Threading Dynamics of Ring Polymers in a Gel

We perform large scale three-dimensional molecu-lar dynamics simulations of unlinked and unknot-ted ring polymers diffusing through a background gel, here a three-dimensional cubic lattice. Tak-ing advantage of this architecture, we propose a new method to unambiguously identify and quan-tify inter-ring threadings (penetrations) and to re-late these to the dynamics of the ring polymers. We find that both the number and the persistence time of the threadings increase with the length of the chains, ultimately leading to a percolating net-work of inter-ring penetrations. We discuss the im-plications of these findings for the possible emer-gence of a topological jammed state of very long rings. Understanding the dynamical and rheological properties of solutions of long polymers is of pri-mary importance in several area of soft matter, ma-terial science and biophysics1. The dynamics of linear polymers in the melt is now understood us-ing the tube and reptation models2,3. These mod-els take advantage of the topological constraint represented by the non-crossability of the chains to describe the diffusion of the polymers along ∗To whom correspondence should be addresse