Scattering functions of knotted ring polymers

TL;DR

This study investigates how the topology of knotted ring polymers influences their scattering functions by simulating Gaussian polygons with various knots, revealing characteristic differences in their scattering profiles.

Contribution

It provides the first detailed simulation-based analysis of scattering functions for knotted Gaussian ring polymers with specific topologies.

Findings

Different knots produce distinct Kratky plots.

Characteristic properties correlate with mean square radius of gyration.

Simulation results align with theoretical expectations.

Abstract

We discuss the scattering function of a Gaussian random polygon with N nodes under a given topological constraint through simulation. We obtain the Kratky plot of a Gaussian polygon of N=200 having a fixed knot for some different knots such as the trivial, trefoil and figure-eight knots. We find that some characteristic properties of the different Kratky plots are consistent with the distinct values of the mean square radius of gyration for Gaussian polygons with the different knots.