Linear rheology of architecturally complex macromolecules: Comb polymers with linear backbones

We present a detailed, systematic study of the linear rheological response of model comb homopolymers consisting of linear backbone chains on which branches of the same polymer are grafted. By using polymers of different molecular weights of backbone and branches, different number of branches, and different chemistries, we explore the relaxation mechanisms of these polymers and find their universal features. We apply a tube model theoretical analysis, originally developed by McLeish and co-workers, which has been appropriately modified in order to account for the effects of the fluctuations of the free ends of the backbone (due to the grafting procedure during synthesis) and the polydispersity on the rheology. The satisfactory fitting of the data with the model indicates that the latter is capable of providing a quantitative understanding of the rheology of branched polymers. More specifically, comb polymers exhibit two distinct relaxation processes, assigned to the branches and the backbone. Relaxation proceeds hierarchically with the grafted branches moving first. The free backbone ends contribute as extra asymmetric branches moving via fluctuations. Finally, important issues relating to the number of grafted branches and the possible tube dilation breakdown (which may explain the physics of the only adjustable parameter p(2)) are discussed.