The mobility and diffusivity of a knotted polymer: Topological deformation effect

The effect of topological deformation on the mobility and diffusivity of a polymer chain in a good solvent is investigated by off-lattice dynamic Monte Carlo simulations. The topological deformation of the polymer is expressed through the knotted structure. The Nernst–Einstein relation is obeyed and thus the diffusivity is proportional to the mobility. As the crossing number of the knotted polymer, which characterizes the extent of the deformation, is increased, the mobility declines. A scaling analysis confirmed by simulations indicates that the deformation yields an extra contribution to the resistance ζN associated with a linear chain, αN−3/5p8/5, where N is the chain length and p is the length-to-diameter ratio associated with a maximum inflated knot. The mobility of the polymer chain is further reduced due to the confinement in a cylindrical tube. Nevertheless, the confinement only slightly increases the friction coefficients ζ and the internal friction constant α. Our numerical results for the Rouse model are qualitatively different from those anticipated on the basis of scaling arguments for the Zimm model.