We present a new strategy for introducing population balances into full-chain constitutive models of living polymers with linear chain architectures. We provide equations to describe a range of stress relaxation processes covering both unentangled systems (Rouse-like motion) and well entangled systems (reptation, contour length fluctuations, chain retraction, and constraint release). Special attention is given to the solutions that emerge when the 'breaking time' of the chain becomes fast compared to various stress relaxation processes. In these 'fast breaking' limits, we reproduce previously known results (with some corrections) and also present new results for nonlinear stress relaxation dynamics. Our analysis culminates with a fully developed constitutive model for the fast breaking regime in which stress relaxation is dominated by contour length fluctuations. Linear and nonlinear rheology predictions of the model are presented and discussed.

中文翻译：

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基于全链管的活性线性聚合物本构模型

我们提出了一种将种群平衡引入具有线性链结构的活性聚合物的全链本构模型的新策略。我们提供方程来描述一系列应力松弛过程，涵盖未纠缠系统（Rouse 状运动）和良好纠缠系统（蠕动、轮廓长度波动、链回缩和约束释放）。与各种应力松弛过程相比，当链条的“断裂时间”变快时出现的解决方案得到了特别关注。在这些“快速突破”限制中，我们重现了先前已知的结果（进行了一些修正），并且还呈现了非线性应力松弛动力学的新结果。我们的分析以一个完全开发的快速断裂本构模型告终，其中应力松弛由轮廓长度波动主导。提出并讨论了模型的线性和非线性流变预测。