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The experimentally determined zero-shear viscosity of entangled branched polymers shows dramatic variation due to the topological arrangements of the branches in branched polymer melts. The position of the branch points, the arm length, and number of the arms are essential to defining the rheological behavior. Recent advances in molecular tube models have led to a much greater understanding of the linear rheology of linear, star, H-shaped, pom-pom, and comb polymers. We correct and extend existing molecular theories for the linear viscoelasticity of comb polymer melts, especially in accounting for (1) polydispersity and (2) the path length of backbone extremities. We compare the predictions with linear rheological data of nearly monodisperse polybutadiene combs. We then predict the zero-shear viscosity for monodisperse comb polyethylenes with varying arm lengths, backbone lengths, and number of arms. For a fixed molecular weight, we find that combs with the longest arms but few branch points give the highest predicted zero-shear viscosities and that they obey an exponential dependence on the length of the arms in the same way as star polymers. We find that combs with short arms, under four entanglements, lie below the 3.4 power law obeyed by linear polymers. All other comb topologies are bounded by these extremes.

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Quiescent and shear-induced crystallizations were performed on several well-defined linear monodisperse hydrogenated polybutadiene blends with a high-molecular-weight long-chain branched (LCB) combshaped additive. The connection between microscopic molecular motion and crystallization kinetics has been quantitatively studied with respect to the formation of either isotropic or oriented shish kebab crystal morphology using time-resolved X-ray scattering techniques. Using a constant preshear rate, the addition of small amounts of LCB combs to the sample blends, at concentrations below and just above the overlap concentration c*, has significantly increased the crystallization rates compared to quiescent conditions. However, only one blend showed the formation of an oriented shish kebab morphology. Also, for these model blends, the transition between isotropic and oriented crystals occurs quite sharply between 5 and 10%, which is around c*. We explain these data by using a shish formation mechanism in which, to form shish kebabs, the combs must be mutually overlapping and the comb Weissenberg number must be in the strong stretch regime.