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.     

Viscometric behavior of ternary concentrated solutions of hydroxypropyl cellulose and ethyl cellulose in m-cresol

The shear viscosity of blend solutions of hydroxypropyl cellulose (HPC) and ethyl cellulose (EC) in m-cresol (both HPC/m-cresol and EC/m-cresol systems form lyotropic liquid crystals) was determined by cone-plate-type and capillary-type viscometers. The textures for the same systems at rest and undergoing shear were also observed with a polarized microscope. At shear rate of 1 s^?1, viscosity exhibited a maximum and a minimum with respect to temperature, and this suggested that the phase of the matrix dominated the viscometric behavior of the ternary systems; the blend composition dependence of the viscosity was not additive, and this suggested that HPC and EC were immiscible. At relatively high shear stress, the blend composition dependence of the viscosity greatly depended on the total polymer concentration of the solutions and was quite different from that at low shear rate; the texture of the anisotropic solutions was also different from that at low shear rate. Our findings suggested that the dependence of viscosity on shear and concentration for pure HPC solution was different from that for pure EC solution.     

Rheological properties of iron oxide particle suspensions

Viscosities of γ-Fe₂O₃ dispersions in epoxy resin, phenol resin, and polyvinyl butyral solutions are measured at shear rate D from 19.2 to 384 sec^?1. Volume fraction of γ-Fe₂O₃ in these dispersions ranges from about 0.002 to 0.03. The concentration dependence of relative viscosity η/η_s is closely represented by the Mooney equation. From this equation, intrinsic viscosity [η] of suspensions is found to decrease from 46.1 at D = 19.2sec^?1 to 14 at D = 384 sec^?1 for epoxy resin solution. The high [η] value indicates the existence of flocs containing immobilized liquid. By increasing the shear rate, the average floc size is reduced to point where at an infinite shear rate, only small clusters or possibly particles remain. Of the three polymers, the lowest [η] value is obtained in the dispersion of the phenol resin solution.     

Shear rheological properties of acrylic copolymers and terpolymers suitable for potentially melt processable carbon fiber precursors

In an effort to generate melt processable polyacrylonitrile (PAN) precursor fibers suitable for conversion to carbon fibers, an acrylonitrile/methyl acrylate (AN/MA) copolymer and two acrylonitrile/methyl acrylate/acryloyl benzophenone (AN/MA/ABP) terpolymers were synthesized at molar ratios of 85/15 and 85/14/1, respectively. The termonomer (ABP) was incorporated to accelerate crosslinking via UV irradiation, which serves to prevent relaxation of orientation and flow as the temperature of the fiber is raised during thermooxidative stabilization. Two molecular weights of the terpolymer and one molecular weight of the copolymer were studied to determine the effect of the termonomer, and the effect of molecular weight (MW), on the steady shear viscosity (η) and magnitude of the complex viscosity (η*). A higher rate of increase of η as a function of time was observed for the high MW terpolymer relative to that of the copolymer over the temperature range used. Using a temperature sweep and monitoring levels of η*, a minimum was observed at lower temperatures for both terpolymers. These results suggest that copolymerization with ABP significantly increased the thermally induced kinetics of crosslinking. Comparison of the η and η* data for the low and high MW terpolymers suggested that molecular weight also significantly reduced the melt stability (increased the kinetics of crosslinking). A chemorhelogical correlation was then used to quantify the effects of the termonomer and of molecular weight on the kinetics of crosslinking of the AN terpolymers. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 2856–2865, 2004     

Water‐soluble polymers. LXXXIII. Correlation of experimentally determined drag reduction efficiency and extensional viscosity of high molecular weight polymers in dilute aqueous solution

The extensional viscosity for aqueous solutions of high molecular weight poly(acrylamide) copolymers and poly(ethylene oxide) homopolymers was measured using a laboratory‐designed screen extensional rheometer. A Bingham model was developed to estimate the average local polymer coil extensional viscosity (η_coil). A strong correlation was found between the measured η_coil values and the polymer extensional viscosity predicted by a bead‐spring model. The dilute aqueous solution drag reduction was measured with a rotating disk instrument under conditions minimizing the effects of shear degradation. Extensional viscosity and drag reduction measurements were performed in deionized water and in 0.514M sodium chloride. The relative drag reduction efficiency values (Δ) in both solvents were found to strongly correlate with measured η_coil values. This is the first report of the accurate prediction of drag reduction behavior for a wide range of polymer types in various solvents from the independently measured molecular parameters η_coil and [η]C. The often‐used relative drag reduction efficiency expressed as the product of [η]C and Δ can now be replaced by the absolute drag reduction efficiency [η]Cη_coil. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 82: 1222–1231, 2001     

