Extensional rheology of concentrated poly(ethylene oxide) solutions

The shear and extensional rheology of three concentrated poly(ethylene oxide) solutions is examined. Shear theology including steady shear viscosity, normal stress difference and linear viscoelastic material functions all collapse onto master curves independent of concentration and temperature. Extensional flow experiments are performed in fiber spinning and opposed nozzles geometries. The concentration dependence of extensional behavior measured using both techniques is presented. The zero-shear viscosity and apparent extensional viscosities measured with both extensional rheometers exhibit a power law dependence with polymer concentration. Strain hardening in the fiber spinning device is found to be of similar magnitude for all test fluids, irrespective of strain rate. The opposed nozzle device measures an apparent extensional viscosity which is one order of magnitude smaller than the value determined with the fiber spinline device. This could be attributed to errors caused by shear, dynamic pressure, and the relatively small strains developed in the opposed nozzle device. This instrument cannot measure local kinematics or stresses, but averages these values over the non-homogenous flow field. These results show that it is not possible to measure the extensional viscosity of non-Newtonian and shear thinning fluids with this device. Fiber spin-line experiments are coupled with a momentum balance and constitutive model to predict stress growth and diameter profiles. A one-mode Giesekus model accurately captures the plateau values of steady and dynamic shear properties, but fails to capture the gradual shear thinning of viscosity. Giesekus model parameters determined from shear rheology are not capable of quantitatively predicting fiber spinline kinematics. However, model parameters fit to a single spinline experiment accurately predict stress growth behavior for different applied spinline tensions.     

Electrical noise generated during capillary flow of aqueous poly(ethylene oxide) solutions

 The relation between the electrical noise generated during flow of aqueous poly(ethylene oxide) PEO solutions in three capillaries of different lengths and entry shape but the same diameter and the flow behaviour was investigated. Flow into the square cut off capillary entry was characterised by a low pressure loss regime followed at higher shear rates by a high pressure loss regime while flow into the trumpet shaped capillary end exhibited only the low pressure loss regime. The high pressure loss flow was associated with strong electrical noise generation. The results suggest that the noise generation mechanism includes a current source supplied by the flow through the capillary volume with an associated streaming potential and a modulation of the current by mixing and turbulence at the capillary entrance. The noise measuring technique can potentionally be used to study disturbances in the entry flow to capillaries. Received: 22 July 1996/Accepted: 9 June 1997     

Effect of poly(ethylene oxide) on the rheological behavior of silica suspensions

The steady-shear viscosity, dynamic viscoelasticity, and sedimentation behavior were measured for silica suspensions dispersed in aqueous solutions of poly(ethylene oxide) (PEO). For suspensions prepared with polymer solutions in which the transient network is developed by entanglements, the viscosity at a given shear rate decreases, shows a minimum, and then increases with increasing particle concentration. Because the suspensions are sterically stabilized under the conditions where the particle surfaces are fully covered with by a thick layer of adsorbed polymer, the viscosity decrease can be attributed to the reduction of network density in solution. But under the low coverage conditions, the particles are flocculated by bridging and this leads to a viscosity increase with shear-thinning profiles. The polymer chains with high molecular weights form flexible bridges between particles. The stress-dependent curve of storage modulus measured by a stress amplitude sweep shows an increase prior to a drastic drop due to structural breakdown. The increase in elastic responses may arise from the restoring forces of extended bridges with high deformability. The effect of PEO on the rheological behavior of silica suspensions can be explained by a combination of concentration reduction of polymer in solution and flocculation by bridging.     

Linear viscoelastic master curves of neat and laponite-filled poly(ethylene oxide)–water solutions

Aqueous solutions composed of dispersed nanoparticles and entangled polymers are shown to exhibit common viscoelasticity over a range of particle and polymer concentrations. Time–temperature superposition and time–concentration superposition are applied to generate rheological master curves for neat and laponite-filled aqueous solutions of poly(ethylene oxide). The shift factors were correlated in terms of temperature and concentration and are found to differ from previous reports for ideal polymer solutions, which can be rationalized with a molecular interpretation of the structure of the laponite–polymer solutions. Laponite addition to the concentrated polymer solution is observed to increase the relaxation time but decrease the elastic modulus, which is a consequence of polymer adsorption and bridging. The addition of small amounts of laponite to stable PEO–water solutions also leads to ageing on the time scale of days.     

