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 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.     

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.     

Interrelationship of strength and flow characteristics of polystyrene

This study investigated the interrelationship between strength and flow characteristics of general-purpose polystyrene (GPPS) used in injection molding applications. The ease of flow was chosen as a measure of processability and was evaluated using the melt flow rate and capillary rheometer techniques. Of the different strength tests that were examined, flexural and notched tensile strength tests were most effective in differentiating between commercial grades of high and low molecular weight GPPS. While characterizing strength of injection molded specimens, the degree of molecular orientation was taken into consideration. For unplasticized resins, increasing the weight average molecular weight by about 100,000 enhanced the flexural strength by 10%, but also increased the viscosity at low shear rates (10 to 100 s^?1). The increase in molecular weight had virtually no effect on viscosity at the highest shear rates (up to 10,000 s^?1). Plasticized resins displayed a 6% loss in flexural strength as well as a significant reduction in viscosity (throughout the shear rate range) as compared with the unplasticized resins. As expected, the improvement in strength achieved by increasing molecular weight leads to a simultaneous increase in the viscosity, i.e., a deterioration of processability. In addition, our study indicates that for samples without preferential molecular orientation, narrowing the molecular weight distribution significantly improves the balance of strength and melt flow rate properties.     

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.     

Effects of ABS rubber particles on rheology,melt failure,and thermoforming

The rubber particles included in rubber modified polymeric materials such as acrylonitrile‐butadiene‐styrene (ABS) polymer and impact modified polymers play an important role in determining their rheological properties, processing behavior, and mechanical properties. In this study both small strain oscillatory shear viscosity in the frequency range from 10^?2 to 10² s^?1 and uniaxial elongational viscosity behavior at two elongation rates ( = 0.1 and 1.0 s^?1) over the range of temperatures from 140°C to 200°C were measured for commercial ABS polymers with different contents and deformability of rubber particles. The influences of rubber content and deformability on rheological properties such as melt elasticity, elongational viscosity, strain hardening and/or softening, the onset of nonuniform deformation, and thermoforming performance were investigated. The Wagner two‐parameter nonlinear viscoelastic constitutive model was used to describe strain hardening behavior, while the Considère criterion was used to determine the onset point of nonuniform deformation. The part thickness distribution obtained through use of a vacuum snap‐back forming process was simulated to investigate the effects of rheological changes associated with different rubber particles on the thermoforming performance. It was found that ABS polymers with larger contents of hard rubber particles exhibited more melt elasticity, stronger strain hardening, a maximum of biaxial elongational viscosity, onset of nonuniform deformation at later time, and better thermoforming performance. Strain hardening and the Considère criterion provide simple, reliable indicators of the thermoforming performance of ABS polymers.     

Rheology of polymer melts in high shear rate

Little is known of the rheology of polymer melts in the high shear rate up to 10⁶ s^?1 or more. A specially designed high-shear-rate rheometer was developed, by which the rheology of polymer melts for shear rates up to 10⁸ s^?1 can be investigated. Two non-Newtonian regions and a transition or the second Newtonian region were observed in the wide range of shear rates up to 10⁷ s^?1. The observed flow curves for various polymer melts are classified into three typical patterns. One is the flow curve typically shown of high-density polyethylene in which a clear second Newtonian region appears after the first non-Newtonian region. The second is the typical flow curve of polystyrene in which a “transition region” appears instead of the second non-Newtonian region. The third is the flow curve shown of acrylonitrile-styrene copolymer, which exhibits behavior between the two types. A generalized flow curve is proposed to explain the observed flow behaviors of various polymers over a wide range of shear rates. The flow behavior in high shear rate results from high orientation and scission of polymer molecules.     

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     

Eine rheo-optische Apparatur für die Durchführung homogener,einfacher Dehnungen an Polymerschmelzen mit simultaner Aufzeichnung der Deformation,der mechanischen Spannung und der Doppelbrechung

The present paper describes a rheo-optical apparatus consisting of an elongational rheometer (with rotary clamps) and a device to measure birefringence. This equipment was designed to perform homogeneous deformations on polymer melts in the simple elongational mode. Elongational experiments were performed on polyisobutylene samples at room temperature using different strain rates (from \documentclass{article}\pagestyle{empty}\begin{document}$\dot \varepsilon$\end{document} 0.01 s^?1 to 1 s^?1). In typical experiments homogeneous elongations up to λ ≈ 200 and stresses up to 2 · 10⁶ Pa were achieved. The stress, the birefringence, and the deformation were obtained by measuring the force, the sample thickness, the optical retardation (the frequency of the sampling was 20 Hz) and the width of the sample (the frequency of the sampling was 3 Hz). It was found that the stress-optical coefficient was constant. The homogeneity of the deformations was carefully controlled because inhomogeneities cause serious errors in the measurements of elongational viscosity and birefringence.     

