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.     

Evaluation of calculated entanglement spacings for undiluted linear amorphous polymers

Conclusions In reality, entanglements based on rheological measurements have been essentially defined operationally as a kinetic or time delay effect present in concentrated polymer systems. This is where intuitively molecular loops or overlap and entanglements of polymer chains are most likely to occur. The evaluation in fig. 2 suggests that the theory of rubber elasticity, even discounting the inherent imprecision of measurements, gives anM _e which is not relatable to polymer composition 1and chain structure. Conversely reliable and internally consistent values ofM _c can come from the molecular weight dependence of: 1.Newtonian viscosities, 2.NMR relaxation times, and 3 the shear dependence of viscosities, see fig. 1. However, entanglement spacings calculated in this way lack adequate theoretical substantiation particularly as to the mechanism of flow. Nonetheless, the correlation ofM _c with composition and structure is convincing and provides a sound empirical correlation and the basis for a renaissance in theoretical interpretation of viscoelastic behavior of linear amorphous polymers. Further theory must rationalize the fact that the shear compliance, which is proportional toM _e , depends on a combination of molecular weight averages involvingZ andZ+1. Yet the break in viscosity-molecular weight curves yieldingM _c has been generally confirmed to depend on only weight average molecular weight. The values ofM _c appear worthy of further experimental and theoretical evaluation. The values ofM _e appear to be based on experimental techniques that at present do not provide sufficient precision to warrant citation of such values molekular weight distribution is thought to have an important yet ill-defined influence on calculated values of M _e .     

Rheological characterization and modeling of end-functionalized polybutadienes

The rheological characterization and modeling of a series of polybutadienes obtained by anionic solution polymerization is presented in this work. The polybutadienes are synthesized using two different initiators: R,R′,R′′-silyloxyalkyllithium (F1) and R,R′,R′′-silylalkyllithium (F3). In addition, a polybutadiene obtained with a conventional alkyllithium initiator (n-butyllithium) is used as a reference. The rheological characterization is carried out under small amplitude oscillatory shear in the stress-controlled mode. Microstructure, molecular weight, and molecular weight distribution are determined by FTIR and GPC. The vinyl content of the polybutadienes synthesized using the functionalized initiators is similar to that obtained with n-butyllithium (8–11%). Materials obtained with F1 show a relatively low polydispersity within a narrow molecular weight range (250,000–300,000 g/mol), while samples obtained with F3 cover a wider range of molecular weights (65,000–670,000 g/mol) and display higher values of polydispersity. In all cases, a parallel reaction using propylene oxide in the termination step is done to place a functional group at the chain ends. The effect of this group on the rheological behavior appears to be negligible. Three rheological models are used and their predictions of the experimental data are compared. The models include the Doi and Edwards reptation model, expressions using a discrete spectrum of relaxation times based in the rubber-like liquid constitutive equation and the fractional Maxwell equation in which a given analytical relaxation-spectrum is used. Relevant relations are obtained between the models' parameters and the molecular properties of these systems, which in turn are related to the presence of functional groups at the polymer chain ends.     

Plastifiziermodelle für die Verarbeitung benetzender und nichtbenetzender Thermoplaste auf Einschnecken-Extrudern

Zusammenfassung Die Untersuchungen mit verschiedenen PVC hart-Ansätzen haben gezeigt, daß das Plastifizierungsmodell vonMaddock undStreet nur auf mittel- und niedrigviskose, benetzende Thermoplaste anzuwenden ist und für hochviskose nicht benetzende Thermoplaste keine Gültigkeit hat.Die Ausbildung des gut plastifizierten und homogenisierten Massenanteils wurde bei der Verarbeitung von PVC hart an der passiven Flanke festgestellt, während nachMaddock undStreet bei der Verarbeitung von PE und PVC weich die gut plastifizierte Zone an der Schubflanke gefunden wurde. Im Unterschied zur Verarbeitung von benetzenden niedrigviskosen Thermoplasten, bei denen über dem gesamten Massenkanalquerschnitt eine gute Durchmischung und Homogenisierung gefunden wurde, findet bei der Verarbeitung hochviskoser nicht-benetzender Thermoplaste in den Zonen 1, 3, und 4 keinerlei Mischeffekt statt. Nur die Zone 2 wird in der gewünschten Form homogenisiert.

