The Rheology of Linear and Long-chain Branched Polymer Melts

By generalising the Doi-Edwards tube model to the Molecular Stress Function theory, the non-linear rheology of polymer melts can be described quantitatively. The strain-hardening of linear polymer melts in extensional flows can be accounted for by a strain energy function, which reflects the increase of strain energy due to tube squeeze. In comparison to linear polymer melts, long-chain branched polymer melts show enhanced strain-hardening. This is due to the fact that while the backbone of the branched macromolecule is stretched by deformation, side chains are compressed. It is demonstrated that the experimentally observed slope of the elongational viscosity after inception of strain-hardening depends on the ratio β of total molar mass to backbone molar mass as predicted by the model. The steady-state (plateau) value of the elongational viscosity depends on the maximum relative stretch, , which can be supported by chain segments and which represents the maximum elastic energy storable in the polymeric system.     

Characterization of elongation viscosity for polyethylene melts

Elongation viscosity is an important characterization of flow properties for polymer melts. In the present article, a new extensional viscosity equation for polymer melts was established by introducing a relaxation time equation based on the Cross model. The elongation viscosities of a low-density polyethylene (LDPE) melt at 200 °C and a metallocene linear low-density polyethylene (mLLDPE) melt at 130 °C were estimated using this equation; then, the calculations of the melt elongation viscosity were compared with the measured data from the extension experiments of the LDPE melt and the mLLDPE melt reported in the reference. Good agreement was found between the predictions and the measured data from the LDPE and mLLDPE melts. In addition, this equation is easy to use for characterization of elongation viscosity during single shaft elongation flow for polymer melts.     

Melt elongation flow behaviour of LDPE/LLDPE blends

The extensional rheological properties of low density polyethylene (LDPE)/linear low density polyethylene (LLDPE) blend melts were measured using a melt spinning technique under temperatures ranging from 160 to 200 °C and die extrusion velocities varying from 9 to 36 mm/s. The results showed that the melt elongation stress decreased with a rise of temperature while it increased with increasing extensional strain rate and the LDPE weight fraction. The dependence of the melt elongation viscosity on temperature roughly obeyed the Arrhenius equation, it increased with increasing extensional strain rate and the LDPE weight fraction when the extensional strain rate was lower than 0.5 s⁻¹, and it reached a maximum when the extensional strain rate was about 0.5 s⁻¹, which can be attributed to the stress hardening effect.     

High‐pressure rheology of polystyrene melts plasticized with CO2: Experimental measurement and predictive scaling relationships

A high‐pressure extrusion slit die rheometer was constructed to measure the viscosity of polymer melts plasticized by liquid and supercritical CO₂. A novel gas injection system was devised to accurately meter the follow of CO₂ into the extruder barrel. Measurements of pressure drop, within the die, confirm the presence of a one‐phase mixture and a fully developed flow during viscosity measurements. Experimental measurements of viscosity as a function of shear rate, pressure, temperature, and CO₂ concentration were conducted for three commercial polystyrene melts. The CO₂ was shown to be an effective plasticizer for polystyrene, lowering the viscosity of the polymer melt by as much as 80%, depending of the process conditions and CO₂ concentration. Existing theories for viscoelastic scaling of polymer melts and the prediction of T_g depression by a diluent were used to develop a free volume model for predicting the effects of CO₂ concentration and pressure on polymer melt rheology. The free volume model, dependent only on material parameters of the polymer melt and pure CO₂, was shown to accurately collapse the experimental data onto a single master curve independent of pressure and CO₂ concentration for each of the three polystyrene samples. This model constitutes a simple predictive set of equations to quantify the effects of gas‐induced plasticization on molten polymer systems. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3168–3180, 2000     

