Rheological properties of poly(vinyl chloride)/plasticizer systems—relation between sol–gel transition and elongational viscosity

Poly(vinyl chloride) (PVC)/di-isononyl phthalate systems with PVC content of 45.5 (PVC8) and 70.4 wt% (PVC6) were prepared by a hot roller at 150 °C and press molded at 180 °C. The dynamic viscoelasticity and elongational viscosity of PVC8 and PVC6 were measured in the temperature range from 150 to 220 °C. We have found that the storage and loss shear moduli, G′ and G″, of PVC8 and PVC6 exhibited the power-law dependence on the angular frequency ω at 190 and 210 °C, respectively. Correspondingly, the tan δ values did not depend on ω. These temperatures indicate the critical gel temperature T _gel of each system. The critical relaxation exponent n obtained from these data was 0.75 irrespective of PVC content, which was in agreement with the n values reported previously for the low PVC concentration samples. These results suggest that the PVC gels of different plasticizer content have a similar fractal structure. Below T _gel, the gradual melting of the PVC crystallites takes place with elevating temperature, and above T _gel, a densely connected network throughout the whole system disappears. Correspondingly, the elongational viscosity behavior of PVC8 and PVC6 exhibited strong strain hardening below T _gel, although it did not show any strain hardening above T _gel. These changes in rheological behavior are attributed to the gradual melting of the PVC crystallites worked as the cross-linking domains in this physical gel, thereby inapplicability of the of time–temperature superposition for PVC/plasticizer systems.     

A study on the melt viscosity of linear and branched poly(butyleneterephthalate)

Linear and branched PBTP samples were synthesized and characterized in terms of the intrinsic viscosity, the melt-flow-index and, for some, the melt viscosity over a range of shear rates at 250 °C.An exponent of 3.2 in the equation relating to was found for linear samples. Both linear and branched samples exhibited Newtonian behaviour over a wide range of shear rates, but for any given melt-viscosity the branched samples became shear thinning at lower shear rates than the linear ones. Correlation between a branching index,, and melt-visocity ratio (0,b/0,l) was in agreement with a previous theoretical study.     

Determination of the steady-state shear viscosity from measurements of the apparent viscosity for some common types of viscometers

Considering a number of model fluids, the relation between the (measurable) apparent viscosity _a and the (true) shear viscosity is studied for some commonly used viscometers, like capillary, slit, plate-plate and concentric cylinders (including the influence of the bottom of the cylinder), as well as for one laboratory type of viscometer. As long as is a purely monotonic function, a shift factor < 1 allows one to deduce from _a . Though in general variable, it frequently suffices for practical purposes to use a constant shift factor (the constant being characteristic of the type of viscometer used). This does not apply to dilute solutions or any fluids with two plateau values for . For plastic fluids, it is shown that Casson or Bingham behavior can — if valid at all — only describe the high shear stress limit of _a .     

Rheo-optical measurements of the first and third normal stresses of homopolymer poly(vinyl methyl ether) melt

Normal stresses play a key role in polymer processing, yet accurate measurements are still challenging. Simultaneous rheo-optical measurements are conducted on a poly(vinyl methyl ether) homopolymer melt over a wide range of temperatures and oscillatory shear frequencies, in an effort to measure the normal stresses, by using quantitative flow birefringence measurements. The stress optical rule holds well for this polymer as expected, with the value of the stress optic coefficient of (6.38±0.19)×10⁻¹¹ cm²/dyn at 30°C. The first and third normal stress difference coefficients, calculated using a single memory constitutive equation applied to the stress and birefringence data, are in excellent agreement. The ratio of the measured third and first normal stress difference coefficients, (1−β)=0.71±0.05, agrees well with the result of the Doi–Edwards model with independent alignment approximation (β=0.28). The measurement of normal stress difference coefficients with such small deviations proves the robust nature of the improved rheo-optical instrument and its ability to measure complete stress tensor.     

Rheological properties of poly(vinyl alcohol)/sodium borate aqueous solutions

Rheological properties were studied for aqueous solutions of poly(vinyl alcohol) containing sodium borate. The solution exhibited a marked shear thickening at a certain critical rate of shear, _c and the flow was unstable at higher rates of shear. The loss modulus exhibited a maximum and the angular frequency corresponding to the maximum, _MAX, was approximately equal to . These features were common to several measurements including various molecular weights and concentrations of polymer and various temperatures. Possible mechanism of shear thickening was discussed based on a temporary network model composed of crosslink points of a finite lifetime.     

