Re-orientational dynamics of ring polymers in dilute solutions

Advances in controlled polymerization have enabled the synthesis of mechanically interlocked polymers like molecular knots and linear[n]catenane. These aesthetic macromolecules with unique topological constraints in the form of mechanical bonds are well known for their fascinating transport and rheological properties in the development of molecular machines and in knotted protein dynamics in biological applications. The diffusion dynamics of such macromolecular structures with large internal degrees of freedom are generally studied by using an equivalent size parameter, i.e., hydrodynamic radius, defined using Zimm theory. Although diffusion rates are expected to depend strongly on the molecular topological constraints in macromolecules, their explicit effects on translational and reorientational dynamics are still unknown. Here, we perform an in silico study on the diffusion dynamics of seven topologically distinct polymer chains in the limit of infinite dilution using multi-particle collision dynamics. The modeled polymers are linear, ring, linear[2]catenane, trefoil knot, linear[3]catenane, cyclic[3]catenane, and Borromean ring. The molecular weights of these macromolecules are selected such that the resulting hydrodynamic radius is approximately equal to each other. We show that while the translational diffusion coefficients of these topologically distinct polymer chains are approximately equal to each other in agreement with the Zimm theory, there are significant differences among the values of the corresponding rotational diffusion coefficients. We show that the presence of mechanical bonds in the polymer chains slows down the rotational diffusion significantly, thus suggesting the role of molecular topology on reaction kinetics of macromolecules.