Chain Size and Knots of Ring Polymers in All-Crossing and Intra-Crossing Melts

TL;DR

This paper uses simulations to study how ring polymers behave in different systems, focusing on their size and knotting patterns.

Contribution

The study reveals how interchain constraints affect knotting probability and derives a new scaling relationship for ring polymer size.

Findings

Interchain constraints increase knotting probability but do not change the scaling of knotting with chain length.

The derived scaling relationship for ring polymer size is R~N1/6 in intra-crossing systems.

Knotted ring polymers show different scaling exponents based on knotting complexity.

Abstract

Using dynamic Monte Carlo simulations based on the bond-fluctuation model, we systematically investigated the size and knots of ring polymers in all-crossing systems and intra-crossing systems. Our results demonstrate that the interchain constraint can increase the knotting probability, but does not alter the scaling relationship between knotting probability and chain length for ring polymers in melts. Having established that, we derived the interchain constraint contribution to the free energy of ring polymers in intra-crossing systems based on the knotting probability and obtained the scaling relationship between the size R and chain length N, i.e., R~N1/6. And, by calculating the mean-squared radius of gyration of ring polymers in intra-crossing systems, we validated these scaling results. Finally, we analyze the size of knotted ring polymers with different types and compare corresponding scaling exponents for size versus chain lengths of ring polymers with different knotting complexities. These results provide fundamental insights into the static properties of ring polymers in melts.

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