Freely Suspended Semiflexible Chains in a Strong Aligning Field: Simple Closed‐Form Solutions for the Small‐Angle Approximation,Macromolecular Theory and Simulations

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Freely Suspended Semiflexible Chains in a Strong Aligning Field: Simple Closed‐Form Solutions for the Small‐Angle Approximation
Macromolecular Theory and Simulations ( IF 1.8 ) Pub Date : 2020-08-11 , DOI: 10.1002/mats.202000049
Philipp A. Kloza ₁ , James A. Elliott ₁

Affiliation

A worm‐like chain model for a single, freely suspended semiflexible macromolecule with an aligning field of arbitrary coupling order is presented. Using a small‐angle approximation and Ginzburg–Landau theory, exact closed‐form solutions of the model are derived in the regime of a strong aligning field in arbitrary dimensions. Expressions for the mean cosine of the chain alignment angle, orientational order parameters, and the two‐point correlation function are found. As a corollary, the persistence length is confirmed as a valid threshold for rigid behavior of the chain. The theoretical results are validated with Monte Carlo simulations in two and three dimensions. It is shown that the solutions for the small‐angle approximation are within

0.1 %

of the simulated values for the exact model for chain‐field alignment angles θ ≲ 20°. As a practical application, the findings are applied to carbon nanotubes in an aligning electric field.

中文翻译：

在强对准场中自由悬挂的半柔性链：小角度逼近的简单封闭形式解决方案

提出了一个具有任意耦合级排列场的，自由悬浮的半柔性大分子的蠕虫状链模型。使用小角度近似和Ginzburg-Landau理论，可以在任意尺寸的强对准场状态下得出模型的精确封闭形式解。找到了链对齐角的平均余弦，方向顺序参数和两点相关函数的表达式。结果，持久长度被确认为链刚性行为的有效阈值。理论结果通过蒙特卡洛模拟在二维和三维上得到验证。结果表明，小角度近似的解在