A Molecular Thermodynamic Model of Complexation in Mixtures of Oppositely Charged Polyelectrolytes with Explicit Account of Charge Association/Dissociation

Abstract

Into an extended Voorn–Overbeek (EVO) free energy model of polyelectrolyte (PE) complexation and phase behavior, we incorporate three classes of short-ranged electrostatic effects, namely counterion association–dissociation, cross-chain ion pairing (IP), and charge regulation by treating each as a reversible chemical reaction leading to a corresponding law of mass action in a self-consistent fashion. The importance of each reaction is controlled by a corresponding chemistry-dependent standard free energy input parameter. Our model also accounts for Born (or ion solvation) energy using a linear mixing rule for the effective dielectric constant. In monophasic systems, the proposed model can qualitatively explain the observed shifts in acidity and basicity observed in potentiometric titration of weak PEs in the presence of salt and oppositely charged PEs in accordance with Le Châtelier’s principle. We demonstrate how a competition between counterion condensation (CC) and IP alone can explain the complex coacervation of strongly charged PEs as well as the existence of a critical salt concentration. Binodal diagrams predicted in our model are also affected by long-ranged electrostatics and are most sensitive to IP strength both for weak and strong PEs. The extent of IP increases in the dense phase at the expense of reduced CC upon coacervation consistent with counter release view of complex coacervation. We compare binodal diagrams predicted by our model against experimental data for both weakly and strongly dissociating polyions pairs and find a plausible parameter set that leads to an acceptable and partial agreement with experiments in the two cases, respectively.

Recent progress in the science of complex coacervation

“…[90][91][92][93][94][95][96] All of these limitations have been appreciated since the original development of Voorn-Overbeek theory, and most theoretical efforts since have focused on moving beyond this simplified picture. 33 Still, the fact that Voorn-Overbeek gets many aspects of the phenomenology qualitatively correct has led to its continued use; 27,28,39,40,97 there are only a few key experimental observations in simple homopolyelectrolyte coacervates that highlight the need to move beyond this simple picture. 35,40,47,98…”

“…[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…”

“…Zhang and Shklovskii developed an early picture, primarily for complexation between two polymer chains, but including a prediction of bulk coacervation when oppositely-charged polyelectrolytes were near stoichiometric ratios. 29 A more recent approach was used for coacervates by Salehi and Larson (Figure 6c), 97 which has been extended in collaboration with Qin (Figure 6d), 40,154 in which there is a fraction of paired charges between the oppositely-charged chains. These approaches are analogous to the theory developed by Olvera de la Cruz for polyelectrolyte condensation with multivalent ionsessentially coacervation where one species has a very small degree of polymerization -where condensed counterions can be modeled as a a fluctuating 'effective charge.'…”

“…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.…”

Patterning Polyelectrolyte Complexes with Alternating Monomer Sequence Distributions

“…Unfortunately, predicting the static and dynamic properties of PECs a priori currently remains out of reach. Promising theoretical developments have been developed over time [4][5][6][7][8][9] , but complementary advancements in the experimental fabrication and simulation of charge-driven assemblies remain critical to establish a stronger universal framework. In particular, expanding the repertoire of available tools to construct designer polyelectrolytes, where the primary sequence of multimonomer building blocks controls emergent properties and self-assembly across multiple length scales, represents the first step toward creating synthetic heteropolymers that can rival intricate membraneless organelle assemblies formed by natural biomolecules in eukaryotic cells.…”