  We measure the rheology of transient hydrogels comprised of a single type of
DNA nanostar that makes both strong and weak bonds. These gels exhibit
power-law frequency-dependence of their storage and loss moduli, with scaling
exponents that depend on the proportions of the two bonds. A diffusive
stress-relaxation model, in which the strong-bond sub-network relieves stress
by diffusing through an effective viscosity imposed by the weak bonds, explains
the scaling of their moduli. The model has implications for the fractal
dimensions of the strong-bond sub-network that are in good agreement with
measurements and makes testable predictions for the viscoelasticity of other
transient hydrogels. Overall, this work demonstrates the power of DNA
nanotechnology to decipher, and potentially rationally design, power-law
rheology.
