The steady flow shear modulus of polymer melts

Relaxation times of polyethylene melts have been measured by Aloisio, Matsuoka, and Maxwell. One implication regarding their observations is that the elastic properties of polymer melts must be time-dependent. In particular, the steady-flow shear modulus depends on the strain rate. Some interpretations of data in the literature have been based on concepts in rubber elasticity where the steady-flow modulus is an equilibrium value, independent of strain rate. We have used Pao's theory for viscoelastic flow together with measurements of relaxation times to discuss the strain rate dependence of the steady-flow shear modulus of melts. The existence of a strain rate-dependent shear modulus leads naturally to a nonlinear relation between shear stress and recoverable shear strain. The conclusions regarding the molecular weight dependence of the modulus also differ from interpretations based on rubber elasticity.     

Experimental study of elongational flow and failure of polymer melts

A new and simple instrument for measurement of elongational flow response of polymer melts in constant uniaxial extension rate experiments is described. Quantitative stress development data are presented for a series of low-density polyethylene (LDPE), high-density polyethylene (HDPE), polystyrene (PS), polypropylene (PP), and poly(methyl methacrylate) (PMMA) melts. For small elongation rate E, linear viscoelastic behavior was observed; while for large E, LDPE and PS showed exponential stress growth, while HDPE and PP showed only linear stress growth. Stress relaxation experiments were carried out for several of the same melts in the instrument. Elongation to break and mechanisms of filament failure were studied. HDPE and PP have a tendency to neck and exhibit ductile failure, while at high E, LDPE and PS seem to show cohesive fracture. The elongational flow stress response data were compared to predictions of nonlinear viscoelastic fluid theory, specifically the Bogue-White formulation. The qualitative differences in responses of the melts studied were explained in terms of different dependences of the effective relaxation times on deformation rate and, more specifically, on values of the a parameter in the theory.     

Shear dependence of thermal conductivity in polyethylene melts

Thermal conductivity measurements with a modified Couette flow cell were obtained as a function of shear rate for two linear polyethylene melts of weight-average molecular weights 27,300 and 56,700, respectively. The lower-molecular-weight polyethylene revealed a maximum decrease in thermal conductivity of 55 percent at 150 s^?1. After shearing at 400 s^?1, approximately 90 minutes was required to recover the value corresponding to the zero shear condition. This was considered consistent with molecular orientation into the flow direction during shear with a subsequent relaxation upon the removal of stress. The higher-molecular-weight polyethylene gave a similar decrease in thermal conductivity at 50 s^?1. Unlike the lower-molecular-weight melt, an increase was observed at higher shear rates. Enhancement of energy transport via cluster flow mechanism was presented as a possible interpretation of these results. A theory of molecular orientation of liquid poly(dimethylsiloxane) (PDMS) under shear flow was previously developed from thermal conductivity and birefringence data of this material. An attempt to clarify the difference in behavior between the two melts examined in this work, and between the polyethylene melts and the PDMS previously studied is presented.     

Dichotomous behavior of polymer melts in isothermal melt spinning

Isothermal melt spinning experiments have been conducted using two polyethylene melts of low density (LDPE) and high density (HDPE) to produce steady state spinline profiles. The data revealed the threadline extensional viscosity exhibiting a contrasting picture : extension thickening behavior for LDPE and extension thinning one for HDPE. A White-Metzner model having a strain rate-dependent relaxation time was then found to be able to simulate this dichotomy in melt spinning fairly well: the fluids whose relaxation times have smaller strain rate-dependence can fit LDPE data with extension thickening extensional viscosity whereas the fluids whose relaxation times have larger strain rate-dependence can fit HDPE data with extension thinning extensional viscosity. This dichotomous nature of viscoelastic fluids is also believed to be able to explain other similar contrasting phenomena exhibited by polymer melts, such as vortex/no vortex in entry flows, cohesive/ductile fracture modes in extension, and more/less stable draw resonance than Newtonian fluids.     

