Rheological and molecular characterization of long-chain branched poly(ethylene terephthalate)

Reactive extrusion with pyromellitic dianhydride (PMDA) and tetraglycidyl diamino diphenyl methane (TGDDM) was conducted to create long-chain branched poly(ethylene terephthalate) (LCB-PET). The mechanical and molecular properties were analyzed by linear and non-linear viscoelastic rheology in the melt state and by size-exclusion chromatography measurements with triple detection. The two tetra-functional chain extenders lead to strong viscosity increases, increasing strain hardening effects, and increasing LCB with increasing chain extender concentration. Molecular stress function model predictions show good agreement with the elongational data measured and allowed a quantification of the strain hardening. Analysis of SEC triple detection data shows a strong increase of the average molar mass, polydispersity, radius of gyration, and hydrodynamic radius with increasing chain extender concentration. Branching was confirmed by a decreasing Mark-Houwink exponent, and the analysis of the contraction of the molecule revealed either star-like, comb-like, random tree-like or hyperbranched structures depending on concentration and type of chain extender.     

Effect of vinyl acetate content and silicate loading on EVA nanocomposites under shear and extensional flow

In this study, three EVAs (ethylene-vinyl acetate co-polymers) with different vinyl contents (VA) ranging from 9 wt% to 28 wt% (EVA9, EVA18 and EVA28) were melt blended with organo-clay to obtain polymer layered silicate nanocomposites. Filler intercalation and exfoliation were evidenced by X-ray diffraction. The melt state viscoelastic properties of EVA nanocomposites were studied to examine the influence of clay in altering the flow properties of these polymeric nanocomposites. The EVA18 and EVA28 nanocomposites exhibited remarkable difference in dynamic and steady shear properties compared to neat polymers. On the other hand, EVA9-5% nanocomposite did not exfoliate and exhibited rheological behaviour very similar to that of the neat polymer. Furthermore, the first normal stress difference was found to be dependent on the silicate loadings when measured at low shear stresses. The uniaxial extensional viscosity measurement indicated that the strain hardening was weaker in EVA nanocomposites compared to neat polymers. Environmental scanning electron (ESE)-microscopy elucidated a possible reason for reduced strain hardening in these systems.     

A new constitutive equation that models extensional flow strain hardening based on evolving natural configurations: stability analysis

Polymer melt viscoelastic fluids often exhibit in elongational flows a significant increase in the elongational viscosity known as strain hardening. This phenomenon could be related to polydispersity, e.g. the presence of a small fraction of very high molecular weight chains whose time frame relaxation spectrum is different from the small chains one. In the present work, we present a fully objective constitutive equation (CE) to primarily model extensional strain hardening based on the new concept of multiple configuration materials. Next, we analyze the CE stability properties with respect to small perturbations about the rest state.     

Comparison of viscous and elastic properties of polyolefin melts in shear and elongation

Viscous and elastic properties of a linear polypropylene (PP) and a long-chain branched low-density polyethylene (LDPE) have been investigated by creep and creep–recovery experiments in shear and elongation. The data obtained verify the ratios between the linear values of the viscosities and the steady-state elastic compliances in shear and elongation predicted by the theory of linear viscoelasticity. In the nonlinear range, no simple correlation between the viscous behaviour in shear and elongation exists. The elongational viscosity of the PP decreases with increasing stress analogously to the shear thinning observed; the linear range extends to higher stresses in elongation than in shear, however. The LDPE shows thinning in shear and strain hardening in elongational flow. For the LDPE, a linear steady-state elastic tensile compliance corresponding to one third of the linear steady-state elastic compliance in shear was determined. For the PP, this theoretically predicted value is approximately reached. Analogous to the viscous behaviour, the linear range extends to higher stresses in elongation than in shear. For both materials, the steady-state elastic compliances in the nonlinear range decrease with increasing stress in shear as well as in elongation. However, the decrease in elongation is more pronounced.     