Response of an HMX based explosive to dynamic loading by the Hopkinson split bar technique

The dynamic compression and localized adiabatic shear in samples of an HMX based explosive was studied using the split Hopkinson bar technique. Dynamic compression tests were performed at strain rates of (0.3–2.0) · 10³ s^?1. Fracture of the explosive samples was found to occur at stresses of 60–80 MPa. The behavior of HMX based samples was also studied in localized shear tests at different strain rates (200–2500 s^?1). The initiation of explosive transformations under the dynamic loads is discussed.     

Assessment of development and relaxation of orientation in a sheared thermotropic liquid crystalline copolyester

Shear-induced chain orientation and relaxation of chain orientation in a thermotropic liquid-crystalline poly(4-hydroxybenzoic acid (73mol%)-co-2-hydroxy-6-naphthoic acid (27 mol%)) (Vectra A950) were studied by means of transmitted light intensity through crossed polarizers in a shear cell. Shear rates ranged between 4 and 1000 s^?1 and the level of chain orientation increased with increasing shear rate and increasing temperature. Overall, the times for relaxation were very short. The longest relaxation times (?21s) were obtained at the lowest shear temperatures and at intermediate shear rates. At high shear rates, the relaxation times were generally short (?2s) and independent of temperature. The rapid relaxation of orientation after high rate shearing (100–1000 s^?1) indicates that shear-induced crystallization is inhibited under these conditions. A certain degree of chain orientation was still present although the relaxation as judged by the transmitted light intensity was complete. Signs of recrystallization were observed if the samples were not preheated to 320°C prior to shearing. By simultanecous shearing and cooling, high degrees of orientation were achieved (f ? 0.7) as revealed by X-ray diffraction and infrared dichroism. Infrared spectroscopy showed that annealing of oriented samples at 250°C led to an increase in thermal stability of the orientation with annealing time.     

Elongational flow field as a tool for investigating helix–coil transition: Observation of helix–coil transition in poly(L-glutamic acid) induced by pH change

Elongational flow technique has been used to investigate helix–coil transition of poly(L -glutamic acid) (PGA) induced by pH change. The elongational flow field was generated by a four-roller mill apparatus of the type originally used by G. I. Taylor¹⁶. The flow-induced nonlocalized birefringence was observed all over the pH range measured. The birefringence, Δn₁₇₆, at a fixed strain rate ε = 176 s^?1 decreases rapidly within a narrow pH range with increasing pH. The Δn₁₇₆ value is considered to contain information about both helix content, θ, of the system and the degree of orientation of polymers in the elongational flow field. From the Δn₁₇₆ value, using rotational diffusion coefficient, D_r, the helix content, θ, was estimated at each iso-pH measurement. pH dependence of θ was obtained and was found to correspond well to those determined by optical rotary dispersion (ORD) studies. Even in a hinged-rod conformation, the PGA molecule is expected to be in an extended structure. On the basis of the hydrodynamic considerations about the molecular conformation, it is concluded that the elongational flow technique is useful to investigate conformational transitions of biopolymers. © 1995 John Wiley & Sons, Inc.     

Rheological behavior of molten epoxide prepolymers

Flow properties of four molten epoxide prepolymers of number average molecular weight 900(I), 1,500(II), 2,100(III) and 4,000(IV), were measured at temperatures ranging from 361 to 463K, and shear rates from 500 to 10,000 s^?1. Apparent shear viscosities showed that all prepolymers used have Newtonian behavior up to shear rates of 2,000 s^?1. Shear thinning occurs at higher shear rates. Flow activation energies at constant shear rates in the range of 500 to 7,000 s^?1 vary for prepolymer III from 5 to 24 kcal/mol, and for prepolymer IV from 9 to 25 kcal/mol. Flow indices in the same shear rate range vary for prepolymer III from 1.0 to 0.7 and for prepolymer IV from 1.0 to 0.3.     

A correlation of Young's modulus with yield stress in oriented poly(vinyl chloride)

The variations of tensile and compressive yield stresses and of Young's modulus of oriented poly(vinyl chloride) sheet with direction and with degree of orientation, represented by birefringence, are shown. Young's modulus was calculated from elastic stiffness constants measured by an ultrasonic pulse method at 5MHz with estimated strain and strain rate amplitudes of 2 × 10^?5 and 100s^?1. Yield strains were about 5 × 10^?2 measured at strain rates of about 2 × 10^?2s^?1. Although the measuring conditions were so different there was found to be a close correlation between tensile yield stress and Young's modulus, the two quantities being connected by a simple linear relationship, as direction of measurement and degree of orientation were varied. Compressive yield stress did not correlate with Young's modulus, and changed little with direction or degree of orientation by comparison with tensile yield stress. The empirical linear relationship between tensile yield stress and Young's modulus, difficult to account for theoretically, might form the basis of a method for determining tensile yield stress ultrasonically.     

Irregularities in steady flow for non-newtonian fluids between cone and plate

Flow irregularities have been visually observed in solutions of polyacrylamide of high molecular weight on shear in a cone-and-plate rheometry (gap angle 2.3°). This anomalous flow was found to depend on molecular weight, concentration, and solvent. The onset of flow irregularities were generally at shear rates < 5 sec^?1. A dimensional analysis shows that the elastic component of the fluid is responsible for the anomalous flow. The onset of flow irregularities has been predicted from measurements of recoverable strain as a function of shear stress.     

