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.

Characterization of the structure and the size distribution of branched polymers formed by co-polymerization of MMA and EGDMA

“…We do not have an explanation of the hump at V e ≈ 23. Such a feature was also observed on other systems [6,8] and could be an artefact of the method. In a first approximation V 0 −V e ∝ log(M ) and therefore the refractive index signal is given by RI ∝ M 2 N (M ), so that the area under the chromatogram is proportional to the total mass injected.…”

“…When the aggregates are still relatively small M w and R gz can be determined from the low q-dependence using equations (5,6). This is no longer feasible if qR gz > 1 even for the smallest accessible scattering angle.…”

“…In this way values of M w and R gz can be obtained even if equations (5,6) are no longer applicable. Figure 2 shows M w as a function of R gz on a double logarithmic scale.…”

“…Large crossover domains can be expected so often no model applies. Nevertheless, the percolation model has given a good description of structural properties of the aggregates in a number systems [5][6][7][8].…”

Phase Diagram of Inhomogeneous Percolation with a Defect Plane

“…Percolation [5] in Z d is a lattice model of polymeric gelation [35,37] and of chemical gelation due to polymerisation of monomers or comonomers [16]. In a percolation model the phenomenon of gelation is understood as a critical phenomenon [7] with characteristic scaling about a critical point called the percolation threshold.…”