Entangled Polymer Rings in 2D and Confinement

TL;DR

This paper investigates the statistical mechanics of entangled polymer loops in 2D with obstacles, revealing a collapse transition to branched polymers characterized by specific scaling laws.

Contribution

It introduces a mean field theory for polymer loops in 2D obstacle environments and demonstrates a collapse transition to branched structures with new scaling behavior.

Findings

Polymer loops undergo a collapse transition in 2D obstacle environments.

The collapsed state is a randomly branched polymer with specific scaling laws.

The effective theory uses the projected area as a key collective variable.

Abstract

The statistical mechanics of polymer loops entangled in the two-dimensional array of randomly distributed obstacles of infinite length is discussed. The area of the loop projected to the plane perpendicular to the obstacles is used as a collective variable in order to re-express a (mean field) effective theory for the polymer conformation. It is explicitly shown that the loop undergoes a collapse transition to a randomly branched polymer with $R\propto lN^\frac{1}{4}$.