Time-dependent knotting of agitated chains

Abstract

Agitated strings serve as macroscale models of spontaneous knotting, providing valuable insight into knotting dynamics at the microscale while allowing explicit analysis of the resulting knot topologies. We present an experimental setup for confined macroscale knot formation via tumbling along with a software interface to process complex knot data. Our setup allows characterization of knotting probability, knot complexity, and knot formation dynamics for knots with as many as 50 crossings. We find that the probability of knotting saturates below 80% within 100 s of the initiation of tumbling and that this saturation probability does not increase for chains above a critical length, an indication of nonequilibrium knot-formation conditions in our experiment. Despite the saturation in knot formation, we show that longer chains, while being more confined, will always tend to form knots of higher complexity since the free end can access a greater number of loops during tumbling.