聚合物体系拉伸流变行为的表征及研究进展

聚合物的拉伸流动在吹膜、纺丝、热成型等加工中扮演着支配的角色,因此掌握聚合物熔体在拉伸条件下的流动行为对于控制和预测其加工性能具有重要意义。相对于剪切流动,拉伸粘度对于大分子的结构、填充粒子的各向异性、共混物中两相的结构等更加敏感。本文简要介绍了当前用于拉伸流变研究的常用装置及其原理,并举例描述了单一组分聚合物、聚合物纳米复合材料和聚合物共混物等体系拉伸流变研究的现状和成果,最后指出了当前拉伸流变研究领域存在的一些不足之处并进行了展望。     

Geometry dependence of the elongation behavior of a polypropylene melt through a micro die

A series of rheological experiments was performed for a polypropylene (PP) melt to explore its elongation behavior through a capillary die. Using an advanced twin-bore capillary rheometer with dies measuring 1.0, 0.5, and 0.25 mm in diameter, the experiments were performed at 210, 220, and 230 °C. The results indicated that the temperature of the PP melt had a significant effect on its extensional viscosity. The different decreases in the extensional viscosity values in the tested dies revealed the geometry dependence of the extensional viscosity. In the case of PP in the 0.25 mm die at 210 °C, the extensional viscosity values under different extensional strain rates were much higher than those in the other dies. Only in the 1.0 mm die did the relationship between the extensional viscosity of PP and its temperature obey the Arrhenius equation due to the larger die size which related to a slight size effect on its elongation behavior. The calculated deviations of the extensional viscosity in the tested dies demonstrated that the increasing pressure applied to the PP melt in the micro channel was related to the geometry dependence of the elongation behavior of the PP melt. The change in the extensional viscosity eventually relied on the interaction of the die geometry, the temperature, and the extensional stress of the PP melt.     

热致性液晶共聚酯的拉伸流动行为

采用入口收缩流动的实验方法研究了改性PET/ 80PHB液晶共聚酯LCP80的拉伸流动行为 ,考察了拉伸速率、温度等对其拉伸粘度、Trouton比的影响 .实验结果表明 ,LCP80的入口压降值很大 ,其中由拉伸引起的入口压降是主要的 .在该文实验条件下LCP80均表现出拉伸稀化现象 ,并且Trouton比值都远大于 3 .根据流动中液晶织态结构的变化解释了实验现象 ,并对入口收缩流动的实验数据处理方法作了改进 ,比Beery的方法更为合理 ,也具有更广的适用性 .     

线型聚乙烯及其共聚物的挤出畸变与熔体粘弹性的关系

采用恒速型双筒毛细管流变仪研究了一类线型聚乙烯熔体的挤出畸变与熔体非线性粘弹性的关系。实验研究了发生畸变时挤出压力的振荡规律,发现线型大分子或带小侧基的大分子熔体,容易发生壁滑和挤出压力振荡;而有较大侧基、或分子量分布宽、或带大量短支链的熔体,挤出畸变现象较轻。挤出畸变与熔体的弹性及熔体．壁面吸附状态紧密相关。容易发生壁滑和挤出压力振荡的熔体,弹性较大(入口压力降大);在壁面的吸附作用强(壁面临界剪切应力大)。稳态剪切粘度大小与挤出畸变和压力振荡的关系不大;而拉伸应力和拉伸粘度大的熔体较易发生壁滑和挤出压力振荡。     

“Experimentation and modeling for the apparent elongation viscosity of polymer melts with the White–Metzner model”

The measurement of the apparent elongation viscosity (η_e) of several polyolefin melts was conducted in this study by using the isothermal fiber‐spinning method. The White–Metzner (W–M) model was used to analyze the spinning flow of the polymer melts and, thus, the elongation viscosity was predicted at elongation strain rates ranging from 0 to approximately 5 s^?1. The values of the model parameters required in the W–M model were obtained by curve fitting the experimental data obtained from the shear measurements. The elongation viscosity predicted using the W–M model was in good agreement with the experimental results of fiber spinning. In addition, η_e could also be estimated directly from the measured shear viscosity (η_S) with a formulation using the W–M model; the subsequently obtained elongation viscosity and Trouton ratio (T_R) were reasonable within a wide range of strain rates. Based on the experimental and theoretical results, the polyolefin with a high molecular weight was observed to have high elongation viscosity, and the polymer with a broad molecular weight distribution also possessed high η_e. The T_R value of the commercial polypropylene (PP‐1040) began to increase from 3 at a deformation rate of 0.1 s^?1 and grew up asymptotically to 10, whereas the T_R of high‐density polyethylene (HDPE‐606) remained nearly at 3 within the entire range of strain rates. Copyright © 2014 John Wiley & Sons, Ltd.     

