Molecular Dynamics of Topological Barriers on the Crystallization Behavior of Ring Polyethylene Melts with Trefoil Knots

Abstract

Topological barriers in ring polyethylene (PE) melts of trefoil knots inhibit crystallization due to self-entanglement, as confirmed by united atom molecular dynamics (UAMD) simulations. In this study, we clarified the decrease in the topological barriers of self-entangled knots with increasing polymer chain length (N) and the localization of the knotted segments in the noncrystallized region. In the UAMD simulations, isothermal crystallization processes were performed at T = 300 K for the trefoil knots using a crystallization time t IC = 200 ns. Here, the trefoil knot gives the simplest nontrivial topology with nonzero crossing number. Crystallization was not observed in trefoil PE knots for N ≤ 120; however, crystallization did take place in the ring PE melt of the trivial knot with trivial topology and zero minimal crossing number. For N = 140, suppression of the growth of a crystalline phase (i.e., the polycrystalline phase) was observed in the trefoil PE melts, whereas such suppression was not detected in the trivial PE melts. In contrast, no significant differences in the crystallization behaviors of the trefoil and trivial PE melts were observed at N = 200. These results indicated that the topological barriers decreased with increasing N. Furthermore, to investigate the relationship between the chain conformation and degree of local crystallization, we developed a new mathematical method for searching the knotted segment of a trefoil knot in a crystallized trefoil PE melt. We found that trefoil knots with large subloops (“large-leaves”) exhibited localization of the knotted segment. In addition, the large leaves of the localized knots dominated in the crystallized region, and the knotted segments of the localized knots were located mainly in the noncrystallized region.

Effects of Trefoil Knots on the Initiation of Polymer Crystallization

“…16 Hagita et al indicated that the shortened segment of a knot in a ring polymer hinders crystallization, and this retardation vanishes with the increase of chain lengths. 17 A trefoil knot is the simplest nontrivial knot projected on a plane with the minimum three crossings. 18 Molecular simulations have demonstrated that the trefoil knots are dominant among the various kinds of topological intrachain knots in polymer single chains 19−21 as well as in melt chains.…”

“…During polymer crystallization, the topological constraints of intrachain knots and interchain entanglements will influence the conformational changes of flexible long-chain polymers. So far, the constraint effects of interchain entanglement on polymer crystallization have been extensively investigated, − but the constraint effects of intrachain knots on polymer crystallization received little attention. − De Gennes proposed that crystallization will reel in the chain and thus tighten the knots . Saitta and Klein reported that the knots enhance local density fluctuations for intramolecular crystal nucleation during stretching of a single polymer chain .…”

“…Saitta and Klein reported that the knots enhance local density fluctuations for intramolecular crystal nucleation during stretching of a single polymer chain . Hagita et al indicated that the shortened segment of a knot in a ring polymer hinders crystallization, and this retardation vanishes with the increase of chain lengths . A trefoil knot is the simplest nontrivial knot projected on a plane with the minimum three crossings .…”