Influence of melt deformation history on orientation in vitrified polymers

An experimental study of the development of orientation in polystyrene melts during flow and its retention in vitrified parts is described. It is shown on the basis of elongational and shear flow experiments that orientation in vitrified polystyrenes may be predicted from a knowledge of the stress field at the time of vitrification and application of stress-optical laws. More generally a relationship between birefringence and principal stress difference is found which correlates (1) on-line isothermal shear flow, (2) on-line non-isothermal elongational flow (melt spinning), and (3) vitrified samples formed in both shear and elongational flow. It is further proposed that orientation in polymer chains in deforming melts is uniquely dependent on stress—specifically, that the ratio of the stress-optical constant C to the intrinsic birefringence Δ° is approximately a constant.     

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.     

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.     

Experimental investigation of the influence of molecular weight distribution on the rheological properties of polypropylene melts

An experimental study of steady shear and elongational flow Theological properties of a series of polypropylene melts of varying molecular weight and distribution is reported. Broadening the molecular weight distribution increases the non-Newtonian character of the shear viscosity function and increases the principal normal stress differences at fixed shear stress. The behavior is compared to earlier rheological property-molecular weight studies. Correlations are developed for these properties in terms of molecular structure. Elongational flow studies indicate that for commercial and broader molecular weight distribution samples, ready failure by neck development occurs and the elongational viscosity appears to decrease with increasing elongation rate. For narrower molecular weight distribution samples, the elongational viscosity is an increasing function of elongation rate, The implication of these experimental results to viscoelastic fluid constitutive equations and polymer melt processing is developed.     

Rheological characterization of controlled-rheology polypropylenes using integral constitutive equations

Controlled-rheology polypropylene melts were prepared via molecular modification of a commercial polypropylene resin. A peroxide-initiated degradation was performed, resulting in materials with different molecular weight distributions. These resins were subjected to rheological characterization, and an integral constitutive equation of the K-BKZ type was used to study the effect of molecular weight characteristics on their rheological properties. Data for the linear viscoelastic spectrum and shear viscosities was used to obtain the model constants. The same constitutive equation has been used to predict the stress and Trouton ratios for simple shear and simple elongational flows, thus giving a quantitative assessment of the viscoelastic character of the melts. The results show the effect of the molecular modification on the rheological behavior of the melts. Polymers produced at higher peroxide concentrations exhibit reduced viscoelasticity manifested in less shear-and strain-thinning behavior. The present work clearly shows the potential of integral constitutive equations in fitting and interpreting experimental data and, thus, giving a much better understanding of the rheological behavior of commercial polymers. © 1996 John Wiley & Sons, Inc.     

Equibiaxial elongational viscosity measurements of commercial polymer melts

The equibiaxial elongational viscosity of six commercially available polymer melts is measured using a novel technique known as continuous lubricated squeezing flow. This technique is a modification of simple lubricated squeezing flow. The systems were chosen in order to investigate the dependence of equibiaxial elongational viscosity on molecular structure. Three of the melts are polyethylene with long chain branching, two are polyethylene with short chain branching, and one is polyisobutylene with linear chains. Each polymer was subjected to strain rates ranging from 0.003 to 0.1 s^?1 and compared to the linear viscoelastic prediction so that the degree of strain hardening could be determined. For a modestly branched polymer, comparison of rheological behavior in both uniaxial and equibiaxial deformations was possible. POLYM. ENG. SCI., 55:1012–1017, 2015. © 2014 Society of Plastics Engineers     

Elongational viscosity of polymer melts: A lubricated skin-core flow approach

Previous work by this research group has shown that the use of a lubricated skin/core flow of polymer melts and a hyperbolic converging die results in an essentially pure elongational flow at a constant elongational strain rate in the core. The previous work was carried out on a laboratory-scale coextrusion system in a planar slit die; tracer particles and an image analysis system were used to confirm the predicted behavior. In this work, the technique was implemented first on the coextruder assembly, as a planar elongational rheometer, and then on a commercial capillary rheometer, as a uniaxial elongational rheometer for polymer melts. The later is achieved by replacing the standard capillary die with a hyperbolic axisymmetric die. A two-laycred billet is prepared for placement in the rheometer barrel by completely encapsulating the core polymer (the polymer to be analyzed) with a low-viscosity polyethylene skin. Commercial grades of polypropylenes, syndiotactic polystyrene, and nylon-66 were analyzed using this technique. Elongational viscosity at high extensional rates can be determined with this method; values in excess of 500 s⁻¹ have already been achieved. © 1996 John Wiley & Sons, Inc.     

