Dynamics of a Ring Polymer in a Gel

Abstract

We present a simple scaling theory of the dynamics of a ring polymer in a gel. In the absence of excluded volume interactions, we predict that the translational diffusion coefficient $D$ varies with the molecular weight $M$ as $D\ensuremath{\sim}{M}^{\ensuremath{-}2}$ and the longest relaxation time $T$ scales as $T\ensuremath{\sim}{M}^{\frac{5}{2}}$. The results of numerical simulations support these findings.