Constitutive models for well-entangled living polymers beyond the fast-breaking limit

Abstract

In well-entangled living polymers, there is a complex relationship between reversible polymerization reactions and stress relaxation dynamics. This relationship is already well-understood in the “fast-breaking” limit, where polymers tend to break apart much faster than they can relax interior tube segments by reptation. For well-entangled living polymers that are not necessarily fast-breaking, we introduce a new suite of computationally efficient partial differential equation models for linear and nonlinear rheology. For linear rheology calculations, we retain full-chain depictions of standard stress relaxation processes (reptation, double reptation, contour length fluctuations, etc.) and replace the reaction terms with a simple “shuffling” approximation. Besides predicting bulk rheology, these shuffling models also yield new insights into the rheological contribution from chains at different sectors of the molecular weight distribution. Generalizing to nonlinear rheology models, additional approximations must be made with respect to reptation and constraint release in order to facilitate applications in computational fluid dynamics. To evaluate... a pair of constitutive models with complementary strengths and weaknesses: LRP-f (living Rolie-Poly, fitted) and STARM-E (simplified tube approximation for rapid-breaking micelles, extended). Nonlinear rheology calculations are provided for both models over a range of flow conditions in both fast-breaking and semi-slow breaking systems. In spite of their differing assumptions and approximations, we find that both models are capable of producing similar results. From this, we conclude that the predictions of the LRP-f and STARM-E models reflect their shared physical basis, and hence either model can be used with reasonable confidence for describing nonlinear rheology in systems of well-entangled living polymers across the fast/slow breaking spectrum.