Electrostatically Stabilized Microstructures: From Clusters to Necklaces to Bulk Microphases

This Viewpoint reveals the universality of the physical mechanisms controlling electrostatically stabilized microstructures in various systems of charged polymers with short-range attractive interactions. Key to this behavior is the competition of short-range attractions with long-range electrostatic repulsions. In dilute solutions of hydrophobic polyelectrolytes and charge-imbalanced polyampholytes, aggregation of single globules driven by the surface tension is restrained by net charge accumulation, stabilizing the finite cluster of the electrostatic blob size, R_cl ≃ ξ_e. Increasing net charge of the chain results in cluster disintegration to single globules and their further transition to beads-on-string necklaces with the bead size D_bead ≃ ξ_e. This intrachain microphase separation is analogous to that in semidilute solutions of these polymers, with the polymer-rich domain size of D_bead ≃ ξ_e. Similar diblock-copolymer-like microphases also form in blends of immiscible polyanions and polycations, with the extra incompatibility-dependent prefactor in the domain size of D ≃ χ_+-^1/6ξ_e originating from decoupling between the domain density and the surface tension. Scaling and the random phase approximation (RPA) approaches to electrostatic microphase separation in solutions and blends of ionic polymers are not contradictory and correspond to the limits of strong and weak segregation, respectively. Upon the addition of salt, both bulk and single-chain systems exhibit multicritical behavior (Lifshitz point) when the Debye radius, r_D, the electrostatic blob, ξ_e, and the blob due to short-range attractions, ξ_att, are all equal to each other, ξ_e ≃ ξ_att ≃ r_D. These findings underscore the universality of characteristic lengths controlling the formation and disintegration of electrostatically stabilized microstructures across different systems.