Extensional viscosity of aqueous solutions of SDS and PVP measured on the rheometrics RFX

An opposed jets extensional rheometer, the Rheometrics RFX, was used to investigate the extensional flow properties of a series of solutions of polyvinylpyrrolidone (PVP) containing varying amounts of an anionic surfactant, sodium dodecylsulphate (SDS). The measurements were made in comparison with data collected for Newtonian fluids of similar viscosity to the polymeric systems of interest. The instrument was used to make measurements of the extensional viscosity as a function of extension rate, and a study of the effect of the residence time within the flow field was made. PVP has been shown to form a complex in aqueous solution with SDS. This study concentrated on the effect the addition of SDS has on the extensional rheology of semi-dilute solutions of PVP, with a molecular weight of 700 000. It was shown that increasing the amount of SDS increased the extensional thickening characteristics of solutions, as shown by a decrease in the critical extension rate for thickening. An increase in the viscosity of the solvent was shown to have an additional effect. By decreasing the distance between the opposed nozzles it was shown that a decrease in the residence time (and hence total average strain) diminished the extensional thickening character of these solutions.     

Electrostatic fiber spinning from polymer melts. II. Examination of the flow field in an electrically driven jet

The flow field in an electrically driven jet has been examined and quantitatively analyzed. Using a model fluid, the nature of the streamlines and magnitude of the stream velocities were investigated with the aid of tracer particle photography. It was found that the velocity field is not purely extensional, but contains rotational components as well. Furthermore, the only portion of the jet completely free of any rotational component is the region about the symmetry axis. The extensional strain rate along the symmetry axis increases rapidly with the applied electric field intensity and can attain values in excess of 50 sec^?1. This suggests that it might be possible to draw continuous oriented fibers from polymer melts by this technique if the jet can be operated at sufficiently high electric field intensity.     

Uniaxial and biaxial stretching of silicone putty

Two novel experimental methods are used. Vertical uniaxial stretching is obtained by attaching a perspex rod to the lower end of a silicone putty cylinder; the rod then descends into water of constant depth. The stress and rate of extension change little during each test, but the rate of extension may be varied from 0.005 to 0.10 s⁻¹ by modifying the experimental conditions. Biaxial stretching is acchieved by placing a disc of silicone putty across the top of an open glass cylinder which is lightly pressurized. The sample expands as a spherical cap, the height of the centre above the cylinder being timed. The stress in the cap passes through a shallow minimum as it expands (at constant pressure) and the slowly varying rate of biaxial extension may be readily determined. This lies in the range 0.003–0.06 s⁻¹. For low rates of uniaxial or biaxial extension, it is possible to plot the extension against time and to show how the extensional viscosity varies with the strain rate (or principal extension ratio). For high rates of extension, a ‘single point’ determination of the extensional viscosity may be made, with the stress and strain rate averaged at the mid-point of the sample's extension. The temperature is 26.5 ± 1.5 °C. The following is shown under the experimental conditions:(a) the extensional viscosity (uniaxial or biaxial) is in the range 1.0 × 105 to 3.0 × 10⁵ Pa s;(b) for extensional strain rates between 0.01 and 0.04 s⁻¹, the uniaxial and biaxial extensional viscosities are of comparable value;(c) both forms of the extensional viscosity tend to decrease with increased extensional strain rate, the biaxial extensional viscosity falling more rapidly and being higher than the uniaxial viscosity at low strain rates and lower at high strain rates;(d) there are no signs of rupture in uniaxial extension (principal extension ratios up to 1.8 and extensional strain rate up to 0.1 s⁻¹);(e) in biaxial extension, the sample tends to rupture more easily as the strain rate is increased. (The sample fails at the principal extension ratio of 2.0 at an extensional strain rate of 0.02 s⁻¹ and fails at a principal extension ratio of 1.3 at an extensional strain rate of 0.07 s⁻¹.)     

