Elongational properties and molecular structure of polyethylene melts

Summary The viscosity and the recoverable strain in the steady state of elongation have been measured on several polyethylenes of different molecular structures. The elongational viscosity as a function of tensile stress runs through a more or less pronounced maximum in the nonlinear range whereas in the linear range the Trouton viscosity is reached. For low density polyethylenes it could be demonstrated that the maximum of the steady-state elongational viscosity and the elasticity expressed by the steady-state compliances in shear and tension sensitively increase if the molecular weight distribution is broadened by the addition of high molecular weight components. A variation of the weight average molecular weight does only shift the elongational viscosity curve but leaves its shape unchanged. Two of the four high density polyethylenes investigated do not show a maximum of the steady-state elongational viscosity, for the others it is less pronounced than in the case of low density polyethylenes. The influence of branching on the elongational behaviour of polyethylene melts in the steady-state and the transient region is qualitatively discussed.With 11 figures and 4 tables     

Flow birefringence of polymer melts: Application to the investigation of time dependent rheological properties

Summary Transient stresses including normal stresses, which are developed in a polymer melt by a suddenly imposed constant rate of shear, are investigated by mechanical measurement and, indirectly, with the aid of the flow birefringence technique. For the latter purpose use is made of the so-called stress-optical law, which is carefully checked.It appears that the essentially linear model of the rubberlike liquid, as proposed byLodge, is capable of describing the behaviour of polymer melts rather well, if the applied total shear does not exceed unity. In order to describe also steady state values of the stresses successfully, one should extend measurements to extremely low shear rates.These statements are verified with the aid of a method which was originally designed bySchwarzl andStruik for the practical calculation of interrelations between linear viscoelastic functions. In the present paper dynamic shear moduli are used as reference functions.

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Zusammenfassung Mit der Zeit anwachsende Spannungen, darunter auch Normalspannungen, wie sie sich nach dem plötzlichen Anlegen einer konstanten Schergeschwindigkeit in einer Polymerschmelze entwickeln, werden mit Hilfe mechanischer Messungen und indirekt mit Hilfe der Strömungsdoppelbrechung untersucht. Für den letzteren Zweck wird das sogenannte spannungsoptische Gesetz herangezogen, dessen Gültigkeit sorgfältig überprüft wird.Es ergibt sich, daß das im Wesen lineare Modell der gummiartigen Flüssigkeit, wie es vonLodge vorgeschlagen wurde, sich recht gut zur Beschreibung des Verhaltens von Polymerschmelzen eignet, solange der im ganzen angelegte Schub den Wert Eins nicht überschreitet. Um auch stationäre Werte der Spannungen in die Beschreibung erfolgreich einzubeziehen, sollte man die Messungen bis zu extrem niedrigen Schergeschwindigkeiten ausdehnen.Die gemachten Feststellungen werden mit Hilfe einer Methode verifiziert, die vonSchwarzl undStruik ursprünglich für die praktische Berechnung von Beziehungen zwischen Zustandsfunktionen entwickelt wurde, die dem linear viskoelastischen Verhalten entsprechen. In der vorliegenden Veröffentlichung dienen die dynamischen Schubmoduln als Bezugsfunktionen.

