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The molecular weight distribution problem and reptation mixing rules

Published online by Cambridge University Press:  17 February 2009

R. S. Anderssen  and
M. Westcott
R. S. Anderssen
Affiliation:
CSIRO Mathematical and Information Sciences, GPO Box 664, Canberra ACT 2601, Australia.
M. Westcott
Affiliation:
CSIRO Mathematical and Information Sciences, GPO Box 664, Canberra ACT 2601, Australia.
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Abstract

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Mixing rules model how the physical properties of a polymer, such as its relaxation modulus G(t), depend on the distribution w(m) of its molecular weights m. They are of practical importance because, among other things, they allow estimates of the molecular weight distribution (MWD) w(m) of a polymer to be determined from measurements of its physical properties including the relaxation modulus. The two most common mixing rules are “single” and “double” reptation. Various derivations for these rules have been published. In this paper, a conditional probability formulation is given which identifies that the fundamental essence of “double” reptation is the discrete binary nature of the “entanglements”, which are assumed to occur in the corresponding topological model of the underlying polymer dynamics. In addition, various methods for determining the MWD are reviewed, and the computation of linear functionals of the MWD motivated and briefly examined.

Type
Research Article
Information
The ANZIAM Journal , Volume 42 , Issue 1 , July 2000 , pp. 26 - 40
Copyright
Copyright © Australian Mathematical Society 2000

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