Entangled linear polymers in fast shear flows: Comparison of tube-model predictions and experimental data

This work addresses the shear response of entangled linear polymers by assessing the current state-of-the-art model and proposing alternative directions. In particular, we examine the performance of the Graham-Likhtman-McLeish-Milner (GLaMM) nonlinear tube model in fast shear flows. Predictions are compared against experimental data for well-characterized, monodisperse, entangled linear polystyrene chains. Unlike previous works using the GLaMM model, finite extensibility is accounted for. Comparison of model predictions and data not only reveals an overall reasonable performance but also highlights limitations. For example, the predictions significantly depend on whether the contribution of contour length fluctuations to the retraction rate is accounted for or not. This specific sensitivity of the model is enhanced as the Rouse-Weissenberg number increases. Possible improvement of the model by modification of the existing mechanisms/model assumptions and/or by incorporation of overlooked mechanisms such as chain tumbling and CCR-driven disentanglement (CCR-D) is discussed. As a possible way to overcome the existing limitations, we propose an alternative approach based on the time marching algorithm (TMA) and focus on the description of the steady-state regime. Compared to the GLaMM model, this approach allows us to keep track of the relaxation state of each entanglement segment in a simple way, while ensuring consistency between chain stretch and constraint release mechanisms. Moreover, it accounts for CCR-D in an indirect manner. A key ingredient is the use of the recently advanced concept of the shear blob and its dependence on the shear rate. Our simple modification of TMA reproduces the experimental steady-state viscosities accurately for all samples and for all shear rates examined.