Electrical fluctuations and entry flow instabilities during capillary flow of aqueous poly (ethylene oxide) solutions

Capillary flow of poly (ethylene oxide) solutions generates voltage fluctuations (noise) between electrodes placed on both sides of the capillary. The noise has a 1/f type spectral distribution, the value of increasing with (shear rate) to a limiting level. Within certain ranges, two sets of harmonic peaks appear in the spectra. It is demonstrated that these peaks are related to the frequency components of the instabilities in the entry flow region. The lower frequency set of harmonics corresponds to axial oscillations (pulsations) of the flow, while the higher frequency peaks are associated with the transverse oscillation of the stream lines in the vicinity of the entry. The corresponding frequencies were measured by visual counting and by spectral analysis of laser light transmitted through the entry region during injection of a coloured solution.The noise measurements were carried out using both platinum and reversible Ag/AgCl electrodes. In the latter case the streaming potential was also measured; its variation due to pressure fluctuations in the instable flow region appears to provide a plausible explanation of flow-induced noise phenomena as observed in elastic solutions.Dedicated to Prof. Dr. J. Schurz on the occasion of his sixtieth birthday.     

Excess thermal noise and low-frequency oscillations during capillary flow of aqueous solutions of poly(ethylene oxide)

The excess thermal noise generated in polymer solutions through narrow capillaries is studied in detail for aqueous solutions of poly(ethylene oxide), , of varying concentration. With increasing flow rate, the excess noise level increases, the noise spectrum assuming a 1/f -form with 1.5. Within a critical flow range, distinct peaks appear in the spectrum, their frequencies being multiples of a fundamental frequency. The latter frequency (f ₀) is found to increase with the flow rate; this variation, as well as that brought about by varying concentration and capillary dimensions, can be accommodated in a single curve correlatingf ₀ with the shear rate at the capillary wall. No such correlation was found for the total noise level. The value off ₀ appeared to be determined by transversal oscillations of the liquid stream entering the capillary. Addition of small amounts of silica particles (Aerosil) led to the disappearance of the peaks in the spectrum.     

Rubber-like behaviour of poly(ethylene oxide) solution in elongational flow

The behaviour of an aqueous poly(ethylene oxide) sucrose solution and of a suspension of glass beads in a similar solution has been examined in elongational flow using a spinline rheometer. Over the accessible strain-rate range of ca. 1 to 10 s^?1 these fluids behaved essentially as elastic materials whereas, at similar strain rates in shear, they show shear-thinning behaviour.     

Rheological characterization of carbon nanotubes/poly(ethylene oxide) composites

Rheological properties of poly(ethylene oxide) nanocomposites embedded with carbon nanotubes (CNTs) were investigated in the present study. It was found that the CNT nanocomposites had a higher effective filler volume fraction than the real filler volume fraction, which yielded a drastic enhancement of shear viscosity. As the CNT loading in the nancomposites increases, non-Newtonian behavior was observed at the low-shear-rate region in the steady shear experiments. Oscillatory dynamic shear experiments showed that more addition of the CNTs led to stronger solidlike and nonterminal behaviors. To identify a dispersion state of the CNTs, field emission scanning electron spectroscopy and transmission electron microscopy were adopted and thermal analysis was also performed by using differential scanning calorimetry. The existence of percolated network structures of the CNTs even at a low CNT loading was verified by rheological properties and electrical conductivities.     

Rheological and molecular characterization of long-chain branched poly(ethylene terephthalate)

Reactive extrusion with pyromellitic dianhydride (PMDA) and tetraglycidyl diamino diphenyl methane (TGDDM) was conducted to create long-chain branched poly(ethylene terephthalate) (LCB-PET). The mechanical and molecular properties were analyzed by linear and non-linear viscoelastic rheology in the melt state and by size-exclusion chromatography measurements with triple detection. The two tetra-functional chain extenders lead to strong viscosity increases, increasing strain hardening effects, and increasing LCB with increasing chain extender concentration. Molecular stress function model predictions show good agreement with the elongational data measured and allowed a quantification of the strain hardening. Analysis of SEC triple detection data shows a strong increase of the average molar mass, polydispersity, radius of gyration, and hydrodynamic radius with increasing chain extender concentration. Branching was confirmed by a decreasing Mark-Houwink exponent, and the analysis of the contraction of the molecule revealed either star-like, comb-like, random tree-like or hyperbranched structures depending on concentration and type of chain extender.     

