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.

Rheological properties of branched polystyrenes: linear viscoelastic behavior

Oscillatory shear measurements on a series of branched graft polystyrenes (PS) synthesized by the macromonomer technique are presented. The graft PS have similar molar masses (M _w between 1.3×10⁵ g/mol and 2.4×10⁵ g/mol) and a polydispersity M _w /M _n around 2. The molar masses of the grafted side chains M _w,br range from 6.8×10³ g/mol to 5.8×10⁴ g/mol, which are well below and above the critical entanglement molar mass M _c of linear polystyrene. The average number of side chains per molecule ranges from 0.6 to 6.7. The oscillatory measurements follow the time–temperature superposition principle. The shift factors do not depend on the number of branches. The zero-shear viscosities of all graft PS are lower than those of linear PS with the same molar mass, which can be attributed to the smaller coil size of the branched molecules. It is shown that the influence of branching on the frequency dependence of the dynamic moduli is weak for all graft PS that were investigated, which can be explained by the low entanglement density.Electronic Supplementary Material Supplementary material is available for this article at This article has already been published online first (DOI: ). Due to an oversight at the publisher's, this version contained several mistakes. The article is herewith republished in its entirety as a "publisher's erratum".     

Comparison of the elongational behavior of various polyolefins in uniaxial and equibiaxial flows

For processing operations with a pronounced elongational component, it was found that the uniformity of extruded items is improved by the presence of strain hardening usually measured in uniaxial elongation. Many processing operations such as foaming, film blowing, and blow molding are dominated by biaxial deformations, however, and therefore, the question arises how strain hardening in uniaxial and biaxial deformation compares. Besides a linear and long-chain branched PP, one classical LDPE, an HDPE pipe extrusion grade with a bimodal MMD, and a LCB-mPE were also characterized. For the measurements in uniaxial elongation the Münstedt tensile rheometer (MTR) and the ARES-EVF were used, while the lubricated flow method was applied for equibiaxial deformation. It was found that the strain hardening in uniaxial elongation is more pronounced. The dependence of strain hardening on strain rate is qualitatively the same in both modes. In the range of strain rates, the chosen long-chain branched LDPE and PP exhibit a strain hardening, which is approximately independent of the elongational rates applied, whereas for the HDPE it becomes smaller with increasing rate.

Transient shear and elongational behavior of blends of PET with a LCP

Blends of polyethylene terephthalate (PET) with a liquid crystalline polymer (LCP) and a compatibilizer were produced by twin screw extrusion and injection molding. Transesterification and compatibilization studies were made in a torque rheometer. The morphology of the injection-molded plaques was studied by scanning electron microscopy. The blends shear growth function was measured in a cone and plate rheometer. The elongational growth function was measured in a modified rotational rheometer. Transesterification was observed in the PET/LCP/compatibilizer 95/5/0 blend. The injection-molded plaques displayed the usual “skin-core” morphology. All the blends were highly shear-thinning, even at low shear rates; thus, a zero-shear viscosity could not be calculated. The compatibilized blend had the highest shear viscosity of all the blends, confirming the strong PET/LCP interphase and the effectiveness of the compatibilizing agent. On the other hand, the 90/10/0 blend had the lowest shear viscosity. All the blends showed strain softening behavior, similar to the PET. The 90/10/0 blend had the highest elongational growth function, while the 95/5/0 had the lowest. The compatibilized blend had an intermediate behavior between both blends.     

Modelling elongational and shear rheology of two LDPE melts

Experimental data of two low-density polyethylene (LDPE) melts at 200°C for both shear flow (transient and steady shear viscosity as well as transient and steady first normal stress coefficient) and elongational flow (transient and steady-state elongational viscosity) as published by Pivokonsky et al. (J Non-Newtonian Fluid Mech 135:58–67, 2006) were analysed using the molecular stress function model for broadly distributed, randomly branched molecular structures. For quantitative modelling of melt rheology in both types of flow and in a very wide range of deformation rates, only three nonlinear viscoelastic material parameters are needed: Whilst the rotational parameter, a ₂, and the structural parameter, β, are found to be equal for the two melts considered, the melts differ in the parameter describing maximum stretch of the polymer chains.     

Influence of long-chain branches in polyethylenes on linear viscoelastic flow properties in shear

 This contribution presents a survey on the influence of long-chain branching on the linear viscoelastic properties zero shear-rate viscosity and steady-state recoverable compliance of polyethylene melts. The materials chosen are linear and slightly long-chain branched metallocene-catalyzed polyethylenes of narrow molecular mass distribution as well as linear and highly long-chain branched polyethylenes of broad molecular mass distribution. The linear viscoelastic flow properties are determined in shear creep and recovery experiments by means of a magnetic bearing torsional creep apparatus. The analysis of the molecular structure of the polyethylenes is performed by a coupled size exclusion chromatography and multi-angle laser light scattering device. Polyethylenes with a slight degree of long-chain branching exhibit a surprisingly high zero shear-rate viscosity in comparison to linear polyethylenes whereas the highly branched polyethylenes have a much lower viscosity compared to linear samples. Slightly branched polyethylenes have got a higher steady-state compliance in comparison to linear products of similar polydispersity, whereas the highly branched polyethylenes of broad molecular mass distribution exhibit a surprisingly low elasticity in comparison to linear polyethylenes of broad molecular mass distribution. In addition sparse levels of long-chain branching cause a different time dependence in comparison to linear polyethylenes. The experimental findings are interpreted by comparison with rheological results from literature on model branched polymers of different molecular topography and chemical composition. Received: 12 July 2001 Accepted: 30 October 2001     

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.     

