Shear viscosity of a crosslinked polymer melt

¹ Institut für Theoretische Physik, Universität Göttingen D-37073 Göttingen, Germany
² Department of Physics, Theoretical Physics, University of Oxford Oxford OX1 3NP, UK

Received: 5 July 1999
Accepted: 24 September 1999

Abstract

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.