Polyelectrolyte complex coacervation by electrostatic dipolar interactions

Abstract

We address complex coacervation, the liquid-liquid phase separation of a solution of oppositely charged polyelectrolyte chains into a polyelectrolyte rich complex coacervate phase and a dilute aqueous phase, based on the general premise of spontaneous formation of polycation-polyanion complexes even in the homogeneous phase. The complexes are treated as flexible chains made of dipolar segments and uniformly charged segments. Using a mean field theory that accounts for the entropy of all dissociated ions in the system, electrostatic interactions among dipolar and charged segments of complexes and uncomplexed polyelectrolytes, and polymer-solvent hydrophobicity, we have computed coacervate phase diagrams in terms of polyelectrolyte composition, added salt concentration, and temperature. For moderately hydrophobic polyelectrolytes in water at room temperature, neither hydrophobicity nor electrostatics alone is strong enough to cause phase separation, but their combined effect results in phase separation, arising from the enhancement of effective hydrophobicity by dipolar attractions. The computed phase diagrams capture key experimental observations including the suppression of complex coacervation due to increases in salt concentration, temperature, and polycation-polyanion composition asymmetry, and its promotion by increasing the chain length, and the preferential partitioning of salt into the polyelectrolyte dilute phase. We also provide new predictions such as the emergence of loops of instability with two critical points.

Recent progress in the science of complex coacervation

“…36 Finally, a theory by Muthukumar, et al predicts the partitioning of salt to the supernatant phase as well, in this case attributed to the presence of strong, favorable interactions between the dipoles formed between paired complexes and the surrounding salt ions. 135 Experimental and computational efforts further probed the Olvera de la Cruz prediction, 99,100 to demonstrate results consistent with the Sing and Perry observations. One notable example is the work of Li et al; 35 salt was again observed to partition into the supernatant phase, in this case for a different set of coacervate-forming polypeptides (poly(L-lysine) and poly(D,Lglutamic acid)), using thermogravimetric analysis to calculate the coexisting salt and polymer concentrations.…”

“…[131][132][133][134] Despite the widespread use of this concept to describe complexation of pair complexes, 29,109 only recently has charge localization been regularly invoked in understanding bulk coacervation. 31,97,135…”

“…173,174 In all of these efforts, connectivity is implicitly considered via the inclusion of counterion condensation, and is parameterized to match observable phase behavior. 40,97,154 Pairing has also been considered in a model by Adhikari and Muthukumar, 135,175 who model coacervation as the attraction between pairs of complexed polyelectrolytes. The advantage of these ad hoc models is that they do not require an explicit description of the locally condensed charges, and instead only need to be appropriately parameterized.…”

“…This initial work by Sing and Perry prompted discussion of salt partitioning in the context of a number of theoretical, 31,31,36,87,135,167,177 computational, 34,35,179 and experimental efforts. 34,35 The immediate follow-up to the Sing and Perry work was the development of the transfer-matrix theory by Sing, 31 which incorporates a phenomenological cubic term in the free energy to account for the excluded volume and packing effects in dense, coacervate systems.…”

Sequence-dependent self-coacervation in high charge-density polyampholytes

“…93 This class of models has a number of manifestations, including a semi-phenomenological 'ion equilibrium' model used by Larson and Qin 94 and a ladder conformation-based model developed by Muthukumar. 95 We have recently developed a model inspired by the concept of charge condensation, that we call the transfer matrix (TM) theory of coacervation. [96][97][98][99][100] This theory accounts for the localization of oppositely-charged small molecule ions or polyelectrolytes near a test polyelectrolyte chain, and maps this localization to a 1-D adsorption model.…”