  Blends of polymers of different topologies, such as ring and supercoiled,
naturally occur in biology and often exhibit emergent viscoelastic properties
coveted in industry. However, due to their complexity, along with the
difficulty of producing polymers of different topologies, the dynamics of
topological polymer blends remains poorly understood. We address this void by
using both passive and active microrheology to characterize the linear and
nonlinear rheological properties of blends of relaxed circular and supercoiled
DNA. We characterize the dynamics as we vary the concentration from below the
overlap concentration c* to above (0.5c* to 2c*). Surprisingly, despite working
at the dilute-semidilute crossover, entanglement dynamics, such as
shear-thinning, elastic plateaus, and multiple relaxation modes, emerge.
Finally, blends exhibit an unexpected sustained elastic response to nonlinear
strains not previously observed even in well-entangled linear polymer
solutions.