Modeling of nonlinear extensional and shear rheology of low-viscosity polymer melts

The hierarchical multi-mode molecular stress function (HMMSF) model developed by Narimissa and Wagner [Rheol. Acta 54, 779–791 (2015), and J. Rheol. 60, 625–636 (2016)] for linear and long-chain branched (LCB) polymer melts were used to analyze the set of transient elongational and shear viscosity data of two LCB low-density polyethylenes (1840H and 2426 k), and a linear poly-(ethylene-co-α-butene), PEB A-780090 as reported by [Li et al. J. Rheol. 64, 177 (2020)], who had developed a new horizontal extensional rheometer to extend the lower limits of elongational viscosity measurements of polymer melts. Comparison between model predictions and elongational stress growth data reveals excellent agreement within the experimental window, and good consistency with shear stress growth data, based exclusively on the linear-viscoelastic relaxation spectrum and only two nonlinear model parameters, the dilution modulus G_D for extensional flows, and in addition a constraint release parameter for shear flow.     

Large transient shearing of molten polymers: Predictions of rate-dependent and nonaffine network models

Analytical expressions of shear stress evolution for arbitrary transient flows are obtained, based on a rate-dependent network (RDN) model as well as on a nonaffine network (NAN) model. Predictions of both models are evaluated for various step histories against experimental results on linear and branched polyethylene melts (LDPE and HDPE). Agreement with experiments justifies the usefulness of the computed stress functions regarding the predictions of shear responses in melt processing. A slow transient process is more adequately simulated by an NAN model than by an RDN model. The very slow reentanglement process following cessation of flow is poorly described by either model. This fact implies that additional relaxation mechanisms are involved. In the linear viscoelasticity of small deformation, elastic relaxation occurs. In processes involving large shear rates, additional parameters are needed to account for the structural changes accompanying the relaxation process. © 1995 John Wiley & Sons, Inc.     

Correlation between entry pressure losses and elongation viscosity of polyethylene melts

The correlation between the entry pressure drop and elongation viscosity during entry converging flow of polymer melts was discussed in this article. The entry pressure drop during extrusion of a low density polyethylene (LDPE) melt and a linear low density polyethylene (LLDPE) melt was measured by means of a capillary rheometer under test conditions with temperature of 170 °C and shear rate varying from 10 to 300 s⁻¹. The results showed that the entry pressure drop increased nonlinearly with an increase of the shear stain rate, and the variation of entry pressure drop of the two melts was close to each other. The melt elongation viscosity of the two resins was estimated using Cogswell equation from the measured entry pressure drop data, and the predictions were compared with the melt extension viscosity measured by using a melt spinning technique published in literature. It was found that the melt extension viscosity from entry converging flow was slightly lower than that from melt spinning technique under the same temperature and extension strain rate.     

A model relating the elastic properties of high-density polyethylene melts to the molecular weight distribution

An earlier model relating the variation of the steady-shear melt viscosity of high-density polyethylene to the molecular weight distribution is applied toward predicting the steady-shear elastic compliance, the first normal stress difference, and relaxation spectrum as a function of shear rate from the molecular weight distribution. The model envisions the cutting off of longer relaxation times as the shear rate is raised such that at any shear rate ${\rm \dot \gamma }$ the molecular weights and their corresponding maximum relaxation times τ_m are partitioned into two classes; the relaxation times are partitioned into operative and inoperative states, depending on whether they are less than or greater than τ_c, the maximum relaxation time allowed at ${\rm \dot \gamma }$. Equations relating molecular weight and relaxation time to the steady-shear elastic compliance and viscosity are assumed valid at nonzero shear rates, except for the partitioning effect of shear rate. The shear rate dependence of the first normal stress difference and the steady-shear viscosity for polyethylene melts is successfully predicted over the range covered by the cone-and-plate viscometer. The assumed proportionality constant between τ_c and 1/${\rm \dot \gamma }$ was determined to be 1.7. Using this relation, the maximum relaxation time at 190°C for a polyethylene molecule of molecular weight M is given by τ_m = 1.4 × 10^?19 (M)^3.33. Reasonable agreement has been obtained between the experimentally determined relaxation spectrum of a polyethylene melt and that predicted from the molecular weight distribution. The agreement is best at the longest relaxation times.     

Effects of stick–slip transition on polymer melt apparent shear viscosity measurement

A twin-bore capillary rheometer is used for the apparent shear viscosity measurement of commercial polyolefin melts based on Ostwald-de Waele model. The effects of stick–slip transition of linear low-density polyethylene (LLDPE) and high-density polyethylene (HDPE) are investigated. The maximum error of apparent shear viscosity calculated by corrected shear rate is 23% when the stick–slip transition occurs. Based on the entanglement‑disentanglement theory, a schematic diagram for shear stress curve containing stick–slip transition is presented to illustrate polymer melt flow in capillary. In this study, the critical stress at the beginning of stick–slip transition at 220 °C is 23.01 kPa higher than that at 190 °C, and why it increases with increasing temperature is discussed with a molecular mechanism in combination with entropy elasticity and entanglement‑disentanglement theory. Through the analysis of ULDPE, PS, EVA, and K-Resin, it can be found that short branches or side groups are helpful to avoid the stick–slip transition. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 48230.     

