Externally steered relaxation of tight polyethylene tangles with different initial knot topologies

Using single-molecule manipulations or sudden changes in solvent, it is possible to introduce knotted-loops (or "tangles") in open linear polymers. It is still unclear how these tangles relax, and in particular, whether it is possible to trap knots locally by adopting very compact loop conformations. Here, we use steered molecular dynamics simulations to study a highly stressed polyethylene chain with three different knot topologies. Starting from stressed configurations, unknotting events are recognized as leading to sudden transitions in overcrossing number. By means of a soft compressing external force, we show that: (1) tangles with different complexities can be unknotted and (2) the potential energy decreases in a way that suggests that a similar relaxation mechanism might be at work for all the tested loop topologies.