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     

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     

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.     

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.     

Exploration of branching topology effects on polymer melt rheology using hierarchical calculation schemes

Hierarchical computational schemes based on tube theories enable calculation of rheological properties for polymers of arbitrary topology. In this study, such a scheme is used to systematically explore key rheological features of model long-chain branched systems. Empirical relations between molecular structure and rheology typically use overall molar mass and branching averages as structural variables, due to lack of knowledge on details of the topological structure or to limited structural variability between available experimental samples. The present approach clarifies the effect of additional structural variation beyond overall molar mass and branching level. For the polymer structures under consideration, arm length is found to dominate zero-shear viscosity, whereas the recoverable compliance scales with the ratio of total molar mass and backbone molar mass. Different topologies are found to lead to a different shear thinning/elasticity balance. The simulation approach provides clear hints for polymer designers that look to obtain specific property balances via topological modifications. This complements the classical empirical approach. Merging the different approaches is expected to synergistically speed up new product development.     

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 properties of electron beam-irradiated polypropylenes with different molar masses

Electron beam-irradiated polypropylene undergoes chain scission initiated by the loss of a proton. The resulting macroradicals can lead to branched molecules. However, the understanding of the influence of irradiation on the branching of polypropylene is still scarce. Therefore, this paper investigates structure?Cproperty relationships in such irradiated polymers. In general, irradiation yields long-chain branches, which develop from a star-like into a tree-like branching architecture with increasing dose. These conclusions can be drawn from the relation between the zero shear-rate viscosity ?? ₀ and the weight average molar mass M _w as well as from the elongational behavior.     

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.     

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.

Detection and quantification of industrial polyethylene branching topologies via Fourier-transform rheology,NMR and simulation using the Pom-pom model

The significance of sparse long-chain branching in polyolefines towards mechanical properties is well-known. Topology is a very important structural property of polyethylene, as is molecular weight distribution. The method of Fourier-transform rheology (FTR) and melt state nuclear magnetic resonance (NMR) is applied for the detection and quantification of branching topology (number of branches per molecule), for industrial polyethylenes of various molecular weight and molecular weight distributions. FT rheology consists of studying the development of higher harmonics contribution of the stress response to a large amplitude oscillatory shear deformation. In particular, when applying large-amplitude oscillatory shear (LAOS), one observes the development of mechanical higher harmonic contributions at 3ω ₁, 5ω ₁,..., in the shear stress response. We correlate the relative intensity, I _3/1, and phase Φ ₃ of these harmonics with structural properties of industrial polyethylene, i.e. polymer topology and molecular weight distribution. Experiments are complemented by numerical simulations, using a multimode differential Pom-pom constitutive model (DCPP formulation), by fitting to the experimental linear and nonlinear viscoelastic behaviours. Simulation results in the nonlinear regime are correlated with molecular properties of the “pom-pom” macromolecular architecture. Qualitative agreement is found between predicted and experimental FT rheology results.     

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.     

Linear viscoelastic behavior of asphalt and asphalt based mastic

The rheological properties of an asphalt mastic and its matrix are investigated. For the purpose of comparison a sample of thermal aged asphalt matrix is also considered. Dynamic and creep shear measurements are reported. The reduced shear rate concept proposed by Ohl and Gleissle is used to correlate mechanical properties of the three materials at the same temperature. We found that the concept gives only qualitative trends. A similar conclusion is found concerning the applicability of the time-temperature superposition principle for each sample. Our experimental results show also that the increase in viscosity due to thermal treatment or to the inclusion of solid particles is not uniform with temperature. The differences in the increase of the Vogel temperature from the asphalt to the mastic, or to the thermally aged asphalt, relate to the different mechanisms involved. Sedimentation of steel spheres in asphalt and mastic, is studied next. The Newtonian wall correction factor for the Stokes drag law holds for the three samples. Despite the similar behavior observed in conventional shear tests, Stokes' law gives the correct trend for the two asphalts although it overestimates the experimental settling velocity by a factor of approximately two in the case of the mastic. Received: 8 June 1999/Accepted: 19 October 1999     

The structure and properties of long-chain branching poly(trimethylene terephthalate)

