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 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.     

Rheology of 1‐butyl‐3‐methylimidazolium chloride cellulose solutions. III. Elongational rheology

The elongational rheology of solutions of cellulose in the ionic liquid solvent 1‐butyl‐3‐methylimidazolium chloride ([Bmim]Cl) was measured at 80, 90, and 100°C; 8, 10, and 12 wt% cellulose; Hencky strains 5, 6, 7; and strain rates from 1 to 100 s^?1. Master curves were generated by shifting the elongational viscosity curves with respect to temperature and Hencky strain. Also, general master curves were generated by simultaneously shifting with respect to both temperatures and Hencky strain. From the Arrhenius plots of the temperature shift factors, the activation energy for elongational flow was determined. The elongational rheology of these solutions was elongational strain rate thinning similar to that of their shear behavior and polymer melts and they were also strain hardening. Both effects and the viscosity increased with cellulose concentration. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Shear and elongational rheology of polyethylenes with different molecular characteristics. II. Elongational rheology

The elongational viscosities of polyethylenes with different molecular characteristics were measured at different Hencky strains and temperatures with a capillary rheometer by the replacement of the capillary cylindrical die with a hyperbolic converging die. The hyperbolic shape of the die established a purely elongational flow field at a constant elongational strain rate throughout the die. The effects of molecular characteristics such as the molecular weight, molecular weight distribution, and long‐chain branching and processing conditions such as the temperature and Hencky strain on the elongational rheology of the polyethylene samples were studied. Good master curves were generated for temperature and Hencky strain shifting and simultaneous shifting with respect to both the temperature and Hencky strain. Both the molecular weight distribution and long‐chain branching seemed to promote strain rate thinning and reduce the elongational viscosity. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 1184–1194, 2007     

Transient elongational viscosity of LLDPE/LDPE blends and its relevance to bubble stability in the film blowing process

Transient elongational viscosity of linear low density polyethylene (LLDPE) and its blends with 10% and 20% of low density polyethylene (LDPE) was measured at two temperatures by a constant strain rate elongational rheometer. In addition, the performance of the blends in the film blowing process was assessed in terms of bubble stability at two processing temperatures. An operating window for stable bubble production was determined. The elongational viscosity measurements on blends revealed stronger strain hardening characteristics at a higher temperature of testing. These results correlate favorably with findings from a bubble stability investigation where it was found that the size of the operating window for stable bubble production increased with increasing extrusion temperature. This work seems to indicate that increasing processing temperature during the film blowing of LLDPE-rich blends could lead to a processability improvement of these blends as far as bubble stability is concerned.     

Measurement of the equibiaxial elongational viscosity of polystyrene using lubricated squeezing

The equibiaxial elongational viscosity of polystyrene was determined using a lubricated squeezing technique. Constant strain rates up to Hencky strains of 4.5 could be maintained by a newly constructed instrument. Test results from controlled stress and controlled strain rate measurement were consistent and yielded well-defined steady-state viscosities. Measurements appeared to be unaffected by sample geometry, although proper lubrication is important in achieving steady state. The measured biaxial viscosity appeared to be strain rate thinning above a biaxial strain rate of ≈ 0.01 s⁻¹ at 160°C. As anticipated in the Newtonian region, biaxial elongational viscosity was approximately six times the shear viscosity. Thinning indices of both shear and biaxial elongational viscosities were 0.75. Data obtained at various temperatures were shifted following the timetemperature superposition principle. The resulting master curve could be fitted by a Carreau model with n ≈ 0.3 and a time constant of 110 s.     

Rheological effects of polyethylenes in film blowing

The aim of this work is to correlate the rheological properties and processability of various polyethylenes during the film‐blowing process. The effect of rheology on the kinematics and dynamics of film blowing for five different polyethylene resins has been extensively studied using a fully instrumented laboratory unit. The complex viscosity, shear viscosity, uniaxial elongational viscosity, and non‐uniform biaxial elongational viscosity, as well as the strain rates and stresses during film blowing, have been determined and correlated to the bubble stability. G′ versus G″ plots were found to be virtually independent of temperature for all polymers investigated. The more elastic polymers (larger G′ values) were found to be more stable in film blowing. Also, the more stable polymer melts were found to be those possessing larger elongational properties.     

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.     

