NDLI: Relaxation time spectrum molecular weight distribution relationships

Content Provider	Springer Nature Link
Author	Friedrich, Christian Loy, Richard J. Anderssen, Robert S.
Copyright Year	2008
Abstract	Single exponential decay $\exp(-t/\tau)$ relationships, which define the molecular weight distribution (MWD) of a polymer as a function of the polymer’s relaxation time spectrum (RTS), have been derived by Wu (Polym Eng Sci 28:538–543, 1988) and Thimm et al. (J Rheol 43:1663–1672, 1999). Experimental validation studies with monodisperse polymers, with quite precisely known MWDs, have been used to test their reliability. It has been established that neither formula is always able to accurately recover the MWDs of monodisperse polymers from their experimentally determined RTS. In this paper, different and more general relationships, based on theoretical results of Anderssen and Loy (Bull Aust Math Soc 65:449–460, 2002a) for decays of the form $\exp(-\theta(t)/\tau)$ , where the derivative of θ(t) is a completely monotone function, are derived, analyzed, and applied. It is shown how to transform these general relationships to equivalent single exponential decay relationships for which Laplace transform solutions are derived. In order to illustrate the interrelationship between an RTS and its corresponding MWD, an explicit analytic solution is given. The paper concludes with a discussion of the rheological implications for the BSW model.
Starting Page	151
Ending Page	162
Page Count	12
File Format	PDF
ISSN	00354511
Journal	Rheologica Acta
Volume Number	48
Issue Number	2
e-ISSN	14351528
Language	English
Publisher	Springer-Verlag
Publisher Date	2008-10-30
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Relaxation time spectrum Molar mass distribution Laplace transformation Monodisperse Complete monotonicity Double reptation Molecular weight distribution BSW spectrum Food Science Polymer Sciences Characterization and Evaluation of Materials Mechanical Engineering Soft Matter, Complex Fluids
Content Type	Text
Resource Type	Article
Subject	Mechanics of Materials Condensed Matter Physics Materials Science

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