Molecular shape transitions driven by an external force: the case of polymer chains with transient knotted loops

We study the simulated relaxation behaviour of grafted polyethylene with transient topological constraints. We employ a "soft" steered molecular dynamics algorithm, whereby chain stress is introduced by a sequence of stretchings/compressions at the free (nongrafted) end of the chain. Each bond perturbation is allowed to dissipate within the chain using constrained molecular dynamics, before the next perturbation is applied. Using a knotted-loop as a model for transient entanglement, we show the occurrence of a range of shape transitions that are not visible in the mean molecular size. During the stretching phase, the formation of rigid and tight knotted loops can be recognized by the variation in entanglement complexity or the local compactness. We show that the stress due to stretching can be removed reversibly during the compression phase, eliciting the delocalization of even very tight knots. We also find that a tight knot is still marginally diffusive along the chain whenever the external stretching couples to chain torsions.