Quantitative rheological evaluation of phase inversion in two-phase polymer blends with cocontinuous morphology

 The present work is focused on the rheological properties of two-phase polymer blends in the phase inversion region. A large number of PS/PMMA- and PSAN/PMMA-blends has been investigated in order to establish a rheological criterion which allows the quantitative determination of the phase inversion concentration φ_PI by rheological means. Three rheological criteria based on the viscous and elastic blend properties such as maximum of dynamic viscosity η′, slope of G′, and maximum of G′ at a constant evaluation frequency have been tested. By correlating the rheological results to data from quantitative morphological analysis we could prove that the chosen rheological criteria are differently suitable for the determination of φ_PI. It has turned out that the G′ criterion is the most robust and most suitable one yielding an excellent correlation with morphological data. Based on these findings we propose a new simple equation for the prediction of φ_PI-values. Received: 14 March 2001 Accepted: 15 May 2001     

Rheological properties of polymer blends with sphere-in-sphere morphology

The linear viscoelastic behavior of polystyrene (PS) and poly(methylmethacrylate) (PMMA) blends with PS as the matrix and amounts of PMMA in the range 10–30 wt% was investigated. Transmission electron microscopy (TEM) revealed a complex morphology which was characterized by the existence of composite particles; the PMMA particles which are enclosed in the PS matrix themselves carry PS inclusions. In order to explain the G* data of these blends a model is presented which consists of a Palierne model for the composite particles and a Palierne model for the whole blend, taking into account composite and neat particles. Simulations show the principal relevance of the assumptions made. Moreover, it is shown that the measurements agree well with the model for the whole measured frequency region and that the fit parameters, the size of the composite particles and the concentration and size of interior particles are in reasonable agreement with data available from TEM. Received: 1 November 1998 Accepted: 5 April 1999     

Large-deformation properties of wheat dough in uni- and biaxial extension. Part I. Flour dough

Rheological and fracture properties of optimally mixed flour doughs from three wheat cultivars which perform differently in cereal products were studied in uniaxial and biaxial extension. Doughs were also tested in small angle sinusoidal oscillation. In accordance with previously published results the linear region was found to be very small. The rheological properties at small deformations hardly depended on the cultivar. A higher water content of the dough resulted in a lower value for the storage modulus and a slightly higher value for tan . For both uniaxial and biaxial extension a more than proportional increase in stress was found with increasing strain, a phenomenon called strain hardening. In uniaxial extension (i) stresses at a certain strain were higher and (ii) the stress was less dependent on the strain rate than in biaxial extension. This indicates that in elongational flow orientational effects are of large importance for the mechanical properties of flour dough. This conclusion is consistent with published data on birefringence of stretched gluten. Fracture stress and strain increased with increasing deformation rate. The observed time-dependency of fracture properties can best be explained by inefficient transport of energy to the crack tip. Presumably, this is caused by energy dissipation due to inhomogeneous deformation because of friction between structural elements, e.g. between dispersed particles and the network. Differences in the rheological properties at large deformations between the cultivars were observed with respect to (i) stress, (ii) strain hardening, (iii) strain rate dependency of the stress, (iv) fracture properties and (v) the stress difference between uniaxial and biaxial extension.     

Strain hardening in bent copper foils

A series of systematic tensile and microbend tests were conducted on copper foil specimens with different thicknesses. The specimens were made of a copper foil having almost unidirectional crystal orientations that was considered to be nearly single-crystal. In order to investigate the effects of slip system interactions, two different crystal orientations relative to the tensile direction were considered in the tests: one is close to coplanar double-slip orientation, and the other is close to the ideal cube orientation (the tensile direction nearly coincides to [0 0 1]) that yields multi-planar multi-slip deformation. We extended the microbend test method to include the reversal of bending, and we attempted to divide the total amount of strain-hardening into isotropic and kinematic hardening components. In the tensile tests, no systematic tendency of size dependence was observed. In the microbend tests, size-dependent kinematic hardening behavior was observed for both the crystal orientations, while size dependence of isotropic hardening was observed only for the multi-planar multi-slip case. We introduce an extended crystal plasticity model that accounts for the effects of the geometrically necessary dislocations (GNDs), which correspond to the spatial gradients of crystallographic slips. Through numerical simulations performed using the model, the origin of the size-dependent behavior observed in the microbend tests is discussed.     

