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Erschienen in: Rheologica Acta 10/2010

01.10.2010 | Original Contribution

Effect of incomplete datasets on the calculation of continuous relaxation spectra from dynamic-mechanical data

verfasst von: Florian J. Stadler

Erschienen in: Rheologica Acta | Ausgabe 10/2010

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Abstract

In this article, the effect of an incomplete frequency range on relaxation spectra calculated with the new spline-based method (Stadler and Bailly, Rheol Acta 48(1):33–49, 2009) presented before is discussed. The range, in which the spectrum can be determined, is limited by the range of the input data, but not directly by the inverse frequency. The actual limits depend on the range of input data. Depending on the shape of the spectrum the relaxation spectrum can be determined from the input data in a range up to three decades larger than the input data. This can be explained by the influence of the modes outside the inverse frequency range. For this purpose, a new concept, the relevance factor analysis, was introduced, which allows for a determination of the limits of spectrum calculation. The characteristic relaxation times are discussed in comparison for to the calculation of \(J_e^{\rm 0}\) and η 0 from the spectrum.

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Fußnoten
1
Another reason for the limitation of TTS for extending the frequency regime is the accessible temperature range, which is limited by crystallization, glass transition, and degradation of the polymer.
 
2
The contributions were calculated by calculating the ratio of G (ω) and G (ω) from the whole range to G (ω) and G (ω) calculated from the reduced relaxation time range. The contributions given in the text refer to the maximum value of this ratio.
 
3
The calculation of the relevance factors is very much straightforward, but requires a lot of computations for complex spectra (and, therefore, anybody should be warned to use arrays with significantly more than 1,000 frequencies by 1,000 relaxation times for numerical reasons). The Matlab®-script written by the author for that purpose can be obtained upon request. To use it, a full Matlab®-installation is required.
 
4
Tests on PBd and telechelic PBd on the TA Instruments ARES (Stadler and van Ruymbeke 2010; Stadler et al. 2009) indicate that the limit for the correction probably is somewhat higher than one decade in modulus.
 
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Metadaten
Titel
Effect of incomplete datasets on the calculation of continuous relaxation spectra from dynamic-mechanical data
verfasst von
Florian J. Stadler
Publikationsdatum
01.10.2010
Verlag
Springer-Verlag
Erschienen in
Rheologica Acta / Ausgabe 10/2010
Print ISSN: 0035-4511
Elektronische ISSN: 1435-1528
DOI
https://doi.org/10.1007/s00397-010-0479-0

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