Flow birefringence of dilute solutions of polyethyleneoxide of high molecular weight at high rates

Summary Birefringence and orientation angle of solutions of Polyox WSR 301 in the concentration range of 50 to 1350 ppm have been measured up to 8000 s^–1. A few marked differences with ordinary flexible polymers have been evidenced: (i) a very low value of the extinction angle at high shear rate, which could be attributed to an unusually high molecular weight; (ii) the independence of this angle on the concentration, which is due to the variation of the flexibility with the concentration, as shown by the study of the concentration dependence of the segmental optical anisotropy; (iii) the concentration dependence of the elongation shows a plateau value forc 150 ppm, which may come from a concentration dependent and reversible association process, as shown from reduced viscosity measurements.

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Zusammenfassung Es wurden die Doppelbrechung und der Orientierungswinkel von Polyox-WSR 301-Lösungen im Konzentrationsbereich 50–1350 ppm bis zu Schergeschwindigkeiten von 8000 s^–1 gemessen. Dabei wurden einige ausgeprägte Unterschiede gegenüber normalen flexiblen Polymeren gefunden: (i) ein sehr niedriger Wert des Auslöschwinkels, was auf ein ungewöhnlich hohes Molekulargewicht schließen läßt: (ii) die Unabhängigkeit dieses Winkels von der Konzentration, was von einer Änderung der Flexibilität mit der Konzentration herrührt, wie sie durch die Untersuchung der Konzentrationsabhängigkeit der optischen Anisotropie der Segmente aufgezeigt wird; (iii) die Existenz eines Plateaus in der Konzentrationsabhängigkeit der Streckung beic 150 ppm, welches auf einen konzentrationsabhängigen reversiblen Assoziationsvorgang hindeutet, der auch durch Messung der reduzierten Viskosität nahegelegt wird.

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With 5 figures     

Linking the viscous and vacancy behavior of high molecular weight hydrocarbons

A new theoretical model that was recently purposed for zero-shear viscosity has now been extended to the three-branch alkanes with pentyl, hexyl, or phenyl attachments. The model links the equilibrium theory of Simha-Somcynsky (SS) statistical thermodynamics of liquids and the transport theory of Eyring Significant Structure (ESS). The predicted quantity of hole fraction as a measure of the free volume, computed from the SS equation of state, plays a primary role in the theory to combine the both theories. The experimental PVT data from 310 to 408 K temperature and 0.1 to 344.5 MPa pressure range have been used. The proportionality constants of the activation energy and the transmission coefficient have been calculated for each species separately and they are in expected trend with the substituted ring structure. Satisfactory agreement in prediction of viscosity from the hole fraction has been obtained.     

Rheological behaviour of poly(ethylene terephthalate) and poly(butylene terephthalate) blends

The presence of up to 4% Poly(butylene terephthalate) (PBT) in blends of Poly(ethylene terephthalate) (PET) with PBT results in an increase in viscosity and a decrease in activation energy, which has been related to the entanglement density. However, further increases in the amount of PBT up to 10% result in decreases in the viscosity, which may be due to partial phase segregation. Various blending rules have been applied to correlate the experimental results and predict the viscosities of the blends.     

Influence of dispersion procedure on rheological properties of aqueous solutions of high molecular weight PEO

The linear and nonlinear viscoelastic behaviors of poly(ethylene oxide) (PEO) in aqueous media have been investigated as a function of concentration and molecular weight. A particular interest has been paid to study the effect of turbulent flow under stirring, inducing both shear and elongational stresses, on the rheological behavior of the polymer solutions. The comparison of intrinsic viscosity and viscoelastic properties between shaken and stirred PEO solutions is discussed at the molecular scale in terms of chain scission and aggregation. Results point out that the effect of the mechanical history on the rheological response of PEO solutions depends also on the concentration regime and molecular weight. Indeed, the influence of the dispersion procedure vanishes by decreasing both the concentration and the molecular weight.     

