  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.
