Small and Medium Amplitude Oscillatory Shear Rheology of Model Branched Polystyrene (PS) Melts

Linear and nonlinear rheological properties of model comb polystyrenes (PS) with loosely to densely grafted architectures were measured under small and medium amplitude oscillatory shear (SAOS and MAOS) flow. This comb PS set had the same length of backbone and branches but varied in the number of branches from 3 to 120 branches. Linear viscoelastic properties of the comb PS were compared with the hierarchical model predictions. The model underpredicted zero-shear viscosity and backbone plateau modulus of densely branched comb with 60 or 120 branches because the model does not include the effect of side chain crowding. First- and third-harmonic nonlinearities reflected the hierarchy in the relaxation motion of comb structures. Notably, the low-frequency plateau values of first-harmonic MAOS moduli scaled with M$^{-2}$$_{w}$ (total molecular weight), reflecting dynamic tube dilution (DTD) by relaxed branches. Relative intrinsic nonlinearity Q$_{0}$ exhibited the difference between comb and bottlebrush via no low-frequency Q$_{0}$ peak of bottlebrush corresponding to backbone relaxation, which is probably related to the stretched backbone conformation in bottlebrush.