Length-scale dependent anomalous diffusion regimes in associative protein hydrogels*

Associative polymer gels are of interest as tunable, responsive materials for biomedical and soft robotics applications. Although theories can describe the effect of crosslink reversibility on network viscoelasticity, diffusion of chains through the network is poorly understood due to the complex interplay between sticker association and strand relaxation. Here, we use forced Rayleigh scattering and neutron spin echo to study self-diffusion in model coiled-coil protein hydrogels over a range of 8 decades of length-squared. We show the first experimental evidence for multiple diffusion regimes spanning from the submolecular to the Fickian, including anomalous caging and superdiffusive regimes, which depend on the concentration and length scale probed. Interpreting these results in the context of Brownian dynamics simulations allows characterization of various diffusive modes and molecular parameters (e.g., sticker dissociation and strand relaxation time) governing transitions between these regimes. Finally, tracer diffusion of single coiled-coils is measured in a matrix of proteins containing 4 such domains to link quantitatively single-sticker dynamics to overall chain diffusion rates at various length scales.