Studies on blown film extrusion. I. Experimental determination of elongational viscosity

Blown-film extrusion experiments were carried out to investigate the elongational flow behavior of viscoelastic polymer melts at different melt temperatures. Materials chosen for study were high-density polyethylene, lowdensity polyethylene, and polypropylene. In the study, isothermal blown-film extrusion experiments were carried out in which the molten blown film traveled upward through a heated chamber of about 13 in. in length maintained at the same temperature as the melt. Axial tension was measured at the take-up roller, the axial profiles of bubble diameter were determined by a photographic technique, and, from the samples collected, the variation in the film thickness along the axial direction was found. These measurements were used later to determine the elongational viscosity, using the force balance equations. It was found, in the experiment, that a careful control of the pressure difference across the thin film permitted one to maintain the bubble diameter constant, and, therefore, depending on the choice of the extrusion conditions, either a uniaxial or biaxial elongational flow was made possible. The experimental results show that, depending on the materials, elongation rate, and melt temperature tested, the elongational viscosity may decrease or increase with elongation rate, and may also stay constant independent of elongation rate. It was observed that the data of elongational viscosity obtained under uniaxial stretching in blown film extrusion is consistent with the data of elongational viscosity obtained earlier by use of the melt-spinning operation.     

Instabilities and failure in elongational flow and melt spinning of fibers

A theoretical and experimental study of instability and failure behavior during melt spinning is presented. From an analysis of system dynamics, draw resonance is shown to be a continuous processing analogue of ductile failure. Using viscoelastic fluid mechanics and the White-Metzner constitutive model, it is shown that melts which exhibit ductile failure in elongational flow tend to show draw resonance in melt spinning. Deformation hardening melts exhibit cohesive fracture in elongational flow and melt-spinning processes.     

Experimental and theoretical investigation of extrudate swell of polymer melts from small (length)/(cross-section) ratio slit and capillary dies

An experimental and theoretical study is presented of extrudate swell from short capillary and slit dies. The polymer melts studied were polystyrene and polypropylene. The swell from slit dies is greater than the swell from capillaries. Decreasing die entry angle for capillary dies decreases swell. The argument is made that elongational How existing in the die entry region and for short dies determines extrudate swell. Dimensional analysis arguments are used to relate extrudate swell to a Weissenberg number based on elongational flow at the die entrance and the detailed die geometry. Correlations are developed. The theoretical study is based on unconstrained elastic recovery following elongational How through the die entrance region.     

An experimental study of the influence of carbon black on the rheological properties of a polystyrene melt

A broad range of experiments on carbon black filled polystyrene melts shows the reinforcing effect of the filler. This study represents one of the most extensive investigations of a series of highly filled polymer melts. Stress relaxation and dynamic experiments characterize the small strain behavior while the steady state shear viscosity, normal stresses, and elongational flow experiments describe the large strain deformation rate response. Extrudate swell and unconstrained shrinkage of extrudates are also measured. Highly filled systems exhibit yield values. This is seen in the dynamic experiments and in the shear and elongational viscosities. Viscosity does not level off at finite values with decreasing deformation rate but continues to increase in an approximately inverse manner. This corresponds to yield values of order 5 × 10⁵ dynes/cm². The storage modulus also does not tend to zero at low frequencies. The small strain dynamic properties and stress relaxation results suggest high memories for small strain experiments. Txtrudate swell values are however small and the systems exhibit minimal delayed recovery. The implications of this are considered. Generally it is argued that at volume loadings between 10 and 20 percent, the system takes on the characteristics of a gel and the response is similar to that of a Schwedoff body.     

Elongational viscosity in the isothermal melt spinning of polypropylene

The elongational viscosity of polypropylene has been investigated by isothermal melt spinning, carried out over a range of experimental conditions. The filament diameter and the elongational force were measured for running filaments and the relationship between elongational viscosity and elongational strain rate reported. The elongational viscosity was observed to decrease in the vicinity of the spinneret and then remained constant before increasing along the thread line. An increase in elongational viscosity did not occur within the isothermal zone until the elongational flow was fully developed. The onset of an increase in elongational viscosity was determined from the constant total elongational strain. The degree of molecular orientation was also studied by birefringence measurements and was investigated as a function of elongational stress. At a high elongational stress, the relation between birefringence and elongational stress departed from linearity and exhibited a rapid increase which can be related to the increase in elongational viscosity.     

Elongational behavior of polyethylene melts—effect of deformation

Transient elongational viscosity of linear low density polyethylene (LLDPE) and two low density polyethylenes (LDPE1 and LDPE2) was measured at one temperature and different deformation rates in constant strain rate elongational rheometer. The elongational viscosity measurements revealed stronger strain hardening characteristics for LDPEs than that observed for LLDPE. The different response to stretching of these polymers is thought to relate to the presence of long chain branches in LDPEs, which affect the elongation viscosity profoundly. The onset of strain hardening for all long chain branched LDPEs as well as for linear LLDPE occurs at the same value of the critical strain, which is independent of temperature or deformation rate. An attempt has been made to explain this phenomenon in terms of the changes that occur in the macromolecular network upon stretching.     

