Scaling properties of branched polyesters

Abstract

The growth of branched polymer structures up to the gel point has been examined in a polyester system at two different branch agent concentrations. Several independent measurements of the size and molecular weight of these polymers were made using elastic light scattering, quasi-elastic light scattering, intrinsic viscosity (SI, and size-exclusion chromatography with low-angle light scattering detection. In all cases, scaling relationships between these various properties were displayed for the whole range of molecular weights examined. The weight-average molecular weight scaled as @, - p)T, where p is the extent of reaction and pc is the extent of reaction at the gel point. The exponent y was found to be 1.8 f 0.3. Scaling exponents from the radius-M, and (+M, relationships were evaluated for unfractionated samples. Using these exponents, another critical exponent of gelation, T, and the exponent relating size to molecular weight for a branched polymer in a good solvent, $, could be evaluated. These were compared with values for the same exponents obtained through size-exclusion chromatography of the polymers. The critical exponent 7 was obtained from this fractionation experiment through the shape of the observed distribution function and from the scaling relation between the molecular weight M-, corresponding to the fraction making the largest contribution to light scattering in this separation, and M, for each sample. Good agreement was observed between these two separate measures of T and the one from the unfractionated samples, as well as from both fractionated and unfractionated samples. The measured values were T = 2.29 f 0.03 and $ = 0.48 f 0.02. The distribution functions for polymers were described by a single universal distribution function. The critical exponents for gelation were compared to percolation and Flory-Stockmayer predictions and were found to favor the percolation results, but the agreement with percolation for the exponent 7 was marginal.