The shear modulus of flowing polyethylene melts

Tests on three low-density polyethylene melts over a range of temperatures and shear rates, using a Weissenberg rheogoniometer, have enabled the reduced shear modulus to be obtained as a function of shear rate at the initiation of shearing and at various subsequent stages. For the two polymers which gave plateau values of modulus during the course of shearing these were in good agreement with figures quoted in the literature, but the initial modulus (measured on one polymer) was an order of magnitude higher. This supports the view that a network structure exists in the polymer at rest and is disrupted in the early stages of shearing. It was not possible to obtain unequivocal evidence that the equilibrium modulus decreases with amount of shearing, as required by the hypothesis that rheological breakdown is caused by a reduction in molecular entanglements.     

Mixing in reactive extrusion of low-density polyethylene melts: Linear vs. branched

The melt flows of linear low-density polyethylene (LLDPE) and branched low-density polyethylene (LDPE) have been compared in a fully intermeshing co-rotating twin-screw extruder. The polyethylene melts were selected in order to investigate the effects of the melt rheology on the mixing. Their shear vicosity curves are quite similar, but the LDPE has a markedly higher apparent extensional viscosity over a wide range of stretch rates. The stagger of the paddles in the mixing zone of the extruder creates axial pressure-driven axial flow can have significant extensional strain components. Residence time distributions obtained in the melt zones of the extruder with tracer dye reveal that the LDPE has a narrower residence time distribution than the LLDPE over a wide range of operating conditions. The axial dispersion for the LDPE is significantly lower than the axial dispersion for the LLDPE. This is attributed to the greater extensional viscosity of the LDPE. During the reactive extrusion process, solid maleic anhydride and polyethylene were added at the feed port but the peroxide provides better control of the crosslinking reaction. Residence time distributions measured for the chemically more reactive LLDPE melt indicate reduced levels of axial mixing with reaction. The reduction in mixing is due to a crosslinking reaction that occurs in parallel to the grafting reaction. This change in mixing is smaller than the difference in mixing between LDPE and LLDPE.     

A relationship between steady-state shear melt viscosity and molecular weight distribution in polystyrene

A model that relates to the molecular weight distribution (MWD) of high-density polyethylene to the steady-state shear melt viscosity has been applied to polystyrene melts. Relations are developed for predicting the rheological flow curve from the molecular weight distribution. Relationships are also developed to predict the MWD from the flow curve, although practical limitations to this procedure are given. From a consideration of predictions of the model and experimental data, it is concluded that the transition for a given molecular species from Newtonian to non-Newtonian flow is sharp. Additionally, the calculated empirical parameter that partitions the MWD into molecules that act in a Newtonian fashion and those that do not is shown to be equivalent to the largest molecular weight homolog that can still undergo Newtonian flow at a given shear rate for monodisperse fractions. The temperature dependence of the relaxation times is found to be somewhat higher than that predicted by the Rouse theory. An activation energy of 30 kcal/mole for η0 was used to fit the experimental viscosity data adequately at 190° and 225°C. The terminal relaxation spectrum for a narrow-MWD polystyrene standard is calculated and found to agree well for long relaxation times with that reported in the literature.     

Linear-low-density polyethylene melt rheology: Extensibility and extrusion defects

This paper investigates three aspects of linear-low-density polyethylene (LLDPE) rheological properties: shear viscosity variations with shear rate and temperature, tensile behavior determined with an extensiometer, and extrusion defects. The differences in shear viscosity variation with shear rate and temperature between LLDPE and LDPE (low-density polyethylene) are shown. These differences, attributed to wider molecular weight distribution and to long chain branching (LCB) in LDPE, involve different extrusion behaviors. The lack of LCB in LLDPE can be demonstrated by comparison of the measured Newtonian viscosity with the value of the same parameter calculated from molecular weight distribution and composition law of Newtonian viscosities. The lack of LCB leads to good melt extensibility, which is shown by tensile properties of polyethylene melts determined with a non-isothermal extensiometer. The melt fracture phenomenon is studied because it promotes surface defects on bubbles in film application. Extrudate distortions are examined at the laboratory extruder outlet. This test shows differences between LLDPE and LDPE, but also between some LLDPE samples.     

