Transfer-Matrix Description of Complex Coacervation

Oppositely-charged polyelectrolytes can undergo associative phase separation in a salt solution via a process known as ‘complex coacervation.’ A notable amount of research has focused on using field-theory extensions of Voorn-Overbeek theory to understand coacervation. However, these methods have difficulty resolving molecular-level features, especially in high charge-density polyelectrolytes. An alternative understanding of coacervation is counterion condensation and release, which postulates coacervation is accompanied by a large change in entropy. The source of this large entropy change is the replacement of a polyelectrolyte’s condensed counterions with the oppositely-charged polyelectrolyte, because the polyelectrolyte’s translational entropy is far less than the counterion’s translational entropy. Inspired by this idea, we have developed a transfer-matrix based theory to describe coacervation in terms of monomer adsorption states. The theoretical values used by this theory are informed by Monte Carlo simulation, and can describe the effects of molecular-level features using physically motivated arguments. This theory could be used in conjunction with more sophisticated theoretical formalisms, thus providing a starting point to describe coacervate-driven self-assembly.