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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Rheologica acta 16 (1977), S. 527-533 
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Résumé Le comportement viscoélastique en régime dynamique de polystyrènes de masses égale et supérieures à la masse critique (M w variant de 37.000 à 670.000) a été étudié dans un très large domaine de fréquences (10−5 à 103 Hz environ, en utilisant le principe de superposition temps-température). Trois approches différentes de l'analyse des propriétés dynamiques ont été abordées, afin de montrer l'intérêt et les limites de chacune d'entre elles (module de cisaillement complexeG * (ω), viscosité complexeη * (ω) et complaisance complexeJ * (ω). Une approche originale de l'étude de la complaisance complexe permet de proposer une expression analytique de celle-ci: $$\begin{gathered} J*(\omega ) = J_g + \frac{1}{{i\omega \eta _0 }} + \frac{{J_p }}{{1 + (i\omega \tau _p )^{1 - \alpha } }} \hfill \\ + \frac{{J_l }}{{1 + (i\omega \tau _l )^{1 - \beta } }}. \hfill \\ \end{gathered} $$ qui s'avère satisfaisante pour représenter les propriétés viscoélastiques de polymères à distribution très étroite de masses moléculaires au-dessus de la masse critique (le termeJ p * (ω) disparaissant pourM ≤ M c). —Les paramètresη 0 etτ p varient de façon identique en fonction de la longueur des chaînes (∝M w 3,4 ). —Les paramètresJ t,τ t etβ caractéristiques de la zone de transition, sont indépendants de la masse moléculaire. —Les paramètresJ p,α sont indépendants de la longueur des chaînes pour des échantillons à distribution très étroite, quoique leurs valeurs soient très sensibles à un élargissement, même minime, de la distribution des masses moléculaires.
    Notes: Summary The dynamic viscoelastic behavior of polystyrenes, with molecular weights above the critical molecular weight (M w ranging from 37.000 to 670.000), has been studied in a broad range of frequencies (10−5 to 103s−1, using time-temperature superposition principle). Three different approaches for the analysis of the dynamic properties have been used in order to show the interest and the limits of each other (complex shear modulusG * (ω), complex viscosityη * (ω), and complex complianceJ * (ω)). A new analysis of the complex compliance shows that it can be fitted by the equation: $$\begin{gathered} J*(\omega ) = J_g + \frac{1}{{i\omega \eta _0 }} + \frac{{J_p }}{{1 + (i\omega \tau _p )^{1 - \alpha } }} \hfill \\ + \frac{{J_l }}{{1 + (i\omega \tau _l )^{1 - \beta } }}. \hfill \\ \end{gathered} $$ This equation is satisfactory in order to represent the viscoelastic properties of narrow MWD polymers above the critical molecular weight (the termJ p * (ω) disappearing forM 〈 M c). Theη 0 andτ p parameters depend on chain length following the same law (∝M w 3,4 ). TheJ t,τ t andβ parameters, characteristic of the transition zone, are independent ofM w. J p andα are independent of chain length for narrow MWD samples; however these values are quite sensitive on a light broadening of the MWD.
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  • 2
    ISSN: 1435-1528
    Keywords: Flow birefringence ; Doppler velocimetry ; constitutive equation ; planar extension ; viscoelastic liquids
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Stress and velocity were determined locally by birefringence measurements and laser Doppler velocimetry for a mildly entangled polystyrene solution flowing at steady state in a rectangular channel with sinusoidally varying wall spacing. Having measured both the velocity and stress fields, we were able to test constitutive equations locally, i.e., without solving the equations of motion for the entire flow. Four were examined for the periodic planar extensions on the channel centerplane: the Newtonian model, the Lodge network model, the Doi-Edwards tube model, and the Wagner-Schaeffer modification of Doi-Edwards. High enough Weissenberg and Deborah numbers were reached to produce sizable departures from the Newtonian predictions. The Doi-Edwards model underpredicted the stress, as did Wagner-Schaeffer, although to a lesser extent. Predictions of the Lodge model were best of all, a surprising result in view of its inadequacy for simple shear deformations. The predictions of the Lodge model, without parameter adjustment, agreed remarkably well with the planar extension data over the accessible range for our apparatus: Deborah numbers up to 2.0, extensional Weissenberg numbers up to 6.5, and a maximum extension ratio of about 2.3.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Rheologica acta 27 (1988), S. 531-539 
    ISSN: 1435-1528
    Keywords: Yield stress ; yield strain ; strain modulus ; dynamic modulus ; microgel solution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Viscosity, modulus, and yield stress for 0–6 wt% aqueous solutions of Carbopol 941 were investigated using constant shear rate, constant shear stress, and dynamic oscillatory experiments. The microgel character of the polymer was evident from the solid-like behavior of the solutions above 1 wt%. Yield stress increased with concentration, but yield occurred at a critical shear strain of 40%, independent of concentration. The static stress-strain relationship became non-linear at ~ 25% strain, in fair agreement with the onset of non-linear response in the storage modulus at ~ 10% strain. Small strain moduli from static and low frequency measurements agreed rather well; modulus values obtained from the recoverable strain after yielding were 30–40% smaller. Solutions flowed at near-constant stress in the low shear rate regime; at higher rates the stress increases with shear rate more rapidly. The viscosity did not obey the Cox-Merz rule. Steady-state viscosity scaled with polymer concentration to the 3/4 power. Results were interpreted using a cellular, deformable sphere model for the polymer, in analogy to emulsions and foams.
