Stress relaxation behavior of PMMA/PS polymer blends

In this work, the stress relaxation behavior of PMMA/PS blends, with or without random copolymer addition, submitted to step shear strain experiments in the linear and nonlinear regime was studied. The effect of blend composition (ranging from 10 to 30 wt.% of dispersed phase), viscosity ratio (ranging from 0.1 to 7.5), and random copolymer addition (for concentrations up to 8 wt.% with respect to the dispersed phase) was evaluated and correlated to the evolution of the morphology of the blends. All blends presented three relaxation stages: a first fast relaxation which was attributed to the relaxation of the pure phases, a second one which was characterized by the presence of a plateau, and a third fast one. The relaxation was shown to be faster for less extended and smaller droplets and to be influenced by coalescence for blends with a dispersed phase concentration larger than 20 wt.%. The relaxation of the blend was strongly influenced by the matrix viscosity. The addition of random copolymer resulted in a slower relaxation of the droplets.     

Stress relaxation after steady shear flow in immiscible model polymer blends

Stress relaxation in immiscible blends is studied for a well defined shear history, i.e. after prolonged steady state shearing. Model systems are used that consist of quasi-Newtonian liquid polymers. Hence the relaxation is dominated by changes in the morphology of the interface. Both shear stress and the first normal stress are considered. The measurements cover the entire concentration range. For dilute blends the interfacial contribution to the stress relaxation compares well with model predictions. Deviations occur when the matrix phase is slightly elastic. In that case the similarity between the relaxation of shear and normal stresses is also lost. The latter is attributed to a wider drop size distribution.Increasing the concentration of the disperse phase results in a complex evolution of the characteristic relaxation times. The normal stresses relax systematically slower than the shear stresses and the concentration curve includes two maxima. Even for equiviscous components the concentration curves are not symmetrical. It is concluded that even a slight degree of elasticity in the matrix phase drastically affects the morphology and the interfacial relaxation of such blends.     

Temperature dependence of the interfacial tension of PS/PMMA, PS/PE, and PMMA/PE blends

The effect of temperature on the interfacial tension for PS/PMMA, PS/PE, and PMMA/PE was measured using the imbedded fiber retraction method. Interfacial tensions for PS/PMMA, PS/PE, and PMMA/PE were measured over temperature ranges of 160–250 °C, 140–220 °C, and 140–220 °C, respectively. The interfacial tension was found to follow a dependence of 3.6–0.013 T dyn/cm, 7.6–0.051 T dyn/cm and 11.8–0.017 T dyn/cm for PS/PMMA, PS/PE, and PMMA/PE, respectively. Comparison of the data with the mean field theory of Helfand and Sapse were made; however, a simple linear fit to the data described the temperature dependence in the experimental window as well as the predictions of the mean field theory. Received: 6 July 1999 Accepted: 23 March 2000     

Stress relaxation after a step strain in uniaxial extension of polyisobutylene and polyethylene

The morphology of molten polymeric materials is known to be less sensitive to shear than to extensional deformations. However, it is not easy to characterise molten polymeric materials in simple extensional flows due to the large number of experimental difficulties involved. This has led to the effective absence of a structure-preserving, morphology probing technique similar to the ones commonly found in shear, i.e., the equivalent of stress relaxation and oscillatory experiments. It is the aim of the present work to demonstrate the usefulness of a recently developed experimental technique that enables stress relaxation experiments after a step strain in uniaxial extension to be performed. Results are presented for two model melts (polyisobutylene, PIB, of different molecular weights) and for a series of linear low-density polyethylenes, LLDPE, in which the molecular structure (molecular weight, MW, molecular weight distribution, MWD and degree of long chain branching, LCB) is changed systematically. It is shown that, for both types of materials, stress relaxation experiments in extension yield quantitatively correct results and that this technique is more sensitive to differences in molecular structure than oscillatory experiments in shear.     

Stress relaxation after oscillatory shear in a thermotropic liquid crystalline polymer

We report investigations of the rheology of a thermotropic liquid crystalline polymer subjected to oscillatory shear. In particular, we have studied its stress relaxation behaviour and found it to be well-represented by the linear viscoelastic model. In our studies, we observed a strong dependence of the relaxation rate on the position in the strain cycle at which the shear is stopped; a result which we show to be a general phenomenon of viscoelastic fluids and not unique to liquid crystalline polymers.     

