A Comparison Between The Solution Properties of Knotted Ring and Star Polymers
Luis F. Vargas Lara, Beatriz Pazmino, Jack F. Douglas
We computationally investigate the solution properties of knotted flexible ring and star polymers by combining molecular dynamics simulation (MD) and path-integral calculations. In particular, we consider knotted rings having a minimal crossing number mc in the range, 0 \leq mc \leq 9, and star polymers having a range of f star arms, 2 \leq f \leq 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 mc and f. Moreover, fluctuations in these properties also decrease with increasing topological complexity, reflecting topological rigidification. The solution properties of stars are found to be similar to knotted rings having a knot complexity f \approx mc + 5. Our findings should be helpful in polymer characterization, and more generally for understanding the role of polymer topology on polymer material properties.