Theoretical correlation of linear and non-linear rheological symptoms of long-chain branching in polyethylenes irradiated by electron beam at relatively low doses

Dynamic and transient shear and elongation flow experiments along with gel permeation chromatography (GPC) and differential scanning calorimetry (DSC) analysis are performed on linear low-density polyethylenes (LLDPEs) irradiated at doses below 25 kGy. GPC data indicate no changes in the molar mass distribution, and there are almost no changes in melt and crystallization temperatures, likewise. Contrary, dynamic shear rheological behavior including thermorheological complexity, type of reduced van Gurp-Palmen curves, and zero shear-rate viscosities all disclose growing levels of long-chain branching with irradiation dose. An inverse tube model is developed for binary blend of linear and star chains and used to extract the fraction of the branched components. Modeling results reveal progressive increase in the length and fraction of star chains, as evidenced by appearance of an anomalous double overshoot in the transient shear viscosities. Detection of strain hardening in extensional stress growth coefficient data, well-quantified by molecular stress function model, is also in agreement with the predictions of tube model.     

Rheological behaviour and molecular structure of long-chain branched semifluorinated thermoplastics

The long-chain branched thermoplastic tetrafluoroethylene–hexafluoropropylene–vinylidenefluoride terpolymers (LCB THV) investigated in this paper are new polymers with a unique combination of properties like a high stability against aging or weathering and a very good chemical resistance. But not much is known about the rheological behaviour of the LCB THV, yet. In this paper, non-linear rheological properties like shear thinning and strain hardening are studied. Two different types of the THV with different contents of comonomers and, therefore, different melting points are examined. The THV with the higher melting point is insoluble. The other with the lower melting temperature is soluble and, therefore, was characterised by size exclusion chromatography coupled with light scattering with respect to its molecular structure. The results of the rheological measurements show a pronounced shear-thinning and strain-hardening behaviour for the long-chain branched materials. Both properties are of great importance for processing operations governed by shear and elongational flows.

Influence of molecular structure on secondary flow of polyolefin melts as investigated by laser-Doppler velocimetry

Laser-Doppler velocimetry (LDV) is applied to investigate velocity profiles in the entrance region of a slit die. Due to the high spatial resolution of the device and the accuracy of the velocity measurements the secondary flow patterns of different polyolefins have quantitatively been analyzed for the first time. A linear polyethylene is compared with two long-chain branched polyethylenes and a conventional linear polypropylene with a long-chain branched one. All materials are rheologically characterized with respect to their viscosity functions, elasticity, and elongational properties. For the two linear materials no indication of secondary flow is found, but the three long-chain branched polymers (two polyethylenes and one polypropylene) exhibit pronounced vortices. Neither viscosity nor elasticity seem to be decisive for the occurrence of secondary flow. The viscosity has an influence, however, on the size of the vortices and the velocities within them. All of the three long-chain branched polymers are strongly strain hardening which gives rise to the conclusion that this behavior may be a necessary condition for the formation of vortices. The linear polypropylene does not show any indication of strain hardening. The linear polyethylene, surprisingly, is significantly strain hardening, but it becomes less pronounced with higher strain rates. As most of the deformation in the entrance region takes place at elongational rates at which the strain hardening of the linear polyethylene is not significant, the findings on the linear polyethylene do not contradict the hypothesis that strain hardening and vortex formation in entrance flow may be related to each other. Received: 27 April 2000 Accepted: 30 November 2000     

Linear and non-linear viscoelastic properties of ethylene vinyl acetate/nano-crystalline cellulose composites

This paper reports on the melt rheological properties of ethylene vinyl acetate containing between 0 and 10 wt.% of nano-crystalline cellulose (NCC). A complete set of rheological tests including frequency sweeps, shear transients, and uniaxial elongations was performed. Frequency sweeps showed that at low frequencies, a pseudo solid-like behavior was obtained for NCC concentrations higher than 5%. This behavior was related to hydrogen bonding between NCC particles and the creation of particle networks as the result of particle–particle interactions. For transient shear tests, all compositions presented a stress overshoot at high shear rates before reaching a steady state. It was found that the amplitude of this overshoot depends on both NCC content and shear rate. On the other hand, the time to reach the maximum was found to be highly shear rate dependent but concentration dependence was rather weak. For uniaxial extensional flow, higher extensional viscosity was observed with increasing NCC content. On the other hand, strain hardening was found to decrease with increasing NCC content.     

