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Full Paper
On the Generalised Stretch Function
Article first published online: 9 FEB 2012
DOI: 10.1002/mats.201100102
Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Additional Information
How to Cite
Kharlamov, A. A. and Filip, P. (2012), On the Generalised Stretch Function. Macromol. Theory Simul., 21: 272–278. doi: 10.1002/mats.201100102
Publication History
- Issue published online: 11 MAY 2012
- Article first published online: 9 FEB 2012
- Manuscript Revised: 1 DEC 2011
- Manuscript Received: 7 OCT 2011
Funded by
- Grant Agency of the Czech Republic. Grant Number: 103/09/2066
- Abstract
- Article
- References
- Cited By
Keywords:
- molecular length;
- recurrence equations;
- rubber;
- strain;
- stretch functions
Abstract
The tube theory represents a powerful tool for the description of polymer behaviour. In this theory, the term in the form of an integral over a full solid angle of a magnitude of deformed unit vector represents the stretch function. This term relates the lengths of the random walk of a molecule in deformed and undeformed states. For the case of the Doi-Edwards model, the integrand is raised to a power of one, however, for other models the power differs from one. The aim of this contribution is to derive an analytical algebraic approximation of a general form of this integral with the integrand raised to an arbitrary power within the physically justified interval between zero and two.