Conformational statistics of randomly-branching double-folded ring polymers

TL;DR

This paper investigates the conformational behavior of double-folded ring polymers constrained by topology, relating their statistics to primitive tree models and analyzing distribution functions of spatial and contour distances.

Contribution

It extends previous tree statistics to the conformational analysis of double-folded rings under tight wrapping conditions, establishing connections between ring and tree exponents.

Findings

Relates ring statistics exponents to primitive tree exponents

Derives distribution functions for spatial and contour distances

Provides insights into the conformational properties of constrained ring polymers

Abstract

The conformations of topologically constrained double-folded ring polymers can be described as wrappings of randomly branched primitive trees. We extend previous work on the tree statistics under different (solvent) conditions to explore the conformational statistics of double-folded rings in the limit of tight wrapping. In particular, we relate the exponents characterizing the ring statistics to those describing the primitive trees and discuss the distribution functions $p(\vec r | \ell)$ and $p(L | \ell)$ for the spatial distance, $\vec r$, and tree contour distance, $L$, between monomers as a function of their ring contour distance, $\ell$.