Elongational rheology of polyethylene melts

Effective elongational viscosities were measured for high‐ and low‐density polyethylene samples using a capillary rheometer fitted with semihyperbolic dies. These dies establish a purely elongational flow field at constant elongational strain rate. The effective elongational viscosities were evaluated under the influence of the process strain rate, Hencky strain, and temperature. Enthalpy and entropy changes associated with the orientation development of semihyperbolic‐processed melts were also estimated. The results showed that elongational viscosities were primarily affected by differences in the weight‐average molecular weight rather than in the degree of branching. This effect was process‐strain‐rate‐ as well as temperature‐dependent. An investigation of the melt‐pressure relaxation and the associated first decay time constants revealed that with increasing strain rate the molecular field of the melt asymptotically gained orientation in approaching a limit. As a result of this behavior, molecular uniqueness became much less distinct at high process strain rates, apparently yielding to orientation development and the associated restructuring of the melt's molecular morphology. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 79: 2170–2184, 2001     

Elongational viscosity at a constant elongational strain rate of polypropylene melt

The measurement of elongational viscosity has been carried out with an improved elongational rheometer, sensitive to small elongational forces and measuring simultaneously the diameter of elongating samples. Force distribution was evaluated for various conditions. The method of reduced variables, successful in linear viscoelastic properties, can be applied to the temperature dependence of elongational viscosity only at small elongational strain rate. For large elongational strain rates, the elongational viscosity was found to be non-linear and a new method characterizing non-linearity was proposed. The non-linearity parameter in elongational viscosity was independent of elongational strain rate and almost independent of temperature. Non-linearity in elongational viscosity is discussed in terms of a structural change in the polymer melt.     

Modeling of the transient viscosity for polymer melts after startup of shearing and elongational deformations

In order to describe the transient stress growth for polymer melts, the empirical model proposed by Seo for the viscosity of steady‐state flow is combined with a phenomenological viscoelastic model of a differential type (the White–Metzner model) along the lines proposed by Souvaliotis and Beris. The relaxation time is taken as a function of the invariant of the stress tensor (hence that of the configuration tensor) rather than that of the rate of the deformation tensor. Numerical results show a good correlation with experimental data. The model predictions approach steady‐state values at long times after the startup. The nonlinear form of the model correlates very well with the experimental data over many decades of the deformation rate, both in shearing and elongational deformations. The proposed model is a simple one that can also describe the overshoot in the transient stress growth. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 510–515, 2003     

Elongational behavior of short glass fiber reinforced polypropylene melts

The Rheometrics Elongational Rheometer was employed to study the uniaxial extensional flow of glass fiber filled polypropylene melts, in which the fiber concentration, c, varied between zero and 40 weight percent. The constant strain rate mode was used for strain rates, \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \varepsilon \limits^. $\end{document}, between 0.003 and 0.6 s⁻¹. Steady state elongational viscosities were observed in most cases for fiber filled polypropylene melts, even at rates at which the stress continued to increase for unfilled polypropylene. The rate of relative stress growth increased with \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \varepsilon \limits^. $\end{document} and was affected by the addition of fibers. The steady elongational viscosity of the fiber reinforced melts was found to decrease with increasing \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \varepsilon \limits^. $\end{document} and to increase with increasing c. Yield stresses were observed in elongational flow at high concentrations, although there was no clear evidence of yield in steady shear.     

Study of kinematics and dynamics of film blowing of different polyethylenes

An extensive experimental study of the effects of material characteristics and processing parameters on the kinematics and dynamics of film blowing is presented. Three polyethylene resins, a high-density polyethylene (HDPE), a low-density polyethylene (LDPE), and a linear low-density polyethylene (LLDPE) were investigated. The convergent flow analysis of Cogswell was used to characterize the elongational flow behavior of the polymers. Strain rates and pressure inside the bubble (P_i) have been determined over a wide range of film blowing conditions. Moreover, on-line bubble temperature and birefringence measurements have been carried out along the length of the bubble. The experimental results reveal that the three polymers display different behaviors. The LLDPE requires the highest P_i value and the LDPE, the lowest. Consistent with this, the LLDPE shows the lowest in-plane birefringence and the LDPE, the highest. Interactions between various process parameters affecting the P_i value are characterized. Bubble instability is correlated to the apparent uniaxial elongational viscosity and P_i. The most stable polymer (LDPE) has the highest elongational viscosity and requires the lowest P_i. Stresses have been calculated with the help of the birefringence and P_i data. The stress and strain rate data were used to calculate an apparent nonuniform biaxial elongational viscosity of the melts, but could not be correlated through any simple constitutive equation.     

Orientation development in thermotropic liquid crystal polymers

Thermotropic liquid crystal polymers are a new class of polymeric materials that consist of rigid backbone molecules and thus, even in the quiescent condition, take extended chain conformation to form optically anisotropic melts. A systematic investigation was carried out on how this type of material responds to two basic flow fields: shear and elongation. Rheological properties of the polymer in these flow fields have also been measured. It was found that a high level of molecular orientation was readily obtained by elongational flow but not with shear flow. Specifically, extraordinarily high orientation was obtained when the melt was subjected to small elongational strains, whiel shear strain or shear rate had little effect. A possible mechanism to explain these behaviors is illustrated based on the existing observations or theories of rodlike molecules. This finding was used to interpret the orientation distribution in the extruded and injection-molded articles.