Rheological behavior of blends of poly(methyl methacrylate) (PMMA) and poly(acrylonitrile-stat-styrene)-graft-polybutadiene (ABS)

The rheological behavior of blends of poly(methyl methacrylate) (PMMA) and poly(acrylonitrile-stat-styrene)-graft-polybutadiene (ABS) was investigated using a cone-and-plate rheometer. The rheological properties measured were shear stress (σ₁₂), viscosity (η), and first normal stress difference (N₁) as functions of shear rate (\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma$ \end{document}) in steady shearing flow, and storage modulus (G′) and loss modulus (G″) as functions of frequency (ω) in oscillatory shearing flow. It has been found that the rheological behavior of blends of ABS and PMMA was very similar to that of blends of poly(styrene-stat-acrylonitrile) (SAN) and PMMA, in that N₁ in logarithmic plots of N₁ versus σ₁₂, and G′ in logarithmic plots of G′ versus G″, vary regularly with blend composition. This has led us to conclude that the rubber particles that are grafted on an SAN resinous matrix in ABS resin plays only a minor role in influencing the compatibility of ABS/PMMA blends, and that the SAN chains attached to the surface of rubber particles, and the SAN matrix phase, play a major role in compatibilizing ABS resin with PMMA.     

Rheological properties of poly(methyl methacrylate)/rigid ladderlike polyphenylsilsesquioxane blends

A series of poly(methyl methacrylate) (PMMA) blends with rigid ladderlike polyphenylsilsesquioxane (PPSQ) were prepared at weight ratios of 100/0, 95/5, 90/10, 85/15, and 80/20 by solution casting and then hot‐pressing. Their rheological properties have been studied under both dynamic shear and uniaxial elongation conditions. Their rheological properties depend on the compositions. The storage modulus, G′, loss modulus, G″, and dynamic shear viscosity, η*, of the PMMA/PPSQ 95/5 blend were slightly lower than those of pure PMMA. However, the values of G′, G″, and η* for the other PMMA/PPSQ blends are higher than those of PMMA. The G′ values increase with an increase in PPSQ content from 5% through 15% PPSQ at low frequencies and then drop as the PPSQ content increases to 20%. Uniaxial elongational viscosity (η_E) data demonstrate that PMMA/PPSQ blends exhibit slightly weaker (5% PPSQ) and much weaker (10% PPSQ) strain‐hardening than PMMA. In contrast, the PMMA/PPSQ 85/15 blend shows strain‐softening. Neither strain‐hardening nor strain‐softening was observed in the 80/20 blend. The special rheological properties for the 95/5 blend is probably due to a decrease in PMMA entanglements brought by the specific PMMA–PPSQ interactions. Rheological properties of PMMA/PPSQ blends with higher PPSQ content (≥10%) are mainly affected by formation of hard PPSQ particles. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 352–359, 2007     

Compatibility,steady and dynamic rheological behaviors of polylactide/poly(ethylene glycol) blends

Understanding the rheological behavior of plasticized polylactide (PLA) contributed to the optimization of processing conditions and revealed the microstructure–property relationships. In this study, the morphological, thermal, steady and dynamic rheological properties of the PLA/poly(ethylene glycol) (PEG) blends were investigated by scanning electron microscope, differential scanning calorimeter, and capillary and dynamic rheometers, respectively. The results illuminated that the melt shear flow basically fitted the power law, whereas the temperature dependence of the apparent shear viscosity (η_a) or complex viscosity (η*) followed the Arrhenius equation. Both the neat PLA and PLA/PEG blends exhibited shear‐thinning behavior. Because the incorporation of PEG reduced the intermolecular forces and improved the mobility of the PLA chains, the η_a, η*, and storage and loss moduli of the PLA/PEG blends decreased. The PEG content (W_PEG) ranged from 0 to 10 wt %, both η_a and η* decreased significantly. However, the decrements of η_a and η* became unremarkable when W_PEG exceeded 10 wt %. The reason was attributed to the occurrence of phase separation, which resulted in the decrease in the plasticization and lubrication efficiencies. This study demonstrated that the addition of the right amount of PEG obviously improved the flow properties of PLA. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 42919.     