---

Summary Studies on various unplasticized PVC formulations show that the plasticizing model ofMaddock andStreet is only valid for wetting thermoplastics with moderate and low viscosity but not for high-viscosity non-wetting thermoplastics.Contrary toMaddock andStreet, who found by processing PE and plasticized PVC the well plasticized zone at the pushing flank, the formation of the homogeneous and well plasticized part of the bulk takes place at the passive flank. Instead of homogenizing and thorough mixing over the whole cross-section of the mass channel in case of low-viscosity wetting thermoplastics no mixing at all is found by the processing of high-viscosity and non-wetting thermoplastics in zones 1, 3 and 4, only in zone 2 the mass is homogeneous.

---

---

Vorgetragen auf der Jahrestagung der Deutschen Rheologen in Bad Ems vom 18.–19. Mai 1967.     

Linear and non-linear rheology of linear polydisperse polyethylene

Rheological techniques, size-exclusion chromatography, and molecular spectroscopy are the most widely used tools for describing polymer molecular structure in polyolefins. The detection of long-chain branching, and to some extent, its quantification, have been based on quantifying the deviation of polyethylene??s (PE) rheological behavior from that of a linear reference. Although metallocene-based PE has been extensively studied, linear polydisperse originating from Ziegler or Chromium-based catalysts are not often thoroughly considered, despite their high industrial importance. Within this work, we study the linear and non-linear rheology of a set of polydisperse PEs, for which the topological linearity is confirmed by GPC-MALLS measurements. Thus, we can safely quantify the effect of broad molecular weight distribution, high and ultra-high molecular weight fractions on rheological quantities and model parameters. Specifically, the zero-shear viscosity, ?? ₀ vs. M _w, relaxation spectra, phase lag vs. the complex modulus plot (van Gurp?CPalmen method) were applied and significant deviations from the ??rheologically linear?? behavior were observed, attributed only to M _w, M _z and polydispersity. Since the elongational viscosity was typical of linear PE, large-amplitude oscillatory shear and FT-Rheology were applied to quantify the non-linear rheological behavior. The latter was described by a single parameter, $Q=I_{3/1}/\gamma_0^2$ , which for linear polydisperse PE was correlated to the high molecular weight fraction and was constant over a broad range of applied Deborah numbers for the respective excitation frequencies. Since we need to correlate structural features such as broad MWD and HMW to polymer performance under processing conditions, we have to extend the analysis of linear rheological parameters, such as zero-shear viscosity, to non-linear parameters, e.g., the Q parameter quantified and used here.     

Structure development during crystallization of polycaprolactone

In this paper, the quiescent crystallization of polycaprolactone (PCL) melts is studied by rheological measurements coupled to calorimetry and optical microscopy. Based on a comparison between the different techniques, we find that the increase in viscoelastic properties during crystallization starts only when a relatively high degree of crystallinity is reached, which corresponds to a much developed crystalline microstructure. Like other semicrystalline thermoplastic polymers, the crystallization of PCL can be seen as a gelation process. In this case, however, we find a peculiar critical gel behavior, as the liquid-to-solid transition takes place at a very high (~20%) relative crystallinity, and this value is independent of temperature. These facts, and the comparison with optical microscopy observations, suggest that the microstructure at the gel point is controlled by the interactions between the growing crystallites. The gel time (from rheometry) and the half-crystallization time [from differential scanning calorimetry (DSC)] both show an Arrhenius-like behavior and have the same pseudoactivation energy. A practical implication of this parallel behavior of t _gel and t _0.5 is that the rheological measurements can be used to extend to higher temperatures the study of crystallization kinetics where DSC is not sufficiently sensitive.This paper was presented at the second Annual European Rheology Conference (AERC) held in Grenoble, France, 21–23 April 2005.     

Rheological characterization of well-defined tetrafluoroethylene/hexafluoropropylene copolymers

The rheology of tetrafluoroethylene/hexafluoropropylene (TFE/HFP) copolymers, also known as Teflon FEP polymers, having different molecular weight and composition (HFP content) was studied by means of a parallel-plate rheometer. Two groups of polymers having different molecular weights with nearly constant polydispersity (around 2.5) were considered; namely, one group having a relatively low melting temperature (amorphous with a high content of HFP) and a second group having a higher melting point (semi-crystalline with a lower content of HFP). The relaxation time spectrum, H(λ), calculated by use of the BSW model (developed for monodisperse linear polymers) followed a scaling relationship in the terminal zone with scaling exponent of 0.13. However, at higher frequencies the model fails to predict adequately the experimental data. The longest relaxation time calculated from both the BSW model and discrete relaxation spectra (λ _i ,g _i ), which was determined by use of a parsimonious fitting software, depends on the molecular weight in a similar way as the zero-shear viscosity does with the well-established scaling factor of 3.4. The critical molecular weight for the onset of entanglements, M _c , was found to be about 100000, a value much higher than those previously reported in literature for other polymers. The rheology of resins in the second group (higher melting point) was found to exhibit a strong dependence on thermal history during oscillatory-shear measurements. The data obtained in experiments at different temperatures without a preheating to a certain value (330°C) exhibited a violation of the time-temperature superposition principle and no well-defined values of the zero-shear viscosity. This is attributed to residual crystallinity even at temperatures well above their melting point (260°C). However, the same experiments with preheating and subsequent cooling to desired temperature resulted into a very good time-temperature scaling. Received: 13 January 1998 Accepted: 6 April 1998     

