Melt viscosity of linear and branched poly(butyleneisophthalate)

Linear and branched poly(butyleneisophthalate) samples were synthesized and characterized in terms of the intrinsic viscosity, the molecular weight and the melt viscosity over a wide range of shear rates at 200 °C. An exponent of about 4.6 in the equation relating ₀ to was found for linear samples; this high value is probably due to the high content of cyclic oligomers in low molecular weight samples. Both linear and branched samples exhibited Newtonian behaviour over a rather wide range of shear rates, but for any given melt-viscosity, the branched samples became shear thinning at lower shear rates than the linear ones. Our experimental data were found to fit a previously proposed correlation between the melt viscosity ratio ( _{0, b} / _{0, 1} ) and a branching index quite well.     

Evaluating Herschel-Bulkley fluids with the back extrusion (annular pumping) technique

A mathematical model was developed to describe the behavior of Herschel-Bulkley fluids in a back extrusion (annular pumping) device. A technique was also developed to determine the rheological properties (yield stress, flow behavior index, and consistency coefficient) of these fluids. Mathematical terms were expressed in four dimensionless terms, and graphical aids and tables were prepared to facilitate the handling of the expressions.Nomenclature a radius of the plunger, m - dv/dr shear rate, s^–1 - F force applied to the plunger, N - F _b buoyancy force, N - F _cb force corrected for buoyancy, N - F _T recorded force just before the plunger is stopped, N - F _Te recorded force after the plunger is stopped, N - g acceleration due to gravity, m/s² - H(t) momentary height between plunger and container bottom, m - K a/R, dimensionless - L length of annular region, m - L(t) depth of plunger penetration, m - n flow behavior index, dimensionless - p static pressure, Pa - P _L pressure in excess of hydrostatic pressure at the plunger base, Pa - p ₀ pressure at entrance to annulus, Pa - P pressure drop per unit of length, Pa/m - Q total volumetric flow rate through the annulus, m³/s - r radial coordinate, measured from common axis of cylinder forming annulus, m - R radius of outer cylinder of annulus, m - s reciprocal of n, dimensionless - t time, s - T dimensionless shear stress, defined in Eq. (3) - T ₀ dimensionless yield stress, defined in Eq. (4) - T _w dimensionless shear stress at the plunger wall - _p velocity of plunger, m/s - velocity, m/s - mass density of fluid, kg/m³ - Newtonian viscosity, Pa s - P p ₀ –p _L , Pa - consistency coefficient, Pa sⁿ - value of where shear stress is zero - _–, ₊ limits of the plug flow region (Fig. 1) - r/R - shear stress, Pa - _y yield stress, Pa - _w shear stress at the plunger wall, Pa - dimensionless flow rate defined in Eq. (24) - dimensionless velocity defined by Eq. (5) - _–, ₊ dimensionless velocity outside the plug flow region - _max dimensionless maximum velocity in the plug flow region - _p dimensionless velocity at the plunger wall     

Growths of mechanical elasticity and electrical conductance of graphene nanoplatelet/poly(lactic acid) composites under strong electric field: correlation with time evolution of higher order structure of graphene nanoplatelets

For a composite of poly(lactic acid) containing graphene nanoplatelets (GNPs) at a low concentration (0.34 vol%), this study examined growths of mechanical and electrical properties under an alternating current (AC) electric field, focusing on field-induced GNP structures governing those properties. The composite was subjected to the AC field (60 Hz) of various intensities E for various times t _E at 190 °C. A fraction of randomly oriented GNPs was aligned by the field and then connected into columns, as suggested from optical microscopy. This structural evolution led to qualitatively similar growths of low-frequency storage modulus and static electrical conductivity. The key quantity for understanding this growth was a time t _E* for occurrence of short circuit that detected formation of GNP columns conductively bridging the electrodes. The growths of both modulus and conductivity for various E were summarized as functions of a reduced variable, t _E/t _E*, confirming the growths commonly reflected the evolution of the GNP columns. However, the modulus grew fast and leveled off by t _E/t _E* ~ 1, whereas the conductivity kept growing gradually even at t _E/t _E* > 1. This difference was discussed in relation to the matrix chains and leftover GNPs out the column.     

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.     

