Supernatant Phase in Polyelectrolyte Complex Coacervation: Cluster Formation, Binodal, and Nucleation

Abstract

This work studies the structure and thermodynamics of the supernatant phase in polyelectrolyte complex coacervation, a relatively unexplored area. By combining the cluster theory in dilute solution with our recently developed mean-field theory for inhomogeneous polyelectrolyte solutions (ZhangP.WangZ.-G. Zhang, P. Wang, Z.-G. Macromolecules20215410994), we systematically investigate the structure of finite-sized clusters formed by oppositely charged polyions in symmetric dilute solutions and how these clusters affect the binodal, spinodal, and nucleation for polyelectrolyte complex coacervation. We find that both the polyion concentration deep inside the cluster and the interfacial tension decrease with increasing the cluster size, reaching their respective bulk coexistence values with corrections inversely proportional to the cluster radius. The polyion concentration in the supernatant phase at coexistence is several orders of magnitude higher than that obtained under the uniform mixing approximation. For most relevant conditions away from the critical point, the supernatant phase consists predominantly of polyion pairs. By examining the nucleation barrier in supersaturated solutions, we can determine a pseudo-spinodal when the barrier is a few multiples of the thermal energy. The location of this pseudo-spinodal is similarly shifted to much higher concentrations than predicted under the uniform mixing approximation. Making the volume approximation for the clusters, we obtain simple analytical expressions for the cluster formation free energy, the modified binodal, and the pseudo-spinodal. In particular, we propose a simple approximate formula for estimating the concentration of the coexisting supernatant phase in terms of the chain length, interfacial tension, and the polyion concentration in the coacervate phase.

Structure and Dynamics of Hybrid Colloid–Polyelectrolyte Coacervates

“…Generally speaking, they are unequal, which can be demonstrated using a more refined analysis. The result similar to eq has been recently reported for the spinodal concentration in the case of conventional PE–PE complex coacervation, which is also preceded by the formation of finite-size neutral pairs (globules). − Similar reasoning applied to regimes II and III yields B n p I I ≃ R 3 ( 1 − ξ e R e R / ξ e ) ≃ prefix− ξ e R 2 normale R / ξ e B n p I I I ≃ R 3 ( 1 − H I I I R e false( Q / q q false) 4 / 3 false( ξ e / R false) 5 / 3 ) ≃ prefix− H I I I R 2…”

Wetting behavior of polyelectrolyte complex coacervates on solid surfaces

“…The phase diagram near the critical salt concentration is not available when accounting for the polyion clusters in the supernatant phase. 70 Further, we expect many aspects of the wetting behavior to be similar, which we will revisit later on.…”

“…In reality, the oppositely charged polyions in the supernatant phase are likely to form dispersed clusters made up of two or more polyions. [67][68][69][70][71] Such a distinction undoubtedly influences the behavior of the supernatant near a solid surface. We recognize this as a limitation of our study; however, using a uniformly mixed assumption allows for the complete phase diagram (Fig.…”

Structural features and electrostatic energy storage of electric double layers in confined polyelectrolyte solutions under low-salt conditions

“…1a). For simplicity, all monomers (or polyelectrolyte segments) and small ions are assumed to have the same volume, 66 of which the solvent is neglected (i.e., implicit solvent). In addition, the local properties of the polyelectrolyte solution (e.g., the concentrations of monomers and small ions, the electrostatic potential, and the physical properties) are assumed to be invariant in the y direction, and thus the mathematical formulation can be simplified as a one-dimensional problem.…”

“…1a). For simplicity, all monomers (or polyelectrolyte segments) and small ions are assumed to have the same volume, 66 of which the solvent is neglected ( i.e. , implicit solvent).…”