Rheology and gelation kinetics of PVC plastisols

Oscillatory rheological experiments at different temperatures and over a wide range of frequencies have been used to investigate the gelation process and, more particularly, the sol–gel transition of various poly(vinyl chloride) (PVC) plastisols. The sol–gel transition process was found to be universal with respect to the temperature and solid volume fraction according to the similarity of the fractal structure in PVC plastisols. The variation of the gel time (t _gel) with temperature for any composition of PVC plastisols was predicted from the Dickinson’s model (E. Dickinson, J Chem Soc Faraday Trans, 93:111–114, 1997). Dynamic viscoelastic properties of PVC plastisols have also been studied as a function of temperature that allowed us to follow the gelation process of various plastisols. Thus, the influence of the type and concentration of PVC resins in gelation process was investigated. The variation of the complex shear modulus at a constant frequency was depicted by a master curve regarding the dependence of the moduli on PVC concentrations.     

Crystallization of alkanes under quiescent and shearing conditions

We report molecular dynamics simulation of crystallization of model alkane systems conducted under constant pressure conditions. We have studied crystallization of n-eicosane (C₂₀H₄₂) and n-hexacontane (C₆₀ H₁₂₂) under quiescent and shearing conditions. We find preshearing before subjecting the melt to quiescent crystallization enhances the crystallization of higher molecular weight hexacontane, whereas, for low molecular weight eicosane, no significant change can be detected. For both alkanes applying steady planar shear significantly speeds up the crystallization. The crystal growth rate increases with the shear rate. However, we find that the critical shear rate above which the crystallization is enhanced, is inversely proportional to the size of the chains. In all cases the Weissenberg numbers of the sheared systems are moderate. We estimate them to be in the range of 0.01–10. Our quiescent simulations for eicosane predict crystallization temperature and lattice parameters of the crystalline phase in good agreement with experimental measurements. We have compared an order parameter used in the simulations against one analogous to that used in dilatometry experiments. Using this order parameter as a measure of crystallinity we predict the crystal growth rate of n-eicosane to be a maximum at ∼300 K in good agreement with experiments. Fitting crystallization growth data to Avrami's model we have calculated Avrami growth functions and exponents for many cases. For quiescent crystallization of n-eicosane we found the Avrami exponent calculated using our order parameter for defining degree of crystallinity, agrees well with that obtained in the experiments. For C60 the crystallization process is very slow at quiescent conditions; however preshearing enhances the crystal growth.     

Creep recovery behavior of metallocene linear low-density polyethylenes

The rheological behavior of two metallocene linear low-density polyethylenes (mLLDPE) is investigated in shear creep recovery measurements using a magnetic bearing torsional creep apparatus of high accuracy. The two mLLDPE used are homogeneous with respect to the comonomer distribution. The most interesting feature of the two mLLDPE is that their molecular mass distributions are alike. Therefore, as one of the mLLDPE contains long-chain branches, the influence of long-chain branching on the elastic properties of polyethylene melts could be investigated. It was found that long-chain branches increase the elasticity of the melt characterized by the steady-state recoverable compliance. The long-chain branched mLLDPE has a flow activation energy of 45 kJ/mol which is distinctly higher than that of the other mLLDPE. The shear thinning behavior is much more pronounced for the long-chain branched mLLDPE. A discrepancy between the weight average molecular mass M _w calculated from size exclusion chromatography measurements by the universal calibration method and the zero shear viscosities of the two mLLDPE was observed. These observations are discussed with reference to the molecular architecture of the long-chain branched mLLDPE. The rheological properties of the long-chain branched mLLDPE are compared with those of a classical long-chain branched LDPE. It is surprisingly found that the rheological behavior is very much the same for these two products although their molecular mass distributions and presumedly the branching structures differ largely. Received: 15 February 1999 Accepted: 10 June 1999     

The effect of molecular weight on the rheological properties of poly(dimethylsiloxane) filled with fumed silica

The viscometric, stress relaxation, and stress growth rheological properties were measured for various molecular weight PDMS fluids filled with fumed silica. The stress growth function exhibited significant overshoot, when the continuous phase molecular weight was slightly greater than the entanglement molecular weight; however, significant overshoot peaks were not observed, when the continuous phase molecular weight was less than or much greater than the molecular weight between entanglements. The experimentally observed transient rheological properties are rationalized in terms of a molecular model, where interparticle interactions occur via entanglements of the polymer adsorbed on the silica surface. When the molecular weight of the adsorbed polymer is greater than the entanglement molecular weight, the strength of the interparticle interaction will increase substantially and the particle diffusivity will substantially decrease.     

