Thermorheological behavior of polyethylene: a sensitive probe to molecular structure

Recent investigations have shown that different topographies in polyethylene (PE) lead to either thermorheological simplicity (linear and short-chain branched PE) or two different types of thermorheologically complex behavior. Low-density polyethylene (LDPE) has a thermorheological complexity, which can be eliminated by a modulus shift, while long-chain branched metallocene PE (LCB-mPE) has a temperature dependent shape of the spectrum and thus a total failure of the time-temperature superposition principle. The reason for that behavior lies in the different relaxation times of linear and long-chain branched chains, present in LCB-mPE. The origin of the thermorheological complexity of LDPE might be the temperature dependence of the miscibility of the different molar mass fractions that differ in their content of short chain branches.     

Influence of molecular structure on rheological properties of polyethylenes

Elastic properties of melts of a long-chain branched low density polyethylene (LDPE) with a broad molecular mass distribution and a short-chain branched linear low-density polyethylene (LLDPE) with a more narrow molecular mass distribution were investigated by creep recovery measurements in shear. The results obtained by means of a magnetic bearing torsional creep apparatus in the linear-viscoelastic region, showed that the steady state recoverable compliance of the LLDPE is greater by a factor of two than that of the LDPE. In the short-time region up to 1000 s, however, the time-dependent recoverable compliance of the LDPE is higher than that of the LLDPE. The retardation times for the LLDPE are considerably longer than for the LDPE. For the LDPE the temperature dependence of the entanglement transition is consistent with that of the terminal zone of the creep compliance. The activation energy of 58 kJ/mole lies in the typical range for long-chain branched polyethylenes. In the case of the LLDPE the creep compliances can be shifted to give a mastercurve with an activation energy of 34 kJ/mole, whereas the recoverable compliances do not follow the time-temperature superposition principle. The molecular characterization using TREF showed that the LLDPE has a bimodal branching structure. In addition to a short-chain branched component, a low percentage of a linear constituent with high molecular mass was found. It is postulated that this linear component forms a dispersed phase in the matrix of the short-chain branched constituent. The resulting interfacial tension could be the reason for the long retardation times, the high steady state recoverable compliance and the fact that the time-temperature superposition principle is not fulfilled in the case of the LLDPE investigated. Received: 1 July 1997 Accepted: 12 November 1997     

Elongational viscosity of LDPE with various structures: employing a new evolution equation in MSF theory

Molecular stress function theory with new strain energy function is used to analyze transient extensional viscosity data of seven low-density polyethylene (LDPE) melts with various molecular structures as published by Stadler et al. (Rheol Acta 48:479–490, 2009) Pivokonsky et al. (J Non Newton Fluid Mech 135:58–67, 2006) and Wagner et al. (J Rheol 47(3):779–793, 2003). The new strain energy function has three nonlinear viscoelastic material parameters and assumes that the total stored energy of a branched molecule is given by different backbone and side chains stretching. The model parameters have been fitted for each LDPE in order to correlate with the supposed macromolecular structure expected from the type of synthesis. Most probable molecular structures for these LDPEs are comb and Cayley tree structures for respectively low- and high-molecular weight parts.     

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.     

Classification of thermorheological complexity for linear and branched polyolefins

Thermorheological complexity in polyolefins has been reported many times but so far it has not been systematically investigated. Here, a classification of the different types of thermorheologically complex behavior is proposed, which categorize the available data in five different types and describe key characteristics. These definitions are based on polyethylene, but other polymers show similar patterns for materials with comparable branching structure. Linear materials are thermorheologically simple as long as many very long short-chain branches do not introduce phase separation. Sparsely branched materials show the most significant thermorheological complexity, with significant shape changes of rheological functions with temperature, while higher amounts of branching (such as trees or combs) reduce thermorheological complexity and increase E_a at the same time. Low-density polyethylene shows a significant modulus shift at different temperatures probably due to excessive low molecular components.     

