纠缠聚合物的持续无规行走的流动变形构象
Flow-deformed conformations of entangled polymers as persistent random walks
摘要：
在流动下的缠结聚合物流体中，在库恩尺度界面上的演变结构和流变学在塑料制品的加工中起着重要作用，并且具有许多其他应用。定量跟踪链构象统计的库恩尺度上是必不可少的发展计算模型的这种现象。为此，我们在这里制定一个双尺度/双模模型的纠缠聚合物链下流动。每一条链都被连续的纠缠分割成两种模式之一：纠缠或悬挂。在链尺度上，理想（非相互作用）链的构象统计遵循其端到端距离的二阶矩的微分演化方程。后者规定持久的随机游走采样构象统计理想的纠缠链的库恩尺度，如下从广义的格林-久保关系和最大熵原理。我们测试它的数值范围内的变形率在启动简单的拉伸和剪切流动。一个自洽的潜力，代表片段的相互作用，修改链构象统计的库恩规模，因为它重新规范化的参数控制的持久性随机游走。广义格林-久保关系，然后反转，以确定如何链端到端的距离的二阶矩是由自洽的潜力改变。这使我们能够设计一个双尺度传播方案的统计权重的纠缠链的子链。后者用于计算纠缠链中每种化学类型的库恩段的局部体积分数，从而确定自洽势。
英文摘要：
Evolving structure and rheology across Kuhn scale interfaces in entangled polymer fluids under flow play a prominent role in processing of manufactured plastics, and have numerous other applications. Quantitative tracking of chain conformation statistics on the Kuhn scale is essential for developing computational models of such phenomena. For this purpose, we formulate here a two-scale/two-mode model of entangled polymer chains under flow. Each chain is partitioned by successive entanglements into strands that are in one of two modes: entangled or dangling. On the strand scale, conformation statistics of ideal (non-interacting) strands follows a differential evolution equation for the second moment of its end-to-end distance. The latter regulates persistent random walks sampling conformation statistics of ideal entangled strands on the Kuhn scale, as follows from a generalized Green-Kubo relation and the Maximum Entropy Principle. We test it numerically for a range of deformation rates at the start-up of simple elongational and shear flows. A self-consistent potential, representing segmental interactions, modifies strand conformation statistics on the Kuhn scale, as it renormalizes the parameters controlling the persistent random walk. The generalized Green-Kubo relation is then inverted to determine how the second moment of the strand end-to-end distance is changed by the self-consistent potential. This allows us to devise a two-scale propagation scheme for the statistical weights of subchains of the entangled chain. The latter is used to calculate local volume fractions for each chemical type of Kuhn segments in entangled chains, thus determining the self-consistent potential.
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