Unifying the Dynamics of Viscoelastic Liquids across the Complex Coacervation Phase Diagram: Time–Polyelectrolyte–Salt Superposition

The dynamics and structure were investigated for polyelectrolyte-rich liquids across the high-salt region of the complex coacervation phase diagram of high molecular weight poly(4-styrenesulfonate), PSS, and poly(diallyldimethylammonium), PDADMA. The total concentration of polyelectrolytes ( W PE ) was increased at different added KBr concentrations ([KBr]) to obtain liquid complex coacervates (CC) and single-phase, saline polyelectrolyte solutions. The dynamic response of these entangled polymer liquids was found to be self-similar at each [KBr], allowing a time–polyelectrolyte superposition using only a polyelectrolyte concentration-dependent horizontal shift factor, a P . This self-similarity was further found among all the samples at different [KBr], allowing the construction of a universal master curve unifying the dynamics of all the samples by applying a second, salt-dependent horizontal shift factor, a S . The CC dynamics were found to have a very strong dependence on the experimentally determined PE concentration with a P ∝ W PE,real 11, while salty solutions of noninteracting PE behaved as polymers in good solvent with a P ∝ W PE,real 4.1 . The extreme scaling in the case of the CC defies the predictions for entangled associating polymers, probably due the large number of stickers per chain. Despite the absence of effective stickers in the salty solutions of fully doped polyelectrolytes, they can mimic the viscoelastic response of the CC up to the solubility limit of the PE. We called these materials quasi -complex coacervates ( quasi -CC) to distinguish them from both CC and individual-polyelectrolyte solutions. Small-angle X-ray scattering revealed that PSS/PDADMA CC, their quasi -CC, and a PSS solution at the same total polymer and salt concentration all have different nanostructures. Unifying the dynamics of viscoelastic liquids across the high-salt region of the phase diagram, time–PE–salt superposition extends the classical time–salt and time–temperature superposition principles to PE systems, marking a step forward in understanding associative polymer dynamics.