Communication: A comparison between the solution properties of knotted ring and star polymers

We computationally investigate the good solvent solution properties of knotted ring and star polymers by combining molecular dynamics (MD) simulation and path-integral calculations. We consider knotted rings having a minimal crossing number m _c in the range, 0 ≤ m _c ≤ 9, and star polymers having a range of f star arms, 2 ≤ f ≤ 20, attached to a common core monomer particle. After generating configurational ensembles of these polymers by MD, we use the path-integration program ZENO to calculate basic configurational properties, i.e., radius of gyration, hydrodynamic radius, intrinsic viscosity, as well as fluctuations in these properties. Our simulations indicate that the configurational properties of knotted rings and star polymers in solution show a similar decrease with increasing m _c and f. Moreover, fluctuations in these properties also decrease with increasing topological complexity. Our findings should be helpful in polymer characterization and more generally for understanding the role of polymer topology in polymer material properties.