Nonlinear viscoelasticity of PP/PS/SEBS blends

The nonlinear viscoelastic behavior of polypropylene/polystyrene (PP/PS) blends compatibilized or not with the linear triblock copolymer (styrene-ethylene-/butylene-styrene, SEBS) was investigated. Start-up of steady-shear at rates from 0.1 to 10 s^–1 was carried out using a controlled strain rotational rheometer and a sliding plate rheometer for strain histories involving one or several shear rates. The shear stress and first normal shear stress difference were measured as functions of time, and the morphologies of the samples before and after shearing were determined. For each strain history except that involving a single shear rate of 0.1 s^–1 the blends showed typical non-linear viscoelastic behavior: a shear stress overshoot/undershoot, depending on the history, followed by a steady state for each step. The first normal stress difference increased monotonically to a steady-state value. The values of the stresses increased with the addition of SEBS. The shear stress overshoot and undershoot and the times at which they occurred depended strongly on the strain history, decreasing for a subsequent shear rate step performed in the same direction as the former, and the time at which stress undershoot occurred increased for a subsequent shear rate step performed in the opposite direction, irrespective of the magnitude of the shear rate. This behavior was observed for all the blends studied. The time of overshoot in a single-step shear rate experiment is inversely proportional to the shear rate, and the steady-state value of N₁ scaled linearly with shear rate, whereas the steady-state shear stress did not. The average diameter of the dispersed phase decreased for all strain histories when the blend was not compatibilized. When the blend was compatibilized, the average diameter of the dispersed phase changed only during the stronger flows. Experimental data were compared with the predictions of a model formulated using ideas of Doi and Ohta (1991), Lacroix et al. (1998) and Bousmina et al. (2001). The model correctly predicted the behavior of the uncompatibilized blends for single-step shear rates but not that of the compatibilized blends, nor did it predict morphologies after shearing.     

Evaluation by means of stress relaxation (after a step strain) experiments of the viscoelastic behavior of polymer melts in uniaxial extension

 As is widely acknowledged, morphology in most materials is far more sensitive to extensional than to shear deformations but, unfortunately, due to the experimental difficulties involved, there are no non-destructive, morphology probing techniques in such flows, i.e., the equivalent of stress relaxation and oscillatory experiments in shear flows. This paper tries to overcome some of those drawbacks by proposing an experimental technique that allows stress relaxation experiments after a step strain in uniaxial extension to be performed. The benefits of this technique are twofold: (a) while the deformation is small enough for the response to be in the linear viscoelastic regime it constitutes a probe of the microstructure of the material and (b) it allows the departure to the non-linear regime to be studied, useful, for example, for the definition of the damping function in uniaxial extensional flow or for the study of the response of materials to fast transient flows with a strong extensional component, such as contraction flows. In this work the proposed technique, which requires a correction to the apparent (theoretical) strain rate in order to allow the calculation of the true Hencky strains attained during the strain step, is tested and validated for two polyisobutylene melts. Received: 9 April 2001 Accepted: 26 July 2001     

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.     

Transient shear and elongational behavior of blends of PET with a LCP

Blends of polyethylene terephthalate (PET) with a liquid crystalline polymer (LCP) and a compatibilizer were produced by twin screw extrusion and injection molding. Transesterification and compatibilization studies were made in a torque rheometer. The morphology of the injection-molded plaques was studied by scanning electron microscopy. The blends shear growth function was measured in a cone and plate rheometer. The elongational growth function was measured in a modified rotational rheometer. Transesterification was observed in the PET/LCP/compatibilizer 95/5/0 blend. The injection-molded plaques displayed the usual “skin-core” morphology. All the blends were highly shear-thinning, even at low shear rates; thus, a zero-shear viscosity could not be calculated. The compatibilized blend had the highest shear viscosity of all the blends, confirming the strong PET/LCP interphase and the effectiveness of the compatibilizing agent. On the other hand, the 90/10/0 blend had the lowest shear viscosity. All the blends showed strain softening behavior, similar to the PET. The 90/10/0 blend had the highest elongational growth function, while the 95/5/0 had the lowest. The compatibilized blend had an intermediate behavior between both blends.     