Design of new HDPE/silica nanocomposite and its enhanced melt strength

Linear polymers are restricted to use in processes that involve severe extensional deformation, such as fiber spinning, film blowing, and thermoforming. To extend their applicability, the extensional properties of polymer melts should be enhanced such that strain hardening, which is defined as an increase in extensional viscosity under a large strain that deviates from the linear viscoelastic curve, is pronounced. In this study, a novel preparation method of linear polymer/inorganic nanocomposites was proposed with a main focus on enhanced melt strength. The design of molecular structure consists of three components—linear polymer, compatibilizer, and surface-modified particles. High-density polyethylene was used as a linear polymer while polyethylene grafted with maleic anhydride was used as a compatibilizer. Silica particles were synthesized and modified on their surfaces by 3-aminopropyltriethoxysilane. The strain hardening behavior of the surface-modified silica composites was pronounced. However, such a result was not observed for the composites of the same composition with pure-silica. In addition, the dispersion of the modified silica was much better than that of pure-silica.     

Prediction of steady-state viscous and elastic properties of polyolefin melts in shear and elongation

The linear and nonlinear steady-state viscosities and elastic compliances were measured in shear and elongational flows for two low-density polyethylenes, a linear polypropylene, and two metallocene catalyzed polyethylenes (one linear and one long-chain branched) by Wolff et al. (Rheol Acta 49:95?C103, 2010) and Resch (dissertation, 2010). Comprehensive data of this type are rarely found in the literature, and comprehensive modeling of both viscous and elastic effects is even rarer. In this contribution, the reliability of a modeling approach proposed by Laun (J Rheol 30(3):459?C501, 1986) and based on the damping function concept is tested. The strain hardening seen for the long-chain branched polymers and its absence in the case of the linear polymer, the stronger decrease of the tensile compliance in comparison to the shear compliance with increasing stress, as well as the extended linear-viscoelastic regime of the shear viscosity in contrast to the shear compliance are correctly modeled. While the modeling of the nonlinear response in shear can be achieved with only one material parameter for most of the polymers considered here, the nonlinear modeling in elongation is achieved with two parameters. The same parameter values are shown to describe viscous as well as elastic properties of the melts, and thus the relations of Laun can be used to test the consistency of viscosity and compliance measurements.     

Simulated properties of Kagomé and tetragonal truss core panels

The finite element method has been used to simulate the properties of panels with Kagomé and tetragonal cores under compressive and shear loading. The simulation has been performed for two different materials: a Cu-alloy with extensive strain hardening and an Al-alloy with minimal hardening. It is shown that the Kagomé core is more resistant to plastic buckling than the tetragonal core under both compression and shear. One consequence is that the Kagomé structure has the greater load capacity and a deferred susceptibility to softening. Another is that the Kagomé core is isotropic in shear: contrasting with the soft orientations exhibited by the tetragonal core.     

Non Linear Rheology for Long Chain Branching characterization,comparison of two methodologies : Fourier Transform Rheology and Relaxation.

In this study we compare three rheological ways for Long Chain Branching (LCB) characterization of a broad variety of linear and branched polyethylene compounds. One method is based on dynamical spectrometry in the linear domain and uses the van Gurp Palmen plot. The two other methods are both based on non linear rheology (Fourier Transform Rheology (FTR) and chain orientation/relaxation experiments). FTR consists in the Fourier analysis of the shear stress signal due to large oscillatory shear strains. In the present work we focus on the third and the fifth harmonics of the shear stress response. Chain orientation/relaxation experiment consists in the analysis of the polymer relaxation after a large step strain obtained by squeeze flow. In this method, relaxation is measured by dynamical spectrometry and is characterized by two relaxation times related to LCB. All methods distinguish clearly the group of linear polyethylene from the group of branched polyethylene. However, FTR and Chain orientation/relaxation experiments show a better sensitivity than the van Gurp Palmen plot. Non linear experiments seem suitable to distinguish long branched polyethylene between themselves.     

