Leipzig 1999 – scientific programme
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PO: Polymerphysik
PO 7: Poster: Polymere Netzwerke
PO 7.2: Poster
Tuesday, March 2, 1999, 14:00–16:00, Foyer
Exact shear viscosity of a crosslinked polymer melt — •Peter Müller, Kurt Broderix, Henning Löwe, and Annette Zippelius — Institut für Theoretische Physik, Universität Göttingen, D–37073 Göttingen, Germany
Starting from a microscopic Rouse model, we calculate exactly the critical behaviour of the mean static shear viscosity η for a randomly crosslinked polymer melt, as the vulcanization transition is approached. Technically, this is achieved by methods from graph theory which relate the viscosity of a random polymer cluster to the Wiener index of a random graph. Using in addition the known cluster statistics from a mean-field-like theory of random graphs, we find that η diverges logarithmically with the distance to the critical point. Replicas provide an alternative to the graph-theoretical methods and yield identical results.
The method presented does also allow to compute exactly the behaviour of the mean static shear viscosity for randomly branched polymers when the number of monomers N of the polymer tends to infinity. In this case it turns out that η∼ N1/2.