Melt shear viscosity of PP/Al(OH)3/Mg(OH)2 flame retardant composites at high extrusion rates

The melt apparent shear viscosity (η_a) of polypropylene (PP) composites filled with aluminum hydroxide [Al(OH)₃] and magnesium hydroxide [Mg(OH)₂] was measured by means of a capillary rheometer under experimental conditions of temperature ranging from 180 to 200°C and apparent shear rate varying from 10 to 2 × 10³ s⁻¹, to identify the effects of the filler particle content and size on the melt viscosity. The results showed that the melt shear flow of the composites obeyed the power law and presented pseudoplastic behavior. The dependence of η_a on temperature was consistent with the Arrhenius equation. The sensitivity of η_a for the composite melts to temperature was greater than that of the unfilled PP, and weakened with increasing apparent shear rate. The η_a increased linearly with an increase of the weigh fraction of the flame retardant, especially in the low apparent shear rate region. The η_a of the composites decreased slightly with an increase of particle size of flame retardant. Moreover, the variation for the η_a with particle size of flame retardant was much less than with apparent shear rate under these test conditions. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Formation of dispersed phase in incompatible polymer blends: Interfacial and rheological effects

The formation of dispersed phase in blends of incompatible polymers during melt extrusion with a co-rotating twin screw extruder was studied, using nylon and polyester as the matrix and ethylene-propylene rubbers as the dispersed phase. A master curve is obtained, i.e., Gηmα/γ = 4p^±0.84, where G is the shear rate, γ the particle diameter, η the interfacial tension, η_m the matrix viscosity, η_d the dispersed-drop viscosity, and p = η_d/η_m. The plus (+) sign applies for p > 1, and the minus (?) sign for p < 1. Thus, the dispersed-drop size is directly proportional to the interfacial tension and the ±0.84 power of viscosity ratio. The dispersed drops are the smaller, when the interfacial tension is the lower and the viscosity ratio is the closer to unity. The interfacial tension is largely controlled by the polarities of the two phases, and can be varied over several orders of magnitude by using appropriate dispersants.     

Flow behavior of concentrated solutions of an SBS block copolymer

The non-Newtonian viscosity of concentrated solutions of a styrene-butadiene-styrene, SBS, block copolymer was measured with a novel capillary viscometer. Polymer concentrations ranged from 0.165 to 0.306 g/cc. Apparent shear rates ranged from 1 to 10⁵ sec^?1. Five different solvents were employed. All of the flow curves can be reduced to a single master curve with the same shape exhibited by monodisperse polystyrenes and the Graessley theory. The shift factor for the shear rate axis, τ₀, approximately parallels the Rouse relaxation time, τ_R, but shows a residual concentration and solvent dependence not predicted by the Rouse form. For different solvents at the same concentration, better solvents show a minimum relative zero shear viscosity, η₀/η_s, and a maximum ratio τ_R/τ₀. It is concluded that all solvent effects are not adequately incorporated into the zero shear viscosity for the purposes of constructing master plots; however, the shape of the master plot is not affected by the solvent or the polymer block structure.     

Lyotropic liquid crystalline solutions of hydroxypropyl cellulose in water: Effect of salts on the turbidity and viscometric behavior

Effect of addition of salt on the viscometric behavior of the dilute or concentrated aqueous solution of hydroxypropyl cellulose (HPC) was determined by means of an Ubbelohde or a cone-plate viscometer. That effect on the turbidity of the dilute system was also determined. As salts, NaCl, LiCl, and thiourea were chosen. The turbidity and viscometric behavior for the dilute system, and the viscometric behavior for the concentrated system were greatly affected by salt type and concentration. With increasing NaCl or LiCl concentration, the cloud point decreased, [η] showed a maximum, Huggins' constant k′ showed a minimum, and the shear viscosity for concentrated isotropic solutions showed a maximum. The 45 wt % solution with no salt showed a viscometric behavior which was characteristic of lyotropic liquid crystals; however, with increasing NaCl concentration, a critical temperature at which the shear viscosity showed a maximum with respect to temperature shifted to lower temperature. This behavior was due to an increase in the turbidity, not due to a phase transformation. On the other hand, an addition of thiourea did not affect so greatly the turbidity and viscometric behavior as an addition of NaCl or LiCl did. We speculated different actions of NaCl and thiourea.     

