Upsurge of Spontaneous Knotting in Polar Diblock Active Polymers

Spontaneous formation of knots in long polymers at equilibrium is inevitable but becomes rare in sufficiently short chains. Here, we show that knotting increases by orders of magnitude in diblock polymers having 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 nonmonotonic behavior to the competition between the rate of knot formation and the knot's lifetime. These findings suggest a nonequilibrium mechanism to generate entangled filaments at the nano- and microscales.