Undershoots in shear startup of entangled linear polymer blends

We revisit the transient response of entangled polymers in shear startup. Evidence from state-of-the-art experiments, modeling and simulations suggests the presence in fast flows of a weak (albeit unambiguous) undershoot, following the overshoot, i.e., while approaching the steady state. Recent sliplink simulations confirmed that the undershoot is not due to slip at the wall, and hence it is intrinsic to polymer rheology. Here, we further examine some features of the undershoot by blending two entangled homopolymers at different compositions. Since blending affects the distribution of relaxation times, it is here shown to also affect the undershoot, probably by broadening the tumbling-time distribution. Indeed, by appropriately modifying our tube-based model, that invokes tumbling to account for the undershoot, and (in parallel) by using simulations, we show how the undershoot depends on the blend composition. We map the experimental results into a diagram of terminal relaxation time versus composition, which identifies regimes where the undershoot is present. Blending is therefore proposed as a molecular mechanism to tailor the shear stress growth function signal, particularly the undershoot.