Entangled dendritic polymers and beyond: Rheology of symmetric Cayley-tree polymers and macromolecular self-assemblies

We present linear rheological data on a series of anionically synthesized, model symmetric Cayley-tree polybutadienes having 2 or 3 generations with entangled branches. The signature of each layer relaxation is evident, in both the plateau modulus (that scales with the volume fraction of the unrelaxed layers) and the terminal relaxation as a distinct contribution, well-separated in time. Using a robust tube-model analysis of the viscoelastic relaxation of entangled polymers of given architecture, which is based on the concept of hierarchy of motion in branched structures, we describe quantitatively the frequency spectra without adjustable parameters; the needed plateau modulus, entanglement molecular weight, and Rouse time of an entanglement segment are taken from the data. Last, but not least, we show that this approach can be successfully applied to account for the rheology of macromolecular self-assemblies, such as the Cayley-tree-like associations of telechelic, mono-co-functionalized star polymers. The implications of the latter findings in providing pathways for the analysis of complex soft superstructures are evident.