Testing the physics of knots with a Feringa nanoengine

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 parts 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 ${W}_{\text{n}}{N}^{\ensuremath{-}1/4}$, 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 support a weak localization of the knots along the contour of flexible cyclic athermal polymers with a localization exponent $t\ensuremath{\approx}0.78$.