We derive a thermodynamically consistent framework for incorporating entanglement dynamics into constitutive equations for flowing polymer melts. We use this to combine the convected constraint release (CCR) dynamics of Ianniruberto–Marriccui into a finitely extensible version of the Rolie–Poly model, and also include an anisotropic mobility as in the Giesekus model. The reversible dynamics are obtained from a free energy that describes both a finitely extensible conformation tensor and an ideal gas of entanglements along the chain. The dissipative dynamics give rise to coupled kinetic equations for the conformation tensor and entanglements, whose coupling terms describe shear-induced disentanglement. The relaxation dynamics of the conformation tensor follow the GLaMM and Rolie–Poly models, and account for reptation, retraction, and CCR. We propose that the relaxation time ${\tau }_{\nu }$ for entanglement recovery is proportional to the Rouse time ${\tau }_R$ which governs polymer stretch within the tube. This matches recent molecular dynamics simulations and corresponds to relaxing the entanglement number before the entire polymer anisotropy has relaxed on the longer reptation time ${\tau }_d$. Our model suggests that claimed signatures of slow re-entanglement on the reptation time in step-strain experiments may be interpreted as arising from anisotropies in reptation dynamics.

中文翻译：

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描述流动下聚合物解缠结的热力学一致本构方程

我们推导出一个热力学一致的框架，用于将纠缠动力学纳入流动聚合物熔体的本构方程。我们使用它来将 Ianniruberto–Marriccui 的对流约束释放 (CCR) 动力学组合成 Rolie–Poly 模型的有限可扩展版本，并且还包括 Giesekus 模型中的各向异性流动性。可逆动力学是从描述有限可扩展构象张量和沿着链的理想纠缠气体的自由能获得的。耗散动力学产生了构象张量和纠缠的耦合动力学方程，其耦合项描述了剪切诱导的解缠结。构象张量的松弛动力学遵循 GLaMM 和 Rolie–Poly 模型，并解释了蠕动、回缩和 CCR。${\tau }_{\nu }$纠缠恢复与劳斯时间成正比${\tau }_R$它控制管内的聚合物拉伸。这与最近的分子动力学模拟相匹配，并且对应于在整个聚合物各向异性在较长的蠕动时间松弛之前松弛纠缠数${\tau }_d$. 我们的模型表明，在步进应变实验中，缓慢重新纠缠对爬行动物时间的声称特征可能被解释为由爬行动物动力学中的各向异性引起的。