Effects of particle softness on the rheology and yielding of colloidal glasses

We studied the linear and nonlinear rheology of colloidal glasses consisting of hard spheres and soft core-shell particles at several volume fractions to explore the effects of particle softness on the mechanical properties and yielding. Creep and recovery and oscillatory shear measurements were used to determine the shear elastic modulus and the yield strain. Both hard and soft sphere glasses exhibited ‘entropic cage elasticity’ below random close packing, whereas for compressed soft spheres at higher effective volume fractions, the yield strain was determined by shell elasticity. The shear modulus followed a strong increase with volume fraction for hard spheres and a much weaker one for soft particles reflecting their interparticle potential. Nonlinear effects, revealed as strong distortions of the stress signal during yielding, were analyzed via Fourier transform rheology and Lissajous plots. The significant contribution of the nonlinearities was analyzed in terms of strain softening and hardening mechanisms within a cycle of oscillation and discussed in relation to particle softness.     

Strain hardening of fibrin gels and plasma clots

Biological macromolecules have unique rheological properties that distinguish them from common synthetic polymers. Among these, fibrin has been studied extensively to understand the basic mechanisms of viscoelasticity as well as molecular mechanisms of coagulation disorders. One aspect of fibrin gel rheology that is not observed in most polymeric systems is strain hardening: an increase in shear modulus at strain amplitudes above 10%. Fibrin clots and plasma clots devoid of platelets exhibit shear moduli at strains of approximately 50% that are as much as 20 times the moduli at small strains. The strain hardening of fibrin gels was eliminated by the addition of platelets, which caused a large increase in shear storage modulus in the low strain linear viscoelastic limit. The reduction in strain hardening may result from fibrin strand retraction which occurs when platelets become activated. This interpretation is in agreement with recent theoretical treatments of semi-flexible polymer network viscoelasticity.Dedicated to Prof. John D. Ferry on the occasion of his 85th birthday.     

Artificial aging and shear deformation behaviour of 6022 aluminium alloy

In this study, the artificial aging behaviour of 6022-T4 alloy is investigated over a wide temperature range. Hardness readings, TEM and XRD analyses were performed. It was shown that 6022-T4 alloy can be substantially hardened through a short aging treatment at temperatures in excess of 200 °C. The strain hardening curves of the 6022 alloy in different aging conditions were measured using the simple shear test and analysed in terms of their respective microstructures. The under-aged and pre-peak-aged exhibited a good combination of strength and strain hardening while the peak-aged alloy was characterised by maximum strength, albeit with a drastic reduction in strain hardening ability. Strain reversal experiments in simple shear were carried out in order to characterize the Bauschinger effect for the different heat treatment conditions. It was shown that the T4 and under-aged conditions lead to permanent softening of the flow stress.     

Recovery of shear modification of polypropylene melts

Long-chain branched polypropylenes (LCB-PP) of different degrees of branching (up to 1 branch/10⁴ carbon atoms) and a linear polypropylene (L-PP) are deformed at different shear conditions (rate, time and deformation) leading to reversible modifications of the entanglement structure. These modifications recover with time. Because of it the intensity of the modification and the rate of recovery are studied. At shear rates between 1?s^?1 and 10?s^?1 lower rates modify stronger. The intensity increases with shear time to a maximum at times of about 1 h where the final deformation does not control the intensity. Obviously, the disentanglement created by shearing competes with the Brownian motion coupling entanglements. Also, the intensity increases with the degree of LCB where the increase is stronger at low degrees. The rate of recovery not influenced noticeably by the initial modification strongly depends on the degree of LCB. The pertinent recovery functions grow exponentially to the limiting value of the unmodified state. Three different recovery processes are found. The fastest one with a recovery time shorter than 10³?s is assigned to linear chains. The process with a time of about 5·10³?s independent of the degree of LCB is assumed to describe the recovery of the backbones. The times for the very slow recovery of the side chains increase with the degree of LCB (between 10⁴ and 10⁵?s for the investigated samples). The recovery strength reflects the initial modification and depends on the degree of LCB. By that, the recovery behaviour provides information on the molecular structure.     

