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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Rheologica acta 26 (1987), S. 375-384 
    ISSN: 1435-1528
    Keywords: Torsional creep ; creep recovery ; time-temperaturesuperposition ; recoverable compliance ; polystyrene
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract The torsional creep and recoverable bahaviour of a technical polystyrene is reported over seven orders of magnitude of the value of the compliance from 10−8 to 10−1 Pa−1 and over more than seven decades in time. The results for the recoverable compliance JR (t) reveal a dispersion region seen between the glass transition and the steady-state recoverable compliance Je. The limiting value of the final dispersion Je = 4.7 · 10−4 Pa−1 indicates a broad molecular-weight distribution. The steady-state recoverable compliance Je is independent of the temperature. The temperature dependence of the final dispersion was found to be indistinguishable from that of viscous flow. However, this temperature dependence differs significantly from that of the glass-rubber transition. A proposal has been made for the construction of creep compliance and recoverable compliance over an extended time scale.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Rheologica acta 23 (1984), S. 378-395 
    ISSN: 1435-1528
    Keywords: Dilatometry ; volume relaxation ; thermal expansion ; glass transition ; secondary transition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Two experimental techniques are described for the determination of the change of specific volume of polymers with temperature and aging time, which allow measurements between − 160 °C and + 200 °C. Four technical amorphous polymers, PS, PVC, PMMA and PC have been investigated. Volume-temperature curves under constant rate of cooling are presented and interpreted with respect to relaxation processes known from other physical investigations. The rate dependence of dilatometric glass transition temperatures is compared with the time dependence of rheometric glass transition temperatures from shear creep data. Volume relaxation data at constant aging temperature are presented. Aging is found to proceed until very low temperatures in the glassy state for e.g. PMMA. For polystyrene, a comparison is made between the predictions of a very simple theory of volume relaxation due to Kovacs with experimental data, using additional information from volume temperature curves and the time temperature shift of the shear creep transition. The theory predicts a rate of volume relaxation which is much lower than that found by experiment.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Rheologica acta 8 (1969), S. 6-17 
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Numerische Formeln werden angegeben, die die Berechnung der dynamischen Nachgiebigkeit aus der Kriechkurve ermöglichen. In diesen Formeln treten Werte der Kriechkurve auf, die zu logarithmisch äquidistanten Zeitpunkten gemessen wurden. Das Verhältnis zweier aufeinanderfolgender Zeitpunkte entspricht stets einem Faktor 2. Für alle Formeln werden obere und untere Schranken für den relativen Fehler abgeleitet. Diese Schranken hängen vom Werte der Dämpfung (tanδ) ab, die bei der Kreisfrequenzω auftritt, für die die Berechnung erfolgt. Die Berechnung der Speicherkomponente der dynamischen Nachgiebigkeit ist desto leichter, je niedriger der Wert der Dämpfung ist. Zu dieser Berechnung benötigt man den Wert der Kriechfunktion zum Zeitpunktt 0=1/ω und deren logarithmische Zeitableitung in einem ziemlich engen Zeitintervall umt 0. Die Berechnung der Verlustkomponente der dynamischen Nachgiebigkeit ist desto leichter, je höher der Wert der Dämpfung ist. Zu dieser Berechnung benötigt man den Wert der logarithmischen Zeitableitung der Kriechfunktion in einem breiten Zeitintervall umt 0.
