Coacervate-driven self-assembly with Transfer Matrix Theory and Self-Consistent Field Theory

Complex coacervation occurs when two oppositely charged polyelectrolytes phase separate in an aqueous salt solution, resulting in a polymer dense coacervate phase and a polymer-dilute supernatant phase. Block copolyelectrolytes, which consists of both charged and neutral blocks, use this driving force to self-assemble into geometries which include micelles, vesicles and hexagonal rods. Coacervate-based materials provide advantages in (for example) the delivery of biologic materials, as encapsulation can be performed in the absence of organic solvent while maintaining stability of proteins. Recent advances in coacervation theory and simulations are used to understand the thermodynamics of coacervation-driven self-assembly. Transfer matrix theory is incorporated into self-consistent field theory (SCFT) to study how parameters like salt concentration, total polymer concentration and charge fraction of block copolyelectrolyes can affect the phase behavior of assembled structures, which is crucial in assisting in the design of materials. We show assembly that is analogous to uncharged block copolymer assembly in solution, and limits to standard coacervate phase behavior in the limit of long charged blocks.