Evaluation of rheological constitutive equations for branched polymers in step shear strain flows

The pom-pom rheological constitutive equation for branched polymers proposed by McLeish and Larson is evaluated in step shear strain flows. Semianalytic expressions for the shear-stress relaxation modulus are derived for both the integral and approximate differential versions of the pom-pom model. Predictions from the thermodynamically motivated differential pompon model of ?ttinger are also examined. Single-mode integral and differential pom-pom models are found to give qualitatively different predictions, the former displays time–strain factorability after the backbone stretch is relaxed, while the latter does not. We also find that the differential pompon model gives quantitatively similar predictions to the integral pom-pom model in step strain flows. Predictions from multimode integral and differential pom-pom models are compared with experimental data on a widely characterized, low-density polyethylene known as 1810H. The experiments strongly support time–strain factorability, while the multimode pom-pom model predictions show deviations from this behavior over the entire range of time that is experimentally accessible.     

Morphology development of a PS/PMMA polymer blend during flow in dies

The morphology development in dilute and semi-concentrated blends (2 and 15 wt% disperse phase) of viscoelastic polymers is studied during flow in dies. In the entrance region the droplets deform into fibrils. In the die itself some of the fibrils can break up depending on their shear history and hence on their radial position. The morphology at the exit of the die is investigated by quenching the extrudate and visualizing the structure via scanning electron microscopy (SEM). For fibrils moving along the die axis, the theory of Tomotika for break-up of a fibril in a quiescent matrix describes the observations satisfactorily. Fibrils flowing off center undergo a shearing flow in the die, which could have an effect on the growth of the Rayleigh disturbances that cause break-up. It is observed that during flow break-up still occurs via Rayleigh instabilities. As a first approximation the theory of Tomotika also predicts the break-up of fibrils flowing off center, if the viscosity at the relevant shear rate is used.     

Rheological behavior of poly(methyl methacrylate)/polystyrene (PMMA/PS) blends with the addition of PMMA-<Emphasis Type="BoldItalic">ran</Emphasis>-PS

In this work, the dynamic behavior of poly(methyl methacrylate)/polystyrene blend to which P(S_0.5-ran-MMA_0.5) was added was studied. Several blend (ranging from 5 to 20 wt% of dispersed phase) and copolymer (up to 20 wt% with respect to dispersed phase) concentrations were studied. The rheological behavior of the blends was compared to Bousmina’s (Rheol Acta 38:73–83, 1999) and Palierne’s (Rheol Acta 29:204–214, 1990) generalized models. The relaxation spectra of the blends were also inferred, and the results were analyzed in light of the analysis of Jacobs et al. [J Rheol 43:1495–1509, 1999]. The relaxation spectra of the blends with smaller dispersed phase (below 10 wt%) and larger copolymer concentrations (above 0.4 wt%) showed the presence of four relaxation times, two corresponding to the blend phases, τ _F , corresponding to the relaxation of the shape of the dispersed phase of the blend and that can be attributed to the relaxation of Marangoni stresses tangential to the interface between the dispersed phase and matrix. The experimental values of and were used to infer the interfacial tension (Γ) and the interfacial complex shear modulus (β) for the different blends, Γ decreased with increasing copolymer concentration. β decreased with increasing blend dispersed phase concentration and decreasing copolymer concentration. The predictions of Palierne’s generalized model were found to corroborate the experimental data once the values of Γ and β, found analyzing the relaxation spectra, were used in the calculations. Bousmina’s model was found to corroborate the data only for larger dispersed phase concentration. Paper was presented at the 3rd Annual Rheology Conference, AERC 2006, April 27–29, 2006, Crete, Greece.     

Uniaxial elongational viscosity of PS/a small amount of UHMW-PS blends

A series of polystyrene (PS) and a small amount of ultra high molecular weight (UHMW) PS blends have been prepared by using tetrahydrofuran (THF). Matrix PS has an M_w of 423,000 (M_w/M_n= 2.36) and UHMW-PS has either an M_w of 3,220,000 (M_w/M_n= 1.05) or 15,400,000 (M_w/M_n=1.30) in the range of concentration from 0 wt% to 1.5 wt%. The influence of a small amount of UHMW on dynamic viscoelasticity was investigated. At the frequency lower than 0.001 rad/s, the enhancement of G′ was observed by the incorporation of a small amount of UHMW. And the degree of enhancement was in the order of M_w of UHMW and its concentration. The measurement of uniaxial elongational viscosity for the blends was performed and the effects of UHMW on strain-hardening properties were analyzed at equal strain-rate conditions. The concentration of UHMW where the strain-hardening becomes substantially stronger was determined. To get more insight into the cause of enhancement of strain-hardening at a certain concentration, the damping function from step-shear stress relaxation was measured. The influence of a small amount of UHMW on the damping function was found to be small. It was interpreted, from time- and strain-dependency points, that the enhancement of strain-hardening by a small amount of UHMW was governed by the long relaxation time. Received: 6 September 2000 Accepted: 11 January 2001     

