Topological effects in ring polymers. II. Influence of persistence length

The interplay of topological constraints and the persistence length of ring polymers in their own melt is investigated by means of dynamical Monte Car lo simulations of a three-dimensional lattice model. We ask if the results are consistent with an asymptotically regime where the rings behove like (c ompact) lattice anumals, in a self-consistent network of topological constr aints imposed by neighboring rings. Tuning the persistence length provides an efficient route to increase the ring overlap required for this mean-fiel d picture to hold: The effective Flory exponent for the ring size decreases down to v less than or equal to 1/3 with increasing persistence length. Ev idence is provided for the emergence of one additional characteristic lengt h scale d,proportional to N-0, only weakly dependent on the persistence len gth and much larger than the excluded volume screening length xi. At distan ces larger than d, the conformational properties of the rings are governed by the topological interactions; at smaller distances rings and their linea r chain counterparts become similar. (At distances smaller than xi both arc hitectures are identical.) However, the crossover between both limits is in tricate and broad? as a detailed discussion of the local fractal dimension (e.g., obtained from the static structure factor) reveals. This is due to v arious crossover effects which we are unable to separate even for the large st ring size (N = 1024) presented here. The increased topological interacti ons 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 rind time scales. The diffusion consta nt of the rings goes down from effectively D(N)proportional to N-1.22 for f lexible rings with low overlap to D(N)proportional to N-1.68 for strongly o verlapping semiflexible rings.