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.     

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.     

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.     

Grafting of polyamide 6 on a styrene–acrylonitrile maleic anhydride terpolymer: melt rheology at the critical gel state

In this work, we studied the melt rheology of multigraft copolymers with a styrene–acrylonitrile maleic anhydride (SANMA) terpolymer backbone and randomly grafted polyamide 6 (PA 6) chains. The multi-grafted chains were formed by interfacial reactions between the maleic anhydride groups of SANMA and the amino end groups of PA 6 during melt blending. Because of the phase separation of SANMA and PA 6, the grafted SANMA backbones formed nearly circular domains which were embedded in the PA 6 melt with a diameter in the order of 20 to 40 nm. The linear viscoelastic behaviour of PA 6/SANMA blends at a sufficiently large SANMA concentration displayed the characteristics of the critical gel state, i.e. the power relations G′ ∝ G′′ ∝ ω ^0.5. In elongation, the PA 6/SANMA blend at the critical gel state showed a non-linear strain hardening behaviour already at a very small Hencky strain. In contrast to neat PA 6, the elasticity of the PA 6/SANMA blends was strongly pronounced, which was demonstrated by recovery experiments. Rheotens tests agreed with the linear viscoelastic shear oscillations and the measurements using the elongational rheometer RME. Increasing the SANMA concentration led to a larger melt strength and a reduced drawability. The occurrence of the critical gel state can be interpreted by the cooperative motion of molecules which develops between the grafted PA 6 chains of neighbouring micelle-like SANMA domains.     

Recoverable deformation and morphology after uniaxial elongation of a polystyrene/linear low density polyethylene blend

The transient recoverable deformation ratio after melt elongation at various elongational rates and maximum elongations was investigated for pure polystyrene and for a 85 wt.% polystyrene/15 wt.% linear low density polyethylene (PS/LLDPE 85:15) blend at a temperature of 170 ^oC. The ratio p of the zero shear rate viscosity of LLDPE to that of PS is p = 0.059 ≈ 1:17. Retraction of the elongated LLDPE droplets back to spheres and end-pinching is observed during recovery. A simple additive rule is applied in order to extract the contribution of the recovery of the elongated droplets from the total recovery of the blend. In that way, the recoverable portion of the PS/LLDPE blend induced by the interfacial tension is determined and compared with the results of a theory based on an effective medium approximation. The effective medium approximation reproduces well the time scale of the experimental data. In addition, the trends that the recoverable deformation increases with elongational rate and maximum elongation are captured by the theoretical approach.     

A parameter investigation of shear-induced coalescence in semidilute PIB–PDMS polymer blends: effects of shear rate, shear stress volume fraction, and viscosity

In this work, drop coalescence of polymer blends under shear flow in a parallel flow apparatus was investigated by optical sectioning microscopy. In each experiment, shear rate was set at values low enough to avoid any break-up phenomena. The time evolution of the drop size distribution was determined by motorized sample scanning and iterative acquisition of stacks of images along sample depth. Drop size and location in the acquired images was found by automated image analysis techniques. A systematic experimental campaign to investigate the effects of shear rate (in the range 0.1–0.5 s⁻¹), volume fraction (2.5–10%), and viscosity of the two phases (3–63 Pa s) at different viscosity ratio (0.1–2.3) was carried out. By comparing data from different experiments, it was found that at any strain value, the average drop size decreases monotonically with the shear stress, calculated as the product of shear rate and matrix viscosity. Furthermore, the coalescence rate slowed down with increasing viscosity ratio. Overall, these results provide an extensive set of data, which can be used as a benchmark for modeling shear-induced coalescence in polymer blends.Paper presented at the Annual Meeting of the European Society of Rheology, Grenoble, April 2005.     

The rheological characterisation of bread dough using capillary rheometry

An Australian hard wheat flour–water dough has been characterised using parallel plate and capillary rheometers over an extensive range of apparent shear rates (10^− 3–10³ s^− 1) relevant to process conditions. Torsional measurements showed that the shear viscosity of the dough increased with strain to a maximum value and then decreased, suggesting a breakdown of the dough structure. Both torsional and capillary experiments revealed the shear-thinning behaviour of the dough. The wall slip phenomenon in capillary rheometry was investigated and found to be diameter dependent and occurred at a critical shear stress of approximately 5–10 kPa. A two-regime power law behaviour was observed, with the power law index approximately 0.3 in the low shear rate range increasing to 0.67 in the high shear rate range. Pressure fluctuation was observed in the capillary data and increased with shear rate, in particular, at shear rates approaching 10⁴ s^− 1. The results demonstrate that capillary rheometry is a viable means of rheologically testing dough at high shear rates provided pressure fluctuation is carefully monitored and capillary rheometry corrections, including wall slip, are accounted for.     

