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

J D Peterson,M E Cates

doi:10.1122/8.0000199

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.

Highlights

INTRODUCTION AND BACKGROUNDFor the past three decades, studies of living polymers have been closely tied to theoretical and experimental interest in wormlike micelles (WLM) [1,2,3,4,5,6,7,8,9]
The living Rolie–Poly” (LRP) model still has a number of notable weaknesses (1) it performs somewhat poorly for linear rheology calculations (2) it does not really consider thermal constraint release, and (3) it so far it lacks a discretization that is suitable for computational fluid dynamics (CFD) calculations
We introduced STARM as a nonlinear constitutive model for linear chain living polymers in the fast-breaking contour length fluctuations (CLFs) limit, where stress relaxation is dominated by CLFs as the breaking time is much faster than the typical stretch relaxation time [18]

Summary

Introduction

For the past three decades, studies of living polymers have been closely tied to theoretical and experimental interest in wormlike micelles (WLM) [1,2,3,4,5,6,7,8,9]. WLMs have become, in many respects, a model system for studying the nonlinear rheology of well-entangled polymeric materials. Principal aim of the present work is to provide a more usable and computationally efficient set of tools for describing the linear and nonlinear rheology of living polymers when the relaxation spectra for stretch and/or orientation cannot be treated as “fast-breaking.”. There are only a few nonlinear constitutive models for living polymers that are not limited to fastbreaking systems [19,20]. The LRP model still has a number of notable weaknesses (1) it performs somewhat poorly for linear rheology calculations (2) it does not really consider thermal constraint release (thermal CR), and (3) it so far it lacks a discretization that is suitable for computational fluid dynamics (CFD) calculations

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Conclusion