Upsurge of spontaneous knotting in polar diblock active polymers

TL;DR

This study demonstrates that active polar diblock polymers exhibit a significant increase in spontaneous knotting and complexity at equilibrium, with a non-monotonic dependence on the fraction of self-propelled monomers, revealing a non-equilibrium mechanism for filament entanglement.

Contribution

It uncovers how activity in diblock polymers enhances knot formation and complexity, identifying an optimal activity level and elucidating the underlying mechanisms.

Findings

Knotting increases with activity in diblock polymers.

Optimal activity level maximizes knot complexity.

Non-monotonic relationship between activity and knot formation.

Abstract

Spontaneous formation of knots in long polymers at equilibrium is inevitable but becomes rare in sufficiently short chains. Here, we show that knotting and knot complexity increase by orders of magnitude in diblock polymers with a fraction $p$ of self-propelled monomers. Remarkably, this enhancement is not monotonic in $p$ with an optimal value independent of the monomer's activity. By monitoring the knot's size and position we elucidate the mechanisms of its formation, diffusion, and untying and ascribe the non-monotonic behaviour to the competition between the rate of knot formation and the knot's lifetime. These findings suggest a non-equilibrium mechanism to generate entangled filaments at the nano-scale.