Effects of Trefoil Knots on the Initiation of Polymer Crystallization

Long-chain polymers make dominant trefoil knots that could influence their crystallization behaviors. We performed dynamic Monte Carlo simulations of polymer crystallization to investigate the constraint effects of one or two trefoil knots on the initiation of crystallization by comparing their parallel results to zero knot, encompassing single chains in the dilute solutions, melt chains in the quiescent bulk phase, and melt chains in the stretching process. The results demonstrated that single chains hold relatively loose knots owing to the volume exclusion of knot monomers, and the constraint effects enhance the thermodynamic stability of crystal nuclei inside the knots to accelerate intramolecular crystal nucleation. In contrast, melt chains hold relatively tight knots owing to polymer interpenetration that screens off the volume exclusion of knot monomers, and the constraint effects retard their dominant intramolecular crystal nucleation due to both shortened segments inside and outside the knots. Meanwhile, the knots show much smaller effects on the dominantly intermolecular crystal nucleation in strain-induced polymer crystallization. In conclusion, the constraint effects of polymer knots mainly influence intramolecular rather than intermolecular crystal nucleation. Our observations shed light on the effects of polymer knots on crystallization behaviors.