Evaluation of molecular weight distribution from dynamic moduli

A method to evaluate molecular weight distribution (MWD) from dynamic moduli is presented here. It relies on the least-square fitting of the dynamic data to a model whose parameters depend on the MWD. In particular, the analytical solution for the relaxation modulus previously obtained from the double reptation model, with the Tuminello step relaxation function and the Generalized Exponential Function (GEX) describing the MWD (Nobile and Cocchini 2000), has been used. A Finite Element Approximation (FEA) has been applied to calculate dynamic moduli from the relaxation modulus as a function of MWD. The sensitiveness of the GEX-double reptation dynamic moduli on the model parameters has also been investigated and the results show that large changes of the M_w/M_n ratio weakly affect the dynamic moduli, while small changes of the M_z/M_w ratio significantly deform the dynamic moduli curves. The use of rheological data to obtain MWD, by the model used in this paper, will, therefore, be able to give rather well defined M_z/M_w ratios, while more uncertainty will be presented in the M_w/M_n results. The so-called GEX-rheological model for the dynamic moduli was applied to fit the experimental data of different polymers in order to obtain the best-fit parameters of the MWD of these polymers, without the need for the inversion of the double reptation integral equation. The stability of the results has been confirmed through the evaluation of the 90% confidence intervals for the first molecular weight averages. Finally, concerning the M_w and M_z values, the predictions obtained from the dynamic moduli measurements differ by less than 10% from those obtained from GPC measurements while, as expected, more uncertainty is present in the M_n predictions. Received: 6 February 2000 Accepted: 22 August 2000     

Dynamic rheological analysis of the gelation behaviour of waxy crude oils

In this work we have characterised the viscoelastic behaviour of paraffin crystals in three different complex crude oils, close to the gelation threshold and after curing the gels under quiescent isothermal conditions, by means of oscillatory shear measurements. An increase in gelation temperature is observed with increasing oils molecular weight. The interactions between wax crystals and the formation of the space-filling network of interlocking wax crystals are thus facilitated by the presence of paraffins with higher molecular weight. The apparent gelation time, obtained from isothermal curing experiments, decreases as the curing temperature was decreased, and it is highly temperature-dependent.The presence and the importance of the ageing of the wax were established under isothermal conditions. It must result from a coarsening of the crystallites presents in the oil and it is, more important, close to the gel point where its full development is very slow taking several days to occur. After ageing the gels, the connective domains or junction zones linking the crystal arrays fail when relatively small strains are applied to the system and the mechanical spectra of the gels reveal an imperfect elastic network, typical rheological characteristics of a particle gel. Despite the compositional differences among the samples, the similarity of their mechanical behaviour is quite remarkable indicating that in all cases the gel-like organisation of the waxy material results from the formation of identical structures in the different oils, which is related not only to the wax content but also to the presence of other material that may reduce the crystallinity of the structure.The low fractal dimensionality obtained indicates elongated substructures. These results, together with the very high elastic modulus obtained at low volume fractions of crystallised material, are indicative of network structures with high degree of porosity: a lattice of wax crystals with large spaces among them filled by the oil and non-precipitated material.This paper was presented at the first Annual European Rheology Conference (AERC) held in Guimarães, Portugal, September 11-13, 2003.     

Network-structure of plasticized epoxy resins by dynamic measurements

Viscoelastic parameters are strongly connected with the glass transition temperature and the degree of cross-linking of polymers. In this paper an attempt was undertaken to analyse the storage modulus in the rubbery plateau and the transition region of a series of plasticized epoxy polymers, in terms of their network structure, by means of dynamic measurements.A series of dynamic tests was carried out at frequencies between 0.1 and 100 Hz and temperatures from 50 °C to 140 °C. By applying the time-temperature superposition principle, composite curves for the storage modulusE () were derived over a wide frequency range.The crosslink density, or the molecular weight, between crosslinks could be changed by adding different amounts of plasticizer in the epoxy polymer, and it was calculated by applying the theory of rubber elasticity. The glass transition temperatureT _g for each substance was found to be influenced by the amount of plasticizer and the molecular weight between crosslinks. This behaviour of the highly crosslinked epoxies was different from that of rubbers or analogous materials.Finally, an estimation of the free volume of the materials tested was attempted by using the WLF-equation.     

