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Unconcatenated and unknotted polymer rings (see panel (a) of the figure) in the melt are subject to strong interactions with neighboring chains due to the presence of topological constraints. We suppose that the rings are not allowed to turn into knotted (not shown) or concatenated configurations (bottom of panel (a)). Basically, due to this non-linkage constraint rings in semi-dilute solutions and melts have been argued to be more compact than gaussian chains.[1,2]
The panel (b) of the figure shows a single ring polymer - a so-called "lattice animals" - in a network of fixed topological obstacles (squares) of mean distance dt. The topological constraints imposes strongly entangled and compact ring conformations. Melts of rings have been argued by our visiting fellow S. Obukhov to behave effectively like these "lattice animals".[2]
We have investigated the interplay of topological constraints and (specifically) the persistence length of ring polymers in their own melt by means of dynamical Monte Carlo simulations of a standard three dimensional lattice model.[3,4,5] We ask whether our results are consistent with an chain length regime where the rings behave like lattice animals with topological constraints imposed self-consistently by neighbouring rings and provide evidence for an additional characteristic length scale dt ~ N 0. Tuning the persistence length provides an efficient route to increase the ring overlap required for this mean-field picture to hold: The effective Flory exponent for the ring size decreases down to 1/3 with increasing chain stiffness.