Predictions for flow-induced scission in well-entangled living polymers: The “living Rolie-Poly” model

In polymeric materials subject to both polymerization reactions and flow, there can be a complex interplay between reactions and stress relaxation processes. For example, reversible scission reactions can “shuffle” stresses across the molecular weight distribution, narrowing the stress relaxation spectra and decreasing the typical stress relaxation time. In addition, flow can stretch chains and make them more likely to break apart, leading to changes in the underlying reaction kinetics. Existing strategies for modeling the coupling between reactions and flow in polymer systems are limited in their range of applicability or dubious in their underlying approximations. Here, we develop a more flexible modeling approach with coupled population balance models that move both material and stress across the molecular weight distribution. The full model, which we call the “living Rolie Poly” (LRP) model, reproduces some earlier findings on linear rheology and offers new insights into nonlinear rheology and the role of flow-induced scission. For systems that are not inclined to shear band in the absence of flow-induced scission, we predict that flow-induced scission produces an additional shear thinning effect for steady shear flow, and in steady extensional flow, we predict that flow-induced scission acts like a finite extensibility correction, preventing the divergence of the steady viscosity. The LRP model is too complex to use in spatially resolved calculations or complex flow geometries at this time, but a “simplified” model with no such limitation arises naturally in the “fast--breaking” limit and shows good agreement with the full LRP model predictions.