Hencky strain shifting of convergent flow measured effective elongational viscosity

The effective elongational viscosity data on a series of polyolefins as a function of the Hencky strain are shifted to a reference Hencky strain using an approach similar to that used for temperature shifting, shearing viscosity data. The basis of this shifting is the order that develops (i.e., the decrease in entropy that occurs) during forced flow through semihyperbolically convergent dies. The entropy decrease is proportional to the orientational contribution to the effective elongational viscosity. The Hencky strain shift factors are obtained from the convergent flow effective elongational rheology and the complex and capillary shear rheology. The commercial grades of polyolefins studied include polypropylene, high density polyethylene, and metallocene and conventionally catalyzed low density polyethylene. The combination of the temperature shift factors given in our companion article and the Hencky strain shift factors in this article enable the creation of master curves for the effective elongational rheology. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 1397–1404, 2003     

Elongational behavior of epoxy during curing

Elongational behavior of epoxy (epoxy/curing agent = 100/0.5, w/w) cured at various conditions over the critical gelation time was investigated. Dynamic viscoelastic measurements of the epoxy system were performed and the critical gelation time of epoxy was determined according to the frequency dependence of G′ and G″ proposed by Winter and Chambon. Elongational behavior of epoxy cured for various times were measured. Epoxy, cured over the critical gelation time, showed strain hardening and elongational behavior similar to a crosslinked rubber. Increase of elongational viscosity of the sample occurred early, and the sample broke at small strain as curing time increased. The effect of strain rate on the elongational stress of epoxy cured near the critical gelation time was measured at various strain rates. For epoxy cured for critical gelation time only, high stress at a small strain rate was represented as strain rate increased. When increasing curing time further, the tensile stress converged on a single curve regardless of strain rate, and samples broke at nearly the same stress and strain. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Determination of steady-state elongational viscosity for rubber compounds using bell-mouthed dies

A bell-mouthed die geometry was designed to cause convergent flow at a constant, uniform, elongational strain rate. An equation was derived, which showed that steady-state elongational viscosity could be calculated from a plot of pressure drop due to elongation against a simple function of die length. To obtain values of pressure drop due to elongation, it was necessary to correct the total pressure drop measured across the bell-mouthed dies for the contribution from shear occurring near the die wall. For this purpose, a simplified shape for the bell-mouthed dies was assumed, comprising several parallel sided segments. Applying a formula to pressure drop data measured across straight dies corresponding to these segments gave an estimate of the pressure drop due to shear across the bell-mouthed dies. Pressure drops due to elongation were determined by subtracting the pressure drop due to shear from the total pressure drop measured across the bell-mouthed dies. Measurements were also carried out with lubrication to validate the shear correction method. The results indicate that for the compound used in this study, a combination of bell-mouthed and straightsided dies can be used in a conventional capillary rheometer to determine steady-state elongational viscosity. An elongational viscosity of 190 kPa s at 90°C and at a strain rate of 10 s⁻¹ was determined for a simple styrene-butadiene rubber compound. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 66: 1139–1150, 1997     

聚合物加工流变学研究新动向

简要介绍了聚合物加工过程中伸长粘度与吹塑成型的关系、伸长流动非线性度与聚合物结构的关系,聚苯乙烯共混物,长玻璃纤维增强聚丙烯和热塑性淀粉的流变行为以及两种新型的流变测定仪。     

An analysis of unsteady one-dimensional stretching of a viscoelastic fluid

The time-dependent response of a viscoelastic liquid to unsteady one-dimensional stretching deformations was examined. Oldroyd's three-constant model for a viscoelastic fluid was used. Two cases representing two different stretching histories were analyzed: a sine stretching pulse and a step stretching pulse. The results show that high elongational viscosity may be easily reached in both cases. As the relaxation time of the liquid becomes comparable to the pulse width, elongational viscosity increases with the increase in maximum stretching rates. Conditions to maintain high levels of elongational viscosity at a subsequently reduced stretching rate were given as functions of the relaxation time and initial stretching rates. In view of recent turbulent boundary layer data, the results were used to discuss possible explanations of turbulent drag reduction in polymer solutions. It was concluded that the basic mechanisms for drag reduction in polymer soluations. It was concluded that the basic mechanisms for drag reducation may be related to the effects of high elongational viscosity and local stabilization of small shear disturbances.     

