Characterization of long-chain branching effects in linear rheology (original) (raw)
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A rheology theory and method on polydispersity and polymer long-chain branching
Polymer, 2007
Model calculations were performed to investigate the sensitivity of zero-shear melt viscosity (h 0 or Eta0) on the molecular weight (MW) polydispersity of linear polymers. Simulated MW distributions (MWD) were generated with the generalized exponential (GEX) distribution function for various levels of polydispersity M w /M n and M z /M w . For linear entangled polymeric chains in the melt, the linear viscoelastic properties were predicted by using the double reptation blending rule and the so-called BSW relaxation time spectrum, named after the authors: Baumgaertel, Schausberger and Winter [Baumgaertel M, Schausberger A, Winter HH. Rheol Acta 1990;29:400e8]. Published rheological parameters appropriate for polyethylene were used in the calculations. It was found that Eta0 depended mostly on M w , but it also significantly depended on the extent of high-MW polydispersity M z /M w . A revision to the fundamental MW dependency of Eta0 was proposed to compensate for this polydispersity effect. To offset the polymer polydispersity differences, we propose a new MW average (M HV or M x with x ¼ 1.5) to replace M w in the historical rheological power-law equation of Eta0 f M w a , where the literature value of exponent ''a'' ranges from 3.2 to 3.6. The use of M HV instead of M w in the power-law equation made the calculated Eta0 independent of the sample high-MW polydispersity. With the removal of the complication from polydispersity effect, the new Eta0 power law can now provide a more robust base for studying polymer long-chain branching (LCB). A new LCB index is thus proposed based on this new melt-viscosity power law. The values of M HV in the new power law can be calculated for polymer samples from the conventional gel permeation chromatographic (GPC) slice data.
Characterization of long chain branching: Dilution rheology of industrial polyethylenes
Synopsis We introduce a method using the rheology of concentrated solutions to differentiate sensitively between nonbranched and branched architecture polymer melts. By modeling the concentration dependent shift in zero-shear viscosity using molecular tube theory for melt rheology, it is feasible to quantify the degree of long chain branching as well as the distribution of sizes of such branches, providing the class of branched material is known. The technique detects branched chains with the order of one entanglement length and greater. We apply the technique, already validated against monodisperse controlled-architecture polymers D. R. Daniels et al. Rheol. Acta 40, 403 2001, to a series of industrially produced metallocene-catalyzed polyethylenes with an octene comonomer and two low density polyethylenes, diluted by the short chain alkane squalane. The dilution method compares favorably with direct solution methods, and holds promise of much greater sensitivity.
Rheological Characterization of Long Chain Branching in a Melt of Evolving Molecular Architecture
Macromolecules, 2001
Long-chain branched polyethylenes are still of great interest today. In some cases their characterization is not an easy task with classical analytic methods (GPC-MALLS and NMR) because of the limited sensitivity at low concentrations of long-chain branches. Rheological methods make a valuable contribution to the characterization due to their high sensitivity with respect to long-chain branches. Using rheology it was possible to get an insight into the influence of different comonomers and comonomer concentrations on the long-chain branch incorporation in LLDPE. A variation of polymerization parameters such as polymerization pressure was found to influence the rheological behavior. From these findings some conclusions with respect to the molecular structure could be drawn.
Macromolecules, 1998
Dynamic viscoelastic results of 23 noncommercial metallocene-catalyzed polyethylenes and poly(ethylene/1-hexene) copolymers, in the range 130-190°C, are presented. The effects of welldetermined structural parameters such as molecular weight, polydispersity, and degree of short chain branching (SCB), are analyzed. The molecular weight varies between 60 000 and 325 000, the polydispersity between 1.8 and 7.3, and SCB between 0 and 48.5 branches/1000 C atoms. It is observed that a group of 11 polymers displays rheological specific features which can be summarized as follows: (a) higher dynamic viscosities at low frequencies than other polyethylenes and ethylene/1-hexene copolymers of similar molecular weight, polydispersity and SCB degree; (b) higher relaxation times than narrow molecular weight distribution polyethylenes of similar dynamic viscosities at low frequencies but similar relaxation times to those of broad molecular weight distribution; (c) higher values of elastic modulus, in comparison with polyethylenes of similar molecular weight, polydispersity, and SCB but of the same order of magnitude as those of broader molecular weight distribution; (d) higher activation energy of flow than linear polyethylenes of the same molecular weight, polydispersity, and SCB level. An analysis of the literature results leads us to suspect that the polymers which show a "dissident" behavior possess a certain very low degree of long chain branching (LCB). The analysis of the samples by SEC coupled with intrinsic viscosimetry reveals that some of these 11 polymers are long chain branched. However, this technique does not appear to be enough sensitive to detect very small amounts of LCB, and an alternative single rheological method, based on the effect of temperature on dynamic viscosity, is proposed to evaluate the possible presence of LCB.
