Unified Entanglement Scaling for Flexible, Semiflexible, and Stiff Polymer Melts and Solutions
Unified Entanglement Scaling for Flexible, Semiflexible, and Stiff Polymer Melts and Solutions
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DOI：
10.1021/acs.macromol.9b02684
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发表时间：
2020-02-25
期刊：
影响因子：
5.5
通讯作者：
Milner, Scott T.
中科院分区：
文献类型：
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作者：
Milner, Scott T.
缠结长度 N-e 是所有缠结聚合物流体的关键参数，目前尚不存在全面的标度理论。我们有一些理论； Lin-Noolandi (LN) 论证预测柔性链的 N-e 缩放比例与聚合物熔体的数据一致。关于 N-e 如何取决于聚合物浓度存在争议，但与 LN 并不明显一致。莫尔斯标度描述了刚性链解的纠缠，与数据一致。 Everaers 提出了一个 ansatz，即 N-e 仅取决于弧长浓度，就好像链条是厚度消失的不可交叉的线一样。该模拟与珠弹簧链的模拟一致，但与 LN 不同，因为它对填充长度没有作用，而填充长度是 LN 缩放中的中心参数。我们提出了一种全面的标度理论，其中一个极限包括 LN，另一个极限包括螺纹 ansatz，并针对刚性链简化为莫尔斯标度。一个新的因素是，两条链之间最接近的距离通常由填充长度或链直径（以较大者为准）决定。如果链条足够柔韧且体积大，则包装长度是相关的；但对于没有侧组的加强型珠弹簧链，填料长度小于链直径，因此适用螺纹缩放。我们的方法呈现了所有体系中纠缠的一致物理图景，即两条链之间的近距离接触。对于解决方案，我们确定链段之间的纠缠概率，并一致地描述爱德华兹和半稀状态之间的交叉。
The entanglement length N-e is a key parameter for all entangled polymer fluids for which no comprehensive scaling theory yet exists. We have pieces of a theory; the Lin-Noolandi (LN) argument predicts N-e scaling for flexible chains that agrees with data on polymer melts. There are arguments for how N-e should depend on polymer concentration, but which are not obviously consistent with LN. Morse scaling describes entanglement for solutions of stiff chains, consistent with data. Everaers proposed an ansatz that N-e depends only on the arclength concentration, as if chains were uncrossable threads of vanishing thickness. This ansatz is consistent with simulations of bead-spring chains, but not with LN, as it has no role for packing length, the central parameter in LN scaling. We propose a comprehensive scaling theory that includes LN in one limit, thread ansatz in another, and reduces to Morse scaling for stiff chains. One new ingredient is that the typical distance of closest approach between two chains is governed by the packing length or chain diameter, whichever is larger. If a chain is sufficiently flexible and bulky, the packing length is relevant; but for stiffened bead-spring chains without side groups, the packing length is smaller than the chain diameter, so thread scaling applies. Our approach presents a consistent physical picture of entanglements in all regimes as close encounters between two chains. For solutions, we determine the entanglement probability between chain segments, and consistently describe the crossover between the Edwards and semidilute regimes.