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.     

Influence of branching on melt viscosity of polydisperse polymers

Summary The relation of melt viscosity to weight-average molecular weight and branching index has been derived for polydisperse polymers, with the most probable distribution of primary chains, having randomly distributed tri- or tetrafunctional branch points. The results are obtained by an extension of theKilb treatment for the intrinsic viscosity calculations. Numerical values of the viscosity functions are given for selected branching indices.

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Zusammenfassung Die Beziehung zwischen der Schmelzviskosität, dem mittleren Molekulargewicht und dem Verzweigungsindex wurde für polydisperse Polymere mit der wahrscheinlichsten Verteilung von primären Ketten, die ihrerseits statistisch verteilte tri- oder tetrafunktionale Verzweigungspunkte besitzen, abgeleitet. Die Ergebnisse wurden aus einer Erweiterung der vonKilb für die Berechnung der Grenzviskosität angewandten Methode erhalten. Für ausgewählte Verzweigungsindizes werden numerische Werte der Viskositätsfunktionen angegeben.

     

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.     

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     

Effect of short chain branching in molecular dimensions and Newtonian viscosity of ethylene/1-hexene copolymers: matching conformational and rheological experimental properties and atomistic simulations

The molecular dimensions in dilute solution and the linear viscoelastic melt properties of a series of linear ethylene/1-hexene random copolymers with variable short chain branching content are reported. The results obtained from size exclusion chromatography and viscosimetry in dilute solution show a molecular contraction as the branching level increases. Additionally, a clear dependence of the Newtonian viscosity with the short chain branching content at T = 463 K is obtained. Both experimental observations are in agreement with previous experimental results found in ethylene/α-olefin copolymers, but more interestingly with recent full atomistic simulations made in our group in this type of macromolecular systems. The dependences observed can be related to the changes observed in the macromolecular conformational features and also in the equilibration entanglement time and the molecular weight between entanglements as the number of short chain branches increases.     

Predicting the rheology of linear with branched polyethylene blends

A series of melt blended commercial linear and branched polyethylenes are used to explore the generality of blending laws. The measured relaxation modulus G(t), and zero shear viscosity ₀ for each blend and blend fraction, have been compared with prediction for miscible blends, particularly using equations derived by Tsenoglou (1987). Plus or minus deviation between theory and measurement is dependent on the relative molecular weights of the blend components. We have found empirically that a generalised form of the blending law for G(t) and for ₀, with a floating index C, provides an improved prediction of the blend fraction data. In particular the function defining C is non-symmetrical, from which we infer the significance of branching as well as molecular weight. The optimum value of the index differs for each of our blends, in the range 1.25 to 4, the variability being accounted for by the different degrees to which branched and linear polymers relax co-operatively in the melt. Blends of two near linear polymers do not fit the floating index prediction and conform more closely, though not precisely, to the original Tsenoglou rule.     

Influence of long-chain branching on time-pressure and time-temperature shift factors for polystyrene and polyethylene

Rheological characterizations were carried out for two polystyrenes. One was a linear polymer with M _w =222,000 g/mol and M _w /M _n =2, while the other was a randomly branched polystyrene with M _w =678,000 g/mol and a broad molecular weight distribution. Experiments performed included oscillatory shear to determine the storage and loss moduli as functions of frequency and temperature, viscosity as a function of shear rate and pressure, and multi-angle light scattering to determine the radius of gyration as a function of molecular weight. The presence of branching in one sample was clearly revealed by the radius of gyration and the low-frequency portion of the complex viscosity curve. Data are also shown for three polyethylene copolymers, one (LLDPE) made using a Ziegler catalyst and two made using metallocene catalysts, one (BmPE) with and one (LmPE) without long-chain branching (LCB). While the distribution of comonomer is known to be much more uniform in LmPE than in LLDPE, the pressure shift factors were the same for these two polymers. The pressure and temperature shift factors of the two polystyrenes were identical, but, in the case of polyethylene, the presence of a small amount of LCB in the BmPE had a definite effect on the shift factors. These observations are discussed in terms of the relative roles of free volume and thermal activation in the effects of temperature and pressure.     

