Disentanglement of Two Single Polymer Chains: Contacts and Knots

Understanding the consequences of the noncrossing constraint is one of the remaining challenges in the physics of walks and polymers. To address this problem, we performed molecular simulations for the separation of only two initially connected, overlapping polymer chains with interactions tuned such that they are nearly random walks. The separation time for a configuration strongly correlates with the number of monomer contacts between both chains. We obtain a broad distribution of separation times with a slowly decaying tail. Knots only play a role for those configurations that contribute to the tail of the distribution. In contrast, when starting from the same initial configuration but allowing for chain crossings, separation is qualitatively faster and the time distribution narrow. The simulation results are rationalized by analytical theory. A theory of contacts based on polymer fractality and criticality is presented, along with the expected effects of knots.