Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA.
Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA.
J Chem Phys. 2019 Sep 21;151(11):114905. doi: 10.1063/1.5113595.
Polymer crystals grown from melts consist of alternating lamellar crystalline regions and amorphous regions. We study the statistics of ties: chains which bridge the adjacent lamellae, loops: chains which come out of one lamella and enter back into the same lamella before reaching the other lamellae, and tails: chains which end in an amorphous region. We develop a theory to calculate the probabilities of formation of ties, loops, and tails with consideration of finite chain length and cooperative incorporation of a chain into multiple lamellae. The results of our numerical calculations based on a field-theoretic formalism show that the fraction of ties increases with increasing chain length, and it decreases with increasing interlamellar separation. In the limiting case of an infinite chain confined between only two walls, we recover the classical results of the gambler's ruin model. We show that the density anomaly encountered in previous theories is avoided naturally in the present theory without forcing the majority of stems to form tight loops. The derived results on the probability of tie chains in the amorphous regions are pertinent to the mechanical properties of semicrystalline polymers.
从熔体中生长的聚合物晶体由交替的层状晶区和非晶区组成。我们研究了连接的统计：连接相邻层片的链，环：从一个层片出来并在到达另一个层片之前重新进入同一层片的链，以及尾部：在非晶区结束的链。我们发展了一种理论，考虑到有限链长和链的协同掺入多个层片中，来计算连接、环和尾部的形成概率。基于场论形式主义的数值计算结果表明，连接的分数随着链长的增加而增加，随着层间距的增加而减小。在仅由两个壁限制的无限链的极限情况下，我们恢复了赌徒破产模型的经典结果。我们表明，在不强制大多数茎形成紧密环的情况下，本理论自然避免了以前理论中遇到的密度异常。在非晶区中连接链的概率的推导结果与半晶聚合物的力学性能有关。