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  • 4
    ISSN: 1435-1528
    Keywords: Key words Polymer melts ; miscible blends ; viscoelasticity ; tracer diffusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Linear viscoelasticity and tracer diffusion were investigated as functions of temperature, component molecular weight and blend composition for entangled, single-phase blends of nearly monodisperse poly(ethylene-alt-propylene) (PEP) and head-to-head polypropylene (HHPP). Both components are non-polar and, despite evidence for slight differences of component glass temperatures in their blends, the viscoelastic data obey time-temperature superposition rather well. The properties of the blends were compared at constant T–T g (blend) with predictions of the tube-model theories. The composition dependence of viscosity agrees best with the double-reptation prediction, as had been found earlier for molecular weight blends. The variation in plateau modulus with composition is consistent with reptation, but the changes are too small to provide a definitive test. The tracer diffusion coefficients, D PEP * and D HHPP * are nearly independent of composition, consistent with the reptation prediction and in sharp contrast with tracer diffusion for blends with specific associations. Results for the recoverable compliance depart from this pattern, varying differently and much less strongly with composition than the predictions of either single or double reptation. It thus seems that microstructural blends may behave in significantly more complex ways than molecular weight blends even for components with only weak dispersive interactions and rather modest differences in glass temperature and plateau modulus.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Rheologica acta 19 (1980), S. 38-50 
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Ein versteiftes und automatisiertes Weissenberg-Rheogoniometer wurde dazu verwendet, stationäre und nicht-stationäre Spannungsmessungen an einer 12%igen Polystyrol-Lösung durchzuführen. Wenngleich die Ergebnisse durchweg mit den früher für die gleiche Lösung mitgeteilten übereinstimmen, so erlaubt doch das neu eingesetzte Daten-Verarbeitungs-System eine genauere Registrierung der Kurzzeit-Signale. Die Ergebnisse der Spann- und Relaxationsversuche werden mit den Voraussagen der Theorie einer finit linearviskoelastischen Flüssigkeit verglichen, welche dasselbe Relaxationsspektrum besitzt wie die Versuchslösung. Auf einem solchen Vergleich basierende einfache Verallgemeinerungen werden untersucht.
    Notes: Summary A stiffened and automated Weissenberg Rheogoniometer has been used to obtain steady-state and transient stress data on a 12 wt.% polystyrene solution. While the results agree generally with those previously reported on the same solution, the present data-acquisition system provides a more accurate recording of short-time responses. Stress growth and relaxation data were compared with the responses predicted for a finite linear viscoelastic fluid with the same relaxation time spectrum as the test solution. Simple generalizations based on such a comparison have been sought.
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  • 6
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Summary The linear viscoelastic properties of polymer solutions are studied through the concentration dependence of the three characteristic parameters of linear viscoelasticity (zero-shear viscosityη 0, limiting complianceJ e 0 and plateau modulusG N 0 ) in various solvents. The polymers are narrow-distribution linear and starbranched polybutadienes. The glass transition temperatures of the solvents are below, equal to, and above, theT g of polybutadiene (respectively tetradecane, low molecular weight polybutadiene, and a commercial oil). The results (η 0 ∞c 4.0,G N 0 ∞c 2.25 andJ e 0 ∞c −2.25) do not agree with the usual mean field behavior assumed for the viscoelastic properties of polymer solutions, and seem to agree partly with recent models for the relaxation and thermodynamics of long chains.
