Prediction of melt viscosity flow curves at various temperatures for some olefin polymers and copolymers

A knowledge of the variation of melt viscosity of thermoplastic polymers with both shear rate and temperature is of considerable importance to plastics engineers as well as to polymer rheologists. The actual measurement of melt viscosity at a large number of temperatures and shear rates is frequently a tedious and time-consuming task. A technique has been developed, based upon the applicability of shear rate-temperature superposition, for predicting the flow curves of a number of olefin polymers and copolymers at various temperatures from experimental data obtained at one temperature for the material in question. The experimental validity for superimposing log shear stress—log shear rate curves at different temperatures along the log shear rate axis has been established for both high and low density polyethylenes, polypropylene, polybutene-1, and poly (ethylene vinyl acetate) copolymers. The temperature dependence of the resultant shift factors has been determined for each system, and the method of utilizing this information to predict viscosities as a function of temperature and shear rate is discussed.     

Melt viscosity behavior of some engineering thermoplastics

Frequently, the enhanced elevated-temperature rigidity of engineering thermoplastics (ETPs) is a consequence of high glass-transition temperature, and many ETPs contain aromatic ring structures in the backbone chain. These factors can lead to difficulty in melt processing, or fabrication, of parts. Thus, the definition of the melt rheology of such systems is of considerable technological, as well as scientific importance. The investigation reported here first defines the viscosity-temperature dependence of five ETPs over a relatively narrow range of temperatures appropriate to melt processing in terms of superposition methodology. The five ETPs studied were bisphenol A polycarbonate, polysulfone, the condensation polymer of bisphenol A and mixed iso- and terephthalic acids, and two experimental condensation polymers: bisphenol A/isophthalic acid and 1,2 bis(4,4′-hydroxy phenyl) ethane/isophthalic acid. Viscous flow energies of activation are examined in terms of polymer chain structure. In the second portion of the investigation it is shown that, for the latter two condensation polymers, the molecular weight, temperature, and shear rate dependence of the viscosity may be expressed in terms of a modified Carreau model. The Newtonian limiting low-shear viscosity dependence on molecular weight and that of the shear rate shift factor (relaxation time) are found to be somewhat greater than that normally observed.     

PVC melt rheology III: The effect of order and molecular weight on the shear rate dependence

The effect of polymerization temperature on the melt flow behavior of PVC of varying molecular weights has been studied over a wide shear rate range. For the same molecular weight, higher melt viscosities are observed for polymers prepared at lower temperatures. The shear rate dependence of the viscosity vs molecular weight plot is shown to be nonlinear over the shear rates examined. The inability to achieve a limiting zero-shear viscosity is discussed.     

An empirical model for the melt viscosity of polymer blends

Summary On the basis of experimental data for blends of polyethylene with different polymers an empirical equation is proposed to describe the dependence of melt viscosity of blends on component viscosities and composition. The model ensures the continuity of viscosity vs. composition curves throughout the whole composition range, the possibility of obtaining extremum values higher or lower than the viscosities of components, allows the calculation of flow curves of blends from the flow curves of components and their volume fractions.     

The influence of molecular weight on the melt rheology of polypropylene

Melt viscosity and melt elasticity data were obtained over a broad range of temperatures and shear rates on a series of four polypropylenes of different molecular weight but approximately the same molecular weight distribution. The superposition technique was used with both temperature and molecular weight to shift flow curves for all four materials at three temperatures each along the shear rate axis to generate a master flow curve at a given temperature and molecular weight. For polypropylenes of this type, and molecular weight distribution shift, factors which can be used to extend the useful range of experimentally obtained flow data were determined. The dependency of apparent viscosity on weight average molecular weight at shear stresses as high as 10⁶ dynes/cm² is shown. The dependency of melt elasticity on molecular weight and temperature is discussed.     

Die wirkungsweise der viskositätsindex-verbesserer

One of the major reasons for using polymeric additives is to obtain a product which has better viscosity-temperature characteristics than a comparable pure mineral oil. Extensive measurements of the viscosity-temperature behaviour of motor oils with and without polymer addition show the necessity of a revision of the generally accepted concept of the mechanism of viscosity index improvement. By addition of polymer the better viscosity-temperature characteristics of light oils, which are however of very limited value for lubrication of engines because of their low viscosity at high temperatures, can be maintained partially in the range of higher viscosities. So it becomes obvious how it is possible to produce multigrade oils both from polymers the polymer coil dimensions of which expand, as well as from polymers, the polymer coils of which contract with increasing temperature. In fact, coil expansion promotes viscosity index improvement to some extent but in no way does this effect play a decisive part.     

