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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

References

[1]Anderssen, R. S. and Mead, D. W., “On the recovery of molecular weight functionals from double reptation models”, J. Non-Newtonian Fluid Mech. 68 (1997) 291–301.CrossRefGoogle Scholar
[2]Bird, R. B., Armstrong, R. C. and Hassager, O., Dynamics of Polymeric Liquids, Vol. 1 (John Wiley and Sons, New York, 1987).Google Scholar
[3]des Cloiseaux, J., “Double reptation vs. single reptation of polymer melts”, Europhys. Lett. 5 (1988) 437–442.Google Scholar
[4]Dealy, J. M. and Wissburn, K. F., Melt Rheology and its Role in Plastics Processing (van Nostrand Reinholdt, New York, 1990).Google Scholar
[5]Doi, M. and Edwards, S. F., The Theory of Polymer Dynamics (Oxford University Press, 1986).Google Scholar
[6]Elliott, D., “The numerical treatment of singular integral equations—a review”, in Treatment of Integral Equations by Numerical Methods (eds Baker, C. T. H. and Miller, G. F.), (Academic Press, London, 1982) 297–312.Google Scholar
[7]Feller, W., An Introduction to Probability Theory and its Applications, Vol. 1 (John Wiley and Sons, 1968).Google Scholar
[8]Fujita, H., Mathematical Theory of Sedimentation Analysis (Academic Press, New York, 1962).Google Scholar
[9]Gehatia, M. and Wiff, D. R., “Determination of a molecular weight distribution from equilibrium sedimentation by applying regularizing functions”, Euro. Polymer J. 8 (1972) 585–597.Google Scholar
[10]de Gennes, P. G., “Reptation of a polymer chain in the presence of fixed obstacles”, J. Chem. Phys. 55 (1971) 572.CrossRefGoogle Scholar
[11]Giddings, J. C., “Field-flow fractionation: analysis of macromolecular, colloidal and particulate materials”, Science 260 (1993) 1456–1465.Google Scholar
[12]Larson, R. G., Constitutive Equations for Polymer Melts and Solutions (Butters worths, Boston, 1988).Google Scholar
[13]Locati, G. and Gargani, L., “Dependence of zero-shear viscosity on molecular weight distribution”, J. Polym. Sci., Polym. Lett. Ed. 11 (1973) 95–101.Google Scholar
[14]MacRitchie, F., “Mechanical degradation of gluten proteins during high speed mixing of dough”, J. Polym. Sci., Polym. Symp. 49 (1975) 85–90.Google Scholar
[15]Maier, D., Eckstein, A., Honerkamp, J. and Friedrich, Chr., “A new mixing rule for polystyrene to calculate the MWD from rheological data”, J. Rheology 42 (1998) 1153–1173.CrossRefGoogle Scholar
[16]Mead, D. W., “Determination of molecular weight distributions of linear flexible polymers from linear viscoelastic material functions”, J. Rheology 38 (1994) 1797–1827.Google Scholar
[17]Tsenoglou, C., “Viscoelasticity of binary homopolymer blends”, ACS Polymer preprints 28 (1987) 185–186.Google Scholar
[18]Tsenoglou, C., “Molecular weight polydispersity effects on the viscoelasticity of entangled polymers”, Macromolecules 24 (1991) 1762–1767.CrossRefGoogle Scholar
[19]Wasserman, S. H., “The relationship between polydispersity and linear viscoelasticity in entangled polymer melts”, Ph. D. Thesis, Princeton University, 1994.Google Scholar
[20]Wood-Adams, P. M. and Dealy, J. M., “Use of rheological measurements to estimate the molecular weight distribution of linear polyethylene”, J. Rheology 40 (1996) 761–778.CrossRefGoogle Scholar
[21]Zeichner, G. R. and Patel, P. D., “A comprehensive evaluation of polypropylene melt rheology”, in Proc. 2nd World Conf. of Chem. Eng., Volume 4, (Montreal, Canada, 1981) 333–337.Google Scholar
[22]The Encyclopaedia Britannica, Vol. 4 (Enc. Brit. Inc., Chicago, 1983), p. 161.Google Scholar