing of thermoplastic polymers is in melt condition. For example, extrusion, or injection moulding, which are the two biggest plastic processing technologies. Nowadays, there is a need to simulate these processes. The simulations are helpful for the plastic product and mold designers. In these simulations one of the most important internal parameters is the shear viscosity, which depends on the temperature, pressure, molecular weight or structure. So easy to see how important is the top priority precise knowledge of the shear viscosity of plastic melts. The importance of polymer melt flow properties during processing has required continuous research of polymer melt rheology. In a previous article, we described how to measure shear viscosity of polycarbonate from 100 to 105 shear-rate regions with standard and non-standard equipments. In this paper a method is shown to calculate the activation energy of flow of high density polyethylene (HDPE), polystyrene (PS) and polycarbonate (PC). It was shown that shear viscosity and activation energy of flow of the polymers depend on the chemical structure. It was found that more rigid molecular structure results higher values.