Viscoelastic flow simulation of polytetrafluoroethylene (PTFE) paste extrusion

Polytetrafluoroethylene (PTFE) is known to be a polymer that shows inherent microstructure formation during cold processing such as paste extrusion. To model such a complex flow, a viscoelastic constitutive equation is proposed that takes into account the continuous change of the paste microstructure during flow, through fibril formation. The mechanism of fibrillation is captured through a microscopic model for a structural parameter ξ that represents the percentage of fibrillated domains of the paste. The proposed viscoelastic constitutive equation consists of a viscous shear-thinning term (Carreau model) and an elastic term (modified Mooney–Rivlin model), the relative contribution of the two depending on ξ. The viscous and elastic parameters of the model are determined by using shear and extensional rheometry on the paste. Finite element simulations based on the proposed constitutive relation with the measured model parameters predict reasonably well the variations of the extrusion pressure with the apparent shear rate and the die geometrical characteristics.     

Rheology of critical LCST polymer blends: poly(styrene-co-maleic anhydrite)/poly(methyl methacrylate)

The shear rheology of a binary polymer blend exhibiting a lower critical solution temperature (LCST) phase diagram and a small dynamic asymmetry (difference of glass transition temperatures between its constituents) has been investigated in the vicinity of phase separation; it is a mixture of a random copolymer of styrene and maleic anhydrite and poly(methyl methacrylate). In the linear viscoelastic regime, the material functions are sensitive to phase separation, and the effects of critical concentration fluctuations, which dominate the mechanical response, are quantified, yielding both the binodal and spinodal curves. The weak dynamic asymmetry is apparently responsible for the reduced magnitude of the observed effects, compared to blends exhibiting much larger contrast in glass transition; therefore, this property affects to some degree the accuracy of the rheologically determined phase diagram. The steady shear properties are weakly sensitive to phase separation, and suggest that shear-induced demixing may be possible. They also indicate the importance of the amount of strain energy introduced to the blend in controlling the effects of flow on phase behavior.This investigation demonstrates that the universal effects of concentration fluctuations can be detected in LCST binary polymer blends, provided that some dynamic asymmetry exists, and further they can be quantified in order to characterize the interplay between rheology and thermodynamics of these systems.Dedicated to the memory of Professor Tasos C. Papanastasiou     

Longitudinal volume viscosity of poly (vinyl chloride)

The volume flow of poly (vinyl chloride) ( = 45,000,T _g = 350 K) has been measured in an Instron Capillary Rheometer.The elastic modulus in longitudinal compression, the longitudinal volume viscosity and initial longitudinal volume viscosity, and retardation times were determined at temperatures both below (324 – 343 K) and above (403 – 453 K) the glass transition temperatureT _g , and at compression rates between approximately 10^–5 and 200 · 10^–5 s^–1.An increase in the longitudinal volume viscosity was observed for decreases in the volume deformation, increases in the compression rate and increases in temperature.T _g decreased at 0.16 K/MPa. The volume flow activation energy was found to be equal to that for shear flow with a constant value of 91.37 kJ/mol.     

Rheological characterization of highly branched poly(ethyleneterephthalate)

Linear and highly branched poly(ethyleneterephthalate) samples were synthesized and characterized in terms of intrinsic viscosity, molecular weight and melt viscosity over a wide range of shear rates at several temperatures, in the range from 265° to 295 °C. Linear samples exhibited Newtonian behavior over a wide range of shear rates, while the branched ones became shear thinning at relatively low shear rates. Our experimental data, as well as data previously reported, were found to be described by a proposed correlation between the melt viscosity ratio and a branching index. Moreover, the activation energy for melt flow was found for the highly branched samples to be a little higher than that of the linear samples.     

Compression creep of molten poly (butylene terephthalate)

Viscoelastic parameters of poly(butylene terephthalate) melt in compression creep have been measured in an Instron Capillary Rheometer. Bulk compression creep complianceB(t) shows plateau regions in the molten state and in the melt crystallized state, both decreasing with increasing stress. Shifting ofB(t) curves provides master curves suitable for analyzing the total (superposed elastic and viscous) bulk compression behavior.Volume viscosity decreases with both increasing stresses and compression rates but seems to be independent of temperature. Its values are larger than those from constant compression rate experiments, possibly due to the presence of elastic effects.     