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a _T shift factor - B _ij Finger deformation tensor - C stress-optical coefficient, (m²/N) - f (p _jl ) undetermined scalar function - G shear modulus, (N/m²) - G(t) time dependent shear modulus, (N/m²) - G() shear storage modulus, (N/m²) - G() shear loss modulus, (N/m²) - G _r reduced shear storage modulus, (N/m²) - G _r reduced shear loss modulus, (N/m²) - H() shear relaxation time spectrum, (N/m²) - k Boltzmann constant, (Nm/°K) - n _ik refractive index tensor - p undetermined hydrostatic pressure, (N/m²) - p _ij ,p _ik stress tensor, (N/m²) - p ₂₁ shear stress, (N/m²) - p ₁₁ –p ₂₂ first normal stress difference, (N/m²) - p ₂₂ –p ₃₃ second normal stress difference, (N/m²) - q shear rate, (s^–1) - t, t time, (s) - T absolute temperature, (°K) - T ₀ reference temperature, (°K) - x the ratiot/ - x position vector of a material point after deformation, (m) - x position vector of a material point before deformation, (m) - ₀, ₁ constants in eq. [37] - ₀, ₁ constants in eq. [37] - shear deformation - (t, t) time dependent shear deformation - _ij unity tensor - n flow birefringence in the 1–2 plane - (q) non-Newtonian shear viscosity, (N s/m²) - ^* () complex dynamic viscosity, (N s/m²) - | ^* ()| absolute value of complex dynamic viscosity, (N s/m²) - () real part of complex dynamic viscosity, (N s/m²) - () imaginary part of complex dynamic viscosity, (N s/m²) - (t — t) memory function, (N/m² · s) - v number of effective chains per unit of volume, (m^–3) - temperature dependent density, (kg/m³) - ₀ density at reference temperatureT ₀, (kg/m³) - relaxation time, (s) - integration variable, (s) - (x) approximate intensity function - ₁ (x) error function - extinction angle - _m orientation angle of the stress ellipsoid - circular frequency, (s^–1) - 1 direction of flow - 2 direction of the velocity gradient - 3 indifferent direction - t time dependence The present investigation has been carried out under the auspices of the Netherlands Organization for the Advancement of Pure Research (Z. W. O.).North Atlantic Treaty Organization Science Post Doctoral Fellow.Research Fellow, Delft University of Technology.With 11 figures and 2 tables     

Morphology development of a PS/PMMA polymer blend during flow in dies

The morphology development in dilute and semi-concentrated blends (2 and 15 wt% disperse phase) of viscoelastic polymers is studied during flow in dies. In the entrance region the droplets deform into fibrils. In the die itself some of the fibrils can break up depending on their shear history and hence on their radial position. The morphology at the exit of the die is investigated by quenching the extrudate and visualizing the structure via scanning electron microscopy (SEM). For fibrils moving along the die axis, the theory of Tomotika for break-up of a fibril in a quiescent matrix describes the observations satisfactorily. Fibrils flowing off center undergo a shearing flow in the die, which could have an effect on the growth of the Rayleigh disturbances that cause break-up. It is observed that during flow break-up still occurs via Rayleigh instabilities. As a first approximation the theory of Tomotika also predicts the break-up of fibrils flowing off center, if the viscosity at the relevant shear rate is used.     

Das viskoelastische Verhalten von Polyamid-6-Schmelzen

Zusammenfassung Das rheologische Verhalten von Polyamid-6-Schmelzen mit verschiedenen Molekulargewichten wurde mit Hilfe von Kapillarviskosimetern, einem modifizierten Weissenberg-Rheogoniometer, einem Parallelplatten-Kriechrheometer und einem Schwingungsviskosimeter untersucht. An Meßbeispielen wird der Einfluß der Feuchte und der Meßzeit auf das Stabilitätsverhalten der Schmelze diskutiert. Auf Grund ihrer gleichartigen Schulz-Flory-Molekulargewichtsverteilungen läßt sich für die Viskositätsfunktionen bei einer Normierung der Viskositäts- und Schergeschwindigkeits-Skala mit der Nullviskosität eine Masterkurve konstruieren, die nicht nur temperaturinvariant, sondern auch vom Molekulargewicht unabhängig ist. Die Strangaufweitungen und Einlaufdruckverluste bei Düsenströmung können als Funktionen der Schubspannung an der Düsenwand ebenfalls temperatur- und molekulargewichtsinvariant dargestellt werden. Die aus dynamischen Messungen, aus Messungen der reversiblen Scherung und der 1. Normalspannungs-differenz im linearen Fließbereich ermittelten Gleichgewichts-Nachgiebigkeiten stimmen überein. Als Folge des konstanten Verhältnisses von ist die Gleichgewichts-Nachgiebigkeit unabhängig vom Molekulargewicht. Die Temperaturabhängigkeit der Nullviskosität folgt einer Arrhenius-Beziehung mit einer vom Molekulargewicht unabhängigen Aktivierungsenergie vonE ₀ = 60 kJ/Mol.

