Stress relaxation behavior of co-continuous PS/PMMA blends after step shear strain

Stress relaxation probing on the immiscible blends is an attractive route to reveal the time-dependent morphology–viscoelasticity correlations under/after flow. However, a comprehensive understanding on the stress relaxation of co-continuous blends, especially after subjected to a shear strain, is still lacking. In this work, the stress relaxation behavior of co-continuous polystyrene/poly(methyl methacrylate) (50/50) blends with different annealing times, strain levels, and temperatures was examined under step shear strain and was correlated with the development of their morphologies. It was found that co-continuous blends display a fast relaxation process which corresponded to the relaxation of bulk polymer and a second slower relaxation process due to the recovery of co-continuous morphology. The stress relaxation rates of co-continuous blends tend to decrease due to the coarsening of instable co-continuous structure during annealing. Furthermore, the stress relaxation of the co-continuous blends is strongly affected by the change of viscosity and interfacial tension caused by the temperature. The contribution of morphological coarsening, viscosity, and interfacial tension variation on the stress relaxation behavior of co-continuous blends was discussed based on the Lee–Park model and time–temperature superposition principle, respectively.     

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     

Rheological behavior of compatibilized and non-compatibilized PA6/EPM blends

The rheological properties of PA-6/EPM polymer blends, non-compatibilized and compatibilized with grafted ethylene propylene rubber (EPM-g-MA), have been investigated. Linear and non-linear (relaxation both in shear and extension) experiments were realized. Stress relaxation experiments coupled with scanning electron microscopy (SEM) analysis showed the existence of one relaxation time and non-deformed droplets for the immiscible blend, and two relaxation times and deformed droplets for the compatibilized ones, the second relaxation being more pronounced for higher compatibilizer contents. These results clearly indicate that, despite the high viscosity and elasticity ratios, if high amounts of compatibilizer are added to the blend, interfacial slip is suppressed and a high-enough adhesion between the phases is achieved for the high-viscosity dispersed phase to be deformed. Paper presented at the 3rd Annual European Rheology Conference, April 27–29, 2006, Crete, Greece     

Rheology of compatibilized immiscible viscoelastic polymer blends

Rheological behavior of a PS/PE model viscoelastic immiscible blend compatibilized by two types of interfacial modifiers was investigated. Dynamic, steady shear, and transient experiments were performed to probe the effect of the interfacial modification on the rheological behavior of the blend. While the effect was relatively small in dynamic and steady shear experiments, significant signature of the presence of the copolymer was observed in transient experiments after start up of shear flow. The magnitude of the departure from Doi-Otha theory (worked out for non-compatibilized blends) was evaluated. Received: 6 March 2000 Accepted: 15 June 2000     

Effect of temperature and molecular weight on the interfacial tension of PS/PDMS blends

The imbedded-fiber retraction (IFR) method was used to study the effect of temperature and PDMS molecular weight on the interfacial tension of PS/PDMS blends. The interfacial tension decreased with increasing temperature and analysis of the temperature dependence using a simple linear fit gave –dγ/dT value of 0.058±0.010 dyn/cm-deg. Reported –dγ/dT values of PS/PDMS blends are highly dependent on the molecular weights of the polymers and can have values that are <0, 0, or >0. Our interfacial tension values were independent of the molecular weight of PDMS and this was attributed to the molecular weights studied here being well above the entanglement values of both polymers. However, analysis of interfacial tension data from this work and the literature showed the following empirical relationship between apparent blend molecular weight, M_b, and interfacial tension of PS/PDMS blends with a correlation of 0.94: γ₁₂=γ₀+k₂M_b ^(–2/3), where γ₀=7.3±0.3 dyn/cm; k₂=–517±41 (dyn/cm)(g/mol)^2/3.     

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.     

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).     

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.     

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.     

The influence of matrix viscoelasticity on the rheology of polymer blends

We examine the effects of matrix phase viscoelasticity on the rheological modeling of polymer blends with a droplet morphology. Two contravariant, second-rank tensor variables are adopted along with the translational momentum density of the fluid to account for viscoelasticity of the matrix phase and the ellipsoidal droplet shapes. The first microstructural variable is a conformation tensor describing the average extension and orientation of the molecules in the matrix phase. The other microstructural variable is a configuration tensor to account for the average shape and orientation of constant-volume droplets. A Hamiltonian framework of non-equilibrium thermodynamics is then adopted to derive a set of continuum equations for the system variables. This set of equations accounts for local conformational changes of the matrix molecules due to droplet deformation and vice versa. The model is intended for dilute blends of both oblate and prolate droplets, and droplet breakup and coalescence are not taken into account. Only the matrix phase is considered as viscoelastic; i.e., the droplets are assumed to be Newtonian. The model equations are solved for various types of homogeneous deformations, and microstructure/rheology relationships are discussed for transient and steady-state conditions. A comparison with other constrained-volume rheological models and experimental data is made as well.     