Characteristics and design procedure of hyperbolic dies

Nozzle profiles capable of generating constant extensional strain rates are termed hyperbolic dies. When used in polymer extrusion, they exhibit greater potential in inducing and retaining polymer molecular orientation than conventional capillary dies. Most mathematical expressions found in the literature involve several processing variables in describing and designing such nozzle profiles. This report reveals that a hyperbolic die profile, although rather complicated, can be expressed with equations in terms of two ordinary geometrical parameters—the exit diameter and the hyperbolic length. This finding greatly simplifies the design procedure of hyperbolic dies. The extensional strain rate of a hyperbolic die can be related to the length-to-diameter ratio for any given exit diameter. Examples of various types of die profiles are presented and their constant extensional strain-rate characteristics are discussed.     

EFFECT OF INTERNAL VISCOSITY OF POLYMERIC FLUIDS UNDER STRONG EXTENSIONAL FLOWS

The dumbbell model with internal viscosity for a dilute polymer solution is investigated based on a balance of viscous drag and restoring Brownian forces.An approximate method is used to obtain the solution of extensional stress in closed form in the case of steady flow.For different internal viscosities,this parametric study shows different asymptotic regimes of the extensional viscosity as a function of strain rate.This analysis may explain the attenuation of pressure drop in strong flows from a phenom...     

Predictions of Some Internal Microstructural Models for Polymer Melts and Solutions in Shear and Elongational Flows

Summary: In this work, the behavior of some internal microstructural models with different mobility tensors has been studied for polymer melts and solutions under steady and transient simple shear and elongational flows. The time evolution equations for conformation and stress tensors in the models reviewed have their root in the Generalized Poisson bracket formalism. Two different families of conformational models have been selected for this study. The first family is based on the Modified Finitely Extensible Nonlinear Elastic (FENE‐P) energy while the second uses a Volume Preserving Conformational Rheological (VPCR) model based on the Hookean Helmholtz free energy function. Several expressions for the mobility tensor based on the previously mentioned energy functions are used to obtain the models. The sensitivity of both families of models to the choice of the mobility tensors on the prediction of material functions in the transient and steady flows is discussed. Also, effects of shear rate on the material functions in start‐up and relaxation shear flows for both models are studied. The predictions of both models are compared with experimental data taken from the literature for some polymer melts. These results show that the family of VPCR models is able to predict the steady shear and elongational flow material functions in an extended range of deformation rates whereas the family of FENE‐P models can predict the behavior of only some specified polymer melts.

Experimental data and VPCR model predictions for steady and elongational viscosity for PS [data of H. Munstedt, 1980].     

Relaxation of entangled polymers in melts

The stress relaxation function of a monodisperse or polydisperse melt, and the corresponding viscosity, have been calculated in the entanglement domain by applying the Doi-Edwards theory which relies on the reptation concept introduced by P. G. de Gennes. Though the theory has been considered as successful, the agreement with precise experiments is only qualitative, and strong anomalies remained to be explained. A new theory is presented here: it is obtained by introducing simple approximations derived from elementary but novel considerations. This theory is shown to be in good agreement with experiments on monodisperse and polydisperse melts. In particular, it explains the well-known fact that the viscosity of a monodisperse polymer melt of molecular mass M seems to increase proportionally to M^3,4 when M is large.     