Large-deformation properties of wheat dough in uni- and biaxial extension. Part II. Gluten dough

Glutens were isolated from flour of three European wheat cultivars which perform differently in cereal products. The rheological and fracture properties of gluten-water doughs were determined in uniaxial and biaxial extension at large deformations and small angle sinusoidal oscillation tests and compared with the mechanical properties of the parental flour doughs. At 25 °C the linear region was in the same range as that of flour dough, while at a higher temperature (45 °C) the linear region was more than an order of magnitude higher. At 45 °C the storage modulus and tan were lower than at 25 °C. Variation in moduli between cultivars was much more pronounced for gluten than for flour doughs.Similarly to flour dough in both uniaxial and biaxial extension the stress () increased more than proportionally with the strain, a phenomenon called strain hardening. The stress at a set strain and strain hardening depended much more strongly on the type of deformation for gluten than for flour dough: was higher in biaxial extension for gluten than for flour dough, but was much higher in uniaxial extension. This indicates that orientational effects in elongational flow are of even larger importance for the mechanical properties of gluten than of flour dough. It is likely that it is the glutenin fraction that, because of its large size, confers these direction dependent properties to gluten and flour doughs. Fracture stresses were much higher for gluten than for flour dough, while fracture strains were in the same range or higher. For gluten dough fracture strains increased less strongly with increasing strain rate than for flour dough. Glutens exhibiting a higher stress at a certain strain had a smaller fracture strain.Our findings confirm the conviction that the large deformation properties of flour dough are mainly governed by the gluten fraction. However, there are also differences. Compared to flour dough gluten dough exhibits (i) a stronger strain hardening, (ii) a larger difference in between uniaxial and biaxial extension and (iii) a smaller strain rate dependency of the fracture strain.     

Effect of a controlled pre-deformation history on extensional viscosity of dilute polymer solutions

We use a modified filament stretching rheometer to quantify the influence of a known controlled pre-shear history on the transient extensional viscosity of a dilute polymer solution. Two different types of pre-deformation are explored; both influence the subsequent stretching significantly, albeit in opposite ways. Small-amplitude oscillatory straining parallel to the direction of stretching enhances strain hardening and accelerates the tensile stress growth toward the steady-state value. Conversely, steady torsional shearing orthogonal to the direction of stretching retards strain hardening and results in a delayed approach to steady-state elongational flow. In both cases, the final steady-state extensional viscosity is the same as that observed with no pre-shearing. Calculations using a finitely extensible nonlinear elastic Peterlin dumbbell model qualitatively capture the trends observed in experiments, enabling interpretation of these observations in terms of the degree of polymer chain stretching imposed by the flow before extensional stretching.     

Capillary flow behavior of bicomponent polymer blends

The flow behavior of bicomponent polymer blends of four types of polymers (polypropylene, polystyrene, high-density polyethylene and polymethyl-methacrylate) was examined using a capillary extrusion rheometer. The viscosity of the blend was generally less than the value calculated by the theoretical or empirical additivity rules proposed in previous reports, whereas the entrance pressure loss, which is considered to be an effect of elasticity, was larger than the estimated value. Thus the variation of the viscosity with blending ratio was inversely proportional to the variation in the elastic property. The cross-section of the material extruded in a roughly dispersed state showed an annularly stratified flow pattern in which the lower viscosity component polymer appeared to form the outer skin layer. However, the observation that the viscosity of the properly blended material at certain blending ratios was sometimes lower than that of either homopolymer could not be explained.     