Uniaxial elongational behavior of poly(vinyl chloride) physical gel

A poly(vinyl chloride) (PVC,  M_w = 102×10³)(\mbox{PVC,}\;{\rm M}_{\rm w} =102\times 10^3) di-octyl phthalate (DOP) gel with PVC content of 20 wt.% was prepared by a solvent evaporation method. The dynamic viscoelsticity and elongational viscosity of the PVC/DOP gel were measured at various temperatures. The gel exhibited a typical sol–gel transition behavior with elevating temperature. The critical gel temperature (T_gel) characterized with a power–law relationship between the storage and loss moduli, G^′ and G^″, and frequency ω, G￠=G^￠￠/tan  ( np/2 ) μ wⁿ{G}^\prime={G}^{\prime\prime}{\rm /tan}\;\left( {{n}\pi {\rm /2}} \right)\propto \omega ^{n}, was observed to be 152°C. The elongational viscosity of the gel was measured below the T_gel. The gel exhibited strong strain hardening. Elongational viscosity against strain plot was independent of strain rate. This finding is different from the elongational viscosity behavior of linear polymer solutions and melts. The stress–strain relations were expressed by the neo-Hookean model at high temperature (135°C) near the T_gel. However, the stress–strain curves were deviated from the neo-Hookean model at smaller strain with decreasing temperature. These results indicated that this physical gel behaves as the neo-Hookean model at low cross-linking point, and is deviated from the neo-Hookean model with increasing of the PVC crystallites worked as the cross-linking junctions.     

Melt viscosity of linear and branched poly(butyleneisophthalate)

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

Rheological behaviour of poly(ethylene terephthalate) and poly(butylene terephthalate) blends

The presence of up to 4% Poly(butylene terephthalate) (PBT) in blends of Poly(ethylene terephthalate) (PET) with PBT results in an increase in viscosity and a decrease in activation energy, which has been related to the entanglement density. However, further increases in the amount of PBT up to 10% result in decreases in the viscosity, which may be due to partial phase segregation. Various blending rules have been applied to correlate the experimental results and predict the viscosities of the blends.     

Pressure-dependent viscosity and free volume of atactic and syndiotactic polystyrene

The effect of pressure on viscosity is an important but often overlooked aspect of the flow properties of polymeric materials. In this work, two polymers (an atactic and a syndiotactic Polystyrene) were characterized to determine the effect of pressure on viscosity. In particular, a device was adopted to increase the exit pressure of a standard capillary rheometer, thus obtaining data of viscosity under high pressure and high shear rates. The Simha-Somcynsky equation of state was applied to the pressure–volume–temperature experimental data of both materials to obtain the dependence of free volume on temperature and pressure. The Doolittle equation was eventually employed to verify the dependence of viscosity on free volume. It was found that, for both materials, a linear relationship holds between the logarithm of zero-shear-rate viscosity (at several temperatures and pressures) and the inverse of free volume.     

Solidification behavior of the theta system 2-propanol/poly(n-butyl methacrylate)

Thermoreversible gelation of the system 2-propanol/poly (n-butyl methacrylate) — as detected by D'SC or dielectric experiments — does not manifest itself in a straightforward manner in the dynamic-mechanical properties. Its occurrence can, however, be seen in many ways: i) For constant composition of the system and a reference temperature lower than T _gel, the storage modulus G is larger than the loss modulus G in the glass transition zone of the master curve and both vary in an almost parallel manner with the angular frequency over almost two decades (whereas this feature is normally found for other gelling systems within the rubber plateau or the flow region). ii) The entanglement molecular weight obtained from G_max is markedly less max than the entanglement molecular weight in the melt divided by ₂, the volume fraction of the polymer. iii) The temperature influences change from WLF like to Arrhenius-like behavior as T is lowered in the case of highly concentrated polymer solutions; analogous considerations hold true as ₂ is increased at constant T. iv) For sufficiently low temperatures, the activation energy of flow exhibits a maximum in the concentration range where the gelation is — according to DSC experiments — most pronounced. Like with ordinary non-gelling systems it is possible to construct master curves. On the basis of Graessley's theory identical dependencies are obtained for the variation of the entanglement parts of the stationary viscosity with shear rate and for the dependence of the entanglement part of the complex viscosity on the frequency of oscillation. Zero shear viscosity and limiting value of the complex viscosity for vanishing as a function of ₂ match smoothly and exhibit two points of inflection.     