Melt viscosity of poly(vinyl chloride) formulations

Commercial, suspension-type PVC resin, poly (vinyl chloride), molecular weight M_w × 10^?4 = 8.6 ± 0.9, polydispersity M_w/M_n = 2.26, was mixed with plasticizer di(2-ethyl hexyl)phthalate (DOP) and organo-tin stabilizer in four different proportions. The mixtures were milled and pressed into sheets for testing. The polymer content in these samples was 97, 80, 60, and 40 wt percent. The viscoelastic properties of the materials were investigated using a Weissenberg rheogoniometer in a cone-and-plate, steady-state shearing mode. The viscosities and primary normal stress difference coefficients were measured at shear rates of 10^?2 ≤ \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \gamma \limits^. $\end{document} (sec^?1) ≤ 10² and at temperatures from 151 to 246°C. The zero shear viscosities, plotted as log η₀ vs 1/T (T is the absolute temperature) did not follow either a straight line dependence, reported for PVC melts at low shear rates at 170–190°C, nor was any discontinuity found near 195°C as by others; the data follows a continuous concave curve. The apparent activation energy of flow increases steeply with decreasing temperature. The data can be represented by a WLF type of equation, but the magnitudes of the parameters of this relation differ from expected values. A crossplot of log η₀ (T = const.) vs log w (where w is the polymer content) also demonstrates a faster increase of η₀ with w than expected from the straight line dependence. The primary normal stress difference coefficient was found to increase with w and decrease with T, paralleling the observed dependencies of η₀.     

Viscoelastic properties of poly(ethylene-co-styrene) copolymers

The viscoelastic properties of narrowly distributed linear poly(ethylene-co-styrene) copolymers with different mole fractions of styrene (x_S = 0–20.5 mol %) and molecular weights (M_w = 64–214 kg/mol) were analyzed in the molten state at different temperatures by means of oscillatory rheometry. Analyzing the thermorheological properties of the polymers, we found that the time temperature superposition principle is fulfilled. The corresponding shift factors follow up to 16.5 mol % of styrene units the Arrhenius behavior of neat polyethylene. For a styrene content of about 20 mol %, the polymers no longer crystallize and a transition from Arrhenius to WLF behavior of pure polystyrene was observed. The zero shear viscosity, η₀, of the polymers was derived from the mastercurves. The determination of the plateau modulus by the well-known tan δ-min criterion is not possible due to the beginning crystallization in the corresponding temperature range. An approximate calculation of this value is based on the characteristic relaxation time λ_x = 1/ω_x, corresponding to the crossover of G′ and G′. Indeed, the characteristic modulus G_px calculated as η₀/λ_x is a good approximation for the plateau modulus G_p. The viscosity–molecular weight and relaxation time–molecular weight scaling relations were established for three copolymers with different molecular weights and nearly the same styrene content. For both material parameters, the scaling exponent is around 3.4, confirming the linear architecture of the investigated polymers. The mixing rules describing the change of such material parameters like zero shear viscosity or plateau modulus independent of styrene content are of logarithmic linear character using the weight fraction of styrene units instead of the mole fraction. The relations found allow the prediction of melt state properties for polymers with arbitrary styrene content. In the future, when catalysts with sufficient activity for the synthesis of high styrene content copolymers are available, these predictions will have to be checked. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 65:209–215, 1997     

Rheological properties of the blends of polychloroprene with poly[ethylene(vinyl acetate)]

Blends of poly[ethylene(vinylacetate)] (EVAc-45; 45% VAc content) and polychloroprene (CR) have been studied with respect to capillary and dynamic flow. It is found that EVAc-45, CR, and their blends are shear thinning (pseudoplastic) in nature. Though shear viscosity (η_a) and dynamic out-of-phase viscosity (η′_E) obeys power law, dynamic elongational viscosity (η′_E) does not follow it due to the synchronization of molecular vibration with the applied frequency at around 11 Hz. Both η_a and η′_E of the blends show positive deviation with respect to their additive values. The relative positive deviation (RPD) in shear flow increases with increasing temperature and shear rate. In the case of dynamic flow, RPD increases with increasing temperature but exhibits a decreasing trend with increasing frequency. RPD can be fitted well into a fifth-order equation with a weight fraction of CR (W_CR) in EVAc-45—CR blends. From rheological point of view, this relative positive deviation indicates blend compatibility between EVAc-45 and CR. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 66: 1759–1765, 1997     