Comparison of the elongational behavior of various polyolefins in uniaxial and equibiaxial flows

For processing operations with a pronounced elongational component, it was found that the uniformity of extruded items is improved by the presence of strain hardening usually measured in uniaxial elongation. Many processing operations such as foaming, film blowing, and blow molding are dominated by biaxial deformations, however, and therefore, the question arises how strain hardening in uniaxial and biaxial deformation compares. Besides a linear and long-chain branched PP, one classical LDPE, an HDPE pipe extrusion grade with a bimodal MMD, and a LCB-mPE were also characterized. For the measurements in uniaxial elongation the Münstedt tensile rheometer (MTR) and the ARES-EVF were used, while the lubricated flow method was applied for equibiaxial deformation. It was found that the strain hardening in uniaxial elongation is more pronounced. The dependence of strain hardening on strain rate is qualitatively the same in both modes. In the range of strain rates, the chosen long-chain branched LDPE and PP exhibit a strain hardening, which is approximately independent of the elongational rates applied, whereas for the HDPE it becomes smaller with increasing rate.

Rheology and morphology of starch/synthetic polymer blends

Corn starch and maleic anhydride functionalized synthetic polymers were melt blended in a Haake twin-screw extruder. The amount of starch in the blends was 60 and 70% by weight. The synthetic polymer used was either styrene maleic anhydride (SMA) or ethylene propylene maleic anhydride copolymer (EPMA). The blends did not exhibit normal thermoplastic behavior; and hence, rheological data was obtained by extrusion feeding the material through a slit die or cylindrical tube viscometer. The starch/SMA blends were extruded through a slit viscometer with a 45% half entry angle, while the starch/EPMA blends were extruded through a cylindrical tube viscometer with a half entry angle of 37.5°. For the blends, data could be obtained at low to moderate shear rates (10< _app<200s^–1). At higher shear rates, blends exhibited slip and/or degradation of starch. The viscosity of the blends exhibited shear-thinning properties. Regrinding and re-extruding through the viscometer a second time showed a significant reduction in shear viscosity for starch/SMA blends. Gel permeation chromatography data indicated that starch macromolecules degraded upon successive extrusion. Extensional viscosity, as estimated from entrance pressure drop method for starch/EPMA blends showed stretch thinning properties. Regrinding and re-extruding showed that the samples were more sensitive to changes in extensional viscosity as observed from the Trouton ratio versus extension rate plot. Optical microscopy showed the presence of starch granules after melt blending, the size of which was related to the torque (or stress) generated during extrusion. The higher the torque, the smaller the size of the starch granules. Successive extrusion runs reduced the number of unmelted granules.Nomenclature A,B Constants associated with power law fluids (Pa s^{m or n}) - e Entrance correction - H Height of slit die (m) - m, n Flow behavior index in shear and extension flow respectively - P _s Shear component of the entrance pressure drop (Pa) - P _e Extensional component of the entrance pressure drop (Pa) - Q volumetric flow rate (m³S^–1) - R _o radius of barrel exit (m) - R ₁ radius of cylindrical die (m) - T _r Trouton ratio - w width of slit die (m) - pressure gradient (Pam^–1) - half die entry angle - P _en Entrance Pressure Drop (Pa) - apparent extension rate (s^–1) - apparent shear rate (s^–1) - _w wall shear stress (Pa) - first normal stress difference in uniaxial extension (Pa)     

Rheology of polymer blends: linear model for viscoelastic emulsions

 Kerner's model for flow of composite elastic media is extended to an emulsion of viscoelastic phases with interfacial tension undergoing deformations of small amplitude. A privileged internal structure inside the suspended drops is discussed in terms of fluid circulation across the interface. It is shown that for usual drop radius and interfacial tension values of emulsions, the rheological behavior predicted by the model, with very simple expression for the complex shear modulus, is quantitatively similar to that predicted by Palierne's model. Predictions of the model are compared with experimental data obtained on a polystyrene/polyethylene blend sheared in a small-amplitude oscillatory mode. Received: 10 August 1998 Accepted: 18 December 1998     

Stress relaxation as a microstructural probe for immiscible polymer blends

Relaxation has been investigated in immiscible blends that consist of slightly viscoelastic components. Both the shear and normal stresses have been measured after cessation of steady shear flow as well as after transient shear histories. The latter can generate a fibrillar structure which can relax by either retraction or break-up via end-pinching or Rayleigh instabilities. Each of these three relaxation mechanisms is reflected in the shape of the stress curves, from which also the corresponding structural time scales can be deduced. The experimental results have been used to evaluate the Doi-Ohta and Lee-Park models for immiscible blends. The scaling relations by Doi-Ohta are confirmed by the experimental results, but none of the existing models can correctly predict the complex relaxation behaviour observed for a highly deformed droplet phase. In the present study an alternative approach has been proposed. The stress relaxation due to fibril break-up via Rayleigh instabilities has been predicted successfully by combining physical models for the structural changes with the basic approach of the Doi-Ohta model.     

