Interfacial Tension of Polyelectrolyte Complex Coacervate Phases

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/η c –1) 3/2 near the critical point of the demixing transition, and that it scales as η 1/2 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/ψ c ) 3/2 near the critical salt concentration ψ c . Our predictions are shown to be in quantitative agreement with experiments and provide a means to design new materials based on polyelectrolyte complexation.