Rheological and thermodynamic interaction effects in plasticized polyvinyl chloride compounds

Earlier work reported the superposition of flow curves for plasticized compounds of vinyl chloride homopolymer with corresponding curves for unplasticized resin. Viscosity shift factors for three plasticizer systems plotted against temperature define an apparent fusion temperature for the bulk polymer. A Brabender Plasticorder, used as a temperature-scanning rheometer, determined fusion temperatures for various plasticized PVC compounds. These data confirm a fusion temperature for bulk polymer near 205°C, and permit calculation of Flory-Huggins χ parameters over substantial ranges of composition and temperature. The thermodynamic parameter correlates well with viscosity shift factors for compounds with polymer volume fractions below 0.6. The possibility is therefore raised of calculating flow characteristics for plasticized PVC compounds from knowledge of χ only. The temperature and composition dependence of χ, estimated for the system PVC-diiso-octyl phthalate, is similar to reported variations in simpler polymer-diluent systems. Thus, PVC-plasticizer systems may follow analogous thermodynamic rules.     

Estimation of melt film variables during the steady‐state penetration phase of thermoplastic vibration welding using a generalized newtonian fluid model

The thickness of the melt film and the temperature profiles within the melt film in the weld zone are key process variables governing the development of weld‐zone microstructures and the resulting development of weld strengths, during vibration welding of thermoplastics. The mathematical model described in this report is aimed at investigating the role of the rheology of the melt—specifically the magnitude and shear‐rate as well as temperature dependence of the melt viscosity—in governing the process variables such as the molten film thickness and the viscosities, stresses, and the temperatures within the melt film during vibration welding. The analysis is focused on the steady‐state penetration phase (phase III) of vibration welding. The coupled steady‐state momentum balance and heat transfer within the melt film, formulated using the Cross‐WLF (Williams‐Landel‐Ferry) relationship for viscosity, are solved in an iterative finite element framework. The model has been implemented for two different polymers displaying significant differences in viscosities and shear thinning behaviors. An attempt has been made to correlate the trends in the estimated melt film variables with the experimentally measured weld quality. POLYM. ENG. SCI., 2012. © 2011 Society of Plastics Engineers     

Rheological study of quaternary ammonium-containing star-shaped polylactic acid

Quaternary ammonium-containing star-shaped polylactic acid (PLA-Q) is analyzed in melt rheology and found to follow a clustering behavior. The viscosity of this polymer is largely higher than its analog, of the same structure, without ammonium ions. This difference is attributed to physical interactions taking place between the ammoniums and hindering the flow of the melt polymer. The frequency sweeps of the storage (G′) and loss (G′′) modulus of the melt PLA-Q are achieved at different temperatures and different shearing times. The iso-temperature and iso-time superposition of the resulting curves were achieved using, respectively, a temperature and a time shift factors, this superposition allowed the determination of the flow activation energy; its value corresponds to an ionic process confirming the ionic interactions. When the two shift factors are used simultaneously, a unique master curve of both G′ and G′′ is obtained; this curve follows the Rouse model indicating the presence of two types of ionic associations within the melt polymer: a large number of multiplets having small size and a small number of clusters of larger size. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2020 , 137, 48337.     

Effects of strain rate and temperature upon tensile properties of acetal copolymers

The strength and elongation to break of an acetal copolymer were measured at four elongation rates, from 0.2 to 20 in./min, at temperatures from 239 K to 339 K. Both strength and elongation results could be reduced to master curves by means of time-temperature superposition. The temperature dependence of the shift factors was given by an equation of the WLF form, with parameters close to those found for most amorphous polymers, at a reference temperature equal to the γ-transition temperature of the polymer. Extrapolation to much higher testing rates and to much slower creep rates was satisfactory. Similar but less extensive tests were run on two other samples with different molecular weights. The yield stress was independent of molecular weight, but elongation increased with increasing molecular weight at all conditions.     

Rheograms of cellulosic polymers from the melt flow index

Data on the variation of melt viscosity over a wide range of shear rates and temperatures are necessary in the processing of cellulosic polymers. An effective method has been proposed to estimate the viscosity vs. shear rate flow curves of a cellulosic resin at temperatures relevant to the processing conditions, from its melt flow index and glass transition temperature. The method involves the use of a master curve obtained by coalescing the rheograms of various grades in terms of a modified viscosity, η˙MFI, and a modified shear rate, γ˙/MFI. Master curves have been reported for cellulose esters and ethers.     