High‐pressure rheology and viscoelastic scaling predictions of polymer melts containing liquid and supercritical carbon dioxide

High‐pressure rheological behavior of polymer melts containing dissolved carbon dioxide (CO₂) at concentrations up to 6 wt % were investigated using a high‐pressure extrusion slit die rheometer. In particular, the steady shear viscosity of poly(methyl methacrylate), polypropylene, low‐density polyethylene, and poly(vinylidene fluoride) with dissolved CO₂ were measured for shear rates ranging from 1 to 500 s^?1 and under pressure conditions up to 30 MPa. The viscosity of all samples revealed a reduction in the presence of CO₂ with its extent dependent on CO₂ concentration, pressure, and the polymer used. Two types of viscoelastic scaling models were developed to predict the effects of both CO₂ concentration and pressure on the viscosity of the polymer melts. The first approach utilized a set of equations analogous to the Williams–Landel–Ferry equation for melts between the glass‐transition temperature (T_g) and T_g + 100 °C, whereas the second approach used equations of the Arrhenius form for melts more than 100 °C above T_g. The combination of these traditional viscoelastic scaling models with predictions for T_g depression by a diluent (Chow model) were used to estimate the observed effects of dissolved CO₂ on polymer melt rheology. In this approach, the only parameters involved are physical properties of the pure polymer melt that are either available in the existing literature or can be measured under atmospheric conditions in the absence of CO₂. The ability of the proposed scaling models to accurately predict the viscosity of polymer melts with dissolved high‐pressure CO₂ were examined for each of the polymer systems. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 3055–3066, 2001     

Characterization of polymer molecular mass distribution from rheological measurements

Various methods for the determination of molecular mass distribution from rheological measurements of polymer melts are introduced. Shear viscosity, entrance pressure loss, recoverable shear, and in particular the dynamic viscoelasticity data G' and G” are discussed as analytical tools to evaluate the molecular mass distribution. Well characterized samples and homologous series of the polymers PS, PE-HD, PP, and PTFE were measured to check the methods. Precise and reliable results can be obtained by calculating the molecular mass distribution from the frequency dependence of the storage modulus.     

Tensile drawing,morphology, and mechanical properties of poly(butylene terephthalate)

The concept of the drawing of a molecular network has been employed to derive a total network draw ratio from the combination of the two deformations occurring in the production of poly(butylene terephthalate), PBT, fibers by the consecutive processes of melt spinning and cold drawing. The mechanical properties of PBT can then be more readily explained in terms of increases in this total network draw ratio. However, the preorientation and crystallization that occurs in the melt-spinning process can occur at different strain rates and temperatures, depending on the wind up speed employed, on the extensional viscosity of the polymer, and on the variation of the extensional viscosity with temperature. Therefore, for polymers such as poly(butylene terephthalate), which can exist in two crystalline forms, the morphology of the final drawn fiber might be expected to depend on the first melt-spinning stage of the process as well as on the total network draw ratio. In this work, density, birefringence, mechanical measurements, and WAXD measurements, which have been made on the melt-spun fibers and on the drawn fibers, are described. Small differences in some of the drawn yarn mechanical properties at the same overall network draw ratio are related to the crystallinity and in particular to differences in the proportion of the α and β phases present in the drawn yarn. These in turn are related to differences in the temperature and stress during melt spinning and drawing. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 2465–2481, 1997     

Modeling of Viscoelastic Fluid Flow Behavior in the Circular Die Using the Leonov-Like Conformational Rheological Constitutive Equations

Summary: In this paper, the flow behavior of Leonov-Like conformational rheological model, which has root in the generalized Poisson bracket formalism based on the conformation tensor, have been studied in the circular die flow. Prediction of the normal stress differences during the flow of these fluids lets us to follow and calculate relaxation dependent phenomena such as die swell. The model predictions have been compared for the four families of mobility expressions. The Study of the model prediction sensitivity to its mobility term shows that model predictions can cover a wide range of rheological behaviors generally observed for polymer melts and solutions in the circular die flow.