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

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 tIC = 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.