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.

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超越快破极限的良好纠缠活性聚合物的本构模型

在纠缠良好的活性聚合物中，可逆聚合反应与应力松弛动力学之间存在复杂的关系。这种关系在“快速断裂”极限中已经很好理解，在这种情况下，聚合物往往比通过蠕动松弛内部管段的速度快得多。对于不一定快速断裂的纠缠良好的活性聚合物，我们引入了一套新的计算效率高的线性和非线性流变学偏微分方程模型。对于线性流变计算，我们保留标准应力松弛过程（蠕动、双蠕动、轮廓长度波动等）的全链描述，并用简单的“改组”近似代替反应项。除了预测体积流变学，这些改组模型还对分子量分布不同部分的链的流变贡献产生了新的见解。推广到非线性流变学模型，必须对爬行和约束释放进行​​额外的近似，以促进计算流体动力学中的应用。评估...一对具有互补优势和劣势的本构模型：LRP-f（活的 Rolie-Poly，拟合）和 STARM-E（快速断裂胶束的简化管近似，扩展）。在快速破乳和半慢破乳系统中的一系列流动条件下，这两种模型都提供了非线性流变学计算。尽管它们的假设和近似不同，但我们发现两种模型都能够产生相似的结果。由此，