The effect of shear rate on the molecular weight determination of acrylamide polymers from intrinsic viscosity measurements

The rheological response of dilute solutions of high molecular weight polyacrylamides at low shear rates has been measured using a capillary viscometer that provided for a fivefold variation in shear rate at each concentration. The non-Newtonian effects were found to be significant for polyacrylamides with number-average molecular weights exceeding 10⁶. The molecular weight average–intrinsic viscosity relationship most widely used in the literature, [η] = 6.80 × 10^?4M , was found to be valid when [η] was measured at high shear rates where the polymer solutions approached Newtonian behavior. A new relationship was developed relating M _n to the intrinsic viscosity extrapolated to zero shear rate.     

Rheological properties of concentrated polymer solution: Polybutadiene in good and θ solvents

The zero shear viscosity, η° of three polybutadiene samples having different molecular weights over a wide range of concentration (1.0–35.0% polymer) in good and θ solvents has been studied. Superposition of viscosity data has been made to give a single composite curve for each solvent by shifting them vertically by a factor (M°/M)^3.4, where M° represents the molecular weight of the reference sample. The shift factor is found to be proportional to M^3.4 in the region of higher concentration, which indicates that the 3.4-power law is valid for the data of polybutadiene. The double-logarithmic plots of relative viscosity η°_r as a function of c⁵M^3.4 yielded a single composite curve approximating a straight line with slope of unity at the higher values of the variables. The results indicate that over a considerable range of the variables (molecular weight and concentration) at a constant temperature, the relative viscosity is a single function of c⁵M^3.4. The results for double-logarithmic plots of zero shear specific viscosity η°_csp as a function of concentration confirmed those observed in polycholoroprene samples studied earlier that the η0_sp values in θ solvents at higher concentration region are found to be higher than those found in good solvents, whereas in the moderately concentrated region the values are just opposite in θ and good solvents. The viscosity crossover in θ solvents is not as sharp as is found in case of polychloroprene samples and that crossover, too, has taken place in the range of concentration of 11.7–31.6% polymer, which is comparatively higher than that of polychloroprene samples (6.06–21.0% polymer). The results indicate some relation between viscosity crossover and polymer polarity, supporting the idea of enhanced intermolecular association in poor solvents. To correlatethe viscosity data obtained in good and poor solvents, two methods, one given by Graessley and the other given by Dreval and coworkers involving the correlating variable c[η], were considered. The plots of relative viscosity η°, versus the correlating variable c[η] in benzene (good solvent) yielded one curve, but in the case of θ solvents (dioxane and isobutyl acetate), the same plots yielded three separate curves instead of a single curve, which is rather unusual. The appropriate correction on the correlating variable for chain contraction in the concentrated region in a good solvent moved the data to a common curve, especially in lower concentration region, but at the higher concentration region a slight overestimation of data seems to have been effected. On the other hand, the plots of log η as a function of correlating variable c[η] yielded a single curve for three samples in the good solvent benzene, but in poor solvents (diozane and isobutyl acetate) the same plots yielded three separate curves for three samples instead of a single curve, the reason for which is not known at present. However, the normalization of the correlating variable c[η] with Martin constant K_M reduced all experimental data of the polymer samples to a common curve. The correlation of the viscosity data by either of the two methods seems to be possible in the case of the nonpolar flexible polymer, polybutadiene.     

