Department of Mathematics and Statistics, University of Reading, Reading RG6 6AX, United Kingdom.
J Chem Phys. 2017 Jul 28;147(4):044907. doi: 10.1063/1.4995422.
The study of dynamics and rheology of well-entangled branched polymers remains a challenge for computer simulations due to the exponentially growing terminal relaxation times of these polymers with increasing molecular weights. We present an efficient simulation algorithm for studying the arm retraction dynamics of entangled star polymers by combining the coarse-grained slip-spring (SS) model with the forward flux sampling (FFS) method. This algorithm is first applied to simulate symmetric star polymers in the absence of constraint release (CR). The reaction coordinate for the FFS method is determined by finding good agreement of the simulation results on the terminal relaxation times of mildly entangled stars with those obtained from direct shooting SS model simulations with the relative difference between them less than 5%. The FFS simulations are then carried out for strongly entangled stars with arm lengths up to 16 entanglements that are far beyond the accessibility of brute force simulations in the non-CR condition. Apart from the terminal relaxation times, the same method can also be applied to generate the relaxation spectra of all entanglements along the arms which are desired for the development of quantitative theories of entangled branched polymers. Furthermore, we propose a numerical route to construct the experimentally measurable relaxation correlation functions by effectively linking the data stored at each interface during the FFS runs. The obtained star arm end-to-end vector relaxation functions Φ(t) and the stress relaxation function G(t) are found to be in reasonably good agreement with standard SS simulation results in the terminal regime. Finally, we demonstrate that this simulation method can be conveniently extended to study the arm-retraction problem in entangled star polymer melts with CR by modifying the definition of the reaction coordinate, while the computational efficiency will depend on the particular slip-spring or slip-link model employed.
由于这些聚合物的末端松弛时间随分子量呈指数增长，因此研究完全缠结的支化聚合物的动力学和流变学对计算机模拟来说仍然是一个挑战。我们提出了一种有效的模拟算法，用于通过将粗粒滑移弹簧（SS）模型与前向通量采样（FFS）方法相结合来研究缠结星形聚合物的臂回缩动力学。该算法首先应用于在不存在约束释放（CR）的情况下模拟对称星形聚合物。FFS 方法的反应坐标是通过找到模拟轻度缠结星形聚合物的末端松弛时间的结果与直接拍摄 SS 模型模拟结果之间的良好一致性来确定的，它们之间的相对差异小于 5%。然后，对于具有臂长可达 16 个缠结的强缠结星形聚合物进行 FFS 模拟，这些缠结远远超出了非 CR 条件下的强制力模拟的可达性。除了末端松弛时间外，该方法还可用于生成所有缠结的松弛谱，这是发展缠结支化聚合物定量理论所需要的。此外，我们提出了一种通过有效链接 FFS 运行过程中每个界面存储的数据来构建可实验测量的松弛相关函数的数值方法。所得到的星形聚合物臂末端向量松弛函数Φ(t)和应力松弛函数 G(t)在末端区域与标准 SS 模拟结果基本一致。最后，我们证明了通过修改反应坐标的定义，这种模拟方法可以方便地扩展到研究具有 CR 的缠结星形聚合物熔体中的臂回缩问题，而计算效率将取决于所采用的特定滑移弹簧或滑移链接模型。