Experimental and numerical study of entry flow of low-density polyethylene melts

The present work deals with experimental and numerical features of entry flows of two polyethylene melts, namely a linear low-density polyethylene (LLDPE) and a low-density polyethylene (LDPE) in an axisymmetric converging geometry. The study also involves rheological characterization of the polymers and determination of flow parameters, at 160°C. For both fluids, the data are fed into a viscoelastic integral Wagner constitutive equation. The numerical flow simulations are performed by using a stream-tube mapping analysis. Consideration of a sub-domain of the total flow domain, the peripheral stream tube, close to the wall of the converging duct permits to relate the results of the numerical simulation to experimental flow characteristics as total and entrance pressure drops. The agreement is good for the total pressure losses, but, concerning LDPE, a lack of consistency remains for the entrance pressure drop.     

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.     

Comparison of the melt fracture behavior of metallocene and conventional polyethylenes

The influence of sparse long-chain branching and molecular weight distribution on the melt fracture behavior of polyethylene melts was investigated. Four commercial polyethylene resins were employed for this study: a conventional low-density polyethylene, a conventional linear low-density polyethylene, a linear metallocene polyethylene, and a sparsely branched metallocene polyethylene. Rheological measurements were obtained for both shear and extensional deformations, and melt fracture experiments were carried out using a controlled rate capillary rheometer. A single capillary geometry was used to focus on the effects of material properties rather than geometric factors. For the linear polyethylenes, surface melt fracture, slip-stick fracture, and gross melt fracture were all observed. Conversely, the branched PE resins did not exhibit a slip-stick regime and the degree of gross fracture was observed to be much more severe than the linear resins. These variations can be explained by the effects that long-chain branching has on the onset of shear-thinning behavior (slip-stick fracture) and the degree of extensional strain hardening (gross melt fracture). Although there is some indication that the breadth of molecular weight distribution indirectly influences surface melt fracture, the results remain inconclusive.     

Silanols cured by borates as lubricants in extrusion of LLDPE. Impact of elasticity of the lubricant on sliding friction

Addition of a viscoelastic material based on silanols cured by boron oxide was used to delay sharkskin and stick–slip instabilities in extrusion of linear low-density polyethylene (LLDPE). Delay of flow instabilities to rates of extrusion 25–35 times higher than without additive and about 40% less extrusion pressure at the same throughput are achieved by the use of this material as an additive (∼0.1%) to LLDPE or as a coating of the extrusion die. Mechanical properties of the lubricant were changed by small variations of composition to investigate the impact of elasticity on lubrication and sharkskin delay. Both lubrication and sharkskin delay were considerably improved when more elastic lubricants were used while the chemical composition of the lubricants was nearly the same. Filling the lubricants with powders of metal oxides or especially particulates having plate-like particles (kaolin, mica, BN) helped to delay the flow instabilities further to even higher throughputs. Together with experimental results, we present a tentative explanation for the importance of elasticity of polymer processing aids in the delay of sharkskin and the stabilization of slip. This paper was presented at Annual European Rheology Conference (AERC) held in Hersonisos, Crete, Greece, April 27–29, 2006.     

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     

A new look at extensional rheology of low-density polyethylene

The nonlinear rheology of three selected commercial low-density polyethylenes (LDPE) is measured in uniaxial extensional flow. The measurements are performed using three different devices including an extensional viscosity fixture (EVF), a homemade filament stretching rheometer (DTU-FSR) and a commercial filament stretching rheometer (VADER-1000). We show that the measurements from the EVF are limited by a maximum Hencky strain of 4, while the two filament stretching rheometers are able to probe the nonlinear behavior at larger Hencky strain values where the steady state is reached. With the capability of the filament stretching rheometers, we show that LDPEs with quite different linear viscoelastic properties can have very similar steady extensional viscosity. This points to the potential for independently controlling shear and extensional rheology in certain rate ranges.     

Uniaxial elongational flow effects and morphology development in LDPE/phosphate glass hybrids

Shear and elongational viscosity measurements were performed on low-density polyethylene/phosphate glass (LDPE/Pglass) hybrid materials in the liquid state. Under shear deformation, the hybrids with low concentrations of Pglass showed a Newtonian region at low frequencies, followed by shear-thinning behavior at high frequencies. High Pglass concentrations displayed shear-thinning behavior over the whole range of frequencies studied. Deviations from the log-additivity rule for viscosity were found to be compositionally dependent and generally indicated an immiscible mixture. The elongational viscosity of the hybrids increased at very low Pglass concentrations (1–2 vol.% Pglass) and then was drastically reduced at higher concentrations (i.e., >10 vol.% Pglass). In addition, elongational flow was found to induce the formation of Pglass fibrils in hybrids containing at least 10 vol.% Pglass. This was correlated to the elongational capillary number; the critical elongational capillary number was estimated to be 0.22. The elongational deformation was also found to greatly increase the overall crystallinity of the system due to molecular orientation of the LDPE polymer chains as confirmed by wide angle X-ray diffraction. A critical composition of 5 vol.% Pglass was found to be the point at which LDPE hybrid rheological properties, molecular orientation, and morphology changed drastically.     

