Polymer threadings and rigidity dictate the viscoelasticity and nonlinear relaxation dynamics of entangled ring-linear blends and their composites with rigid rod microtubules

Mixtures of polymers of varying topologies and stiffnesses display complex emergent rheological properties that often cannot be predicted from their single-component counterparts. For example, entangled blends of ring and linear polymers have been shown to exhibit enhanced shear thinning and viscosity, as well as prolonged relaxation timescales, compared to pure solutions of rings or linear chains. These emergent properties arise in part from the synergistic threading of rings by linear polymers. Topology has also been shown to play an important role in composites of flexible (e.g., DNA) and stiff (e.g., microtubules) polymers, whereby rings promote mixing while linear polymers induce de-mixing and flocculation of stiff polymers, with these topology-dependent interactions giving rise to highly distinct rheological signatures. To shed light on these intriguing phenomena, we use optical tweezers microrheology to measure the linear and nonlinear rheological properties of entangled ring-linear DNA blends and their composites with rigid microtubules. We show that the linear viscoelasticity is primarily dictated by the microtubules at lower frequencies, but their contributions become frozen out at frequencies above the DNA entanglement rate. In the nonlinear regime, we reveal that mechanical response features, such as shear thinning, stress softening and multi-modal relaxation dynamics are mediated by entropic stretching, threading, and flow alignment of entangled DNA, as well as forced de-threading, disentanglement, and clustering. The contributions of each of these mechanisms depend on the strain rate as well as the entanglement density and stiffness of the polymers, leading to non-monotonic rate dependences of mechanical properties that are most pronounced for highly concentrated ring-linear blends rather than DNA-MT composites.