Linear rheology of comb polymers with star-like backbones: Melts and solutions

We investigate the linear rheology of model star-comb homopolymers consisting of star-like backbone chains with grafted branches. We show that the tube-based theory in the framework of full dynamic dilution, appropriately modified to account for the effects of the fluctuations of the free segments (the segments of the star arms between the outer branching points and the arms' free end-monomers) of the backbone star arms, and the polydispersity accurately describes the linear viscoelastic spectrum. For these branched polymers, the relaxation is found to proceed hierarchically, similar to combs with linear backbones. However, in contrast to the latter, here, there is no reptation. The higher functionality star combs with sparse branching are particularly interesting because they resemble a Cayley tree structure and are treated in the context of asymmetric star polymers. We also employ solutions of star combs and test our model in static dilution conditions. In the region where despite the presence of both static (solvent) and dynamic dilution the polymers remain entangled, our model is particularly successful without adjusting any parameters.