We present an extensive analysis of the relaxation dynamics of entangled linear polymer melts via long-time molecular dynamics simulations of a generic bead–spring model. We study the mean-squared displacements, the autocorrelation function of the end-to-end vector, P(t), the single-chain dynamic structure factor, S(q, t), and the linear viscoelastic properties, especially the shear stress relaxation modulus, G(t). The simulation data are compared with the theoretically expected scaling laws for different time regimes of entangled melts, and with analytical expressions that account for different relaxation mechanisms in the tube model, namely, reptation, contour length fluctuation (CLF), and constraint release (CR). CLF involves a t^1/4 scaling regime in the time-dependence of (1 – P(t)). With increasing chain length, a gradual development of this scaling regime is observed. In the absence of CR, the tube model further predicts that at long times, the chain dynamics is governed by one central quantity, the “surviving tube fraction” μ(t). As a result, one expects S(q, t) ∝ G(t) ∝ P(t) in that time regime. We test this prediction by comparing S(q, t) and G(t) with P(t). For both quantities, proportionality with P(t) is not observed, indicating that CR has an important effect on the behavior of these two quantities. Instead, to a very good approximation, we find G(t) ∝ P(t)² at late times, which is consistent with the dynamic tube dilation or double reptation approximations for the CR process. In addition, we calculate nonlocal mobility functions, which can be used in dynamic density functional theories for entangled inhomogeneous polymer blends, and discuss the effect of entanglements on the shape of these functions.

中文翻译：

---

通过分子动力学模拟分析缠结线性聚合物熔体的弛豫动力学


我们通过通用珠子-弹簧模型的长期分子动力学模拟，对纠缠线性聚合物熔体的松弛动力学进行了广泛的分析。我们研究了均方位移、端到端矢量的自相关函数 P（t）、单链动态结构因子 S（q， t） 和线性粘弹性，尤其是剪切应力松弛模量 G（t）。将仿真数据与理论上预期的缠缠熔体不同时间状态的缩放定律以及解释管模型中不同松弛机制的解析表达式进行比较，即重复、轮廓长度波动 （CLF） 和约束释放 （CR）。CLF 涉及时间依赖性为 （1 – P（t）） 的 t^1/4 缩放机制。随着链长的增加，观察到这种缩放机制的逐渐发展。在没有 CR 的情况下，管模型进一步预测，在很长一段时间内，链动力学由一个中心量控制，即“幸存管分数” μ（t）。因此，在该时间范围内，人们期望 S（q， t） ∝ G（t） ∝ P（t）。我们通过将 S（q， t） 和 G（t） 与 P（t） 进行比较来检验这一预测。对于这两个量，未观察到与 P（t） 的比例，表明 CR 对这两个量的行为有重要影响。 相反，对于一个非常好的近似值，我们发现 G（t） ∝ P（t）² 在后期，这与 CR 过程的动态管膨胀或双重复近似一致。此外，我们计算了非局部迁移率函数，该函数可用于纠缠不均匀聚合物共混物的动态密度泛函理论，并讨论了纠缠对这些函数形状的影响。