Linear and branched poly(butyleneterephthalate): Activation energy for melt flow

Poly(butyleneterephthalate) (PBTP) samples of different molecular weights, both linear and branched, were synthetized by mass polymerization and studied in the molten state with a melt-flow-index apparatus at different temperatures in the range 245–270 °C. In our experimental conditions ( 20 s^–1) the behaviour of PBTP samples was Newtonian, as reported previously. The flow activation energyE _a,0 was found to increase with degree of branching: typicallyE _a,0 was about 47 and 63–79 kJ/mol for linear and branched polymers respectively.Presented in part at the IX. International Congress on Rheology, Acapulco, Mexico, October 8–13, 1984     

The instability of water-mud interface in viscous two-layer flow with large viscosity contrast

The temporal instability of parallel viscous two-phase mixing layers is extended to current-fluid mud by considering a composite error function velocity profile. The influence of viscosity ratio, Reynolds number, and Froude number on the instability of the system are discussed and a new phenomenon never discussed is investigated based on our numerical results. It is shown that viscosity can enlarge the unstable wave number range, cause new instability modes, and certainly reduce the growth rate of Kelvin—Helmholtz (K—H) instability.     

Extensional rheology of concentrated poly(ethylene oxide) solutions

The shear and extensional rheology of three concentrated poly(ethylene oxide) solutions is examined. Shear theology including steady shear viscosity, normal stress difference and linear viscoelastic material functions all collapse onto master curves independent of concentration and temperature. Extensional flow experiments are performed in fiber spinning and opposed nozzles geometries. The concentration dependence of extensional behavior measured using both techniques is presented. The zero-shear viscosity and apparent extensional viscosities measured with both extensional rheometers exhibit a power law dependence with polymer concentration. Strain hardening in the fiber spinning device is found to be of similar magnitude for all test fluids, irrespective of strain rate. The opposed nozzle device measures an apparent extensional viscosity which is one order of magnitude smaller than the value determined with the fiber spinline device. This could be attributed to errors caused by shear, dynamic pressure, and the relatively small strains developed in the opposed nozzle device. This instrument cannot measure local kinematics or stresses, but averages these values over the non-homogenous flow field. These results show that it is not possible to measure the extensional viscosity of non-Newtonian and shear thinning fluids with this device. Fiber spin-line experiments are coupled with a momentum balance and constitutive model to predict stress growth and diameter profiles. A one-mode Giesekus model accurately captures the plateau values of steady and dynamic shear properties, but fails to capture the gradual shear thinning of viscosity. Giesekus model parameters determined from shear rheology are not capable of quantitatively predicting fiber spinline kinematics. However, model parameters fit to a single spinline experiment accurately predict stress growth behavior for different applied spinline tensions.     

Temperature dependence of the viscosity of highly starch-filled poly(hydroxy ester ether) biodegradable composites

 The temperature dependence of the viscosity of starch-filled poly(hydroxy ester ether) (PHEE) biodegradable composites was analyzed using Arrhenius and WLF equations. Corn starch/PHEE materials were extruded using a twin screw extruder with starch volume fractions from 0.27 to 0.66. Dynamic strain sweep measurements were carried out at 10 rad/s at six different temperatures from 100 °C to 150 °C. Both Arrhenius and WLF equations model equally well the temperature effect on viscosity of PHEE and starch/PHEE composites with starch volume fractions up to 0.36. Arrhenius equation with stress correction describes the stress dependence of viscosity of starch/PHEE composites with higher starch volume fractions. The activation energy using both Arrhenius equation and Arrhenius equation with stress correction is 62.7 kJ/mol for pure PHEE and starch/PHEE composites. Received: 10 September 1999 Accepted: 27 March 2000     

Effect of maleic anhydride content on the rheology and phase behavior of poly(styrene-co -maleic anhydride)/ poly(methyl methacrylate) blends

