Modeling of Phase Behavior of Coacervates

Abstract

Coacervates are dense phases formed by mixing polyelectrolytes with oppositely charged species, such as polyelectrolytes, surfactant micelles, colloids, globular proteins. They can be found in novel applications, such as delivery of therapeutics and DNA transfection into cells, stabilization of vaccines, microfiltration membranes, water treatment, and food processing. Other applications include everyday consumer products, including shampoo. Coacervation is even found in biological structures; specifically, there are dense coacervate droplets, known as organelles, inside cells, which are formed through association of intrinsically disordered proteins (IDPs). However, despite the ubiquity of coacervates, it has remained a challenge to predict if a coacervate forms under given conditions and elucidate roles of physiochemical factors in coacervation. This challenge motivates us to investigate the phase behavior of coacervates through developing new thermodynamic theories that can ultimately guide rational design of the aforementioned applications. In this doctoral work, we first study single-phase polyelectrolyte or surfactant micelle solutions using models that capture both the effects of chemical specificity using local (specific) binding free energies and more general long-range electrostatic correlations. We apply our model to: counterion binding to polyelectrolytes in Chapter 2, charge regulation of weak polyacids in Chapter 3, and counterion binding to surfactant micelles in Chapter 4. Our model yields expressions for the binding constants of counterion binding and protonation that include contributions from the local binding free energies and electrostatic correlations. Our models yield predictions in agreement with simulation and with experimental results for counterion binding to polyelectrolytes, protonation (or charge regulation) of polyelectrolytes, and counterion binding to micelles. These studies highlight the roles of both local, specific binding free energies and electrostatic correlations in ion binding, with electrostatic correlation tending to lower the charge density of the polyelectrolytes (or micelles). One can in essence incorporate these single-phase theories into a coacervate model to explore coacervation formed from mixing polyelectrolytes with oppositely charged species, including polyelectrolytes and surfactant micelles. In Chapters 5 and 6, however, we limit our investigations to coacervates formed from oppositely, strongly charged polyelectrolytes, and leave other types of coacervate for future. We focus on the salt partitioning between a coacervate and its co-existing dilute solution in Chapter 5, and on overcharging of coacervates in Chapter 6. In agreement with experiments, our model predicts that the partitioning behavior of salt ions depends on the aforementioned (specific) binding free energy, with ions that strongly bind to polyelectrolytes partitioning preferentially into the coacervate phase and weakly binding ones partitioning more into the dilute phase. Through a comparison of stoichiometric and non-stoichiometric mixtures of polyanions and polycations, we elucidate the forces driving coacervate “overcharging” in which an excess of one of the two polyelectrolytes can be driven into a coacervate. As in stoichiometric mixtures of polyelectrolytes, we find that the driving forces for the transfer of excess polyelectrolyte into a coacervate are also entropic: namely with significant contributions from both counterion release and combinatorial entropy. Lastly, we review current views on polyelectrolyte coacervate formation in Chapter 7, and draw conclusions and suggest future lines of research in Chapter 8. These findings and agreements of our theory predictions with experimental and simulation results demonstrate the capability of our theory, which can be used to guide developing coacervate-based products.