(475b) Bridging Field Theory and Ion Pairing in the Theory of Polymer Complex Coacervation

Polymeric complex coacervation is an associative phase separation process that is driven by the electrostatic attraction between oppositely-charged polyelectrolytes in solution. This phase separation results in a polymer-dense ‘coacervate’ phase and a polymer-dilute ‘supernatant’ phase, with the coacervate phase in particular finding widespread use in industrial applications (such as food and personal care products) and as a model system for biomolecular condensates. There has been significant effort in the polymer physics community to study these materials, using a wide variety of theoretical approaches to understand the underlying physics of this phase separation phenomenon. One approach, the transfer matrix theory, maps the problem of coacervation to a one-dimensional adsorption model to keep track of its interactions with surrounding particles. This model has been successful at making predictions of coacervate phase behavior, and how it is affected by several molecular effects such as polyelectrolyte stiffness, monomer sequence, multivalent salts, pH, and polymer architecture. However, the transfer matrix model relies on several empirical fit parameters whose connection to molecular structure has been unclear. We can now show, using cluster expansions, how to derive expressions for these parameters that relate to underlying polymer connectivity and interactions. These parameters give reasonable predictions for phase behavior consistent with known phase behavior in polyelectrolyte coacervates, and provide the foundation for more rigorously explaining molecular effects on coacervation.