Linear viscoelastic model for elongational viscosity by control theory

Flows involving different types of chain branches have been modelled as functions of the uniaxial elongation using the recently generated constitutive model and molecular dynamics for linear viscoelasticity of polymers. Previously control theory was applied to model the relationship between the relaxation modulus, dynamic and shear viscosity, transient flow effects, power law and Cox–Merz rule related to the molecular weight distribution (MWD) by melt calibration. Temperature dependences and dimensions of statistical chain tubes were also modelled. The present study investigated the elongational viscosity. We introduced earlier the rheologically effective distribution (RED), which relates very accurately and linearly to the viscoelastic properties. The newly introduced effective strain-hardening distribution (RED_H) is related to long-chain branching. This RED_H is converted to real long-chain branching distribution by melt calibration and a simple relation formula. The presented procedure is very effective at characterizing long-chain branches, and also provides information on their structure and distribution. Accurate simulations of the elongational viscosities of low-density polyethylene, linear low-density polyethylene and polypropylene, and new types of MWDs are presented. Models are presented for strain-hardening that includes the monotonic increase and overshoot effects. Since the correct behaviour at large Hencky strains is still unclear, these theoretical models may aid further research and measurements.     

Instability phenomena in tubular film,and melt spinning of rheologically characterized high density,low density and linear low density polyethylenes

An experimental study of instabilities in melt spinning, ribbon drawdown and tubular film extrusion of moleculary and rheologically characterized high density (HDPE) low density (LDPE) and linear low density (LLDPE) polyethylenes is presented. The characteristics of the instabilities occuring in these processes are described. The draw resonance instability is found to occur in melt spinning and ribbon drawdown. Special attention is given to tubular film extrusion which has received little treatment in the literature. Three distinctive tubular film instabilities are described. These involve (i) an axisymmetric periodic fluctuation in bubble diameter; (ii) a fluctuation of frostline height and tension; (iii) a helical motion of the bubble. The characteristics and occurrence of these phenomena are discused. In the melt spinning and ribbon drawdown, th LDPE is the most stable and the broad molecular weight distribution HDPEs the most unstable. In tubular film extrusion, the LDPEs are again the most stable but the narrower distribution HDPEs and LLDPEs are much more unstable than the broader distribution HDPE. These results are discussed in terms of convected Maxwell model representations.     

Viscoelastic properties of POSS–styrene nanocomposite blended with polystyrene

Polyhedral oligomeric silsesquioxane (POSS) are hybrid nanostructures of about 1.5 nm in size. These silicon (Si)-based polyhedral nanostructures are attached to a polystyrene (PS) backbone to produce a polymer nanocomposite (POSS–styrene). We have solution blended POSS–styrene of with commercial polystyrene (PS), , and studied the rheological behavior and thermal properties of the neat polymeric components and their blends. The concentration of POSS–styrene was varied from 3 up to 20 wt.%. Thermal analysis studies suggest phase miscibility between POSS–styrene and the PS matrix. The blends displayed linear viscoelastic regime and the time–temperature superposition principle applied to all blends. The flow activation energy of the blends decreased gradually with respect to the matrix as the POSS–styrene concentration increased. Strikingly, it was found that POSS–styrene promoted a monotonic decrease of zero-shear rate viscosity, η ₀, as the concentration increased. Rheological data analyses showed that the POSS–styrene increased the fractional free volume and decreased the entanglement molecular weight in the blends. In contrast, blending the commercial PS with a PS of did not show the same lubrication effect as POSS–styrene. Therefore, it is suggested that POSS particles are responsible for the monotonic reduction of zero-shear rate viscosity in the blends.     

