PRISM-Based Theory of Complex Coacervation: Excluded Volume versus Chain Correlation

Abstract

Aqueous solutions of oppositely charged polyelectrolytes can undergo liquid–liquid phase separation into materials known as complex coacervates. These coacervates have been a subject of intense experimental and theoretical interest. Efforts to provide a physical description of complex coacervates have led to a number of theories that qualitatively (and sometimes quantitatively) agree with experimental data. However, this agreement often occurs in a degeneracy of models with profoundly different starting assumptions and different levels of sophistication. Theoretical difficulties in these systems are similar to those in most polyelectrolyte systems where charged species are highly correlated. These highly correlated systems can be described using liquid state (LS) integral equation theories, which surpass mean-field theories by providing information on local charge ordering. We extend these ideas to complex coacervate systems using PRISM-type theories and are able to capture effects not observable in traditional coacervate models, particularly connectivity and excluded volume effects. We can thus bridge two traditional but incommensurate theories meant to describe complex coacervates: the Voorn–Overbeek theory and counterion release. Importantly, we hypothesize that a cancellation of connectivity and excluded volume effects provides an explanation for the ability of Voorn–Overbeek theory to fit experimental data despite its well-known approximations.