High shear strain rate rheometry of polymer melts

The rheology of a range of polymer melts has been measured at strain rates above those attained during conventional rheometry using an instrumented injection molding machine. Deviations from shear thinning behavior were observed at high rates, and previously unreported shear thickening behavior occurred for some of the polymers examined. Measured pressure and volumetric throughputs were used to calculate shear and extensional viscosity at wall shear strain rates up to 10⁷ s^?1. Parallel plate rheometry and twin bore capillary rheometry were used to provide comparative rheological data at low and medium shear strain rates, respectively. Commercial grades of polyethylene, polypropylene, polystyrene, and PMMA were studied. Measured shear viscosity was found to follow Newtonian behavior at low rates and shear thinning power law behavior at intermediate strain rates. At shear strain rates approaching or above 10⁶ s^?1, shear viscosity reached a rate‐independent plateau, and in some cases shear thickened with further increase in strain rate. A relationship between the measured high strain rate rheological behavior and molecular structure was noted, with polymers containing larger side groups reaching the rate‐independent plateau at lower strain rates than those with simpler structures. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Extensional flow of mica-filled polyethylene

Extensional flow of mica-filled high density polyethylene was studied at 150°C in a Rheometrics elongational rheometer. The constant strain-rate mode at a rate of 10⁻³ to 1.0 s⁻¹, and the constant stress mode were used. The mica content was 0, 25, 40, and 60 weight percent. In both testing modes, the steady state elongational viscosities were obtained; those for the filled samples were about ten to twenty times larger than the shear viscosity at corresponding (low) rates of deformation.     

The effect of strain rate on the toughening mechanisms of rubber-modified plastics

The impact modification mechanisms of polycarbonate (PC) blended with polyethylene (PE) and blends of polyxylenol ether (PXE)/high impact polystyrene (HIPS), were studied using a volume dilation technique. With two extensometers, measurements of volume change during tensile deformation were made on the plastics. Strain rates of 2 × 10^?5 s^?1 to 4 s^?1 were achieved with a MTS servo-hydraulic testing machine. Analysis of both systems were supported with scanning and transmission electron microscopy. Results on the PC/PE system indicate that the impact modification mechanism is one of voiding and shear banding. The mechanism appeared to be rate sensitive: the amount of voiding increased with rate. The toughening mechanism in the PXE/HIPS blends is identified as a combination of crazing and shear banding. The amount of shear banding that occurs is proportional to the amount of PXE in the blends. The point of craze initiation was found to be delayed by increasing strain rate. The stress for craze initiation appears to be greater than for shear banding.     

Rheological properties of poly(trimethylene terephthalate) in capillary flow

The shear viscosity, extensional viscosity, and die swell of the PTT melt were investigated using a capillary rheometer. The results showed that the PTT melt was a typical pseudoplastic fluid exhibiting shear thinning and extensional thinning phenomena in capillary flow. There existed no melt fracture phenomenon in the PTT melt through a capillary die even though the shear rate was 20,000 s^?1. Increasing the shear rate would decrease the flow activation energy and decline the sensitivity of the shear viscosity to the melt temperature. The molecular weight had a significant influence on the flow curve. The flow behavior of the PTT melt approached that of Newtonian fluid even though the weight‐molecular weight was below 43,000 s^?1 at 260°C. The extensional viscosity decreased with the increase of the extensional stress, which became more obvious with increasing the molecular weight. The sensitiveness of the extensional viscosity to the melt temperature decreased promptly along with increasing the extensional strain rate. The die swell ratio and end effect would increase along with increasing the shear rate and with decreasing the temperature, which represented that the increase of the shear rate and the decrease of temperature would increase the extruding elasticity of the PTT melt in the capillary die. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 705–709, 2005     

Photon-correlation velocimetry of polystyrene solutions in extensional flow fields

A cross slot device has been used to produce elongational flow fields in dilute solutions of narrow fractions of high molecular weight ($\text{M}\text{?}{}_{\mathrm{w}}$ between 2.8 × 10⁶ and 2 × 10⁷) atactic polystyrene. Strainrates obtainable were sufficient to extend individual molecules. Photon-correlation microvelocimetry has been used to measure velocity profiles in a channel of the cross slot as a function of distance from the centre of the cross, polymer concentration and flow rate. It has been found that in solutions of concentration about or greater than $\text{c1}$ and at flow rates sufficient to extend the polymer molecules a minimum in velocity is observed at the centre of the channel. This minimum sets in at flow rates around that at which extension of the polymer molecules is first observed through birefringence observations, but the depth of the minimum decreases rapidly with decreasing polymer concentration below $\text{c1}$. The velocity profile evolves into the usual parabolic profile away from the region of elongational flow. At higher strain rates a birefringence in the solution near the channel walls was also observed and preliminary measurements indicate that two symmetrical minima or shoulders in the velocity profile may be associated with this observation.