  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.

Statistical Mechanics;Soft Condensed Matter;Chemical Physics