Melt rheology of poly(lactic acid): Consequences of blending chain architectures

The rheology of blends of linear and branched poly(lactic acid) (PLA) architectures is comprehensively investigated. Measurement of the melt rheological properties of PLA is complicated by degradation effects but the addition of 0.35 wt% tris(nonylphenyl) phosphite (TNPP) provides excellent stabilization over a range of temperatures. Master curves of dynamic viscosity constructed using time‐temperature superposition show significant dispersion for unstabilized samples; this behavior is accompanied by a loss of molecular weight. TNPP stabilized samples show excellent superposition throughout the entire frequency range and minimal loss in molecular weight. For the linear architecture, the Cox‐Merz rule is valid for a large range of shear rates and frequencies. The branched architecture deviates from the Cox‐Merz equality and blends show intermediate behavior. Both the zero shear viscosity and the elasticity (as measured by the recoverable shear compliance) Increase with increasing branched content. The viscosities of both the unstabilized samples and the TNPP stabilized samples roughly obey a log additivity mixing rule. The recoverable shear compliance is monotonic in blend composition and a mixing rule for this property is also presented. For the linear chain, the compliance is independent of temperature but this behavior is apparently lost for the branched and blended materials. Tensile and thermal properties of the blends are also measured and found to be roughly equal within the statistical error of the experiments. The results suggest that excellent control over rheological behavior of PLA is possible through blending chain architectures without compromising mechanical properties.     

A theoretical analysis of non-isothermal flow in wire-coating co-extrusion dies

A theoretical study of non-isothermal superimposed flow of two polymer melts in wire coating co-extrusion dies has been carried out. Numerical methods have been employed to solve the coupled momentum- and energy-balance equations. Various combinations of three polymers—namely, high density polyethylene (HDPE), polystyrene (PS) and low density polyethylene (LDPE) have been studied and least squares curve fitted quadratic polynomials have been used for constitutive equations for all three polymers in non-Newtonian high shear rate regions. A multitude of thermal and mechanical boundary conditions can be treated by this algorithm. It was found that temperature and velocity profiles in the die depend significantly on the arrangement of the polymers. Maximum temperature rise has been noted to increase sharply with wire velocity but it can be reduced by increasing the die radius. When the thickness of the outer layer is increased from zero, the shear stress at the wall undergoes a dramatic change (if the viscosities of the polymers are different) at small values of the flow rate ratio and it reaches an asymptotic value at large values of flow rate ratio. It was also found that viscosity ratio at the interface can be reduced by changing the initial temperatures of the liquids. It was observed in some cases that large errors in the calculation of rheological and thermal variables for this problem can be made if temperature rise due to viscous dissipation is not considered.     

The effect of viscous heating on the observed temperature dependence of mechanochemical reactions

The temperature dependence of mechanochemical reactions of high polymers is investigated in light of viscous dissipation in the flow field. The viscosity of the polymer melt is assumed to depend exponentially upon temperature, and the power-law model is used to describe the shear stress–shear rate relationship. Using equations previously reported in in the literature for the temperature profile generated in capillary flow, evidence that such an experimental system operates under decidedly nonisothermal conditions is presented. These equations, together with the classical Arrhenius equation for the temperature dependence of chemical reactions, predict that the average reaction rate in a capillary decreases, passes through a minimum, and increases as the capillary wall temperature is increased. Good agreement exists between the temperature at the minimum rate found in this work and that found experimentally for polystyrene, natural rubber, and polyisobutylene.     

Rheology of 1‐butyl‐3‐methylimidazolium chloride cellulose solutions. I. Shear rheology

In this article, shear rheology of solutions of different concentrations obtained by dissolution of cellulose in the ionic liquid (IL) solvent 1‐butyl‐3‐methylimidazolium chloride ([Bmim]Cl) was studied by measuring the complex viscosity and dynamic moduli at different temperatures. The obtained viscosity curves were compared with those of lyocell solutions and melt blowing grade polypropylene melts of different melt flow rates (MFR). Master curves were generated for complex viscosity and dynamic moduli by using Carreau and Cross viscosity models to fit experimental data. From the Arrhenius plots of the shift factors with respect to temperature, the activation energies for shear flow were determined. These varied between 18.99 and 24.09 kCal/mol, and were compared with values for lyocell solutions and different polymeric melts, such as polyolefins, polystyrene, and polycarbonate. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Benzyl triphenyl phosphonium chloride as an additive for polyvinylidene fluoride: Melt rheology,crystallization, and electrical properties

