Interfacial Structure and Tension of Polyelectrolyte Complex Coacervates

Abstract

We develop a simple inhomogeneous mean-field theory to study the interfacial structure and tension of polyelectrolyte complex coacervates in equilibrium with a supernatant solution. Our theory treats the electrostatic correlation by combining the Debye–Hückel theory with the first-order thermodynamic perturbation theory within the local density approximation, and incorporates the conformation entropy contribution for both polyions using Lifshitz’s ground-state dominance approximation. Using this theory, we systematically examine the interfacial properties of both symmetric and concentration-asymmetric coacervates. The interfacial tension γ is generally rather low, on the order of 1 mN/m or less. For asymmetric coacervates, an intricate electric double layer forms in the interfacial region, which can even contain several oscillations under certain conditions. The interfacial tension generally decreases with increasing the stoichiometric asymmetry, the added-salt concentration, and the initial polymer concentration of the mixture. We further find that the interfacial tension can be quantitatively related to the degree of phase separation S, where S is the Euclidean distance in composition between the two coexisting phases. In particular, we find that γ as a function of S for different concentration asymmetries collapses approximately to two master curves, which merge together and follow γ ∼ S 3 for small S.

Wetting behavior of polyelectrolyte complex coacervates on solid surfaces

“…To elucidate the main physics in this system, we use a simple inhomogeneous mean-field theory extended from a theory for studying the interfacial behavior of polyelectrolyte complex coacervates developed by Zhang and Wang. 28 The central difference from ref. 28 is that the polyelectrolyte solution, either coacervate or supernatant, is in contact with a solid surface rather than its coexisting phase.…”

“…28 The central difference from ref. 28 is that the polyelectrolyte solution, either coacervate or supernatant, is in contact with a solid surface rather than its coexisting phase. Under the conditions studied, we find that the supernatant to coacervate wetting transition generally occurs via a first order prewetting transition with a second order transition occurring as one approaches the bulk critical salt concentration.…”

“…The denominator in eqn ( 11) is the interfacial tension, which we calculate using the methods described in our earlier work. 28 Fig. S6 (ESI †) gives g sup,co for the phase diagram in Fig.…”

“…1,[16][17][18] In the past decade, there has also been significant progress in characterizing the interfacial properties of the coacervate-supernatant interface-notably, the interfacial tension. 19,20 Experiments and theory of symmetric mixtures of polyelectrolytes have characterized the scaling of interfacial tension with the salt concentration relative to the critical salt concentration [21][22][23][24][25][26][27][28][29] (g B [f crit AE À f AE ] 3/2 ) and with the chain length. 22,24,30 Simulations and theory also give access to additional interfacial properties, such interface thickness and excess adsorption.…”

“…25 Access to the interfacial profiles is particularly important for asymmetric mixtures of polyelectrolytes, where local charge separation can lead to spatially varying, and usually nonmonotonic, profiles of the electrostatic potential. 28,31 Compared to the coacervate-supernatant interface, the supernatant and coacervate phases near solid surfaces are relatively unexplored. Of central importance for solid substrates is the adsorption and corresponding wetting (or drying) behavior of the coacervate phase.…”