Branched poly(ethylene terephthalate) correlations between viscosimetric properties and polymerization parameters

Samples of poly(ethylene terephthalate) (PET) modified with small amounts of trimesic acid groups and hence containing long chain branching have been prepared. From the content of trifunctional modifier and from the experimental value of the extent of reaction, the weight-average molecular weight $\text{M}\text{?}{}_{\mathrm{w}}$ and branching density $\text{B}\text{?}{}_{\mathrm{w}}$ have been calculated, assuming that all the end-groups are equally reactive and intramolecular reactions are absent. The values of $\text{M}\text{?}{}_{\mathrm{w}}$ and $\text{B}\text{?}{}_{\mathrm{w}}$ have been correlated with the experimental values of intrinsic viscosity [η] and the Newtonian melt viscosity η₀. General relations of the following type have been obtained:

$\text{f}{}_1\text{([η],}\text{M}{}_{\mathrm{w}}\text{,}\text{B}{}_{\mathrm{w}}\text{) = 0; f}{}_2\text{(η}{}_0\text{,}\text{M}{}_{\mathrm{w}}\text{,}\text{B}{}_{\mathrm{w}}\text{) =0; f}{}_3\text{(η}{}_0\text{, [η],}\text{B}{}_{\mathrm{w}}\text{) = 0; f}{}_4\text{(η}{}_0\text{, [η],}\text{M}{}_{\mathrm{w}}\text{) = 0;}$

In particular, [η] and η₀ increase on increasing $\text{M}\text{?}{}_{\mathrm{w}}$ and decrease on increasing $\text{B}\text{?}{}_{\mathrm{w}}$, but, at equal [η] values, η₀ increases with $\text{B}\text{?}{}_{\mathrm{w}}$. Through the last relation, the reliability limits of which should be experimentally checked, and from measurements of [η] and η₀, it is possible to calculate $\text{M}\text{?}{}_{\mathrm{w}}$ of a branched PET.     

Dynamic rheological behavior of poly(ether ketone ketone) from solid state to melt state

High performance thermoplastic poly(ether ketone ketone) (PEKK) polymers with various meta phenyl links ratio were investigated by dynamical mechanical analysis. Analyses were carried out in a wide range of temperature from solid state (torsion rectangular mode) to the melt state (torsion parallel plates mode) as function of thermal history and environmental conditions. In the solid state, this study was focused on the secondary relaxations in the vitreous state. A complementary investigation conducted with different poly(aryl ether ketones) allowed us to propose a molecular interpretation of PEKK sub‐vitreous relaxations. In the molten state, storage modulus (G′), loss modulus (G″), storage viscosity (η′), and loss viscosity (η″) were studied to determine zero shear‐rate viscosity (η₀) and thermal activation energy E_a. Master curves were built and the shift factor a_T was determined. Thermal activation energies were extracted from an Arrhenius model on the shift factor temperature's dependency. Finally, E_a and η₀ were determined thanks to the dynamic viscosity fit with Cross model and Cole–Cole representation. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 46456.     

A phenomenological master curve for viscosity—structure data for two phase polymer systems in simple shear flow

A master curve hypothesis is established based on a mass balance and an assumption of continuous stress through interfaces for well dispersed two phase systems with “defined” zero shear viscosity. The master curve, which is in reasonable accordance with experimental data is represented in a double logarithmic plot of log (η_T/_T,0) against log \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{{\eta _{T,0} M_C H\rho}}{{c^2 RT}}\dot \gamma _T} \right) $\end{document}. M_c is the molecular weight between entanglements, H = M?_w/M?_n, ρ is the density, c is the polymer concentration, all defined for the continuous phase. η_T and η_T,0 are the viscosity and zero shear viscosity of the blend, η_T is the apparent shear rate, R the gas constant, and T is absolute temperature.     

