Bridging Field Theory and Ion Pairing in the Theory of Polymer Complex Coacervation

Complex coacervation is a phase separation phenomenon, driven by the electrostatic attraction between oppositely-charged macromolecular species. A recent surge of interest in coacervation between polyelectrolytes has been driven by both fundamental advances in experimental characterization of these systems, along with recognition of their relevance for both biological systems such as biomolecular condensates as well as industrially-relevant consumer products. Concomitantly, there have been several theories capable of predicting complex coacervation that are used to explain these experimental observations. While there has been a general conceptual consensus on the underlying physics of coacervation, these theoretical approaches have so far remained distinct. Polymer field theory, liquid state theory, ion pairing theories, and scaling theories all provide useful insights, but how the assumptions of each candidate theory are interrelated remains largely unexplored. In this manuscript, we attempt to show how two such classes of models can be derived from a single starting point, using cluster expansions as the basis for discussing which interactions are included in both field theory and ion pairing theory. This allows us to compare and contrast these approaches, evaluate conditions where each model should be relevant, and suggest ways in which existing models can be improved or parameterized.