A generic stress-strain model for metallic materials with two-stage strain hardening behaviour

Constitutive equations are often used to describe the stress-strain behaviour of metallic materials. This allows the execution of parametric studies for various purposes. Despite the large number of developed stress-strain equations, all frequently applied ones fail to accurately describe a strain hardening behaviour in two distinct stages, which many metallic materials tend to show. For this purpose, the authors developed a new stress-strain model, based on the well-known Ramberg-Osgood equation, which focuses on this two-stage strain hardening behaviour. This article describes the model and its analytical background, along with a graphical method to derive suited model parameters. To validate the proposed methodology, it is applied on stress-strain curves of two high-strength steels, an aluminium alloy and a duplex stainless-steel alloy. Whereas a good correspondence for the stainless-steel alloy is confined to limited plastic strains, excellent agreements are observed for the steels and the aluminium alloy. Following the proposed method, it was possible to obtain model parameter values that give a good correspondence within a detectable strain range.     

Rheology of polymer blends

Rheological properties of blends of amorphous and crystalline polymers were studied for a broad range of compositions and temperatures. It was established that below the melting pointT _m the viscoelastic properties of blends of crystalline polymers are similar to those of polymers filled with mineral fillers. In both cases these properties are influenced by the existence, in such systems, of a temporary structural network formed by mineral or polymeric particles and its subsequent breakdown under the action of shear stresses. It was found that an anomalous decrease in the melt viscosity of the main component on addition of a small amount of a second polymer depended on deformation conditions. The comparison of data on viscoelastic properties and thermodynamic interaction between the components in the melt, estimated from the parameter ₂₃ of a new Flory theory, shows that the sharp drop of viscosity takes place in the region of microphase separation due to the appearance of an excess free volume in the interphase region. Calculation of the relaxation spectra for various blends also revealed marked changes when various amounts of a second component were added to the main polymer.     

Effect of interfacial tension on linear viscoelastic behavior of immiscible polymer blends

When interfacial tension is increased from zero to infinity, the storage dynamic modulus predicted by Palierne's model varies in a nearly Gaussian fashion with almost equal asymptotic values at the limits of low and high interfacial tension. We report a simple physical discussion of such an effect. Received: 13 January 1999 Accepted: 22 March 1999     

Anisotropic strain hardening behavior in simple shear for cube textured aluminum alloy sheets

Finite element (FE) simulations of the simple shear test were conducted for 1050-O and 6022-T4 aluminum alloy sheet samples. Simulations were conducted with two different constitutive equations to account for plastic anisotropy: Either a recently proposed anisotropic yield function combined with an isotropic strain hardening law or a crystal plasticity model. The FE computed shear stress–shear strain curves were compared to the experimental curves measured for the two materials in previous works. Both phenomenological and polycrystal approaches led to results consistent with the experiments. These comparisons lead to a discussion concerning the assessment of anisotropic hardening in the simple shear test.     

Uniaxial deformation and relaxation of polymer blends: relationship between flow and morphology development

Uniaxial elongational flow followed by stress relaxation of a dilute mixture of polystyrene/polymethylmethacrylate) PS/PMMA with PS (5 wt%) as a dispersed phase was investigated. The behavior of the blend was found to be dominated by the PMMA matrix during elongation and by the interface during the relaxation at long time. Such a behavior was related to drop deformation and shape recovery during the relaxation process as was confirmed by morphological analyses on samples quenched within the rheometer just after elongation and at various times during the relaxation process. The morphology and the rheological material functions variation were compared to the Yu model (Yu W, Bousmina M, Grmela M, Palierne JF, Zhou C (2002) Quantitative relationship between rheology and morphology in emulsions. J Rheol 46(6):1381–1399).     

