Topological effects in ring polymers (II): Influence of persistence length

Abstract

The interplay of topological constraints and 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) {\em lattice animals} in a self-consistent network of topological constraints imposed by neighbouring rings. Tuning the persistence length provides an efficient route to increase the ring overlap required for this mean-field picture to hold: The {\em effective} Flory exponent for the ring size decreases down to $\nu \stackrel{<}{\sim} 1/3$ with increasing persistence length. Evidence is provided for the emergence of one additional characteristic length scale $\dtop \propto N^0$, only weakly dependent on the persistence length and much larger than the excluded volume screening length $\xi$. At distances larger than \dtop 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.