Self-Similar Conformations and Dynamics in Entangled Melts and Solutions of Nonconcatenated Ring Polymers.
Self-Similar Conformations and Dynamics in Entangled Melts and Solutions of Nonconcatenated Ring Polymers.
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DOI：
10.1021/acs.macromol.5b02319
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发表时间：
2016
期刊：
影响因子：
5.5
通讯作者：
Rubinstein M
中科院分区：
文献类型：
--
作者：
Ge T;Panyukov S;Rubinstein M
建立了非级联缠结环聚合物自相似构象和动力学的标度模型。拓扑约束迫使这些环状聚合物形成分形维数为df = 3的紧凑构象，我们称之为分形多环小球（FLG）。这个结果是基于猜想，在所有长度尺度上的环的子部分的重叠参数是相同的，并且等于Kavassalis-Noolandi数OKN 10-20。纠缠环的动力学是自相似的，并且随着尺寸不断增加的环在各自的扩散时间逐渐重新排列而继续进行。与较小的重排环相关的拓扑约束通过增加有效摩擦系数来影响较大环的动力学，但对限制较大环的纠缠管没有影响。因此，定义为相关拓扑约束之间的平均间距的管直径随着时间t而增加，导致“管膨胀”。在分子动力学模拟中的原始路径的分析表明，一个完整的管膨胀与管直径的顺序的时间依赖性的特征环的大小。时间t处的特征环被定义为在时间t期间扩散了等于其尺寸的距离的环形部分。我们推导出动态标度指数的纠缠环的分形维数和基本的原始路径和一个参数表征管膨胀的程度。结果再现了一个单一的非级联纠缠环的不同动力学模型的预测。我们证明了传统的单环模型推广到多环动力学是不自洽的，并开发了一个FLG模型与自洽的多环动力学和完整的管膨胀。这个自洽的FLG模型预测，非级联缠结环聚合物的最长弛豫时间与它们的聚合度N成比例关系，为τrelax ~ N7/3，而这些环的扩散系数成比例关系，为D3 d ~ N−5/3。对于环的缠结溶液和熔体，我们预测幂律应力松弛函数G（t）~ t−3/7在t < τ松弛时没有橡胶平台，相应的粘度与聚合度N的标度为η ~ N4/3。这些理论预测与最近的计算机模拟结果吻合得很好，并与非级联纠缠环熔体的实验结果一致。
A scaling model of self-similar conformations and dynamics of nonconcatenated entangled ring polymers is developed. Topological constraints force these ring polymers into compact conformations with fractal dimension df = 3 that we call fractal loopy globules (FLGs). This result is based on the conjecture that the overlap parameter of subsections of rings on all length scales is the same and equal to the Kavassalis–Noolandi number OKN ≈ 10–20. The dynamics of entangled rings is self-similar and proceeds as loops of increasing sizes are rearranged progressively at their respective diffusion times. The topological constraints associated with smaller rearranged loops affect the dynamics of larger loops through increasing the effective friction coefficient but have no influence on the entanglement tubes confining larger loops. As a result, the tube diameter defined as the average spacing between relevant topological constraints increases with time t, leading to “tube dilation”. Analysis of the primitive paths in molecular dynamics simulations suggests a complete tube dilation with the tube diameter on the order of the time-dependent characteristic loop size. A characteristic loop at time t is defined as a ring section that has diffused a distance equal to its size during time t. We derive dynamic scaling exponents in terms of fractal dimensions of an entangled ring and the underlying primitive path and a parameter characterizing the extent of tube dilation. The results reproduce the predictions of different dynamic models of a single nonconcatenated entangled ring. We demonstrate that traditional generalization of single-ring models to multi-ring dynamics is not self-consistent and develop a FLG model with self-consistent multi-ring dynamics and complete tube dilation. This selfconsistent FLG model predicts that the longest relaxation time of nonconcatenated entangled ring polymers scales with their degree of polymerization N as τrelax ~ N7/3, while the diffusion coefficient of these rings scales as D3d ~ N−5/3. For the entangled solutions and melts of rings, we predict power law stress relaxation function G(t) ~ t−3/7 at t < τrelax without a rubbery plateau and the corresponding viscosity scaling with the degree of polymerization N as η ~ N4/3. These theoretical predictions are in good agreement with recent computer simulations and are consistent with experiments of melts of nonconcatenated entangled rings.