Dynamics of ring polymers in the presence of fixed obstacles

The configurations and dynamics of a polymer ring (R) inside a strongly crosslinked polymer gel (G) are discussed and compared to those of linear (L) and branched (B) polymers in G. R is not topologically connected to G in the sense that the contour line of R can be reduced to a point without crossing any of the chains of G. This topological requirement leads to the correspondence between the configurations of R in G and the set of lattice trees (randomly branched polymers). But the dynamics of R in G is much faster than that of entangled B, and is similar to the dynamics of entangled L.