Branched viscoelastic surfactant solutions and their response to elongational flow

Several years ago, Münstedt and Laun reported on the influence of branching on the elongational flow properties of polymer chains (Münstedt and Laun, 1981). They concluded that, in addition to the molecular weight distribution, the degree of branching strongly affects the degree of strain thickening of the elongational viscosity in such a way that the maximum in this material function increases with branching. In a recent paper by Lin, a ternary system of dodecyldimethylamine oxide-sodium laureth sulphate-sodium chloride surfactant solutions was investigated by CryoTEM and rheology (Lin, 1996). He reported a linear relation between the added sodium chloride and the branching of the wormlike micelles. In this paper we present an investigation of these surfactant solutions in elongational flow. Our results indicate that for branched micellar systems the presence of branching enhances the maximum of the elongational viscosity in the same manner as in the case of polymer melts.     

Degree of branching of polypropylene measured from Fourier-transform rheology

In this study, linear and branched polypropylenes (PP) were compared under medium strain amplitude oscillatory shear (usually strain amplitude range from 10 to 100%) with Fourier-transform rheology (FT rheology). On a log–log diagram, the third relative intensity (I ₃/I ₁), which is a parameter to represent nonlinearity, shows a linear relationship with the strain amplitude in the range of medium strain amplitude. The slope of I ₃/I ₁ of linear PP with various molecular weight and molecular weight distribution was 2 as most constitutive equations predict, while that of branched PP was 1.64, which is lower than that of linear PP. When the linear and branch PP were blended, the slope of I ₃/I ₁ was proportional to the composition of the branch PP. Therefore, it is suggested that the degree of branching can be defined in terms of the slope of I ₃/I ₁ under medium amplitude oscillatory shear.     

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.     

Non-Newtonian flow and normal stress phenomena in solutions of polystyrene in toluene

Summary Non-Newtonian flow and normal stress phenomena are studied with solutions of polystyrene in toluene with varying temperature, concentration and molecular weight.The temperature dependence of normal and shear stresses of a solution with fixed concentration can be described in terms of the shift factor,a _T , which is commonly used in the study of linear viscoelastic phenomena of polymeric systems.From the measurements of normal and shear stresses the elasticity contribution to flow behavior of polymer solution can be evaluated, and its dependences on concentration and molecular weight are discussed. Each of the tested solutions shows more or less non-Newtonian viscosity behavior, especially very strongly in solutions with high concentration and high molecular weight. And these solutions are mainly Hookean in shear, but non-Hookean character appears in solutions with high concentration and with rather low molecular weight.The zeroshear viscosityversus concentration relationship is found to obey ac ⁵-dependence in a certain range of concentration, while in the same concentration range the reciprocal of steady shear compliance shows ac ^1,5 c ²-dependence. The zeroshear viscosityversus molecular weight relationship of solutions at a fixed concentration obeys the well-knownM ^3,4-dependence above a certain critical value of molecular weight which is dependent on the concentration. While the reciprocal of compliance is almost independent of molecular weight above this value, and it seems to be somewhat affected by the type of polymers such as molecular weight heterogeneity and/or degree of branching of the polymer.