    Notes: Summary Numerical formulae are given for calculation of storage and loss compliance from the course of the creep compliance for linear viscoelastic materials. These formulae involve values of the creep compliance at times which are equally spaced on a logarithmic time scale. The ratio between succeeding times corresponds to a factor of two. A method is introduced by which bounds for the relative error of those formulae can be derived. These bounds depend on the value of the damping, tanδ. The calculation of the storage compliance is easier with the lower damping values. This calculation involves the value of the creep compliance at timet 0=1/ω, and that of its derivative with respect to the logarithm of time in a rather narrow region aroundt 0. In contrast the calculation of the loss compliance is more difficult with the lower damping values. This calculation involves the value of the derivative of the creep compliance with respect to the logarithm of time in a broad interval aroundt 0.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Rheologica acta 10 (1971), S. 165-173 
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Numerische Formeln werden gegeben, die die Berechnung des dynamischen Moduls aus der Spannungsrelaxationskurve ermöglichen. In diesen Formeln treten Werte der Spannungsrelaxationskurve auf, die zu logarithmisch äquidistanten Zeitpunkten gemessen wurden. Das Verhältnis zweier aufeinanderfolgender Zeitpunkte entspricht stets einem Faktor 2. Für alle Formeln werden obere und untere Schranken für den relativen Fehler abgeleitet. Diese Schranken hängen vom Werte der Dämpfung (tanδ) ab, die bei der Kreisfrequenz ω auftritt, für die die Berechnung erfolgt. Die Berechnung der Speicherkomponente des dynamischen Moduls ist desto leichter, je niedriger der Wert der Dämpfung ist. Zu dieser Berechnung benötigt man den Wert der Spannungsrelaxationsfunktion zum Zeitpunktt 0=1/ω, und deren logarithmische Zeitableitung in einem ziemlich engen Zeitintervall umt 0. Die Berechnung der Verlustkomponente des dynamischen Moduls ist umständlich, Zu dieser Berechnung benötigt man den Wert der logarithmischen Zeitableitung der Spannungsrelaxationsfunktion in einem breiten Zeitintervall umt 0. Insbesondere erfordert diese Berechnung viel Information über den Verlauf der Spannungsrelaxationskurve bei Zeitent〈t 0. Die Folgerungen dieses bei der Berechnung vonG″(ω) auftretenden „Kurzzeit-Verstümmelungsproblemes“ werden auseinandergesetzt. Wenn neben den Ergebnissen der Spannungsrelaxationsmessung im Langzeitbereich noch solche einer Schwingungsmessung im Kurzzeitbereich zur Verfügung stehen, kann das Problem der Berechnung des Verlustmoduls aus der Spannungsrelaxationskurve wesentlich vereinfacht werden.
    Notes: Summary Numerical formulae are given for calculation of storage and loss modulus from the known course of the stress relaxation modulus for linear viscoelastic materials. These formulae involve values of the relaxation modulus at times which are equally spaced on a logarithmic time scale. The ratio between succeeding times corresponds to a factor of two. Bounds for the relative error of those formulae were derived. These bounds depend on the value of the damping, tanδ, at the angular frequency,ω. The lower the damping values, the easier is the calculation of the storage modulus. This calculation involves the value of the relaxation modulus at timet 0=1/ω, and that of its derivative with respect to the logarithm of time in a rather narrow region aroundt 0. By contrast, the calculation of the loss modulus is difficult. This calculation involves the value of the derivative of the relaxation modulus with respect to the logarithm of time in a broad interval aroundt 0. Especially the behaviour of the relaxation modulus at timest〈t 0 affects the calculation of the loss modulus significantly. The consequences of this “short time truncation problem” for the calculation of the loss modulus are discussed. If the results of dynamic measurements are available in the short time region in addition to those of the stress relaxation measurement in the long time region, the calculation of the loss modulus from the stress relaxation measurement is considerably simplified. The short time truncation problem can then be solved by using information aboutG″ as obtained from the dynamic measurements at short times (high frequencies).
    Type of Medium: Electronic Resource
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  • 5
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Rheologica acta 13 (1974), S. 209-215 
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Summary Two compounds or rigid PVC, one of the emulsion type, the other of the suspension type, were processed at different temperatures by means of a highly instrumented 30-mm research extruder. During processing, measurements were made of the axial distribution of pressures and temperatures at the inner wall of the barrel, of the axial temperature distribution in the hollow screw and of the radial temperature distribution of the melt close to the screw tip. The melts were forced through capillaries and slit dies and their viscosity behaviour was measured. Extrudates were subjected to an immersion test in acetone, in which they showed very significant differences in behaviour that depended on the temperatures at which they were processed. These differences did not show up in impact strength or yield strength in stress strain testing.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Rheologica acta 14 (1975), S. 581-590 
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Numerische Formeln werden gegeben, die die Berechnung des Spannungsrelaxationsmoduls aus dem dynamischen Modul ermöglichen. In diesen Formeln treten Werte des Speichermoduls und Verlustmoduls auf, die bei logarithmisch äquidistanten Frequenzen gemessen wurden. Das Verhältnis zweier aufeinanderfolgender Frequenzen entspricht stets einem Faktor 2. Für alle Formeln werden obere und untere Schranken für den relativen Fehler abgeleitet. Diese Schranken hängen vom Werte der Dämpfung (tanδ) ab, die bei der Kreisfrequenzω 0 auftritt, für die die Berechnung erfolgt. Die Berechnung des Relaxationsmoduls ist um so einfacher, je niedriger der Wert der Dämpfung ist. Zu dieser Berechnung benötigt man entweder den Wert des Speichermoduls bei der Kreisfrequenzω 0=1/t und die Werte des Verlustmoduls in einem ziemlich engen Frequenzintervall umω 0, oder den Wert des Speichermoduls bei der Kreisfrequenzω 0 und den Wert der logarithmischen Frequenzableitung des Speichermoduls in einem Frequenzintervall umω 0.