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)     

Three views of viscoelasticity for Cox–Merz materials

A slight rearrangement of the classical Cox and Merz rule suggests that the shear stress value of steady shear flow, , and complex modulus value of small amplitude oscillatory shear, G^∗(ω) = (G^′2 + G^″2)^1/2, are equivalent in many respects. Small changes of material structure, which express themselves most sensitively in the steady shear stress, τ, show equally pronounced in linear viscoelastic data when plotting these with G^∗ as one of the variables. An example is given to demonstrate this phenomenon: viscosity data that cover about three decades in frequency get stretched out over about nine decades in G^∗ while maintaining steep gradients in a transition region. This suggests a more effective way of exploiting the Cox–Merz rule when it is valid and exploring reasons for lack of validity when it is not. The τ −G^∗ equivalence could also further the understanding of the steady shear normal stress function as proposed by Laun.     

The effect of mixing particles of different size on the electrorheological response under steady shear flow

 The effect of mixing particles of different sizes on the electrorheological response of suspensions under steady shear flow was investigated. Two sizes, 15 μm and 50 μm, of monodisperse spherical sulfonated poly(styrene-co-divinylbenzene) particles were used. Several electrorheological fluids were made containing different proportions of small and large particles dispersed in silicone oil, but with constant overall particulate concentration. It was found that the mixed size system produced the highest electrorheological response under the shear rates used (10 s⁻¹ to 500 s⁻¹), which is the opposite trend to previous studies of bimodal systems with larger size ratios. Received: 21 December 2000 Accepted: 29 March 2001     

Measurements and model predictions of transient elongational rheology of polymeric nanocomposites

Transient elongational rheology of two commercial-grade polypropylene (PP) and the organoclay thermoplastic nanocomposites is investigated. A specifically designed fixture consisting of two drums (SER Universal Testing Platform) mounted on a TA Instruments ARES rotational rheometer was used to measure the transient uniaxial extensional viscosity of both polypropylene and nanoclay/PP melts. The Hencky strain rate was varied from 0.001 to 2 s^− 1, and the temperature was fixed at 180°C. The measurements show that the steady-state elongational viscosity was reached at the measured Hencky strains for the polymer and for the nanocomposites. The addition of nanoclay particles to the polymer melt was found to increase the elongation viscosity principally at low strain rates. For example, at a deformation rate of 0.3 s^− 1, the steady-state elongation viscosity for polypropylene was 1.4 × 10⁴ Pa s which was raised to 2.8 × 10⁴ and 4.5 × 10⁴ Pa s after addition of 0.5 and 1.5 vol.% nanoclay, respectively. A mesoscopic rheological model originally developed to predict the motion of ellipsoid particles in viscoelastic media was modified based on the recent developments by Eslami and Grmela (Rheol Acta 47:399–415, 2008) to take into account the polymer chain reptation. We show that the orientation states of the particles and the rheological behavior of the layered particles/thermoplastic hybrids can be quantitatively explained by the proposed model.     

Strain recovery of model immiscible blends without compatibilizer

Strain recovery after the cessation of shear was studied in model immiscible blends composed of polyisobutylene drops (10–30% by weight) in a polydimethylsiloxane matrix. Blends of viscosity ratio (viscosity of the drops relative to the matrix viscosity) ranging from 0.3 to 1.7 were studied. Most of the strain recovery was attributable to interfacial tension, and could be well-described by just two parameters: the ultimate recovery and a single retardation time. Both these parameters were found to increase with the capillary number of the drops prior to cessation of shear. For blends that had reached steady shear conditions, the ultimate recovery decreased with increasing viscosity ratio, whereas the retardation time increased with increasing viscosity ratio. The retardation time was well-predicted, but the ultimate recovery was over-predicted by a linear viscoelastic model developed previously by Vinckier et al. (Rheol Acta 38:65–72, 1999).     