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Summary The rheological behaviour of nylon 6 melts of different molecular weights was investigated by means of capillary viscometers, a modified Weissenberg rheogoniometer, a sandwich creep apparatus, and an oscillatory viscometer. The influence of moisture content and residence time on the stability behaviour of the melts is demonstrated by measurements. Due to the comparable Schulz-Flory molecular weight distributions of the melts a mastercurve for the viscosity functions can be constructed by normalizing the viscosity and the shear rate by means of the zeroshear viscosity. The mastercurve is not only temperature invariant but also independent of the molecular weight. Temperature and molecular weight invariant plots are also obtained for the extrudate swell and entrance pressure losses as functions of the wall shear stress. Coincident values for the steady-state compliance are determined from oscillatory measurements, the recoverable shear strains, and the primary normal stress differences in the linear range of shear flow. As a consequence of the constant ratio the steady-state compliance is independent of the molecular weight. The temperature dependence of the zeroshear viscosity follows an Arrhenius relation with a constant activation energy ofE ₀ = 60 kJ/Mol.

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Auszugsweise vorgetragen auf dem Wissenschaftlichen Kolloquium zu Ehren von Professor Dr.Paul Schlack am 19. Dezember 1977 in Stuttgart.

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Herrn Professor Dr.Paul Schlack zum 80. Geburtstag gewidmet.

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Mit 16 Abbildungen     

Fracture and Fragmentation of Silicon Dies

Different failure modes of silicon are observed. Experimental results are not able to explain these variations clearly and therefore numerical simulations have been performed. In order to reduce high computational costs a simplified method to introduce weakened areas on silicon chips is presented. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

BSSE-correction scheme for consistent gaussian basis sets of double- and triple-zeta valence with polarization quality for solid-state calculations

Revised versions of our published pob-TZVP [Peintinger, M. F.; Oliveira, D. V. and Bredow, T., J. Comput. Chem., 2013, 34 (6), 451–459.] and unpublished pob-DZVP basis sets, denoted as pob-TZVP-rev2 and pob-DZVP-rev2, have been derived for the elements H Br. It was observed that the pob basis sets suffer from the basis set superposition error (BSSE). In order to reduce this effect, we took into account the counterpoise energy of hydride dimers as an additional parameter in the basis set optimization. The overall performance, portability, and SCF stability of the resulting rev2 basis sets are significantly improved compared to the original pob basis sets. © 2019 Wiley Periodicals, Inc.     

Manifestation of spinodal decomposition in oscillatory shear measurements

The linear dynamic moduli of a PαMSAN/PMMA blend have been measured during spinodal decomposition and the subsequent coarsening of the co‐continuous morphology. The feasibility of probing this morphology development by rheological measurements has been investigated. During phase separation, the storage modulus shows a power law behaviour at low frequency and its value decreases as time proceeds. However, effects of the dynamic measurement on the morphology development have been observed, even for strain amplitudes as low as 0.01. This effect of oscillatory shear on the coarsening of a co‐continuous structure is consistent with the predictions of the Doi‐Ohta theory.     

On the effects of dephasing due to local gradients in diffusion tensor imaging experiments: relevance for diffusion tensor imaging fiber phantoms

The effect of susceptibility differences between fluid and fibers on the properties of DTI fiber phantoms was investigated. Thereto, machine-made, easily producible and inexpensive DTI fiber phantoms were constructed by winding polyamide fibers of 15 microm diameter around a circular acrylic glass spindle. The achieved fractional anisotropy was 0.78+/-0.02. It is shown by phantom measurements and Monte Carlo simulations that the transversal relaxation time T(2) strongly depends on the angle between the fibers and the B(0) field if the susceptibilities of the fibers and fluid are not identical. In the phantoms, the measured T(2) time at 3 T decreased by 60% for fibers running perpendicular to B(0). Monte Carlo simulations confirmed this result and revealed that the exact relaxation time depends strongly on the exact packing of the fibers. In the phantoms, the measured diffusion was independent of fiber orientation. Monte Carlo simulations revealed that the measured diffusion strongly depends on the exact fiber packing and that field strength and -orientation dependencies of measured diffusion may be minimal for hexagonal packing while the diffusion can be underestimated by more than 50% for cubic packing at 3 T. To overcome these effects, the susceptibilities of fibers and fluid were matched using an aqueous sodium chloride solution (83 g NaCl per kilogram of water). This enables an orientation independent and reliable use of DTI phantoms for evaluation purposes.