Volume 48, Number 4, November II 1999
|Page(s)||421 - 427|
|Section||Condensed matter: structure, mechanical and thermal properties|
|Published online||01 September 2002|
Shear viscosity of a crosslinked polymer melt
Institut für Theoretische Physik, Universität Göttingen D-37073 Göttingen, Germany
2 Department of Physics, Theoretical Physics, University of Oxford Oxford OX1 3NP, UK
Accepted: 24 September 1999
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 β associated with the gel fraction and the crossover exponent ϕ of a random resistor network.
PACS: 64.60.Ht – Dynamic critical phenomena / 82.70.Gg – Gels and sols / 83.10.Nn – Polymer dynamics
© EDP Sciences, 1999
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