Testing the physics of knots with a Feringa nanoengine

TL;DR

This study uses a computational model to analyze how polymer loops connected to a nanoengine contract and fold, revealing scaling behaviors and knot localization properties in polymers.

Contribution

It introduces a scaling framework for polymer knot behavior under nanoengine constraints, supported by simulation data.

Findings

Polymer size and folding follow scaling predictions based on confinement.

Conformation data collapses when plotted against a specific scaling variable.

Knots exhibit weak localization along the polymer contour with an exponent around 0.78.

Abstract

We use the bond fluctuation model to study the contraction process of two polymer loops with $N$ segments that are connected each to the bottom and top part of a Feringa engine. The change in the size of the molecules as well as the folding of the two strands follows approximately scaling predictions that are derived by assuming that the strands are confined inside an effective tube. Conformation data can be overlapped when plotting it as a function of $W_{\text{n}}N^{-1/4}$, where $W_{\text{n}}$ is the winding number of the two strands that is proportional to the number of blobs inside the ``knotted'' region of the molecule and $N$ is the degree of polymerization of the strands. Our data also supports a weak localization of the knots along the contour of a-thermal polymers with a localization exponent $t\approx0.78$.