Theory of melt polyelectrolyte blends and block copolymers: phase behavior, surface tension, and microphase periodicity.

Polymer mixtures such as blends or block copolymers are of great interest in energy applications and functional materials, and often, one or more of these species contain charges. The traditional fashion in which such materials are studied uses Self-Consistent Field Theory (SCFT) methods that incorporate electrostatics using Poisson-Boltzmann (PB) theory. We adapt a new and rigorous approach that does not rely on the mean-field assumptions inherent in the PB theory and instead uses Liquid State (LS) integral equation theory to articulate charge correlations that are completely neglected in PB. We use this theory to calculate phase diagrams for both blends and block copolyelectrolytes using SCFT-LS and demonstrate how their phase behavior is highly dependent on chain length, charge fraction, charge size, and the strength of Coulombic interactions. Beyond providing phase behavior of blends and block copolyelectrolytes, we can use this theory to investigate the interfacial properties such as surface tension and block copolyelectrolyte lamellar spacing. Lamellar spacing provides a way to directly compare the SCFT-LS theory to the results of experiments. SCFT-LS will provide conceptual and mathematical clarification of the role of charge correlations in these systems and aid in the design of materials based on charge polymers.