Incorporating Molecular Structure into a Transfer Matrix Theory of Complex Coacervation

Polymeric complex coacervation is a phase-separation process involving two oppositely-charged polyelectrolytes in an aqueous salt solution, where a polymer-dense phase is formed due to electrostatic interactions between the polyelectrolyte species. The resulting coacervate materials have seen widespread use in industry as viscosity modifiers and encapsulants, and are used in polymer research as an interaction motif for charge-driven self assembly. Despite this utility, a fundamental physical description of this process has remained elusive; a recent resurgance of interest in coacervation has led to a number of candidate theories. Here we present a transfer matrix theory that maps coacervate structure to a one-dimensional adsorption model, leading to a theory that can predict both coacervate phase behavior and local charge correlation features. We show that straightforward modifications to the theory can be used to account for a number of molecular features, including divalent ions, linear charge density, polymer stiffness, and polymer architecture. Comparison to simulation and experiment shows that we can capture qualitative trends that inform the molecular design of polymer complex coacervates.