Assessment of nonlinear strain measures for extensional and shearing flows of polymer melts

From stress-strain experiments in extensional and shearing flows, nonlinear strain measures and effective damping functions are derived for a polyisobutylene melt. The strain measures determined in planar extensional flow and in simple shear flow coincide. Experimental results are compared with predictions of two molecular theories, the Doi-Edwards model and the molecular stress function approach of Wagner and Schaeffer. Discrepancies between theories and experiment lead to a reconsideration of the classification of extensional flows. The symmetry of the flow field is identified and quantified as an important parameter influencing the strain measure, and a unifying strain measure for general extensional and shearing flows of polymer melts is presented.     

Correlation between rheological behaviour in uniaxial elongation and film blowing properties of various polyethylenes

Six various low density polyethylenes and one blend were rheologically characterized in elongation. Their different strain-hardening behaviour could qualitatively be related to their molecular structure. All the materials were blown to films on laboratory equipment under various conditions. The take-up force and the film homogeneity were determined quantitatively, the bubble stability was visually assessed. The bubble stability increased with growing take-up force. The take-up force was found to be the stronger the higher the elongational viscosity was. The homogeneity of film thickness is not related to the bubble stability but to the occurrence of strain hardening in the uniaxial elongational experiment at high Hencky strains. Measurements of the uniaxial elongational behaviour of polyethylene melts are a valuable and promising way to assist the development and optimisation of film blowing materials.

Nonlinear shear behavior and interlaminar shear strength of unidirectional polymer matrix composites: A numerical study

Detailed finite element implementation is presented for a recently developed technique (He et al., 2012) to characterize nonlinear shear stress–strain response and interlaminar shear strength based on short-beam shear test of unidirectional polymeric composites. The material characterization couples iterative three-dimensional finite element modeling for stress calculation with digital image correlation for strain evaluation. Extensive numerical experiments were conducted to examine the dependence of the measured shear behavior on specimen and test configurations. The numerical results demonstrate that consistent results can be achieved for specimens with various span-to-thickness ratios, supporting the accurate material properties for the carbon/epoxy composite under study.     

Time-harmonic Green's function and boundary integral formulation for incremental nonlinear elasticity: dynamics of wave patterns and shear bands

Superimposed dynamic, time-harmonic incremental deformations are considered in an elastic, orthotropic and incompressible, infinite body, subject to plane, homogeneous—but otherwise arbitrary—deformation. The dynamic, infinite body Green's function is found and, in addition, new boundary integral equations are obtained for incremental in-plane hydrostatic stress and displacements. These findings open the way to integral methods in incremental, dynamic elasticity. Moreover, the Green's function is employed as a dynamic perturbation to analyze interaction between wave propagation and shear band formation. Depending on anisotropy and pre-stress level, peculiar wave patterns emerge with focussing and shadowing effects of signals, which may remain undetected by the usual criteria based on analysis of weak discontinuity surfaces.     

Rheological study of heterogeneities in melt blends of ZN-LLDPE and LDPE: Influence of M<Subscript>w</Subscript> and comonomer type,and implications for miscibility

The influences of molecular weight and LLDPE comonomer type on the heterogeneity (immiscibility) of Ziegler-Natta LLDPE and LDPE blends are investigated with rheological methods. Dynamic and steady shear measurements were carried out in a Rheometrics Mechanical Spectrometer 800.Blends of low-M_w (<10⁵)LLDPE (butene) and LDPE are likely homogeneous and miscible as revealed by the dependence of their on blend composition at 140 °C. Blends of high-M_w (10⁵)LLDPE (butene) and LDPE mixed and tested at 190 °C were only partially miscible; heterogeneity and immiscibility was likely to occur around the 50/50 composition and in the LDPE-rich blends. Blends were likely miscible in the LLDPE-rich range. Increasing the LLDPE branch length (comonomer) from butene to octene slightly increased the miscibility of LLDPE/LDPE blends. It is suggested that the molecular order in polyethylenes (see Hussein and Williams (1999) J Non-Newtonian Fluid Mech 86:105–118; (1998) Macromol Rapid Commun 19:323–325) and mismatch of the molecular conformations of different polyethylene structures provide explanations for the immiscibility of polyethylenes. Agreement was observed between the measured G() and G() and theoretical predictions of Palierne and Bousmina-Kerner models, which are based on two-phase emulsion behavior.