Rheological behaviors of PVA/H2O solutions of high‐polymer concentration

The dynamic viscoelastic properties of poly(vinyl alcohol) (PVA)/H₂O solutions with concentrations of 10 to 25 wt % have been characterized by controlled‐stress rheometry at 30°C. Parameters relating to the linear and nonlinear viscoelasticities include complex viscosity (η*), storage modulus (G′), loss tangent (tan δ), relaxation time (λ), thixotropy, and creep. Change curves of η*, G′, tanδ, and λ with frequency (ω) have been obtained for the PVA/H₂O solutions. Creep and recovery testing yielded compliance (J′) curves with loading and unloading. Shear stress versus rate profiles of the PVA solutions have been obtained through thixotropic measurements. The PVA concentration has been found to have a profound influence on the rheological properties of the aqueous solutions. Four aqueous solutions of 10, 15, 20, and 25 wt % PVA at 30°C exhibited shear‐thinning and showed different transition behaviors of η* and G′ with frequency, and different degrees of creep under constant stress to recovery with time. The 10 wt % PVA solution was viscous and displayed the lowest η* and G′; the 25 wt % PVA solution was viscoelastic and displayed the highest η* and G′; the 15 and 20 wt % PVA solutions showed η* and G′ values and creep to recovery behaviors intermediate between those of the 10 wt % and 25 wt % PVA solutions. The different rheological properties of these PVA/H₂O solutions are considered to correlate with interchain hydrogen bonds and shear‐induced orientation in the solutions. Shearing is able to break the intrachain and interchain hydrogen bonds, and, at the same time, the orientation creates new interchain hydrogen bonding. The reorganization of hydrogen‐bonding mode contributes to the transitions of the macroscopic viscoelasticity with frequency. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

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.     

Rheological characterization of carbon black/polystyrene solution systems

Steady‐shear measurements of suspensions of carbon blacks (CB) in polystyrene (PS)/di‐(butyl phthalate) (DBP) solution were investigated as a function of volume fraction (?) of CB to clarify the effect of the primary particle size and the structure of CB aggregates on the rheological properties. The suspensions show a typical shear‐thinning behavior in the range of a shear rate studied. The Casson model was applied to evaluate the viscosity at infinite of shear rate η_∞ and the yield stress σ_y for the suspensions. Relative viscosity η_∞/η_m, (η_m: medium viscosity) thus obtained was compared to the high‐frequency viscosity for the ideal hard‐sphere silica suspensions to evaluate the effective volume fraction ?_eff of CB aggregates. The ?_eff value was larger for the higher‐structure CB with higher DBP absorption value, irrespective of the primary particle size. The yield stress σ_y had almost the same ?_eff dependence for neutral furnace CB/(PS/DBP) suspensions, although it was larger for acetylene black (AcB)/(PS/DBP) suspensions. These results demonstrated that the effective volume fraction is the most important quantity to characterize the CB aggregates on the rheological properties. It was also found that the correction of the medium viscosity changes due to polymer adsorption on the CB surface is important since neutral furnace CB adsorbs PS polymers but AcB hardly adsorbs PS polymers in the solution. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Long-range hydrodynamic response of particulate liquids and liquid-laden solids

In viscous particulate liquids, such as suspensions and polymer solutions, the large-distance steady-state flow due to a local disturbance is commonly described in terms of hydrodynamic screening—beyond a correlation length ξ the response drops from that of the pure solvent, characterized by its viscosity η₀, to that of the macroscopic liquid with viscosity η > η₀ For cases where η >> η₀ we show, based on general conservation arguments, that this screening picture, while being asymptotically correct, should be refined in an essential way. The crossover between the microscopic and macroscopic behaviors occurs gradually over a wide range of distances, ξ < r < (η / η₀)^1/2 ξ In liquid-laden solids, such as colloidal glasses, gels, and liquid-filled porous media, where η → ∞, this intermediate behavior takes over the entire large-distance response. The intermediate flow field, arising from the effect of mass displacement rather than momentum diffusion, has several unique characteristics: (i) It has a dipolar shape with l/r ³ spatial decay, negative transverse components, and vanishing angular average. (ii) Its amplitude depends on the liquid properties through η₀ and ξ alone; thus, in cases where ξ is fixed by geometry (e.g., for particulate liquids tightly confined in solid matrices), the large-distance response is independent of particle concentration. (iii) The intermediate field builds up non-diffusively, with a distance-independent relaxation rate, making it dominant at large distances before steady state has been reached. We demonstrate these general properties in three model systems.     

