Viscoelasticity of randomly branched polymers in the critical percolation class

We report viscosity, recoverable compliance, and molecular weight distribution of a series of randomly branched polyester samples below their gel point. From the static characterization we determine τ=2.17±0.08 (95%) for the exponent controlling the mass distribution, indicating that this system belongs to the critical percolation universality class. We find that viscosity diverges at the gel point with an exponent s=1.36±0.09 (95%), in agreement with a simple bead-spring (Rouse) model without hydrodynamic or topological interactions. Similarly, the recoverable compliance diverges at the threshold with an exponent t=2.71±0.30 (95%), consistent with the idea that kBT of elastic energy is stored per correlation volume. The complex shear modulus obeys a power law in frequency with exponent u=0.659±0.015 (95%), thereby confirming the dynamical scaling law u=t/(s+t). (c) 1995 The American Physical Society