Double-Semidilute Liquid and Gel Coacervates formed by Oppositely Charged Polyelectrolytes

We develop a scaling model for two qualitatively different classes of coacervates formed by oppositely charged polyelectrolytes. The weakly interacting coacervates are liquids with electrostatic interaction energy per charge less than thermal energy kT. The strongly interacting coacervates are gels with cross-links formed by ion pairs of opposite charges attracting each other with energy stronger than kT. The liquid coacervate is a double-semidilute solution with two correlation lengths and two qualitatively different types of conformations of weaker and stronger charged polyelectrolytes. Weaker charged chains form a screening “coat” around stronger charged chains. The conformations of weaker charged chains in this screening coat is analogous to a semidilute solution of uncharged polymers. The conformation of stronger charged polyelectrolytes in liquid coacervates is similar to their conformation in semidilute polyelectrolyte solutions. The strongly interacting coacervates form bottlebrush gels for longer polyelectrolytes with higher charge density and star-like gels for shorter higher charge desity chains.