    Abstract: Zusammenfassung Das linear-viskoelastische Verhalten von Polymerlösungen wird anhand der Abhängigkeit der drei charakteristischen Parameter (Nullviskositätη 0, NullkomplianzJ e 0 und PlateaumodulG N 0 ) von der Konzentration in verschiedenen Lösungsmitteln untersucht. Bei den Polymeren handelt es sich um lineare und sternförmig verzweigte Polybutadiene mit enger Molmassenverteilung. Die Glasübergangstemperaturen der Lösungsmittel (Tetradecan, niedermolekulares Polybutadien bzw. ein kommerzielles Ol) sind niedriger, gleich oder höher als diejenigen des Polybutadiens. Die Ergebnisse (η 0 ∼c 4,0,G N 0 ∼c 2,25 undJ e 0 ∼c −2,25) stimmen nicht mit den Voraussagen der üblicherweise zugrundegelegten, durch Mittelwertbildung gekennzeichneten Theorien überein, sondern scheinen zumindest zum Teil denen neuer thermodynamischer bzw. Relaxationstheorien langkettiger Polymerer zu entsprechen.
    Notes: Résumé L'évolution des propriétés viscoélastiques linéaires de polymères en solution est caractérisée par l'étude des variations des trois paramètres caractéristiques de la viscoélasticité linéaire (viscosité limiteη 0, complaisance limiteJ e 0 et module de plateauG N 0 ) en fonction de la concentration dans différents solvants. Les polymères étudiés sont des polybutadiènes linéaires et branchés en étoile, à distribution étroite de masses moléculaires. Les solvants étudiés ont des températures de transition vitreuse inférieure, égale ou supérieure à celle du polybutadiène (respectivement le tétradécane, un polybutadiène de faible masse moléculaire et une huile commerciale). Les résultats obtenus (η 0 ∞c 4,0,G N 0 ∞c 2,25 etJ e 0 ∞c −2,25) sont en désaccord avec le comportement conforme aux modèles de champ moyen généralement admis, et semble partiellement en accord avec les modèles récents de la relaxation et de la thermodynamique des longues chaînes flexibles.
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Rheologica acta 16 (1977), S. 291-301 
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Der Spannungsaufbau beim Anfahren einer stationären Scherströmung und die Spannungsrelaxation nach dem Anhalten derselben werden in einem steifer gemachten Weissenberg-Rheogoniometer für drei Polystyrol-Lösungen über einem weiten Schergeschwindigkeitsbereich gemessen. Die zeitabhängige Schubspannungσ und die erste NormalspannungsdifferenzN 1 werden aus dem Drehmoment und der Axialverschiebung bestimmt. Aus umfangreichen Nebenuntersuchungen kann man schließen, daß die Ergebnisse von Verfälschungen durch instrumentelle Effekte weitgehend frei sind. Die Lösungen haben Null-Viskositäten von 890, 3900 und 67000 Poise. Für eine Untersuchung der Verträglichkeit der Daten mit Stoffgesetzen vom „strain rate“-Typ wurde dievan Es-Christensen-Gleichung zugrundegelegt, für Stoffgesetze vom „relative strain“-Typ entsprechend dieKearsley-Zapas-Gleichung. In beiden Fällen wurden wesentliche Abweichungen gefunden. Ebenso wurde das Modell vonMarrucci geprüft. Ähnlich wie beimCarreau-Modell B sind die Voraussagen des Anlauf-Verhaltens durch dieses Modell durchgängig in qualitativer Übereinstimmung mit den Beobachtungen, aber einige systematische quantitative Unterschiede sind auch hier vorhanden.
    Notes: Summary Stress development at the onset of steady shear flow and stress relaxation from steady state were measured in a stiffened Weissenberg Rheogoniometer over wide ranges of shear rate for three polystyrene solutions. Time dependent shear stressσ and first normal stress differenceN 1 were obtained from the torque and axial thrust. From extensive auxiliary tests we believe these data to be free of spurious effects associated with instrument compliance. The solutions have zero shear viscosities of 890, 3900 and 67 000 poise. Tests for consistency with strain rate constitutive models were made using thevan Es-Christensen relation and with relative strain models using theKearsley-Zapas relations. Substantial deviations were found in both cases. TheMarrucci model was also examined. As in theCarreau model B, the predicted start-up curves from theMarrucci model are in general qualitative accord with observations, but some systematic quantitative discrepancies remain.
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