The β phase of polyvinylidene fluoride (PVDF) crystals is polar and has very good piezoelectric and dielectric properties as compared with the nonpolar α phase. Benzyl triphenyl phosphonium chloride (BTPC) has been previously shown to directly nucleate the β phase from melt, instead of α phase, and is an additive of practical importance. Different amounts of BTPC were melt mixed into PVDF using a micro twin screw extruder to study the rheology of the blends using oscillatory and steady shear viscometry. Data at different temperatures were found to superimpose onto a master curve using time‐temperature superposition. The complex viscosity and steady shear viscosity increased significantly upon addition of 0.5% BTPC and decreased slightly with further addition of BTPC. The storage modulus exhibited a plateau at low frequencies indicating structure formation in the melt on addition of BTPC. The horizontal shift factors derived from the time‐temperature superposition were found to follow an Arrhenius temperature dependence and the flow activation energy for each blend was obtained. Pure PVDF and PVDF films with 1% and 3% BTPC were melt extruded using a laboratory twin screw extruder. The film containing 3% of BTPC gave the highest fraction of β phase crystals (75%). Small angle light scattering results showed that the size of spherulites decreased with increase in the weight fraction of BTPC. The dielectric constant and conductivity of the films at low frequencies increased significantly with concentration of BTPC, as did the dielectric loss and AC electrical conductivity. POLYM. ENG. SCI., 54:2420–2429, 2014. © 2013 Society of Plastics Engineers     

Properties of random and block copolymers of butadiene and styrene. II. Melt flow

Flow curves, log (rate of shear) versus log (shear stress), as functions of temperature were obtained for several butadiene-styrene copolymers of fixed (25%) styrene content, differing in monomer sequence distribution. A random copolymer of constant composition along the polymer chain and narrow molecular weight distribution (MWD) exhibited behavior similar to linear, narrow MWD polybutadienes; the flow was Newtonian at low shear stresses, and the flow curves for various temperatures were accurately superimposable by a shift along the log (shear rate) axis. In a random copolymer varying in composition along the polymer chain, non-Newtonian behavior was more pronounced, and temperature-shear rate superposition did not succeed, a trend further perpetuated in copolymer of a single long styrene block sequence. The latter resemble branched polymers, as would be expected from association of the styrene blocks. With two styrene blocks, association produces network structures below the glass transition of polystyrene with consequent loss of flow. Disruption of these associations above T_g (styrene) imparts the greatest thermoplasticity to these elastomers. There is evidence, however, that some of the associations persist at temperatures well in excess of T_g (styrene).     

Observation of melt fracture of polypropylene resins in capillary flow

Melt fracture, shear viscosity, extensional viscosity, and die swell of two polypropylene resins were studied using a capillary rheometer. A modified Bagley plot with consideration of pressure effects on melt viscosity and end effect was used. From the true wall shear stress the shear viscosity was calculated. Extensional viscosity was calculated from the end effect. Both shear and extensional viscosities of different molecular weights and temperatures correlated well under the time-temperature Williams-Landel-Ferry (WLF) superposition. Die swell increased when shear stress increased, and was higher for shorter dies at a given shear rate. When shear rates increased the extrudate staged from smooth to gross melt fracture with regular patterns (spurt), and then turned into irregular shapes. In the regular stage the wavelength of extrudates was measured, and corresponding frequency was calculated. The frequency increased when molecular weight decreased and when melt temperature increased. The shift factor based on shear viscosity also brought frequency data of different molecular weights and temperatures into master curves. The frequency decreased slightly when die lengths increased from L/R=10 to 60. A small maximum was observed when shear rates increased.     

Melt rheological behavior of PP–SAN blend

A study of melt rheology of the blend of styrene-acrylonitrile (SAN) and polypropylene (PP) in composition range 0–50 wt % SAN content is presented. Measurements are made on a capillary rheometer at temperatures of 210, 230, and 250°C. The data are presented as flow curves and variations of melt viscosity and melt elasticity as functions of shear rate and blend composition. Scanning electron micrographs are presented to illustrate the dispersion and other characteristics of the SAN droplets. Results of melt rheology are interpreted in terms of the role of SAN droplets in the blend.     

Characterization of poly(3-octylthiophene). II: Melt rheological characterization

The poly(3-alkythiophenes) are electrically conducting polymers which are of particular interest due to their melt-processibility. We have studied the melt properties of poly(3-octylthiophene) (P3OT) by dynamic rheological measurements at temperatures between 180 and 250°C. The samples investigated have molecular weights in the range M_w = 30,000 to 400,000 and have been carefully characterized by dilute solution techniques, Residual iron chloride, a reagent used in the polymerization of these materials, was found to cause a high degree of crosslinking in the polymer melt. By contrast, samples which had been carefully purified demonstrated a negligible rate of crosslinking in a nitrogen atmosphere; however, the presence of air and higher temperatures were found to increase the rate of crosslinking substantially. The temperature dependence of the viscoelastic properties was characterized according to the principles of time-temperature superposition, and the influence of molecular weight was also evaluated. Overall, the rheological behavior was determined to be similar to that commonly observed for linear flexible polymers, which is in agreement with the results of our solution characterization of these materials.