The Role of Structure in Polymer Rheology: Review
Polymers, 2022
The review is devoted to the analysis of the current state of understanding relationships among the deformation-induced structure transformations, observed rheological properties, and the occurrence of non-linear effects for polymer liquids (melts, solutions, and composites). Three levels of non-linearity are the base for consideration. The first one concerns changes in the relaxation spectra of viscoelastic liquids, which are responsible for weak non-linear phenomena. The second one refers to the strong non-linearity corresponding to such changes in the structure of a medium that leads to the emergence of a new relaxation state of a matter. Finally, the third one describes the deformation-induced changes in the phase state and/or the occurring of bifurcations and instability in flow and reflects the thermodynamic non-linear behavior. From a structure point of view, a common cause of the non-linear effects is the orientation of macromolecules and changes in intermolecular interactio...
Applied Rheology, 1999
Based on a recently introduced generalized mixing rule, which contains the results of the reptation and double reptation model as special cases, it is possible to determine the molecular weight distribution (MWD) from rheological data. By evaluating data from bimodal PS-mixtures Maier et al. (1998) have shown how the MWD can be estimated from the relaxation shear modulus, G(t), using an inversion method. Thimm et al. (1999) derived an analytical relation between the relaxation time spectrum and the MWD, which is able to reproduce the result of Maier et al. (1998) with less computational effort. In this article we compare both methods by evaluating data from three different series of polymer mixtures: Polystyrene (PS), Polymethylmethacrylate (PMMA) and isotactic Polypropylene (iPP). We compare the MWD obtained from rheological data with results from size exclusion chromatography (SEC) and discuss differences. Kurzfassung Ausgehend von einer kürzlich eingeführten, verallgemeinerten Mischungsregel, die die Ergebnisse des Reptations-und Doppelten Reptationsmodells als Spezialfälle enthält, ist es möglich, die Molekulargewichtsverteilung zu bestimmen. Maier et al. (1998) haben durch Auswertung der Daten von bimodalen PS-Mischungen gezeigt, wie die Molekulargewichtsverteilung mittels eines Rechenverfahrens, das auf Regularisierung beruht, aus dem Relaxationsschermodul G(t) geschätzt werden kann. Thimm et al. (1999) haben eine analytische Beziehung zwischen dem Relaxationszeitspektrum und der Molekulargewichtsverteilung hergeleitet, die in der Lage ist, die Ergebnisse von Maier et al. (1998) mit weniger Rechenaufwand zu reproduzieren. In diesem Artikel vergleichen wir beide Methoden, indem wir Daten von drei unterschiedlichen Mischungsreihen von Polymermischungen analysieren: Polystyrol, Polymethylmethacrylat und isotaktisches Polypropylen. Wir vergleichen die Molekulargewichtsverteilungen, die aus den rheologischen Daten bestimmt werden, mit Ergebnissen einer SEC-Analyse und diskutieren Unterschiede. Résumé A partir d'une loi de mélange géneralisée récemment introduite, et qui contient les résultats des modèles de reptation et de reptation double comme cas particulier, il est possible de déterminer, avec des données rhéologiques, la distribution en poids moléculaire (DPM). Maier et al. (1998) ont étudie un mélange bimodal de polystyrène (PS) et ont montré comment la DPM de ce mélange pouvait être calculée a partir de la relaxation du module de cisaillement G(t) et en utilisant une méthode d'inversion. Thimm et al. (1999) ont développé une relation analytique entre le spectre des temps de relaxation et la DPM qui est capable de reproduire les résultats de Maier et al. (1998) tout en économisant du temps de calcul. Dans cet article, nous comparons ces deux méthodes en les appliquant a l'étude de 3 séries différentes de mélanges de polymères: polystyrène (PS), polymethylméthacrylate (PMMA) et polypropylène isotactique (iPP). Nous comparons les DPM obtenues a partir des données rhéologiques avec les DPM obtenues au moyen de la chromatographie par exclusion de taille (Size Exclusion Chromatography, SEC) et nous discutons les différences observées.