Rheological behavior of partially hydrolyzed poly(vinyl acetate-co-ethylene)

The rheological behavior of partially hydrolyzed poly(vinyl acetate-co-ethylene) (VAE) was investigated, using a Rheometrics Dynamic Mechanical Spectrometer. For the investigation, measurements of storage modulus (G′), loss modulus (G″) and loss tangent (tan δ) of the materials were recorded as functions of temperature at a fixed frequency (i.e., using temperature scans) and, also, as functions of frequency at a fixed temperature (i.e., using frequency scans). For the hydrolysis, three different grades of copolymer (containing 34, 47, 62 mol% of vinyl acetate) were used to yield poly(vinyl acetate-co-ethylene-co-vinyl alcohol) (VAEOH) with varying amounts of hydroxyl group. For comparison purposes, the viscoelastic properties of blends of VAE copolymer with poly(vinyl alcohol) (PVOH), having varying blend compositions, were also measured. The blends were prepared by first mixing a solution of VAE copolymer, which was dissolved in a toluene/dichloroethane mixed solvent, and an aqueous solution of PVOH, and then freeze drying the mixture to a constant weight. Also measured were the glass transition temperature (T_g) of the VAE copolymers and the T_g and melting point (T_m) of the VAEOH terpolymers, using a DuPont Thermal Analyzer equipped with a 910 DSC Module. It has been found that (1) introduction of hydroxyl group into the backbone of the amorphous VAE copolymer has made the resulting VAEOH terpolymer semicrystalline; (2) the T_m, T_g, G′, and the complex viscosity (η^*) of the VAEOH terpolymers increase with increasing amounts of hydroxyl group; (3) the physical blending of PVOH with VAE copolymer has not affected the T_g of the VAE copolymer; (4) the G′ and η^* of the VAE/PVOH blends are found to increase with the amount of PVOH in the blend. The use of logarithmic plots of G′ versus G″ has been found to be very useful for discerning the differences in the structure of the materials tested.     

Dynamic rheological properties of polyetherimide/polyetheretherketone/liquid crystalline polymer ternary blends

The dynamic rheological properties of poly(etherimide)/poly(etheretherketone)/liquid crystalline polymer (LCP) ternary blends were measured in order to correlate these properties with the morphology obtained after extrusion. The viscosity radio, η_d/η_m, where η_d = disperse phase viscosity and η_m = matrix viscosity, had to be redefined. Below 50 wt% LCP, η_d = η_LCP, η_m = η_PEEK+PEI and η_d/η_m < 1. Above 50 wt% LCP, η_d = η_PEEK+PEI, η_m = η_LCP and η_d/η_m > 1. Fibrillar morphologies were obtained in both cases, except below a concentration of 20 wt% LCP. At low concentrations of LCP the ternary blends had lower viscosities than the component polymers, showing a flow promotion effect of the LCP on the PEI- and PEEK-rich phases.     

An empirical approach for predicting kinematic viscosities of biodiesel blends

Kinematic viscosity (η) is an important property of diesel fuels, including biodiesels, which are marketed mostly as the blends in many countries around the world. In this study, the free energy of viscous flow (ΔG_vis) for a non-associated liquid mixture is assumed to be the summed of ΔG_vis of individual components. Hence, the Eyring’s equation, η = Ae(−ΔG_vis/RT), is transformed to ln η_blend = a + bn₁ + c/T + dn₁/T (where, a, b, c and d, T and n₁ are thermodynamically related constants, absolute temperature and mole fraction of biodiesel, respectively). The transformed equation is used to predict kinematic viscosity of biodiesel blends (η_blend) of different degree of blending at any temperatures from pour point to 100 °C. The predicted kinematic viscosities are in good agreement with those reported in literatures at all temperatures. The highest deviation is ±5.4% and the average absolute deviation (AAD) is less than 2.86%. The transformed equation can also be used to predict kinematic viscosities of pure fatty acid methyl esters in diesel fuel. Methyl ricinoleate is an exception. The AAD is 4.50% and the deviation is as high as 12.80%. The high deviation suggests that molecular interactions between methyl ricinoleate and diesel fuel is high and cannot be ignored.     

