Shear viscosity of a crosslinked polymer melt

Details Shear viscosity of a crosslinked polymer melt Shear viscosity of a crosslinked polymer melt

1998-11-27

arxiv.org/abs/cond-mat/9811388v3

Europhys. Lett., 48 (4), pp. 421-427 (1999)

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1209/epl/i1999-00500-3

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 $k=\phi-\beta$ between the critical exponent $k$ of the viscosity, the thermal exponent $\beta$ associated with the gel fraction and the crossover exponent $\phi$ of a random resistor network.

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