Transfer Matrix Model of of pH Effects in Polymeric Complex Coacervation

Oppositely-charged polyelectrolytes can undergo an associative phase separation driven by electrostatic attraction. This process is known as polymeric complex coacervation and leads to the formation of a polymer dense coacervate phase and a coexisting polymer-dilute supernatant phase. Complex coacervates have uses in personal care products and as biomolecular encapsulants, applications that require a full understanding of the fundamental molecular physics of coacervation. We aim to reconcile a notable difference between most experiments and theoretical models. Experiments often use weak polyelectrolytes whose charge state depends on solution pH, while theoretical models typically assume strong polyelectrolytes. There have only been a few models to try to account for pH effects on complex coacervation. We modify the transfer matrix theory of coacervation to account for pH effects. We demonstrate that asymmetric phase diagrams can exist when charge stoichiometry is not equal, leading to a partitioning of one salt species into the coacervate phase to maintain electroneutrality which can suppress phase separation. We also demonstrate that mixtures off-stoichiometric in volume fraction but stoichiometric in charge have the greatest propensity to form coacervate phases.