Comparison of optical and mechanical measurements of second normal stress difference relaxation following step strain

Relaxation of the second normal stress difference (N ₂) following step strain of a concentrated monodisperse polystyrene solution has been studied using mechanical and optical rheometry. Measurements of normal thrust in a parallel plate geometry are corrected for strain inhomogeneity and combined with independent measurements of the first normal stress difference (N ₁) to determine N ₂. Optical experiments were performed using a novel configuration where flow birefringence data collected using multiple light paths within the shear plane are combined with the stress-optical law to determine all three independent stress components for shearing deformations. This technique eliminates end effects, and provides an opportunity to oversample the stress tensor and develop consistency checks of experimental data. N ₂ is found to be nonzero at all accessible times, and relaxes in roughly constant proportion to N ₁. This reflects nonaffine distribution of chain segments, even well within the regime of chain retraction at short times. Data collected with the two techniques are reasonably consistent with each other, and with results of previous studies, generally lying between the predictions of the Doi-Edwards model with and without the independent alignment approximation. The normal stress ratio –N ₂/N ₁ shows pronounced strain thinning in the nonlinear regime.     

Stress relaxation of a polymer melt after extensional flow

The relaxation behaviour of a stretched polymer melt is described with the aid of the semi-empirical constitutive equation of Wagner. The theoretical predictions based on this model, are in fair agreement with the experimental results, as far as the period of stress decay following the stress build-up is not too long.     

Effects of compatibilization on rheological properties of PS/PB blends and investigation of Doi–Ohta scaling relationship in double start-up of shear experiments

The rheological properties for the blends of polystyrene and polybutadiene were investigated and the effect of compatibilizer styrene butadiene rubber (SBR), on the blends were studied and the results compared with the non-compatibilized blends. The frequency sweep, step shear strain and shear stress growth experiments were carried out for the blends. The results showed that with addition of compatibilizer the changes in behavior of the rheological properties of blends are observed. These rheological variations could be related to the reduction of interfacial tension and size of dispersed phase. Furthermore, the validity of Doi–Ohta scaling relationship in double start-up experiments was studied. It is shown that this scaling relationship becomes more reliable with increasing the amount of PB and compatibilizer.     

Finite shear strain behavior of a crosslinking polydimethylsiloxane near its gel point

A power law distribution of relaxation times, large normal stress differences, and physical rupture of molecular network strands dominate the shear behavior of polymers at the gel point (critical gels). This is shown in a series of well-defined experiments with increasing magnitude of shear on a model-network polymer system consisting of a linear, telechelic, vinyl-terminated poly-dimethylsiloxane (PDMS) and a four-functional siloxane crosslinker. Stable samples were prepared by stopping the crosslinking reaction at different extents of reaction in the vicinity of the gel point (GP). The Gel Equation has been shown to be valid up to strains of about 2 when using a finite strain tensor. Larger strains have been found to disrupt the network structure of the crosslinking polymer, and introduce a mechanical delay to the gel point. A sample that was crosslinked beyond the gel point (p>p _c ) can be reduced from the solid state to a critical gel, or even to a viscoelastic liquid, depending on the magnitude of shear strain. As a consequence, the relaxation exponent of a critical gel created under the influence of shear is less than that of a quiescently crosslinked critical gel.     

Elastic recovery of immiscible blends 1. Analysis after steady state shear flow

Due to the interfacial tension, immiscible blends can show an elastic recovery that is substantially larger than that of their pure components. Here it is attempted to relate the elastic recovery after steady shear flow to the underlying morphology. On the one hand, the predictions of the Palierne and the Doi-Ohta models are calculated for the flow conditions during recoil. On the other hand, systematic recoil experiments after steady state shearing have been performed on a model blend. As the component polymers hardly show any recoil under the stresses applied in these tests, the measured recovery can be attributed completely to the action of the interface. Comparison of the model predictions with the experimental results shows that the recoverable strain can be derived quantitatively from the linear Palierne theory. Although the droplet deformation remained limited during the preshear, the retardation time predicted by this model has to be multiplied by the aspect ratio of the droplet phase to the power 2/3 to describe the experiments. For conditions in which the material does not show an intrinsic length scale, particular scaling relations as derived from the Doi-Ohta theory are found to apply also to recoil. Received: 5 August 1998 Accepted: 17 November 1998