Polymer Knots in Thin Films: Thickness Dependence, Local Effects, and Stiffness

We study how confinement affects topology and conformations in polymer films of varying thickness $h$. The knotting probability exhibits a maximum at intermediate thicknesses near the bulk radius of gyration $h\approx R_{\mathrm{g},\mathrm{b}\mathrm{u}\mathrm{l}\mathrm{k}}$, vanishes at small $h$ and approaches bulk values for large $h$. Close to walls, the entanglement length increases monotonically and conformations become flatter. A layer-resolved analysis of structural and topological properties allows us to reconstruct the explicit thickness dependencies by integrating layer-resolved properties of a thick film.