Rheological behavior of compatible polymer blends. I. Blends of poly(styrene-Co-acrylonitrile) and poly(ε-caprolactone)

The rheological behavior of blends of poly(styrene-co-acrylonitrile) (SAN) and poly(ε-caprolactone) (PCL) was investigated, using a cone-and-plate rheometer. For the study, blends of various compositions were prepared by melt blending using a twin-screw compounding machine. The rheological properties measured were shear stress (σ₁₂), viscosity (η), and first normal stress difference (N₁) as functions of shear rate (γ) in steady shearing flow, and dynamic storage modulus (G′) and loss modulus (G″) as functions of angular frequency (ω) in oscillatory shearing flow, at various temperatures. It has been found that logarithmic plots of N₁ versus σ₁₂, and logarithmic plots of G′ versus G″, become virtually independent of temperature but vary regularly with blend composition, and that the zero-shear viscosity of the blends, (η_o)_blend, follows the relationship, 1/log(η_o)_blend = w_A/log η_0A + w_B/log η_0B, where η_0A and η_0B are the zero-shear viscosities of components A and B, respectively, and w_A and w_B are the weight fractions of components A and B, respectively. The physical implications of the relationship found are discussed.     

Effect of rheological parameters on the miscibility and polymer–filler interactions of the black-filled blends of polyethylene–vinyl acetate and polychloroprene

Miscibility of 30 phr loaded black-filled (N110) blends of polyethylene-vinyl acetate (EVAc, VAc content 28%) and polychloroprene (CR) are investigated through shear and dynamic deformations. Both shear (η_a) and dynamic elongational (η′_E) viscosities are conducive to their miscibility as both show positive deviation for all blends, though dynamic out-of-phase (η″_E) viscosity shows negative-positive deviation. Both η_a and η′_E follow the power law relationship with shear rate (γ˙_wa) and frequency (ω), respectively. Both storage (E′) and loss (E″) modulii increases with frequency. The higher dissipative energy at around 11 Hz may be due to its syncronization with molecular vibrations of the polymer segments. The effect of rheological parameters like strain rate and temperature on the relative change in shear (RV_S) and dynamic elongational (RV_D) viscosities is reported for the variation of blend composition with 30 phr loaded black-filled compounds. The variation of both RV_S and RV_D follows a third order polynomial equation with carbon black loading in 50/50 EVAc/CR blend; all the polynomial constants are function of temperature and strain rate. © 1996 John Wiley & Sons, Inc.     

Development and relaxation of orientation in sheared concentrated lyotropic solutions of hydroxypropylcellulose in m-cresol

Shear-induced orientation and the relaxation of orientation after the cessation of shear in 45 and 50 wt% solutions of cholesteric hydroxypropylcellulose (HPC) in m-cresol have been studied in situ by infrared spectroscopy and polarised microscopy. The shearing experiments were conducted at 30-80 °C at shear rates of 1-300 s⁻¹, which covered the director tumbling, wagging and a small part of the steady-state shear rate regimes. The steady-state order parameter was proportional to the shear rate and the proportionality constant increased with increasing HPC concentration and decreasing temperature. The concentrated solutions studied showed steady-state alignment even in the tumbling regime. Three different shear-rate regions with different behaviours of the solutions after the cessation of shear were found in these concentrated HPC solutions. At low shear rates (1-5 s⁻¹, referring to the 50% HPC solution) the polymer remained isotropic during shear but became gradually more oriented a few minutes after the cessation of shear, an observation that was substantiated by polarized microscopy. The order parameter reached a final plateau value and stayed constant at this level for long periods of time (∼24 h). At intermediate shear rates (from 5 to 50 s⁻¹ for the 50% HPC solution), a detectable order parameter was recorded at steady shear and, after the cessation of shear, the structure returned to an almost isotropic state within a few minutes, after which the orientation gradually started to increase to approach a plateau value after about 150 min. At even higher shear rates (∼100 s⁻¹ for to the 50% HPC solution), the initial steady shear order parameter relaxed to an almost isotropic state and remained constant at this level for time periods extending up to 24 h.     

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     

梳状聚合物二醇的结构与流变性能关系

制备了一系列支链结构不同的梳状聚合物二元醇(CPD),并用FTIR对其结构进行了表征。着重研究了CPD梳状支链结构和温度对其流变性能的影响,并测定了CPD的流动活化能ΔE_η0。研究发现,梳状支链的长度增加和极性增大,CPD的黏度增加,出现剪切变稀行为的剪切速率降低。CPD的η-γ曲线出现两次剪切变稀行为,在两次行为之间存在一平台,这一平台随温度增加向高剪切速率方向移动,并逐渐变短,最后在50℃时消失。随梳状支链长度增加和极性增大,CPD的流动活化能ΔE_η0增加。