Binary blends of metallocene polyethylene with conventional polyolefins: Rheological and morphological properties

The rheology and morphology of four sets of binary blends of polyethylene synthesized with metallocene catalysis (metallocene polyethylene: MCPE) with polyolefins prepared using Ziegler‐Natta catalysts have been investigated. The blend systems are MCPE with high density polyethylene (MCPE‐HDPE), polypropylene (MCPE‐PP), poly(propylene‐co‐ethylene) (MCPE‐CoPP), and poly(propylene‐co‐ethylene‐co‐1‐butylene) (MCPE‐TerPP). Cole‐Cole plots [storage melt viscosity (η′) versus loss melt viscosity (η″)], plots of the dynamic storage modulus (G′) versus the dynamic loss modulus (G″), and plots of the log melt viscosity (η*, η′, and η″) versus blend compositions were constructed. The morphology of the blends after microtoming and etching was studied. The phase morphology of MCPE‐HDPE appeared homogeneous, whereas the other three blends were heterogeneous. Rheological and morphological investigations indicated that the MCPE‐HDPE blend was miscible, but the other three blends were immiscible in the melt as well as in the solid state. These observations can be rationalized in terms of the similarity of the chemical structures of the polyolefins.     

Stereocomplex formation between enantiomeric poly(lactic acid)s. X. Binary blends from poly(D-lactide-CO-glycolide) and poly(L-lactide-CO-glycolide)

Binary blend films from lactide-rich poly(D -lactide-co-glycolide) (PDLG) and poly(L -lactide-co-glycolide) (PLLG) were obtained by casting methylene chloride solutions of the two mixed copolymers with different D- and L-lactide contents (X_DI and X_LI ), and their crystallization was studied by differential scanning calorimetry (DSC). Four combinations were selected from the binary (A-B) blends: mixing of the same polymer [X_DI (A) = X_DI (B) or X_LI (A) = X_LI(B)], blending under X_DI (B) = X_LI (A), blending of a D -lactide homopolymer [X_DI(B) = 1] with other PDLGs, and blending of a D -lactide homopolymer [X_DI(B) = 1] with other PLLGs. Racemic crystallites were exclusively formed between PDLG and PLLG when they had high lactide unit contents. The melting point and enthalpy of fusion of the racemic crystallites decreased with a decrease in X_DI of PDLG or X_LI of PLLG, suggesting that glycolide units in the polymer disturbed the growth of the racemic crystallites. A similar behavior was also observed for the homocrystallization in nonblended copolymer films. Homocrystallites composed entirely either of D -lactide unit or L-lactide unit sequences were formed when one component was crystallizable and the other component had the same sign of optical rotation or very different lactide content. An interesting finding was that even nonhomocrystallizable lactide-poor PDLG and PLLG could form racemic crystallites when both were blended. © 1994 John Wiley & Sons, Inc.     

Influence of the glycosidic linkage on the solution conformation of glucans

In order to gain a better understanding of the influence of β-glycosidic linkages on the solution conformation of glucans, a comparison was made between the carboxymethyl derivatives of cellulose (CMC, 100% 1,4-), barley glucan (CMGG, 30 : 70 1,3 : 1,4-) and curdlan (CMCd, 100% 1,3-glycosidic), each with an average degree of substitution of DS = 1.0–1.5 and molar masses of 144 000–720 000 g mol^–1. For this purpose curdlan and barley glucan were chemically modified, whereas carboxymethylcellulose was available as a commercial sample. Via congo red analysis it was proved for the microbial β-1,3-glucans curdlan (unsubstituted) and scleroglucan (one β-1,6-linked glucose side group on every third monomer unit) that substituents in glucan derivatives weaken an existing helical structure but that reduction of the molar mass with ultrasound has no influence on the helices. The molecular parameters M_w, M_n, R_G, L_P and [η] were determined by means of SEC/MALLS measurements and viscometry and the chain mobility was quantified using the ¹³C NMR relaxation times, T₁, of the different polymers. From this it was possible to derive [η]-M_w relationships. For all samples, the exponent ν of the R_G-M_W relationship lay in the range 0.54–0.59, from which it is possible to deduce a coiled solution structure. However, β-1,3-glucans occupy 25% less volume than β-1,4-glucans and exhibit less chain mobility. Hence β-1,4-glucans should be considerably more viscous than β-1,3-glucans, as was indeed demonstrated by rheological flow curves of 6% solutions of the carboxymethylglucan derivatives. The zero-shear viscosity, η₀, decreases by 3 decades in the order of CMC > CMGG > CMCd.     

