The mobility and diffusivity of a knotted polymer : Topological deformation effect(2/2)

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 poly-mer, which characterizes the extent of the deformation, is increased, the mobility de-clines. A scaling analysis confirmed by simu-lations indicates that the deformation yields an extra contribution to the resistance æN as-sociated with a linear chain, áN -3/5 p 8/5 , 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. Neverthe-less, the confinement only slightly increases the friction coefficients æ and the internal friction constant á. Our numerical results for the Rouse model are qualitatively different from those anticipated on the basis of scaling arguments for the Zimm model