Characterization of the flow properties of sodium carboxymethylcellulose via mechanical and optical techniques

Sodium carboxymethylcellulose (NaCMC) in solution represents a complex rheological system, since it forms aggregates and associations and hence higher-level structures and, depending on the synthesis, is only found in a molecularly dispersed form in exceptional cases. Rheo-mechanical investigations of the viscoelasticity showed that the Cox-Merz rule is not fulfilled. The aim was therefore to examine whether rheo-optics could be employed to provide more detailed conclusions about the parameters that influence the flow behavior of NaCMC than has hitherto been available with mechanical methods. The flow birefringence, Δn ^′, rises as the degree of polymerization increases, and exhibits the same dependence on molar mass as does the viscosity: Δn ^′∝M _w ^3.4. As the degree of polymerization increases while the shear rate remains constant, the polymer segments become more distinctly aligned in the direction of shear. Hence increasing the degree of polymerization also affects the solution structure, i.e. the interaction of the molecules with one another. The stress-optical rule only applies to a limited extent for this system. The stress-optical coefficient, C, is almost independent of the shear rate, but is strongly influenced by the concentration and attains a limiting value of 3 × 10⁻⁸ Pa⁻¹. C was determined for a polymer in dilute solution and the curve obtained also enabled transitions in the solution structure to be recognized. Received: 1 May 1998 Accepted: 5 October 1998     

The orientational behavior of multiwall carbon nanotubes in polycarbonate in simple shear flow

This paper describes the changes in the orientation of multiwall carbon nanotubes (MWCNT) in polycarbonate as determined by transient and oscillatory shear rheology. It is well known from rheological studies on composites with macroscopic fibers that the overshoot in transient shear viscosity is caused by the change in orientation distribution of these fibers. This study shows that although an overshoot in transient shear viscosity of MWCNT/polycarbonate is measured at shear rates as low as 0.1 s^− 1, the MWCNT network is disturbed only at considerably higher shear rates. Scanning electron microscopy micrographs and oscillatory shear show that MWCNT in thermoplastic composites will only be oriented at high shear rates. Simultaneous measurements of the electrical conductivity during rheological start-up shear and oscillatory measurements show large differences between electrical and mechanical relaxation behaviors. The viscosity of the composite seems to depend strongly on the MWCNT network density, whereas the proximity of the tubes at the network points seems to determine the electrical properties of the MWCNT composite.     

Polypropylene-polyethylene blends

Summary Die swell behaviour and morphology of melt blends of isotactic polypropylene (PP) and high density polyethylene for pure polymers and blends with 25, 50 and 75 weight % PP are described in the present study. A light interference contrast microscopy technique was used for the morphological characterization of melt blends and extrudate samples of the blends obtained with an Instron capillary rheometer. The results indicate that the domains from blends where the dispersed phase has higher viscosity than the continuous phase remain as continuous domains in the extrudate whereas domain destruction takes place when blends where the continuous phase has the higher viscosity are extruded.The die swell behaviour as well as the fiber forming properties of extrudates of melts having unstable domains extruded at high shear stresses resemble the behaviour of homopolymers, whereas samples with stable domains are significantly different, die swell increases with temperature at constant shear stress and stable fibers cannot be obtained after necking.With 10 figures and 1 table     

Rheology and birefringence of Fomblin YR at very high shear rates

The rheological and structural properties of perfluoropolyether (PFPE) lubricant films including viscosity, shear stress, and birefringence were measured at relatively low to extremely high shear rates using a rotational optical rheometer. The viscosity of various films with different thicknesses exhibit Newtonian behavior up to a shear rate 1 × 10⁴ s⁻¹, with a transition to shear-thinning behavior obvious at higher shear rates. Birefringence of these films was also measured for the first time, and these results indicate chain alignment with shear in the shear-thinning regime. The shear rate at which alignment occurs is similar to that of the onset of shear thinning. This correlation between chain alignment and shear thinning provides direct evidence that the ability of PFPEs to lubricate hard drives at high shear rates is a direct consequence of the ability of the applied shear field to align the molecules on a molecular level.     