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)     

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     

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.     

Rheology of polymer blends: non-linear model for viscoelastic emulsions undergoing high deformation flows

Non-linear rheology of a mixture of two viscoelastic immiscible liquids undergoing high deformation flow was considered. Using Grmela's formalism (Grmela 1986, 1989, 1993a, b) and the coarse grained picture given by Onuki (1987) and Doi and Ohta (1991), we have derived a set of highly non-linear time-dependent transport equations that take into account a direct coupling between the rheology and morphology. Breakup, coalescence, and the high deformation of the interface were considered. Models of Doi and Ohta (1991), Lee and Park (1994), and Grmela et al. (1998) are recovered as special cases. The parameters of?the model were given a physical meaning in both shear and elongational flows and the predictions of the model were ¶compared to the predictions of the previous models on the basis of experimental results obtained on two model?blends PDM/PB polydimethylsiloxane/poly(1-butene) and PP/PS polypropylene/polystyrene blends.     

Rheology of polymer blends with matrix-phase viscoelasticity and a narrow droplet size distribution

A Hamiltonian framework of non-equilibrium thermodynamics is adopted to construct a set of dynamical continuum equations for a polymer blend with matrix viscoelasticity and a narrow droplet size distribution that is assumed to obey a Weibull distribution function. The microstructure of the matrix is described in terms of a conformation tensor. The variable droplet distribution is described in terms of two thermodynamic variables: the droplet shape tensor and the number density of representative droplets. A Hamiltonian functional in terms of the thermodynamic variables is introduced and a set of time evolution equations for the system variables is derived. Sample calculations for homogenous flows and constant droplet distribution are compared with data of a PIB/PDMS blend and a HPC/PDMS blend with high viscoelastic contrast. For the PIB/PDMS blend, satisfactory predictions of the flow curves are obtained. Sample calculations for a blend with variable droplet distribution are performed and the effect of flow on the rheology, droplet morphology, and on the droplet distribution are discussed. It is found that deformation can increase or decrease the dispersity of the droplet morphology for the flows investigated herein.     

高应变率大变形下的聚丙烯/尼龙共混高聚物损伤型本构特性

对两种采用不同相容剂的聚丙烯（PP）和尼龙（PA）共混高聚物材料在大变形下的粘弹性力学行为进行研究,着重考察应变率效应和损伤的演化,从而分析不同的界面分子设计对共混体系材料宏观性能的作用。在准静态及冲击实验研究的基础上,基于ZWT非线性粘弹性模型,并结合了遗传算法,分别得到了能有效描述两种共混高聚物大变形阶段计及损伤的非线性粘弹性本构关系。两种材料在不同加载条件下表现出明显不一致的性能,原因在于其损伤演化的率相关性,且两种材料的大变形机制存在一定的差别,能用ZWT方程进行描述的范围也不一样。     

压缩-剪切复合应力下PMMA材料的静态力学特性研究

通过压缩具有一定倾斜角(0°,10°,15°,20°和25°)试件和双剪切模型试件,实现了单轴压缩、压缩-剪切复合应力以及纯剪切三种应力状态,得到PMMA(聚甲基丙烯酸甲酯)在相应应力状态下的应力-应变曲线,同时对不同应力状态下试件的破坏模式进行了分析。结果表明:在不同受力环境中材料的强度和破坏的机理不同;同单轴压缩状态下相比,材料在压缩-剪切复合应力状态下屈服极限、强度极限以及破坏应变均不同程度的增大,呈现明显的"剪切增强"现象。单轴压缩与压缩-剪切应力状态下试件的破坏模式均为在试件短对角面上出现明显的剪切屈服带,由应力分析得出试件剪应力在短对角面上达到最大,引起在此平面上分子链间滑动从而产生应变软化形成剪切屈服带;双剪切试件的破坏模式为与剪切面呈45°的斜面。     

Uniaxial extensional flow behavior of immiscible and compatibilized polypropylene/liquid crystalline polymer blends

In this work liquid crystalline polymer (LCP) and thermoplastic (TP) blends with and without compatibilizer were studied with respect to their elongational flow behavior, under uniaxial extensional flow. This knowledge is important because in processes involving dominantly extensional deformations, like the case of the formation of the LCP fibrillation, transient extensional flow properties become more important than transient or steady-shear properties. In systems characterized by disperse phase morphologies (10 and 20 wt%) the LCP acts as a plasticizer, decreasing the viscosity of the system and increasing its durability with respect to that of the matrix. On the other hand, for a system in which a co-continuous morphology is present (40 wt% LCP) fibrils and droplets deformation occurs simultaneously, leading to a much higher strain hardening and durability. Moreover, the addition of compatibilizers to the blends gives rise to an increase of the strain hardening and to a decrease of the durability, which is in accordance with the mechanical properties, namely a higher Young’s modulus and lower elongation at break, in comparison with noncompatibilized systems.     

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     

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