Effect of elongational viscosity on axisymmetric entrance flow of polymers

A finite element simulation of the flow in a channel with an abrupt contraction is presented. The effects of the shear and elongational viscosities of a polymer on the entrance flow are analyzed employing a truncated power‐law model. The power‐law index and the strain rate characterizing the transition from Newtonian to power‐law behavior for the elongational viscosity are treated as being independent of the values of these two parameters for the shear viscosity. The effect of flow rate on entrance flow is also analyzed. It is confirmed that the Trouton ratio is important in determining the recirculating vortex and the extra pressure loss in entrance flow. Extra pressure loss and vortex length predicted by a finite element simulation of entrance loss are compared with the corresponding predictions from Binding's approximate analysis.     

New extensional rheometer for elongational viscosity and flow birefringence measurements: some results on polystyrene melts

A new extensional rheometer allowing the simultaneous measurement of elongational viscosity and flow birefringence is described. Polystyrene melts have been tested at different temperatures and strain rates. It appears that the time-temperature superposition principle holds for elongational tests in the temperature range investigated, with the same shift factors as for linear shear experiments. It has been verified that the stress optical behaviour of the melts is linear for small values of the stress whereas significant deviations appear at higher stresses.     

纤维素溶液吹膜过程中拉伸黏度的测定

通过非等温吹塑薄膜挤出实验研究了纤维素的NMMO(N-甲基吗啉-N-氧化物，亦称N-甲基氧化吗啉)溶液在不同工艺条件下的拉伸流动行为。讨论和推导了挤出过程中的理论数学模型，测定了纤维素溶液在加工过程中膜泡半径和膜厚随加工方向的变化，并对沿加工方向上拉伸速率和表观拉伸黏度的变化进行了探讨。研究表明：质量份数为9％的纤维素溶液在加工过程中拉伸黏度受拉伸速率与温度的综合影响，沿加工方向呈现先微降，再渐升的趋势；在加工过程中随着牵引速度和膜泡内外压力差(△P)的增大，膜泡的厚度变小，拉伸速率变大，拉伸黏度变小。     

Radial temperature differences during the melt spinning of fibers

In this investigation, a numerical model was developed to predict the temperature distribution in a fiber during melt spinning. This model uses the implicit Crank–Nicolson method to solve the governing differential equation for the problem. The model was applied to a series of numerical experiments on a liquid crystalline fiber which is melt-spun. These simulations used typical sets of operating conditions to determine the effect of various operating parameters on the predicted radius profile, spinline tension, and temperature distribution. The effects of spinneret capillary diameter, mass flow rate, ambient air temperature, spinning temperature, and elongational viscosity were investigated. The results of the various runs showed that ambient air temperature and mass flow rate had a significant effect on the predicted radius profile, spinline tension, and temperature distribution. The spinning temperature was an important parameter, but its only significant effect was on the spinline tension. Spinneret capillary diameter and elongational viscosity had little effect on the predicted results.     

Elongational flow properties of low-density polyethylene and linear low-density polyethylene from nonisothermal melt spinning experiments

Low-density polyethylene (LDPE) and also linear low-density polyethylene (LLDPE) resins can be characterized by the degree of strain hardening and down-gaging during elongation. A new method for the determination of the apparent elongational flow characteristics is presented. In a small scale apparatus, a molten monofilament is stretched under nonisothermal conditions similar to those found in tubular film extrusion. Measurement of resistance to elongational flow and apparent elongational strain rates permit the comparison of the process-ability of different resins under specified conditions. The effect of melt temperature and extension ratio are examined. The importance of the molecular structure of both LDPE and LLDPE resins on these properties is also outlined.     

Shear and extensional flow of a thermotropic liquid crystalline polymer

The flow of a thermotropic liquid crystalline polymer (unfilled and glass fiber filled) was studied using a capillary rheometer and an instrumented injection molding machine. Despite different thermal histories, the techniques gave similar results. From 330 to 350°C, viscosity was independent of temperature. At 340°C, where most measurements were carried out, pronounced shear-thinning occurred and the shear flow curves were nonlinear, the power law exponent decreasing from 0.51 at a shear rate of 10 s⁻¹ to 0.35 at 10⁴ s⁻¹. A previously reported model was used to derive elongational flow curves from die entry pressure data. Because of the nonlinearity of the flow curves, quadratic log-stress vs. log-strain rate plots were needed to model behavior over the strain rate region studied. The elongational flow curves were similar in shape to the shear flow curves, with an effective Trouton ratio of 30. Despite orientation and structure present in the melt, the extensional viscosities and Trouton ratios were within the range found with normal thermoplastic melts. The results suggest that extensional flow may be inhomogeneous, the flowing units possibly being partially ordered domains.     

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