Dynamics of liquid coacervates formed by oppositely charged polyelectrolytes

Mixtures of oppositely charged polyelectrolytes can undergo a phase separation to form a polymer rich phase, called a coacervate, and a polymer depleted phase. The polymer rich phase can be a soft, viscous liquid, or a solid complex. Both types have drawn much attention in the literature due to their technological applications as well as their role in biological systems. Models have been developed to predict thermodynamic properties of the coacervates. However, much less attention has been given to modeling coacervate dynamics. We develop a scaling theory to predict the dynamics of entangled and unentangled asymmetric liquid coacervates formed from oppositely charged polyelectrolytes. The theory predicts the scaling of properties such as the relaxation modulus and shear viscosity of the coacervate, and the diffusivity of the polyelectrolyte chains. The scaling theory highlights the different dynamic regimes of the system, and how the dynamic properties can be tuned by experimentally controllable parameters such as the degree of polymerization or the number density of charges along the polyelectrolyte backbone, providing a means with which to rationally design dynamic properties for technological applications.