Scaling Properties of Branched Polyesters. 2. Static Scaling above the Gel Point

We report experimental data on gel fraction, gel equilibrium swelling, sol intrinsic viscosity, and molecular weight distribution of the sol for a series of polyester samples above the gel point. The data are analyzed in terms of scaling relations suggested by percolation theory. We determine the Fisher exponent tau that describes the power law distribution of molecular weights at the gel point, by five independent methods above the gel point, and conclude tau = 2.35 +/- 0.03 (95 %). This is in excellent agreement with the previously reported analysis of tau below the gel point for the same polyester system. The measured tau is intermediate between the expectations of three-dimensional percolation theory (tau = 2.2) and the mean-field Flory-Stockmayer theory (tau = 2.5). We interpret the intermediate exponent in terms of a crossover between the two limiting theories and estimate the prefactor for the Ginzburg criterion from the experimental data. We also find that network strands are not able to completely disintersperse when the network is swollen in a good solvent.