A rheological evaluation of linear and branched controlled-rheology polypropylenes
The Canadian Journal of Chemical Engineering, 1994
Commodity linear and branched polypropylene resins have been modified by means of peroxide initiated chemical degradation in a reactive extrusion process. Data collected from molar mass and linear viscoelastic property measurements have been used to evaluate the L'crossover modulus" and "modulus separation" rheological polydispersity measures and a theoretical justification is provided for the modulus separation index. In the past, these empirical methods have been used successfully to relate molar mass characteristics to rheological properties. Results obtained in this study confirm the validity of the modulus separation index for linear polymers and suggest that it should be used carefully in the analysis of data from branched polymers. Linear viscoelastic data are used to estimate the terminal relaxation time spectra of both the linear and branched materials and a new correlation between modulus separation and relaxation time polydispersity is given. Des rCsines de commoditt de polypropylene 1inCaires et ramifiCes ont CtC rnodifikes par dkgradation chimique au peroxyde dans un procCdC d'extrusion rCactive. Des donntes venant de mesures des propriCtCs viscoClastiques liniaires et de masse molaire ont ttC utilisees pour Cvaluer les mesures rhCologiques de polydispersitC de "module de croisement" et de "sCparation des modules", et une justification thCorique est donnee pour I'indice de skparation des modules. Dans le passe, ces mCthodes empiriques ont CtC utiliskes avec succb pour relier les caractkristiques de masse molaire aux propriCtCs rhCoIogiques. Les rCsultats obtenus dans cette Ctude confirment la validite de I'indice de separation des modules pour les polymkres lintaires et suggkrent qu'on devrait les utiliser avec prudence dans l'analyse des donntes de polymtres ramifies. On utilise des donntes viscoelastiques IinCaires pour estimer le spectre de temps de relaxation terminal des rnateriaux 1inCaires et rarnifiks, et on donne une nouvelle corrtlation entre la sCparation des modules et la polydispersitt de temps de relaxation.
Effect of long branches on the rheology of polypropylene
Journal of Rheology, 2004
In order to study the rheology of long chain branched polymers, branches have been added on linear polypropylene precursors in varying amounts using reactive modification with peroxydicarbonates. The branched polypropylene samples show distinct strain hardening, something absent from the linear melt; this considerably improves the melt strength of the modified polymer. The zero shear viscosity and the elasticity measured by the relaxation spectrum also increase with the number of branches per molecule. Two models are applied to describe strain hardening of the viscosity during the course of elongation. The model parameters were found to vary systematically with the degree of branching and, therefore, their values can be used as a measure of this. Consequently, fluidity, elasticity, strain hardening, and melt strength are all related to the degree of long chain branching.
Journal of Rheology, 2013
Low-density polyethylene was thermo-oxidatively degraded at 170 C, i.e., degraded in the presence of air, by a one thermal cycle (1C) treatment during times between 30 and 90 min, and by a two thermal cycles (2C) treatment, i.e., after storage at room temperature, an already previously degraded sample was further degraded during times between 15 and 45 min. Characterization methods include gel permeation chromatography (GPC), Fourier transform infrared (FTIR) spectroscopy, as well as linear and nonlinear rheology. A reduction of molar mass was detected for all degraded samples by GPC, as well as an increase of the high molar mass fraction of the 1C sample degraded for the longest time. Intrinsic viscosity measurements indicate also a reduction of molar mass with increasing degradation times for both 1C and 2C samples. Thermo-oxidation is confirmed for 1C and 2C samples by analyzing specific indices in FTIR. Linear viscoelasticity seems to be in general only marginally affected by thermo-oxidative exposure, while the enhanced strain-hardening effect observed in uniaxial extension experiments presents a clear evidence for an increased long-chain branching (LCB) content in both 1C and 2C samples. Elongational viscosity data were analyzed by the molecular stress function (MSF) model as well as the Wagner-I model, and for both models, quantitative description of the experimental data for all samples was achieved by fit of only one nonlinear model parameter. Time-deformation separability was confirmed for all samples degraded, 1C as well as 2C, for cumulative degradation times of up to 90 min. The characterization by GPC was confronted with the characterization obtained from nonlinear rheology. It can be stated that elongational rheology is a powerful method to detect structural a)