Linear Elasticity of DNA Hydrogels as a Function of DNA Nanostar Valence

Crosslink valence, or the number of network strands that connect at a junction, is a key structural feature of hydrogel networks. To better understand the effect of crosslink valence on network mechanics, we measure the linear, frequency-dependent elastic response of hydrogels made of DNA nanostars of valence f = {4, 5, 6} using bulk rheology. A DNA nanostar (DNAns) is a cross-linking structure of defined valence that self-assembles when a solution of partially-complementary DNA strands is slowly cooled from near boiling to room temperature. When designed with short, self-complementary sequences at one end of each strand, DNAns experience temperature-dependent binding interactions which support network formation. When the time scale of deformation is shorter than the lifetime of the binding interactions, the storage modulus (G') of the DNAns hydrogel exceeds the loss modulus (G'') and plateaus to a constant value G'_p. For all f, G'_p scales with DNAns concentration to a power 1 < x < 2, suggesting that the hydrogel is a flocculated fractal network rather than a cross-linked polymer network. We report the fractal dimension of hydrogels made from DNAns of different valence, and compare the magnitude of G'_p to theoretical predictions.