PubMed2000
The interplay of topological constraints and the persistence length of ring polymers in their own melt is investigated by means of dynamical Monte Carlo simulations of a three-dimensional lattice model. We ask if the results are consistent with an asymptotically regime where the rings behave like (compact) lattice animals in a self-consistent network of topological constraints imposed by neighboring rings. 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 nu less, similar1/3 with increasing persistence length. Evidence is provided for the emergence of one additional characteristic length scale d(t) approximately N0, only weakly dependent on the persistence length and much larger than the excluded volume screening length xi. At distances larger than d(t) the conformational properties of the rings are governed by the topological interactions; at smaller distances rings and their linear chain counterparts become similar. (At distances smaller than xi both architectures are identical.) However, the crossover between both limits is intricate and broad, as a detailed discussion of the local fractal dimension (e.g., obtained from the static structure factor) reveals. This is due to various crossover effects which we are unable to separate even for the largest ring size (N=1024) presented here. The increased topological interactions also influence the dynamical properties. Mean-square displacements and their distributions depend crucially on the ring overlap, and show evidence of the existence of additional size and time scales. The diffusion constant of the rings goes down from effectively D(N) approximately N-1.22 for flexible rings with low overlap to D(N) approximately N-1.68 for strongly overlapping semiflexible rings.