Small-angle neutron scattering from symmetric blends of poly(dimethylsiloxane) and poly(ethylmethylsiloxane)

We present results of a small-angle neutron scattering (SANS) study of the structure and thermodynamic properties of symmetric blends of deuterated poly(dimethylsiloxane) (d-PDMS) and poly(ethylmethylsiloxane) (PEMS) as a function of temperature (T) (40≤T≤300 °C) and the molecular weight (M_w) (4700≤M_w≤23,200). The radius of gyration (R_g) of d-PDMS was measured using the high-concentration labeling method and revealed unperturbed chain dimensions at all temperatures regardless of the polymer M_w. The random phase approximation (RPA) fits the data for low M_w blends, however it fails to describe the SANS data for M_w>10,000 g/mol. This observation is explained by the fact that for high M_w blends the correlation length of the concentration fluctuations ξ is always large (ξ>R_g), implying that these blends remain microscopically inhomogeneous at all temperatures studied in this work. At the same time, the low M_w blends are randomly mixed (ξ<R_g) at all T and can reach the ‘ideal mixing’ or Θ condition (χ=0).     

Shear degradation of poly(vinyl acetate) in toluene solutions by high-speed stirring

A poly(vinyl acetate) (PVAc) of M?_w 750,000 and M?_w/M?_n 5.10 in toluene solution was sheared in a Virtis-60 homogenizer. The polymer concentration was 3.0 to 12.0 g/100ml, and test temperature was 10 ± 0.5°C. The extent of degradation was measured by gel permeation chromatography (GPC). It was concluded that on shearing (i) the molecular weight decreases rapidly at the beginning of shearing and thereafter decreases ever more slowly toward a limiting value, (ii) the molecular weight distribution is narrowed, (iii) no degradation occurs up to 5000 rpm and thereafter increases with stirring speed, (iv) degradation is more at lower concentrations but concentration is not a sensitive variable, and (v) the chain scission occurs randomly. The Mark-Houwing relationship for PVAc in THF at 25°C was derived as [η] = 2.47 × 10^?4 × M?_v^0.644.     

Thermal analyses of poly(3-hydroxybutyrate), poly(3-hydroxybutyrate-co-3-hydroxyvalerate), and poly(3-hydroxybutyrate-co-3-hydroxyhexanoate)

Thermal analyses of poly(3-hydroxybutyrate) (PHB), poly(3-hydroxybutyrate-co-3-hydroxyvalerate) [P(HB–HV)], and poly(3-hydroxybutyrate-co-3-hydroxyhexanoate) [P(HB–HHx)] were made with thermogravimetry and differential scanning calorimetry (DSC). In the thermal degradation of PHB, the onset of weight loss occurred at the temperature (°C) given by T_o = 0.75B + 311, where B represents the heating rate (°C/min). The temperature at which the weight-loss rate was at a maximum was T_p = 0.91B + 320, and the temperature at which degradation was completed was T_f = 1.00B + 325. In the thermal degradation of P(HB–HV) (70:30), T_o = 0.96B + 308, T_p = 0.99B + 320, and T_f = 1.09B + 325. In the thermal degradation of P(HB–HHx) (85:15), T_o = 1.11B + 305, T_p = 1.10B + 319, and T_f = 1.16B + 325. The derivative thermogravimetry curves of PHB, P(HB–HV), and P(HB–HHx) confirmed only one weight-loss step change. The incorporation of 30 mol % 3-hydroxyvalerate (HV) and 15 mol % 3-hydroxyhexanoate (HHx) components into the polyester increased the various thermal temperatures T_o, T_p, and T_f relative to those of PHB by 3–12°C (measured at B = 40°C/min). DSC measurements showed that the incorporation of HV and HHx decreased the melting temperature relative to that of PHB by 70°C. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 82: 90–98, 2001     

Polymer rheology: Influence of molecular weight and polydispersity

Literature data on the non-Newtonian flow of bulk polymer and of polymer solutions are correlated on the basis of a four-parameter equation, η = η_∞ + (η₀ ? η_∞)/[1 + (τD)^m], η being the viscosity at shear rate D, and η₀ and η_∞ limiting values at D = 0 and D = ∞, respectively. The parameters η₀, η_∞, and τ all show dependence on molecular weight, and in general there is good correlation between τ and η₀. There is evidence that τ is related to a molecular weight higher than the weight-average. The exponent m shows dependence on molecular weight distribution and approaches an upper limit of unity for a monodisperse linear polymer. For linear unblended polymers it may be expressed empirically by m = (M?_n/M?_w)^1/5.