Characterization of physical aging by time-resolved rheometry: fundamentals and application to bituminous binders

Physical aging is a ubiquitous phenomenon in glassy materials and it is reflected, for example, in the time evolution of rheological properties under isothermal conditions. In this paper, time-resolved rheometry (TRR) is used to characterize this time-dependent rheological behavior. The fundamentals of TRR are briefly reviewed, and its advantages over the traditional Struik’s physical aging test protocol are discussed. In the experimental section, the TRR technique is applied to study physical aging in bituminous binders. Small-diameter parallel plate (SDPP) rheometry is employed to perform cyclic frequency sweep (CFS) experiments over extended periods of time (from one to 8.6 days). The results verify that the mutation of rheological properties is relatively slow during physical aging (mutation number N′_mu?<<?1), thus allowing rheological measurements on a quasi-stable sample. The effects of temperature, crystallinity, and styrene-butadiene-styrene (SBS) polymer modification on the physical aging of bitumen are evaluated. The time-aging time superposition is found to be valid both for unmodified and for polymer-modified bitumen. Vertical shifts are necessary, in addition to horizontal time-aging time shifts, to generate smooth master curves for highly SBS-modified bitumen.     

Gelation behavior of polysaccharide-based interpenetrating polymer network (IPN) hydrogels

We report the preparation and rheological characterization of interpenetrating polymer network (IPN) hydrogels made from alginate and hydrophobically modified ethyl hydroxyl ethyl cellulose (HMEHEC). To our knowledge, there have been no studies of the gelation behavior of IPNs. We found that the rheology of these systems can be easily tuned, with the elastic modulus of the IPN strongly dependent on the relative ratio of HMEHEC to alginate. The sol–gel transition of these systems was found to satisfy the Winter–Chambon criterion for gelation at various crosslinker densities. From the power law relationship of the dynamic moduli (G ^′ ~G ^″ ~ω ⁿ), the exponent n appears to be dependent on both the crosslinker density and relative amount of two polymers. The value of n was found to be ~0.5 for all samples for stoichiometric amounts of crosslinker. The effect of molecular weight of HMEHEC on the gel point and viscoelastic exponent has also been reported. Alginate seems to dominate the kinetics of the process but the effect of high molecular weight HMEHEC on the gel point, especially at lower proportion was also evident.     

Novel bitumen/isocyanate-based reactive polymer formulations for the paving industry

Reactive modification is lately gaining acceptance as a successful way to give added value to bitumen, a crude oil refining by-product. In order to study the effect of both bitumen type and processing method, isocyanate-based reactive modification was carried out with four types of bitumen from different sources, by following two different procedures (“water-free” and “water-involved” processing). The polymer used (MDI–PPG) was synthesized from the reaction of 4,4^′-diphenylmethane diisocyanate with a low molecular weight polypropylene glycol. The results obtained demonstrate that the addition of small quantities of this reactive polymer to bitumen endows the resulting modified binder with an improved performance at high in-service temperatures. Interestingly, two different modification pathways have been identified: the first one, which occurs during mixing, is the result of chemical reactions between -NCO groups of the reactive polymer with functional groups containing active hydrogen atoms (mainly, –OH), such as those typically present in the most polar bitumen fractions; the second one has been proved to be a consequence of series reactions involving water. Both pathways, but mainly the latter, lead to bituminous paving materials showing a more complex microstructure, with the consequent change in their rheological response. Finally, very different degrees of modification, depending on the colloidal features of the as-received bitumen, were observed.     

Molecular mass dependence of the zero shear-rate viscosity of LDPE melts: evidence of an exponential behaviour

The molecular mass dependence of the zero shear-rate viscosity of low-density polyethylene (LDPE) melts is revisited for a series of LDPE samples of different molecular masses and densities. The long-chain branching structure and absolute weight average molecular masses are determined using a state-of-the-art size exclusion chromatography system coupled with multi-angle laser light-scattering. Creep experiments in a stress-controlled rotational rheometer are used to determine the zero shear-rate viscosity. The experimental results give evidence of an exponential molecular mass dependence of zero shear viscosity. It is demonstrated that these results can qualitatively be explained by comparison with recent theoretical predictions of the rheological properties of comb-branched model polymers.