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Zusammenfassung Nicht-Newtonsches Fließen und Normalspannungsphänomene wurden an Lösungen von Polystyrol in Toluol bei verschiedenen Temperaturen und Konzentrationen sowie bei verschiedenem Molekulargewicht untersucht.Die Temperaturabhängigkeit der Normal- und Schubspannungen einer Lösung bestimmter Konzentration kann durch den Schift-Faktora _T , der allgemein bei der Betrachtung linearer viskoelastischer Phänomene polymerer Systeme gebraucht wird, beschrieben werden. Aus den Messungen der Normal- und Schubspannungen wurde der Elastizitätsbeitrag zu dem Fließverhalten der polymeren Lösung abgeleitet und seine Abhängigkeit von der Konzentration und dem Molekulargewicht diskutiert.Jede der geprüften Lösungen zeigte mehr oder weniger nicht-Newtonsches Viskositätsverhalten, besonders stark ausgeprägt in Lösungen mit hoher Konzentration und hohem Molekulargewicht. Die Lösungen zeigten bei Scherbeanspruchung hauptsächlichHookeschen Charakter. Der nicht-Hookesche Charakter trat eher auf in Lösungen mit hoher Konzentration und bei niedrigerem Molekulargewicht.Die Anfangsviskositäts-Konzentrationsbeziehunggehorcht einerc ⁵-Abhängigkeit in einem gewissen Konzentrationsbereich, während bei derselben Konzentration der reziproke Wert der Komplianz (Nachgiebigkeit) bei stationärem Scheren einec ^1,5- bisc ²-Abhängigkeit aufweist. Oberhalb eines gewissen kritischen Wertes des Molekulargewichts, der von der Konzentration abhängt, gilt die bekannteM ^3,4-Beziehung zwischen der Anfangsviskosität und dem Molekulargewicht.Der reziproke Wert der Komplianz (Nachgiebigkeit) hängt fast nicht von dem Molekulargewicht oberhalb eines kritischen Wertes ab, aber das scheint durch den Typ der polymeren Substanz, wie Polymolekularität oder durch den Verzweigungsgrad, beeinflußt zu sein.

     

Rheological characterization of highly branched poly(ethyleneterephthalate)

Linear and highly branched poly(ethyleneterephthalate) samples were synthesized and characterized in terms of intrinsic viscosity, molecular weight and melt viscosity over a wide range of shear rates at several temperatures, in the range from 265° to 295 °C. Linear samples exhibited Newtonian behavior over a wide range of shear rates, while the branched ones became shear thinning at relatively low shear rates. Our experimental data, as well as data previously reported, were found to be described by a proposed correlation between the melt viscosity ratio and a branching index. Moreover, the activation energy for melt flow was found for the highly branched samples to be a little higher than that of the linear samples.     

Thermorheological properties of LLDPE/LDPE blends

The thermorheological behavior of a number of linear low-density polyethylene and low-density polyethylene (LLDPE/LDPE) blends was studied with emphasis on the effects of long chain branching. A Ziegler–Natta, LLDPE (LL3001.32) was blended with four LDPEs having distinctly different molecular weights. The weight fractions of the LDPEs used in the blends were 1, 5, 10, 20, 50, and 75%. Differential scanning calorimetry (DSC) analysis has shown that all blends exhibited more than one crystal type. At high LDPE weight fractions, apart from the two distinct peaks of the individual components, a third peak appears which indicates the existence of a third phase that is created from the co-crystallization of the two components. The linear viscoelastic characterization was performed, and mastercurves at 150 °C were constructed for all blends to check miscibility. In addition, Van Gurp Palmen, zero-shear viscosity vs composition, Cole–Cole, and the weighted relaxation spectra plots were constructed to check the thermorheological behavior of all blends. In general, good agreement is found among these various methods. The elongational behavior of the blends was studied using a uniaxial extensional rheometer, the SER universal testing platform from Xpansion Instruments. The blends exhibit strain-hardening behavior at high rates of deformation even at LDPE concentrations as low as 1%, which suggests the strong effect of branching added by the LDPE component.     

Melt viscosity of linear and branched poly(butyleneisophthalate)

Linear and branched poly(butyleneisophthalate) samples were synthesized and characterized in terms of the intrinsic viscosity, the molecular weight and the melt viscosity over a wide range of shear rates at 200 °C. An exponent of about 4.6 in the equation relating ₀ to was found for linear samples; this high value is probably due to the high content of cyclic oligomers in low molecular weight samples. Both linear and branched samples exhibited Newtonian behaviour over a rather wide range of shear rates, but for any given melt-viscosity, the branched samples became shear thinning at lower shear rates than the linear ones. Our experimental data were found to fit a previously proposed correlation between the melt viscosity ratio ( _{0, b} / _{0, 1} ) and a branching index quite well.     

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.     

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.