Interfacial Tension of Polyelectrolyte Complex Coacervate Phases

Abstract

We consider polyelectrolyte solutions which, under suitable conditions, phase separate into a liquid-like coacervate phase and a coexisting supernatant phase that exhibit an extremely low interfacial tension. Such interfacial tension provides the basis for most coacervate-based applications, but little is known about it, including its dependence on molecular weight, charge density, and salt concentration. By combining a Debye–Hückel treatment for electrostatic interactions with the Cahn–Hilliard theory, we derive explicit expressions for this interfacial tension. In the absence of added salts, we find that the interfacial tension scales as N –3/2(η/ηc–1)3/2 near the critical point of the demixing transition, and that it scales as η1/2 far away from it, where N is the chain length and η measures the electrostatic interaction strength as a function of temperature, dielectric constant, and charge density of the polyelectrolytes. For the case with added salts, we find that the interfacial tension scales with the salt concentration ψ as N –1/4(1−ψ/ψc)3/2 near the critical salt concentration ψc. Our predictions are shown to be in quantitative agreement with experiments and provide a means to design new materials based on polyelectrolyte complexation.

Polyelectrolyte assisted charge titration spectrometry: Applications to latex and oxide nanoparticles

“…2c, lower panel). These polymer phases are similar to those found by Priftis et al on branched poly(ethyleneimine) complexed with linear poly(glutamic acid) [51,65], indicating that electrostatics driven reactions between charged polymers share general features as far as the structure, the phase or the thermodynamics are concerned [32]. The main result of this study is that the PACTS technique allows an accurate determination of the charge stoichiometry.…”

“…"# = 1.2 ± 0.1. Such a scattering feature on mixing oppositely charge species was observed for various systems, including synthetic and biological polymers, phospholipid vesicles and surfactants [19,31,32,47,48,51,52,63]. It is interpreted in terms of complexation, charge neutralization and the formation of structures or phase much larger the initial components.…”

The Effect of Salt on the Complex Coacervation of Vinyl Polyelectrolytes

“…This critical entropic dependence on the release of counter-ions is considered to be the main reason why complex coacervation is sensitive to the overall concentration of salt ions present. High salt concentrations decrease the entropic driving force for complex formation and ultimately destabilize the liquid-liquid phase separation [1][2][3]11,12,36,[42][43][44]. In contrast to this inhibitory effect on complex formation under conditions of high salt, the presence of small amounts of salt may, in fact, enhance complex formation by softening electrostatic interactions, favoring more accessible polymer conformations, and enabling chain rearrangement [4,36,45].…”

“…Electrostatically-driven self assembly can be tuned through a variety of parameters, including the chemical nature of the charged species, the size or length of the charged particle or molecule, particle shape, polydispersity, charge density, pH, and ionic strength [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Consideration of these variables is critical in the design of self-assembled materials.…”

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

“…Excellent agreement between experiment and theory is possible, 34 and extensions to (for example) adapt Cahn-Hilliard models of interfaces can describe interfacial surface tension effects. 57 However this theory carries with it the approximations inherent to the linearized, mean field Debye-Hückel theory.…”