The motion of long bubbles through viscoelastic fluids in capillary tubes

The penetration of long gas bubble through a viscoelastic fluid in a capillary tube has been studied in order to investigate the influence of viscoelastic material properties on the hydrodynamic coating thickness and local flow kinematics. Experiments are conducted for three tailored ideal elastic (Boger) fluids, designed to exhibit similar steady shear properties but substantially different elastic material functions. This allows for the isolation of elastic and extensional material effects on the bubble penetration process. The shear and extensional rheology of the fluid is characterized using rotational and filament stretching rheometers (FSR). The fluids are designed such that the steady-state extensional viscosity measured by the FSR at a Deborah number (De) greater than 1 differs over three orders of magnitude (Trouton ratio = 10³–10⁶). The experiment set up to measure the hydrodynamic coating thickness is designed to provide accurate data over a wide range of capillary numbers (0.01 < Ca < 100). The results indicate that the coating thickness in this process increases with an increase in the extensionally thickening nature of the fluid. Experiments are also conducted using several different capillary tube diameters (0.1 < D < 1 cm), in order to compare responses at similar Ca but different flow De. Suitable scaling methods and nonlinear viscoelastic constitutive equations are explored to characterize the displacement process for polymeric fluids. Bubble tip shapes at different De are recorded using a CCD camera, and measured using an edge detection algorithm. The influence of the mixed flow field on the bubble tip shape is examined. Particle tracking velocimetry experiments are conducted to compare the influence of viscoelastic properties on the velocity field in the vicinity of the bubble tip. Local shear and extension rates are calculated in the vicinity of the bubble tip from the velocity data. The results provide quantitative information on the influence of elastic and extensional properties on the bubble penetration process in gas-assisted injection molding. The bubble shape and velocity field information provides a basis for evaluating the performance of constitutive equations in mixed flow. Received: 19 January 1999 Accepted: 30 June 1999     

Non-linear rheology and flow-induced transition of a lamellar-to-vesicle phase in ternary systems of alkyldimethyl oxide/alcohol/water

 The time-dependent transformation of an ionically charged lamellar phase (L _α-phase) into a vesicle phase under the influence of shear is investigated using rheological and conductivity measurements. The L _α-phase consists of the zwitterionic surfactant tetradecyldimethylaminoxide (C₁₄DMAO), hexanol, oxalic acid and water. The experiments were carried out on the L _α-phase in a well defined state. It was prepared by a special route from the neighbouring L ₃-phase that consists of 100 mM C₁₄DMAO, 250 mM hexanol and 5 mM oxalicdiethylester (OEE). The OEE hydrolyses in the L ₃ -phase to oxalic acid and ethanol. The result is a virgin L _α-phase which consists of stacked bilayers and which has not been exposed to shear. When this low-viscous phase is subjected to shear it is transformed into a highly viscous vesicle phase. The transformation of the L _α-phase into vesicles under constant shear was monitored by recording the viscosity and conductivity with time. It is observed that at least three different time constants can be distinguished in the transformation process. The conductivity passes through a minimum (τ₁) in the direction of shear. The viscosity first passes through a minimum (τ₂) and then over a maximum (τ₃). It is concluded that τ₁ belongs to the complete alignment of the bilayer parallel to the wall, τ₂ to the beginning of the break-up of the bilayers to the vesicles and τ₃ to the complete transformation of the L _α- to the vesicle phase. When the shear rate was varied, it was noted that the product of the time constants and shear is constant. Received: 30 June 1999/Accepted: 30 August 1999     

Behaviour of a simple crystallisation model in tube and channel flow

A formulation describing the rheology of crystallising polymers is discussed. For some semi-crystalline polymers where spherulites form as part of the crystallisation process, the use of a suspension-type model is appropriate. Whilst it is possible to so describe simple shearing and elongational rheology during on-going crystallisation with such models, the flow through a capillary tube is much more complex and numerical solution is usually necessary. To give some insight into this complex flow, a ‘step function’ or ‘amorphous-frozen’ model of the viscosity changes due to crystallisation has been devised so that a semi-analytical approach is feasible. We use this simple model and compare the results with recently published experiments in tubes and channels at high (O(10³ s^− 1)) shear rates using poly(butene-1). A direct correlation between simple shear and tube flow crystallisation onset times is found.