Theory of statistics of ties, loops, and tails in semicrystalline polymers
Theory of statistics of ties, loops, and tails in semicrystalline polymers
复制标题
DOI：
10.1063/1.5113595
复制
发表时间：
2019-09-21
影响因子：
4.4
通讯作者：
Muthukumar, Murugappan
中科院分区：
文献类型：
--
作者：
Adhikari, Sabin;Muthukumar, Murugappan
从熔体中生长的聚合物晶体由交替的层状结晶区和无定形区组成。我们研究的统计关系：链桥接相邻的层，环：链出来的一个层，并进入同一层之前到达其他层，和尾巴：链结束在一个无定形区域。我们发展了一个理论来计算的概率形成的领带，环，和尾巴考虑有限的链长度和合作纳入一个链到多个lameries。我们的数值计算结果的基础上的场论形式主义表明，该分数的领带增加的链长，并减少与增加层间分离。在无限长链仅限于两壁之间的极限情况下，我们恢复了赌徒破产模型的经典结果。我们发现，在以前的理论中遇到的密度异常，自然避免在本理论中，而不迫使大多数的茎形成紧密的循环。在无定形区域的概率的结链的衍生结果是有关的半结晶聚合物的机械性能。
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.