  Ring polymers remain a major challenge to our current understanding of
polymer dynamics. Experimental results are difficult to interpret because of
the uncertainty in the purity and dispersity of the sample. Using both
equilibrium and non-equilibrium molecular dynamics simulations we have
systematically investigated the structure, dynamics and rheology of perfectly
controlled ring/linear polymer blends with chains of such length and
flexibility that the number of entanglements is up to about 14 per chain, which
is comparable to experimental systems examined in the literature. The smallest
concentration at which linear contaminants increase the zero-shear viscosity of
a ring polymer melt of these chain lengths by 10% is approximately one-fifth of
their overlap concentration. When the two architectures are present in equal
amounts the viscosity of the blend is approximately twice as large as that of
the pure linear melt. At this concentration the diffusion coefficient of the
rings is found to decrease dramatically, while the static and dynamic
properties of the linear polymers are mostly unaffected. Our results are
supported by a primitive path analysis.
