Europhys. Lett, 48 (4), pp. 421-427 (1999)
Shear viscosity of a crosslinked polymer melt
K. Broderix 1,2, H. Löwe 1, P. Müller 1 and A. Zippelius 1
1 Institut für Theoretische Physik, Universität
D-37073 Göttingen, Germany
2 Department of Physics, Theoretical Physics, University of Oxford
Oxford OX1 3NP, UK
(received 5 July 1999; accepted in final form 24 September 1999)
PACS. 64.60.Ht - Dynamic critical phenomena.
PACS. 82.70.Gg - Gels and sols.
PACS. 83.10.Nn - Polymer dynamics.
We investigate the static shear viscosity on the sol side of the vulcanization transition within a minimal mesoscopic model for the Rouse-dynamics of a randomly crosslinked melt of phantom polymers. We derive an exact relation between the viscosity and the resistances measured in a corresponding random resistor network. This enables us to calculate the viscosity exactly for an ensemble of crosslinks without correlations. The viscosity diverges logarithmically as the critical point is approached. For a more realistic ensemble of crosslinks amenable to the scaling description of percolation, we prove the scaling relation between the critical exponent k of the viscosity, the thermal exponent associated with the gel fraction and the crossover exponent of a random resistor network.
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