Rheological characterization of cross-linked poly(methyl methacrylate)

Poly(methyl methacrylate) (PMMA) with various degrees of cross-linking were prepared from methyl methacrylate and a cross-linker, and the effect of dilution of the polymerizable mixture by a thermoplastic PMMA on the cross-linked PMMAs was evaluated. The rheological properties were characterized in linear viscoelasticity and in uniaxial extensional flow. A critical gel is formed at concentrations of the cross-linking agent neopentyl glycol dimethacrylate (NPG) of approximately 250 mol ppm both in the case of PMMAs, which are not diluted by an addition of thermoplastic PMMA to the monomer (Recipe-A), and of PMMAs, which were obtained by an addition of 25 wt% low molecular weight thermoplastic PMMA to the monomer (Recipe-B). Significant strain hardening is observed for concentrations of NPG at and above 100 mol ppm for PMMAs based on Recipe-A and for all PMMAs produced by Recipe-B. At the same NPG concentration of 30 mol ppm, PMMA produced by Recipe-A shows very little strain hardening, while PMMA produced by Recipe-B shows significant strain hardening. This is due to the difference in the molecular weight distribution: PMMA from Recipe-A is mono-modal with M _w /M _n = 2.5, while PMMA from Recipe-B is bimodal with M _w /M _n = 5.6. Surprisingly, the strain-hardening tendency is strongly increasing with increasing NPG concentration, and at the same NPG concentration, the strain hardening of PMMAs produced by Recipe-B is higher than that of PMMAs produced by Recipe-A. This difference can be attributed to the dilution effect of the (unreacted) thermoplastic PMMA in Recipe-B PMMAs. The elongational flow behavior was also analyzed by the Molecular Stress Function (MSF) model.     

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.     

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.     

Wall slip and melt fracture of poly(lactides)

The wall slip and melt fracture behaviour of several commercial polylactides (PLAs) as well as their rheological properties under shear and extensional have been investigated. The PLAs have had weight-average molecular weights in the range of 10⁴–10⁵ g/mol and studied in the temperature range of 160–200°C. The solution properties and linear viscoelastic behaviour of melts indicate linear microstructure behaviour. PLAs with molecular weights greater than a certain value were found to slip, with the slip velocity to increase with decrease of molecular weight. The capillary data were found to agree well with linear viscoelastic envelope once correction for slip effects was applied. The onset of melt fracture for the high molecular weight PLAs was found to occur at about 0.2 to 0.3 MPa, depending on the geometrical characteristics of the dies and independent of temperature. Addition of 0.5 wt.% of a polycaprolactone (PCL) into the PLA that exhibits melt fracture was found to be effective in eliminating and delaying the onset of melt fracture to higher shear rates. This is due to significant interfacial slip that occurs in the presence of PCL.     

Effect of nanofillers on the phase separation and rheological properties of poly(methyl methacrylate)/poly(styrene-co-acrylonitrile) blends

The viscoelastic characteristics of the blends of poly(methyl methacrylate)/poly(styrene-co-acrylonitrile) (PMMA/SAN) were investigated at various temperatures below, near, and above the phase separation temperature. The investigated polymer system is characterized by a lower critical solution temperature. Rheological behavior of the blends in the region of a phase separation was compared with change of the light scattering intensity. The presence of nanofillers in the blend results in that the phase separation occurs at a higher temperature. At the isothermal conditions, the phase separation begins earlier and proceeds with a higher rate as compared with the same blend without filler. The results of the study show the considerable change of the viscoelastic characteristics of PMMA/SAN when the polymer system passes from the homogeneous state to the heterogeneous one. Such characteristics as the dependence of the storage modulus (G ^′) on the loss modulus (G ^″), the dependence of the loss viscosity (η ^″) on the dynamic viscosity (η ^′), the dependences of the complex viscosity (η*), and the free volume fraction (f) on the blend composition are the most sensitive to the phase separation. The phase separation affects the characteristics G ^′(ω), where ω is the frequency only in a low-frequency range. Temperatures of phase separation were estimated using dependence G ^′(T) at ω, which is the constant in the range of low frequencies.     

