Determining polymer molecular weight distributions from rheological properties using the dual-constraint model

Although multiple models now exist for predicting the linear viscoelasticity of a polydisperse linear polymer from its molecular weight distribution (MWD) and for inverting this process by predicting the MWD from the linear rheology, such inverse predictions do not yet exist for long-chain branched polymers. Here, we develop and test a method of inverting the dual-constraint model (Pattamaprom et al., Rheol Acta 39:517–531, 2000; Pattamaprom and Larson, Macromolecules 34:5229–5237, 2001), a model that is able to predict the linear rheology of polydisperse linear and star-branched polymers. As a first step, we apply this method only to polydisperse linear polymers, by comparing the inverse predictions of the dual-constraint model to experimental GPC traces. We show that these predictions are usually at least as good, or better than, the inverse predictions obtained from the Doi–Edwards double-reptation model (Tsenoglou, ACS Polym Prepr 28:185–186, 1987; des Cloizeaux, J Europhys Lett 5:437–442, 1988; Mead, J Rheol 38:1797–1827, 1994), which we take as a “benchmark”—an acceptable invertible model for polydisperse linear polymers. By changing the predefined type of molecular weight distribution from log normal, which has two fitting parameters, to GEX, which has three parameters, the predictions of the dual-constraint model are slightly improved. These results suggest that models that are complex enough to predict branched polymer rheology can be inverted, at least for linear polymers, to obtain molecular weight distribution. Further work will be required to invert such models to allow prediction of the molecular weight distribution of branched polymers.