    Notes: Summary Numerical formulae are given for calculation of stress relaxation modulus from the known course of the storage and loss modulus with frequency for linear viscoelastic materials. The formulae involve values of the storage modulus and/or loss modulus at frequencies equally spaced on a logarithmic frequency scale, the ratio between successive frequencies beeing two. A method is introduced by which bounds for the relative errors of these formulae can be derived. These bounds depend on the value of the damping, tanδ, at the angular frequency,ω, for which the calculation is made. The less the damping, the simpler the calculation of the stress relaxation modulus. This calculation involves either the value of the storage modulus at a frequencyω 0 = 1/t, and the values of the loss modulus in a rather narrow frequency region aroundω 0, or the value of the storage modulus at frequencyω 0 and the derivative of the storage modulus with respect to the logarithm of frequency in a frequency region aroundω 0.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Rheologica acta 19 (1980), S. 137-152 
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Es wurden genaue Messungen der Scher-Kriechfunktion im Glas-Kautschuk-Übergangsgebiet in einem ausgedehnten logarithmischen Zeitintervall mit Hilfe eines Torsionspendel- und Kriechautomaten durchgeführt. Untersucht wurden kommerzielles PS, PMMA und PVC sowie zwei leicht vernetzte Kautschuke, NR und PU. Für die drei Kunststoffe wurde das spezifische Volumen als Funktion der Temperatur bei verschiedenen Kühlgeschwindigkeiten bestimmt. Die Scher-Nachgiebigkeit erfüllte das Zeit-Temperatur-Verschiebungsprinzip. Im Temperaturbereich über der Glastemperatur kann die Zeit-Temperatur-Verschiebungsfunktion mit großer Genauigkeit durch die W.L.F.-Gleichung beschrieben werden. Die W.L.F.-Konstantenc 1 undc 2 sind jedoch für die verschiedenen Polymere verschieden und stimmen nicht mit den Universalwerten dieser Konstanten überein. Spezifisches Volumen im gummielastischen Zustand und thermischer Ausdehnungskoeffizient im Glaszustand hängen nicht von der Kühlgeschwindigkeit ab. Spezifisches Volumen im Glaszustand und die Glastemperatur nehmen mit steigender Kühlgeschwindigkeit zu. Die Ergebnisse konnten mit Hilfe einer einfachen Hypothese beschrieben werden, in der das freie Volumen einerseits aus dem spezifischen Volumen definiert wird, das oberhalb der Glastemperatur zusätzlich auftaut, andererseits durch seinen Zusammenhang mit der molekularen Beweglichkeit eingeführt wird (Doolittle-Gleichung). Diese Hypothese enthält drei unabhängige Parameter, nämlich die thermodynamische GlastemperaturT ∞, den Ausdehnungskoeffizienten des relativen freien Volumensα f und den ParameterB der Doolittle-Gleichung. Durch Kombination der Meßresultate können alle drei Parameter bestimmt werden. Wir finden fürB Werte zwischen 0,24 und 0,42 und für das beim Glasübergang eingefrorene relative freie Volumenf g Werte zwischen 0,8 und 1,1%.
    Notes: Summary Accurate measurements of the shear creep compliance in the glass rubber transition region have been performed by means of a combined torsional pendulum and torsional creep apparatus over a broad experimental window for commercial PS, PMMA and PVC and for two slightly crosslinked rubbers, NR and PU. For the three plastic materials, specific volume vs. temperature curves were obtained by volume dilatometry under different rates of cooling. Shear creep compliance was found to obey the time-temperature superposition principle. In the temperature region above the glass transition temperature, the time-temperature shift function could be accurately described by a W.L.F. equation. However, the W.L.F. constantsc 1 andc 2 differed for the different polymers and were different from the universal W.L.F. values. No choice for a reference temperature could be found to make the W.L.F. constants of the different polymers to coincide within experimental scatter. Specific volumes in the rubbery state and the thermal expansion coefficients in the glassy state were found to be independent of rate of cooling. Specific volumes in the glassy state and glass transition temperature both increased with rate of cooling. A simple hypothesis could be used to discuss the results, in which free volume is defined by the excess specific volume above glass transition on the one hand, and by its relation to mobility (the Doolittle equation), on the other. This hypothesis contains three independent parameter values, viz. the “thermodynamic glass transition temperature”T ∞, the thermal expansion coefficient of the free volume fraction,α f, andB of the Doolittle equation. By combining the results of both measurements, all three parameters can be separately determined. Values forB are found between 0.2 and 0.4, values of the fractional free volume frozen at the glass transition are found between 0.8 and 1.1%.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Rheologica acta 30 (1991), S. 300-300 
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Colloid & polymer science 252 (1974), S. 759-759 
    ISSN: 1435-1536
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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