Rheological properties of concentrated latex suspensions of poly(styrene-butadiene)

Concentrated suspensions of charged latex particles of poly(styrene-butadiene) have been used as model systems to investigate the influence of surface charges on the rheology of colloidal suspensions. The suspensions were found to behave as elastic solids at small strains and to require a finite stress to flow. This was related to an ordered structure of the suspensions at rest, resulting from electrostatic and van der Waals forces. Important shear-thinning effects were observed as a consequence of structure rearrangements under shear. At a fixed shear rate, the steady-shear viscosity as a function of the ionic strength exhibits a minimum. Under oscillatory shear flow, the behavior of the concentrated suspensions was found to be non-linear above a very small strain amplitude. The non-linear output signal from dynamic experiments was analyzed using a fast Fourier transform algorithm. A maximum in the third harmonic intensity as a function of the strain amplitude was observed and the intensity of higher harmonics decreased with increasing ionic strength. The behavior of the suspensions could be adequately described using the structural model of Yziquel et al. (Yziquel F, Carreau PJ, Moan M, Tanguy PA (1999) Rheological modeling of concentrated colloidal suspensions. J Non-Newtonian Fluid Mech 86:133–155).     

Rheological properties of poly(dimethylsiloxane) filled with fumed silica: I. Hysteresis behaviour

The apparent viscosity and primary normal stress difference were measured for dispersions of fumed silica in poly(dimethylsiloxane). Dispersions with less than 4.75% by weight of filler exhibit hysteresis in both the viscosity and normal stress, when the shear rate was increased and then decreased in discrete steps. The shape of the hysteresis loops were sensitive to the details of the deformation history. By using the appropriate deformation history, the material properties determined during the increasing shear rate part of the hysteresis experiment compare favourably with the steady-state rheological properties. The rheological properties of the dispersion were quite sensitive to the age of the fluid with no hysteresis behaviou exhibited by dispersions less than three days old. For dispersions with at least 4.75% by weight of fumed silica, neither the apparent viscosity nor the primary normal stress coefficient exhibited significant hysteresis behaviour. The relationship between the observed rheological behaviour and the dispersion's microstructure is discussed.     

Indentation lifetime of swollen poly (β-hydroxyethyl methacrylate) networks

Summary An original indentation lifetime method was used in the investigation of the ultimate properties of crosslinked poly(-hydroxyethyl methacrylate) gels swollen with water to equilibrium. The method consists in the determination of the time (indentation lifetime,) which is needed to produce a failure in a polymer sample by means of a thin cylindrical indentor under constant load. The curves obtained by plotting the indentation lifetimex in dependence on stress at various temperatures can be superimposed to yield a universal dependence; the temperature dependence of the shift factorsa _T obeys theWLF equation. It was found that thea _T values corresponded to the shift factors of the viscoelastic statical measurements at much shorter times.From the temperature dependence of the indentation lifetime, the valuesT _s from theWLF equation were determined for samples swollen to equilibrium and prepared at various concentrations of the crosslinking agent or diluent at polymerization. The difference found between the dependence of theT _s values on the concentration of the crosslinking agent and diluent and the same dependence determined in dry samples by measuring the creep compliance was elucidated. The non-monotonous dependence of the indentation lifetime values on stress was explained in terms of the specific deformation and stress geometry of the indentation test.

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Zusammenfassung Zur Untersuchung des Festigkeitsverhaltens im Wasser gequollener vernetzter Gele des Poly--Hydroxymethylmethacrylates wurde eine Methode der Penetrationslebensdauer verwendet. Die Methode beruht in der Bestimmung der Zeit (Penetrationslebensdauer), die zur Zerstörung eines Prüfkörpers durch einen konstant belasteten dünnen zylindrischen Indentor nötig ist. Die Kurven der Penetrationslebensdauer in Abhängigkeit von der Druckspannung, die verschiedenen Temperaturen entsprechen, können in eine gemeinsame Abhängigkeit superponiert werden; die Temperaturabhängigkeit der Temperaturreduktionsfaktorena folgt derWLF-Gleichung. Diea _T -Werte entsprechen den statischen viskoelastischen Temperaturreduktionsfaktoren bei viel kürzeren Zeiten.Für gleichgewichtsgequollene Proben, die mit verschiedenen Konzentrationen des Vernetzungs- bzw. Verdünnungsmittels bei der Polymerisation hergestellt wurden, wurdenT _s -Werte aus derWLF-Gleichung festgestellt. Es wurde der Verlauf derT _s -Werte in Abhängigkeit von der Vernetzungsmittelkonzentration diskutiert im Vergleich mit derselben Abhängigkeit, die bei trockenen Proben mit Hilfe der Kriechmessung gefunden wurde. Der amonotone Verlauf der Penetrationslebensdauerwerte in Abhängigkeit von der Spannung wurde der spezifischen Verformungs- und Spannungsgeometrie zugeschrieben.