 We investigated the thermo- rheological behavior of high glass transition, high molecular weight and small dynamic asymmetry blends of poly(styrene-co-maleic anhydride) (SMA) and poly (methyl methacrylate) (PMMA) with varying amounts of maleic anhydride (MA) content, namely 8 wt%, 14 wt% and 32 wt%, in the SMA component. The phase separation (binodal) temperature of each blend was determined rheologically using a combination of dynamic frequency and temperature sweeps in parallel plate geometry; it was marked by a change in slope of the elastic modulus and the occurrence of a peak in tan δ in temperature sweeps. Failure of the time-temperature superposition principle and observation of two peaks in the Cole-Cole plots corroborated these findings. The blends displayed lower critical solution temperature (LCST) behavior with the critical temperatures exhibiting a non-monotonic dependence on the MA content. From rheological and thermal measurements it was concluded that SMA/PMMA blends containing 14% MA were more miscible than those containing 8% or 32% MA, a finding attributed to the compositional dependence of the interplay between SMA-SMA and SMA-PMMA interactions in the different samples. MA also influenced the dynamic asymmetry and pretransitional concentration fluctuations. The phase diagrams corresponding to each blend were modeled using a two-parameter temperature dependent interaction parameter, based on the concept of generalized Gibbs free energy of mixing. The fitted values of interaction parameter were in good agreement with values calculated explicitly using the Flory-Huggins theory. Received: 16 February 2001 Accepted: 11 July 2001     

Compression creep of molten poly (butylene terephthalate)

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

Recoverable strains and retardation times of monodisperse suspensions of silicon dioxide spheres in poly(dimethylsiloxane)

Steady-state viscosities η, steady-state recoverable strains γ _rs and characteristic retardation time τ _1/2 were measured for suspensions of monodisperse silicon dioxide (SiO₂) spheres in poly(dimethylsiloxane) (PDMS) with various volume fractions Φ of the suspended spheres at various creep stresses σ ₀. Two different regions are found in plots of η/η _m vs γ _rs, where η/η _m denotes the relative viscosity of the suspensions. In one region, η/η _m is proportional to γ _rs, while γ _rs is independent of η/η _m in the other region. In both regions, τ _1/2 is the functions of the shear strain rate in the steady-state of creep test independently of Φ. The origin of the elasticity is related to the ‘maximally distorted’ cages recovered owing to the repulsive interaction between the SiO₂ spheres and recovery of the cages in the shear-induced clusters of the suspended spheres.     

Evolution of viscosities and morphology for the two-phase system polyethylene oxide/poly(dimethylsiloxane)

Shear viscosities and oscillatory viscosities were measured for the two-phase system polyethylene oxide/poly(dimethylsiloxane) at 70 °C as a function of composition. This blend exhibits the usual droplet/matrix structures in the vicinity of the pure components and a region of co-continuity within which two droplet/matrix structures coexist. A stepwise reduction in the shear rate, , leads to a rapid increase in viscosity followed by a much slower exponential decay; plots of the corresponding rate constants as a function of composition exhibit two discontinuities marking the boundaries of co-continuity; a similar dependence is obtained for the time independent final viscosities . Keeping the blend composition constant and determining as a function of yields a curve that passes a distinct maximum, where the viscosities are very close to that of the less viscous pure component on both ends of this dependence. The dynamic mechanical measurements of the blends yield at low frequencies storage moduli G′ that are orders of magnitude larger than that of the components because of the deformation of the interfaces. At high frequencies, the loss moduli G″ reflect the increasing alignment of the drops suspended in the matrix phases. The composition dependencies of G′ and of the complex viscosities can again be used to determine the limits of co-continuity.     

Viscoelastic properties of semidilute poly(methyl methacrylate) solutions

Viscoelastic properties were examined for semidilute solutions of poly(methyl methacrylate) (PMMA) and polystyrene (PS) in chlorinated biphenyl. The number of entanglement per molecule, N, was evaluated from the plateau modulus, G _N . Two time constants, _s and ₁, respectively, characterizing the glass-to-rubber transition and terminal flow regions, were evaluated from the complex modulus and the relaxation modulus. A time constant _k supposedly characterizing the shrink of an extended chain, was evaluated from the relaxation modulus at finite strains. The ratios ₁/ _s and _k / _s were determined solely by N for each polymer species. The ratio ₁/ _s was proportional to N ^4.5 and N ^3.5 for PMMA and PS solutions, respectively. The ratio _k / _s was approximately proportional to N ^2.0 in accord with the prediction of the tube model theory, for either of the polymers. However, the values for PMMA were about four times as large as those for PS. The result is contrary to the expectation from the tube model theory that the viscoelasticity of a polymeric system, with given molecular weight and concentration, is determined if two material constants _s and G _N are known.