The viscosity of monomolecular melts of poly(vinyl chloride)

PVC melts are predicted to be homogeneous with single molecules as the stable flow units (monomolecular melts) at corresponding values of high temperatures and/or high shear stresses. Under these conditions, it is found that the zero shear viscosity in simple shearing flow of rigid compounds depends on the average molecular weight by weight to the 3.5 power for molecular weights between 24,000 and 100,000. All data measured under conditions where monomolecular melts are predicted fall on a master curve of reduced viscosity versus reduced shear rate when a relaxation time proportional to η0/c²T is used. It is, therefore, concluded that monomolecular melts of PVC compounds follow the same structure–viscosity relations as found for other linear melts in viscometric flow.     

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     

Structure-property relationships in blends of linear low- and conventional low-density polyethylene as blown films

Three-layer coextruded blown (either blend or composite) films, made of low-density polyethylene and linear lowdensity polyethylene (1:1 ratio) of identical density, were compared. The tensile properties of both systems are nearly as high as those of the linear polyethylene while high strain rate properties including impact strength and tear resistance of the composite film are superior. Some structural insight was obtained by thermal analysis and thermoelastic measurements. Structure property relationships are discussed in light of the unique behavior, structure, and morphology of linear low-density polyethylene. The two polyethylenes are only compatible to a rather limited extent mainly affecting their blend behavior. However, a strong mutual reinforcement effect was observed.     

Rheology and processing of linear low density polyethylene resins as affected by alpha-olefin comonomers

The effects of the higher alpha-olefin comonomers on the rheology and processing behavior of linear low density polyethylenes were investigated. Four linear low density polyethylene resins polymerized with butene, hexene and octene comonomers and a low density polyethylene were characterized in terms of their shear viscosity, first normal stress difference, storage and loss moduli, shear stress growth, stress relaxation upon step strain, stress relaxation upon the cessation of steady shear, and uniaxial extensional stress growth material functions. Differences in first normal stress difference, relaxation moduli, damping function parameters, and uniaxial extensional stress growth behavior were noted. The observations were elucidated in terms of the processability considerations in blown film extrusion process.     

Mixture Rules for Critical Shear Values of Extruded Linear PE/Branched PE Blends

Oscillatory flow and elastic turbulence belong to the types of flow instabilities frequently encountered during extrusion of polymer melts. The onset of these defects corresponds to the flow conditions when the critical shear stresses or the critical shear rates are attained. The critical values of shear stresses and shear rates were experimentally determined for linear polyethylene/branched polyethylene blends (IPE/bPE) that were prepared with various weight ratios. Consequently, mixture rules of the logarithmic type are proposed. These rules relate the critical value of shear stress (shear rate) of blend to the critical values of shear stresses (shear rates) of the individual pure components, weight fractions, and interaction parameters. There is a good agreement between the proposed mixture rules and experimentally determined critical values.     

Thermal,dynamic mechanical,and rheological behavior of linear low-density polyethylene/poly(octadecene-co-maleic anhydride) blends

Blends of linear low-density polyethylene (LLDPE) and a 50:50 copolymer of octadecene and maleic anhydride (C₁₈-MAH) were characterized by calorimetry, dynamic mechanical testing, and rheometry. In the solid state, the blends are essentially immiscible. No evidence was obtained for cocrystallization of the LLDPE with the paraf-finic side-chains of the C₁₈-MAH. Interactions between the blend components were observed in three ways. First, presence of the C₁₈-MAH in the LLDPE melt increases the nucleation rate for LLDPE crystallization. Second, side-chain crystallization in a portion of the C₁₈-MAH component equivalent to approximately 15% of the total blend is apparently suppressed in the blends. Third, although the mechanical loss of the blends is essentially a sum of the pure components, the β relaxation of the LLDPE is absent in blends containing more than 20% C₁₈-MAH. The blends are also immiscible in the melt. The steady and dynamic shear rheology is dominated by the immiscibility and mismatch in viscosity, η, between the two polymers. A linear dependence on blend composition was found for log η in dynamic (small strain) tests. Nonlinear behavior with positive and negative deviations from linearity was found for log η in steady shear (large strain) tests.