Rheological behavior of suspensions of modified and unmodified cellulose nanocrystals in dimethyl sulfoxide

The rheological behavior of cellulose nanocrystal (CNC) and modified CNC (mCNC) suspensions in dimethyl sulfoxide (DMSO) was investigated. The efficiency of the surface modification of CNCs by grafting an organic acid chloride to produce hydrophobic CNCs has been verified by X-ray photoelectron spectroscopy (XPS). The thermal degradation temperature of the mCNCs was found to be 165 versus 275 °C for CNCs. The CNC suspensions in DMSO at 70 °C underwent gelation at very low concentration (1 wt%) after 1 day. The network formation was temperature sensitive and did not occur at room temperature. For gels containing 3 wt% CNCs, the complex viscosity at 70 °C increased by almost four decades after 1 day. For the mCNCs in DMSO, a weak gel was formed from the first day and temperature did not affect the gelation. Finally, the effect of adding 10 wt% of polylactide (PLA) to the solvent on the rheological properties of CNC and mCNC suspensions was investigated. The properties of suspensions containing 1.9 wt% CNCs and mCNCs increased during the first and second days, and PLA did not prevent gel formation. However, the reduced viscosity and storage modulus of the CNC and mCNC gels with PLA were lower than those of samples without PLA.     

Melt rheology of long-chain-branched polypropylenes

Rheological properties of long-chain-branched isotactic polypropylene (PP) via copolymerization with a very small amount of nonconjugated α,ω-diene monomer using metallocene catalyst system in both linear and nonlinear regions were investigated, comparing with conventional linear and long-chain-branched PP modified at postreactor. Although comonomer incorporation was equal to 0.05 mol% or less, it caused high molecular weight, broad molecular weight distribution, and long-chain branching. A detailed study on the effect of diene incorporation on the polymer properties was conducted, comparing with modified PP in postreactor. Polymer chain microstructures were characterized by gel permeation chromatography with multiangle laser light scattering (MALLS), differential scanning calorimetry, and rheological means: dynamic viscoelasticity, step-strain, uniaxial elongational flow measurements, and large amplitude oscillatory shear. The PP, which incorporated a small amount of diene monomer, showed significantly improved viscoelastic behaviors. The diene-propylene copolymer containing long-chain branches showed extremely long relaxation mode under shear and outstanding viscosity increase under elongational flow, so-called strain hardening. The difference in microstructure of diene-propylene copolymer with modified PP with long-chain branches is investigated by MALLS and rheological characterizations.     

Rheology of SiO 2 /(acrylic polymer/epoxy) suspensions. III. Uniaxial elongational viscosity

Uniaxial elongational viscosity of SiO₂/(acrylic polymer/epoxy (AP/EP)) suspensions with various SiO₂ volume fractions (?) in a blend of acrylic polymer and epoxy was investigated at various temperatures (T). The matrix polymer ((AP/EP) blend) contained 70?vol.% of EP. At ?????35?vol.% at T????80°C, where the suspensions were in sol state, strain-hardening behavior was observed. This strain hardening of the suspensions is attributable to the elongational flow properties of (AP/EP) medium. At critical gel state (??=?35?vol.% and T?=?100°C) and in gel state (?????40?vol.%), the elongational viscosity exhibited the strain-softening behavior. These results strongly suggest that the strain softening results from the strain-induced disruption of the network structure of the SiO₂ particles therein.