Cyclic plastic deformation and cyclic hardening/softening behavior in 304LN stainless steel

Low cycle fatigue experiments have been conducted on 304LN stainless steel in ambient air at room temperature. Uniaxial ratcheting behavior has also been studied on this material and in both engineering and true stress controlling modes. It is shown that material’s cyclic hardening/softening behavior in low cycle fatigue and in ratcheting is dependent not only on material but also on the loading condition. Improvement of ratcheting life and mean stress dependent hardening are observed in the presence of mean stress. A method based on the strain energy density (SED) is used to represent cyclic hardening/softening behavior of the material in this work. The decrease of SED with cycles is an indication that the life in low cycle fatigue and in ratcheting is improved. The SED represents the area of the hysteresis loops.     

Rheology of immiscible blends with particle-induced drop clusters

We consider the effects of 2.7-μm-diameter hydrophobic silica particles added to droplet–matrix blends of polyethylene oxide (PEO) and polyisobutylene (PIB). The particles adsorb on the surface of the PEO drops but protrude considerably into the PIB phase. Hence, it is possible for a single particle to adsorb onto two PEO drops simultaneously. Such particles are called “bridging” particles, and they the glue drops into noncoalescing clusters. Flow visualization studies show that shearing the sample promotes bridging-induced clustering of drops and that the structure of the clusters depends on the shear rate. Rheologically, the most significant consequence of bridging-induced drop clustering appears to be a plateau in G′ at low frequencies characteristic of gel-like behavior. The gel-like behavior develops fully after shearing the sample, and the kinetics of gel formation are faster with increasing shear stress or increasing drop volume fraction. The gel-like behavior suggests that the bridging-induced drop clusters form a weak network. Apart from particle bridging, optical microscopy also reveals that particles can organize into a hexagonal lattice on the drops’ surfaces, a phenomenon that has only been noted in aqueous systems previously. Finally, rheology and flow visualization both suggest that particles promote coalescence of drops. This is surprising in light of much past research that shows that particles that are preferentially wetted by the continuous phase generally hinder coalescence in droplet–matrix systems.     

Strain hardening of fibrin gels and plasma clots

Biological macromolecules have unique rheological properties that distinguish them from common synthetic polymers. Among these, fibrin has been studied extensively to understand the basic mechanisms of viscoelasticity as well as molecular mechanisms of coagulation disorders. One aspect of fibrin gel rheology that is not observed in most polymeric systems is strain hardening: an increase in shear modulus at strain amplitudes above 10%. Fibrin clots and plasma clots devoid of platelets exhibit shear moduli at strains of approximately 50% that are as much as 20 times the moduli at small strains. The strain hardening of fibrin gels was eliminated by the addition of platelets, which caused a large increase in shear storage modulus in the low strain linear viscoelastic limit. The reduction in strain hardening may result from fibrin strand retraction which occurs when platelets become activated. This interpretation is in agreement with recent theoretical treatments of semi-flexible polymer network viscoelasticity.Dedicated to Prof. John D. Ferry on the occasion of his 85th birthday.     

Shear and normal stress relaxation in polymer blends: stress predictions from interface velocity and Laplace pressure terms

We derived for the first time the relationships among shear stress and normal stress differences for ellipsoidal interfaces under large step shear strains considering interface velocity term and Laplace pressure term in the expression of the stress tensor for mixtures of two Newtonian fluids. In the derivation, orientation angle of the interface is assumed to be given by the affine deformation assumption and is independent of time based on experimental results for blends with 0.048 ≤ K ≤ 0.54 where K is the ratio of droplet viscosity to matrix viscosity. For ellipsoidal droplets, the shear stress is only proportional to the first normal stress difference. On the other hand, for spheroidal droplets, proportionality among the shear stress, the first and the second normal stress differences was derived, and the ratio of the second normal stress difference to the first normal stress difference was given as a function of step strain. The shear stress and the first normal stress difference obtained experimentally satisfy the derived relationship, indicating applicability of the stress expression for polymer blends.