Rheological properties of polyethylene/metaboric acid thermoplastic blends

The rheological properties of molten low-density polyethylene/metaboric acid blends were studied. It was found that the blend behavior can be rather different, depending on volume fraction of the inorganic component. Specifically, at some concentration of metaboric acid, the dynamic moduli and the Newtonian viscosity of the blends demonstrate a jump-like change. The concentration threshold depends on temperature and equals to 21.9 and 14.1 vol %, at 150 and 180 ^°C, respectively. In the concentration range below the threshold, the gain in the content of inorganic component results in an enhancement of the blend dynamic moduli and viscosity, without changing the general character of the rheological behavior of composition in the region of linear response. On the other hand, at higher concentrations of metaboric acid, the yield stress is observed, and the elastic modulus in the linear region of mechanical behavior becomes virtually independent of frequency. It was suggested that the rheological behavior of blends is related to a spontaneous change in their structure as well as planar molecular structure of the inorganic component.     

Comparative investigations of surface instabilities (“sharkskin”) of a linear and a long-chain branched polyethylene

An experimental study of the physical origin and the mechanisms of the sharkskin instability is presented. Extrusion flows through a slit die are studied for two materials: a linear low density polyethylene (LLDPE) which exhibits sharkskin instability for flow rates larger than an onset value and a low density polyethylene (LDPE) which does not show any instability over a broad range of flow rates. By combining laser-Doppler velocimetry (LDV) with rheological measurements in both uniaxial extension and shear, the distributions of tensile and shear stresses in extrusion flows are measured for both materials. The experimentally measured flow fields appear to be qualitatively similar for both the unstable (LLDPE) and stable case (LDPE): around the die exit the flow accelerates near the boundaries and decelerates around the flow axis. The fields of the axial gradients of the axial velocity component are, however, quite different in the two cases. In the unstable case there exists a strongly non-uniform transversal distribution of velocity gradients near the die exit. This non-uniformity of the distribution of gradients is significantly smaller in the stable case. Significant differences in the extensional rheological properties of the two materials are found as well. Due to its branched structure, the LDPE is able to sustain higher tensile stresses prior to failure. Measurements of the distributions of tensile stresses around the die exit reveal a stress boundary layer and a stress imbalance between the boundaries and the bulk. The magnitude of the stress imbalance exceeds the melt strength in the experiments with the LLDPE which causes the failure of the material in the superficial layers and results in the emergence of the sharkskin instability. In the experiments with the LDPE, the magnitude of the stress imbalance remains smaller than the melt strength which explains the lack of an instability. The measured shear stresses around the die exit are significantly smaller than the tensile stresses, suggesting that the shear component of the flow plays no significant role in the emergence of the sharkskin instability.     

Molecular architecture and linear viscoelasticity of homogeneous ethylene/styrene copolymers

We have studied correlations between molecular features and the linear rheology of two series of carefully synthesized ethylene/styrene copolymers. The materials were polymerized using two single-site catalyst systems; a commercial constrained geometry catalyst and an ansa-metallocene single-site catalyst designed on purpose. The copolymers obtained are characterized by a narrow molecular weight distribution and a broad range of different styrene content. The thermorheological properties and the shape of the viscoelastic fingerprint of the samples obtained from the ansa-metallocene catalyst are those featured by linear polymers. The flow activation energy in these materials depends on the amount of comonomer, but the values are much higher than those corresponding to aliphatic copolymers with the same amount of comonomer, likely due to the hindrance effect of the styrene units in flow behavior. The results obtained for the samples polymerized by the constrained geometry catalyst indicate a complex molecular architecture. In fact, the samples show characteristic features like thermorheological complexity, increased values of the flow activation energy, and a bimodal linear viscoelastic fingerprint in the terminal zone. From these results it can be argued that these materials are actually blends of linear and branched species, these later with the highest relaxation times and flow activation energy values.     

Flow instability for binary blends of linear polyethylene and long-chain branched polyethylene

The rheological properties and flow instability are studied for binary blends composed of a long-chain branched polyethylene and a linear polyethylene. It is found that the blends containing a linear-polyethylene with high shear viscosity exhibit higher oscillatory moduli, drawdown force, and strain-hardening behavior. The blends showing the anomalous rheological phenomena show sharkskin failure in low shear rate region as compared with a pure linear polyethylene. Moreover, the blends exhibit severe gross melt fracture at low output rate. Enhanced strain-hardening in elongational viscosity and large entrance angle at a die entry will be responsible for the severe gross melt fracture for the blends.