(332b) Complex Coacervation in Polyelectrolyte Brushes

We develop a scaling theory of interaction and complex coacervation between mobile linear polyelectrolytes (PEs) and planar brush of the oppositely charged PEs. In contrast to coacervation in bulk, coacervation in brush is primarily driven by the entropy gain due to the counterion release. This is due to the planar geometry of the brush, that retains counterions inside itself in the free (non-complexed) state. At moderate grafting density and low salt concentration, brush and free counterions form the thin layer of polyelectrolyte complex coacervate, whose structure and density are identical to that of the macroscopic coacervates phase. At higher grafting density, mobile chains penetrate the brush to form a surface complex denser than macroscopic coacervate. Its structure is controlled by the balance between entropic elasticity and nonelectrostatic short-range interactions, so brush can be considered quasi-neutral. When salt concentration exceeds the theoretically predicted threshold and Coulomb interactions are sufficiently screened, guest polyions do not penetrate the brush and it remains free. Complexation-induced lateral microphase separation and formation of the finite-size clusters of the surface interPE complex is predicted for brushes with moderately low grafting density. Different scenarios of intra-brush coacervation are summarized in the scaling diagram of the brush regimes. Power laws for the brush thickness, density, and structural features as the functions of the salt concentration and grafting density are provided.