Relationship between linear viscoelastic properties and molecular structure for linear and branched polymers

The prediction of linear viscoelasticity (LVE) of a polymer melts from the knowledge of their structure has received tremendous attention in recent years. Quite accurate quantitative predictions are obtained for linear polymers, including inverse predictions of molecular weight distributions from knowledge of rheological response. The situation for branched polymers is much more complicated for at least two reasons. First, because of the incredible variety of architectures that can be, and are actually, made in the lab or by industry. Second, because branched polymers are characterised by very broad distributions of relaxation times, which are very dependent on details of the architecture. The main objective of this work is to propose a model suitable for predicting LVE of arbitrary mixtures of (a)symmetric stars and linear molecules, where the interrelation of relaxation processes (as reptation, tube length fluctuations or constraint release process) cannot be predicted a priori. We validate it on a large set of experimental data taken from the literature, from our own experiments or from co-workers. Next, we use it to detect long chain branching (LCB) in sparsely branched polycarbonate samples. This characterization technique, based on the analysis of the relaxation moduli, is compared to solution characterization. A similar work is performed for polyethylene samples, on which we compare our method to classical methods based on the measurement of their intrinsic viscosity or on the analysis of their activation energies spectrum. The success of our model in describing the relaxation of an already broad range of polymer structures gives some hope for understanding the dynamics of more complex systems. Indeed, its structure allows us to easily extend it to H or comb polymers and then, to proceed to polymers always closer to the industrial polymers.