A multifunctional epoxide chain extender (ADR4370S) was used to increase the molecular weight of poly(trimethylene terephthalate) (PTT). And the effects of ADR4370S content on the molecular structure, melt viscosity, and rheological properties of PTT were studied. It is found that a star-type topological structure is formed in PTT by introduction of ADR4370S, and the balance torque, intrinsic viscosity, and molecular weight are increased by increasing ADR4370S dosage. The rheological measurement results show that the elastic modulus, complex viscosity, and shear thinning behavior of long-chain branching PTT are increased with the concentration of ADR4370S. The presence of broadened relaxation time spectrum and a long relaxation time mode for the PTT with 1.50 wt% ADR4370S demonstrate that the cross-linking reaction occurs, and the gel forms in the PTT system.     

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.     

Investigation of the linear flow regime of commercial polymers by numerical conversion of MVM creep measurements

A new experimental and numerical method has been developed to characterize the terminal flow behavior of polydisperse, commercial grade polymer melts over a wide dynamic range of time/frequency scales. Experimentally, an MVM rheometer specifically designed for long time scale (t 10⁴ s) creep measurements is used to measure the creep compliance of three commercial polymers: two high density polyethylenes and one polystyrene. The long time scale MVM creep data are complemented in the short time scale regime by creep data from an industrial plate-plate rheometer. The time-dependent creep data is combined and converted to a discrete retardation spectra using a nonlinear regularization algorithm to address the ill-posed nature of the interconversion. The retardation spectrum is analytically converted to dynamic moduli and compared with independently measured dynamic moduli. In the overlapping frequency region, calculations and measurements show excellent agreement and the combined data span a much larger dynamic range than either independent data set. The calculated and measured dynamic moduli data are combined and a retardation spectrum with a vastly expanded dynamic range is generated. Combining long time scale MVM creep compliance data and dynamic moduli data exploits the intrinsic sensitivities of controlled strain and controlled stress rheological experiments and is a powerful means to greatly expand the experimentally accessible dynamic range of time/frequency. This approach is particularly useful for commercial polymers with broad molecular weight distributions and commensurately large distributions of relaxation times.     

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.     

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

Several poly(butyleneisophthalate)s of different molecular weight, both linear and randomly branched, were synthetized by bulk polymerization and studied in the molten state with a capillary rheometer in the temperature range 190–220°C. The viscosity shift factors showed to be well correlated to temperature by an Arrhenius-type equation. The melt-flow activation energy at constant shear stressE was found to be 15±1 kcal/mol for both linear and branched samples, whereas for polydisperse poly(butyleneterephthalate) and poly(ethyleneterephthalate) it was found previously that random long-chain branching substantially increases the activation energy.An analysis of our results and of those available in the literature shows that the influence of branches on the temperature coefficient of viscosity of polymers is still a subject open to discussion.     

Melt strengthening of poly (lactic acid) through reactive extrusion with epoxy-functionalized chains

Poly (lactic acid) is an industrially mature, bio-sourced and biodegradable polymer. However, current applications of this eco-friendly material are limited as a result of its brittleness and its poorly melt properties. One of the keys to extend its processing window is to melt strengthen the native material. This paper considers the chain extension as a valuable solution for reaching such an objective. An additive based on epoxy-functionalized PLA was employed during reactive extrusion. The reaction times as a function of chain extender ratios were determined by monitoring the melt pressure during recirculating micro-extrusions. Once residence times were optimized, reactive extrusion experiments were performed on a twin screw extruder. Size exclusion chromatography provided information about the molecular weight distributions (MWD) of the modified PLAs and revealed the creation of a high molecular weight shoulder. The rheological experiments highlighted the enhancement of the melt properties brought about by the chain extension. Shear rheology revealed some enlarged and bimodal relaxation time spectra for the extended materials which are in accordance with the MWD analysis. Such a modification directly amplified the shear sensitivity of modified PLAs. Regarding the rheological temperature sensitivity, it was found to be decreased when the chain extender content is raised as shown from the Arrhenius viscosity fit. The reduction of the polar interactions from neat to highly chain-extended PLAs is here proposed to explain this surprising result. Chain extension was also found to impact on the elongational melt properties where strain hardening occurred for modified PLAs. Investigation of the chain extension architecture was made from the rheological data and revealed a long-chain branched topology for the modified PLAs.