Shear viscosity of a crosslinked polymer melt

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 $k=\ddot{I}•-{\hat{I}}^2$ between the critical exponent $k$ of the viscosity, the thermal exponent ${\hat{I}}^2$ associated with the gel fraction and the crossover exponent $\ddot{I}•$ of a random resistor network.

8 pages, uses Europhysics Letters style; Revisions: results extended