Electrostatically Stabilized Microphase Separation in Polyelectrolyte Blends: Analogy to Nuclear "Pasta" Phases

We develop the weak segregation theory of microphase separation in stoichiometric blends of oppositely and weakly charged polyelectrolytes, which would be immiscible in the absence of charged units. Short-range repulsions between polycation and polyanion monomers induce the formation of oppositely charged domains, whose size is controlled by their excess Coulomb energy. The diagram of blend morphologies is constructed in the framework of a Leibler’s mean-field approach and, to account for fluctuations, within a Brazovskii-Fredrickson-Helfand approximation. Phase behavior of the polyelectrolyte blends is fully analogous to that of neutral diblock copolymers. In asymmetric blends, increasing incompatibility between polyelectrolytes triggers the usual cascade of first order phase transitions, disordered blend → bcc → hex → lam. We also discuss that microphase separation in polyelectrolyte blends (and hence neutral diblock copolymers) and the formation of nuclear “pasta” phases arising within neutron stars are governed by similar physical principles, despite the six orders of magnitude difference in the periods of these structures (nanometers vs femtometers, respectively).