We measured the linear and nonlinear rheology of model polyisoprene comb polymers with a moderate number (5−18) of short (marginally entangled to unentangled) branches and highly entangled backbones. The hierarchical modes of relaxation were found to govern both the linear and nonlinear response. Appropriate modification of tube-model theory for entangled branches, inspired by recent work on asymmetric star polymers (where the short branch behaves as effectively larger on small time scales), provided a framework for quantitative predictions of the linear viscoelastic spectra. The extended nonlinear stress relaxation data over a wide time range (via time−temperature superposition) obeys time−strain separability and allows extraction of two damping functions: one for the branches at short times and one for the diluted backbone at long times. Both exhibit signatures of the comb architecture. The comb damping function at short times, shifted relative to the branch relaxation, is dominated by the retraction of branches and backbone end segments. The backbone damping function is rationalized by considering it as a linear chain that feels a smaller effective strain due to the prior branch relaxation.

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The stress relaxation dynamics of a series of second and third generation dendritic star polymers have been investigated experimentally in the linear regime with small amplitude oscillatory shear and also by nonlinear step shear deformations. In linear rheology, the relaxation dynamics of dendritic star melts agree with the expected relaxation hierarchy, where the characteristic tan(δ) minima that appear at high frequency correspond to the faster relaxing parts of the given dendritic topology. On the other hand, the degree of dilution, estimated from the ratio of the second plateau modulus G II to the rubbery plateau modulus G N , was much less than the expectation of the hierarchical theory, which implies a relatively slower rate of dilution due to multiple arms and generations. The nonlinear damping behavior of the second generation dendritic architecture was similar to that of H-shaped/multiarm architectures, featuring a novel damping transition from less strain softening to agreement with the Doi-Edwards damping function as the branch-point withdrawal motion. The third generation dendritic polymers exhibited much weaker strain dependence than second generation samples, suggesting a stronger stretching effect due to multiple branching generations even with arms of a few entanglements at each generation. Such a stretching effect even with small arms at each generation induced extensional hardening in the linear polymer matrix maintaining the shear viscosity.