Interfacial Tension of Polyelectrolyte Complex Coacervate
Phases
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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 <i>N</i><sup>–3/2</sup>(η/η<sub>c</sub>–1)<sup>3/2</sup> near the critical
point of the demixing transition, and that it scales as η<sup>1/2</sup> far away from it, where <i>N</i> 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 <i>N</i><sup>–1/4</sup>(1−ψ/ψ<sub>c</sub>)<sup>3/2</sup> near the critical salt concentration ψ<sub>c</sub>. Our predictions are shown to be in quantitative agreement
with experiments and provide a means to design new materials based
on polyelectrolyte complexation