Shear-thickening flow of suspensions of carbon nanofibers in aqueous PVA solutions

The suspensions of carbon nanofibers in aqueous poly(vinyl alcohol) solutions were prepared in the presence of spherical carbon black particles, and the steady-shear viscosity and dynamic viscoelasticity were measured for complex suspensions. Although the single suspensions of carbon black are highly stable, the flocculation of carbon nanofibers is promoted by the addition of carbon black particles. The complex suspensions show remarkable shear thickening in the steady-flow and strain hardening in oscillatory shear with large amplitude. The nonlinear responses strongly depend on the carbon black concentration, whereas the dynamic viscoelasticity at low strains in the linear ranges is not significantly influenced. As the highly elastic effects arise from the long-range motion of particles, the possible mechanism may be the orientation of nanofibers in strong shear fields. The suspensions show the time-dependent behavior of viscosity when the time-scale of measurements is shorter than that of structural recovery to the isotropic states.     

The effect of molecular weight on the rheological properties of poly(dimethylsiloxane) filled with fumed silica

The viscometric, stress relaxation, and stress growth rheological properties were measured for various molecular weight PDMS fluids filled with fumed silica. The stress growth function exhibited significant overshoot, when the continuous phase molecular weight was slightly greater than the entanglement molecular weight; however, significant overshoot peaks were not observed, when the continuous phase molecular weight was less than or much greater than the molecular weight between entanglements. The experimentally observed transient rheological properties are rationalized in terms of a molecular model, where interparticle interactions occur via entanglements of the polymer adsorbed on the silica surface. When the molecular weight of the adsorbed polymer is greater than the entanglement molecular weight, the strength of the interparticle interaction will increase substantially and the particle diffusivity will substantially decrease.     

Turbulent expansion flow of low molecular weight shear-thinning solutions

A Laser-Doppler anemometer and a pressure transducer were used to carry out detailed measurements of the mean and root mean square of the velocity and wall-pressure in an axisymmetric sudden expansion flow, with 0.4 and 0.5% by weight shear-thinning aqueous solutions of a low molecular weight polymer (6,000), after appropriate rheological characterisation. In spite of their very low molecular weight, these solutions still exhibited elongational elastic effects through drag reduction of up to 35% relative to Newtonian turbulent pipe flow, as shown by Pereira and Pinho (1994). The results showed small variations of the recirculation bubble length with polymer concentration and Reynolds number and reductions of the normal Reynolds stresses of up to 30%, especially in the tangential and radial directions. The reduction in normal Reynolds stresses within the shear layer is an elongational elastic effect, but this elasticity needs to be considerably more intense, such as with high molecular weight polymers, in order to strongly affect the mean flow characteristics. The observed mean flow patterns with these low molecular weight polymer solutions were indeed similar to those exhibited by Newtonian and inelastic fluids.     

Viscoelastic properties of semidilute poly(methyl methacrylate) solutions

Viscoelastic properties were examined for semidilute solutions of poly(methyl methacrylate) (PMMA) and polystyrene (PS) in chlorinated biphenyl. The number of entanglement per molecule, N, was evaluated from the plateau modulus, G _N . Two time constants, _s and ₁, respectively, characterizing the glass-to-rubber transition and terminal flow regions, were evaluated from the complex modulus and the relaxation modulus. A time constant _k supposedly characterizing the shrink of an extended chain, was evaluated from the relaxation modulus at finite strains. The ratios ₁/ _s and _k / _s were determined solely by N for each polymer species. The ratio ₁/ _s was proportional to N ^4.5 and N ^3.5 for PMMA and PS solutions, respectively. The ratio _k / _s was approximately proportional to N ^2.0 in accord with the prediction of the tube model theory, for either of the polymers. However, the values for PMMA were about four times as large as those for PS. The result is contrary to the expectation from the tube model theory that the viscoelasticity of a polymeric system, with given molecular weight and concentration, is determined if two material constants _s and G _N are known.