Structure and Viscoelasticity of Hybrid Colloid-Polyelectrolyte Coacervates

We theoretically consider complex coacervation between polyelectrolytes (PEs) and oppositely charged colloids, such as globular proteins, solid nanoparticles, or spherical micelles of ionic surfactants. A scaling theory of stoichiometric colloid-PE (“hybrid”) coacervates is developed to predict their structure, viscoelasticity, and critical concentration of coacervation. At low concentrations, PEs adsorb at the colloids to form electrically neutral finite-size complexes. Attractions of these clusters arise due to bridging between the adsorbed PE layers and, above the threshold concentration, macroscopic phase separation sets in. The internal structure of hybrid coacervate is controlled by (i) the strength of the PE adsorption and (ii) the ratio of the PE shell thickness to the colloid radius. Different scaling regimes of hybrid coacervates are distinguished, and the respective scaling diagram is constructed in the coordinates of the colloid charge Q and radius R. At the high charge of colloids, the shell is thick and the most volume of the hybrid coacervate is occupied by PEs, which define its osmotic and rheological properties. In contrast to usual PE-PE coacervates, hybrid coacervates have an inhomogeneous structure: The local polymer density decreases with the distance from the colloid surface. Hybrid coacervates have higher average density but simultaneously lower surface tension as compared to usual PE-PE counterparts. Rouse and reputation models are applied to describe PE dynamics and diffusion of colloids in the condensed phase. In Θ solvent, the coacervate viscosity increases with the colloid charge as η_Rouse ∼Q^4/5 when PEs are unentangled and as η_rep ∼Q^28/15 for entangled systems. The diffusion coefficients of colloids are strongly decreasing functions of Q and R. Obtained predictions are compared to the experimental results on hybrid coacervates formed from globular supercationic green fluorescent proteins (GFPs) and RNA polyanions.