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

Abstract

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.

Dynamical Monte Carlo study of equilibrium polymers. II. The role of rings

“…In line with our previous work on conventional polymers studied in Ref. 21, we find b g0 /bϷ0.3 and b g1 /bϷ1/ͱ6. This result holds again for both simulation methods.…”

“…The found values for b are essentially identical to what was obtained previously for monodisperse linear polymers. 16,21 In a similar fashion, one may define and measure the prefactors b g0 and b g1 from the radii of gyration R g0 and R g1 . In line with our previous work on conventional polymers studied in Ref.…”

Density effects in entangled solutions of linear and ring polymers

“…In order to maximize mutual chain interpenetration at relatively moderate chain length [10] and hence reduce the computational effort, we have introduced an additional bending energy penalty between consecutive triplets of neighbouring beads along the chain in order to control polymer stiffness:…”

“…More recently a new class of systems has emerged and started receiving similar systematic attention: entangled solutions and melts of unconcatenated and unknotted circular (ring) polymers [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Why are ring polymers so special and, as we will shortly see, challenging?…”

Confinement-Induced Glassy Dynamics in a Model for Chromosome Organization

“…Although the origin of chromosomal territories is controversial because equilibrium polymer configurations with many loops naturally produce segregated domains as well [14,15], a major non-equilibrium effect, glassy dynamics of the genome under strong confinement, should not be overlooked from a contributing factor in chromosome folding. The relaxation time of a polymer via disentanglement [16] (τ rep ∼ N 3 [12,13,17,18]) could be far longer, effectively permanent for higher organisms, than the cell cycle time (τ cell ) [12,13] for a large N .…”