A. Rosa, E. Orlandini, L. Tubiana and C. Micheletti
Structure and dynamics of ring polymers: entanglement effects because of solution density and ring topology
Macromolecules, 2011, 44 , 8668-8680
Link to arXiv preprint ,
Link to online article
Abstract
The effects of entanglement in solutions and
melts of unknotted ring polymers have been addressed by several
theoretical and numerical studies. The system properties have been
typically profiled as a function of ring contour length at fixed
solution density. Here, we use a different approach to investigate
numerically the equilibrium and kinetic properties of solutions of
model ring polymers. Specifically, the ring contour length is
maintained fixed, while the interplay of inter- and intra-chain
entanglement is modulated by varying both solution density (from
infinite dilution up to $\approx$ 40% volume occupancy) and ring
topology (by considering unknotted and trefoil-knotted chains). The
equilibrium metric properties of rings with either topology are found
to be only weakly affected by the increase of solution density. Even
at the highest density, the average ring size, shape anisotropy and
length of the knotted region differ at most by 40% from those of
isolated rings. Conversely, kinetics are strongly affected by the
degree of inter-chain entanglement: for both unknots and trefoils the
characteristic times of ring size relaxation, reorientation and
diffusion change by one order of magnitude across the considered range
of concentrations. Yet, significant topology-dependent differences in
kinetics are observed only for very dilute solutions (much below the
ring overlap threshold). For knotted rings, the slowest kinetic
process is found to correspond to the diffusion of the knotted region
along the ring backbone.