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

Structure and Dynamics of Hybrid Colloid-Polyelectrolyte Coacervates

We develop a scaling theory for the structure and dynamics of "hybrid" complex coacervates formed from linear polyelectrolytes (PEs) and oppositely charged spherical colloids, such as globular proteins, solid nanoparticles, or spherical micelles of ionic surfactants. At low concentrations, in stoichiometric solutions, PEs adsorb at the colloids to form electrically neutral finite-size complexes. These clusters attract each other through bridging between the adsorbed PE layers. Above a threshold concentration, macroscopic phase separation sets in. The coacervate internal structure is defined by (i) the adsorption strength and (ii) the ratio of the resulting shell thickness to the colloid radius, H/R. A scaling diagram of different coacervate regimes is constructed in terms of the colloid charge and its radius for Θ and athermal solvents. For high charges of the colloids, the shell is thick, H ≫ R, and most of the volume of the coacervate is occupied by PEs, which determine its osmotic and rheological properties. The average density of hybrid coacervates exceeds that of their PE-PE counterparts and increases with nanoparticle charge, Q. At the same time, their osmotic moduli remain equal, and the surface tension of hybrid coacervates is lower, which is a consequence of the shell's inhomogeneous density decreasing with the distance from the colloid surface. When charge correlations are weak, hybrid coacervates remain liquid and follow Rouse/reptation dynamics with a Q-dependent viscosity, η _Rouse ∼ Q ^4/5 and η _rep ∼ Q ^28/15 for a Θ solvent. For an athermal solvent, these exponents are equal to 0.89 and 2.68, respectively. The diffusion coefficients of colloids are predicted to be strongly decreasing functions of their radius and charge. Our results on how Q affects the threshold coacervation concentration and colloidal dynamics in condensed phases are consistent with experimental observations for in vitro and in vivo studies of coacervation between supercationic green fluorescent proteins (GFPs) and RNA.

Structure and Flocculation of Ion Associates of Carrageenan and Poly(diallyldimethylammonium chloride) Depending on the Component Ratio

Carrageenan is a polysaccharide of a plant origin, commonly used as a thickening and gelling agent in the food, pharmaceutical, and cosmetic industries. Due to the negative charges of its sulfate groups, carrageenan macromolecules strongly interact with oppositely charged polyions. The ionic complexes of carrageenan with poly(diallyldimethylammonium chloride) were obtained at the molar ratios 4:1, 2;1, 1:1, 1:2, and 1:4. The structure and characteristics of the polyanion-polycation associates were studied by XRD, IR, optical microscopy, and via sedimentation and particle size measurements. It was found that the suspended particles flocculate and settle fastest when the molar ratio of the polyions is near 1:1. Turbidimetric titration experiments enabled us to measure the molar ratio of cationic to anionic groups at the onset of flocculation, and the value in question was found to be 1:1.32. In other words, a mass of 511 mg carrageenan corresponds to one millimole of ester sulfate (monobasic) groups. The measurement of the onset of flocculation has been employed for the accurate determination of carrageenan in real samples of food products. The color and turbidity of the sample do not interfere with the determination results.

Driving force and pathway in polyelectrolyte complex coacervation

There is notable discrepancy between experiments and coarse-grained model studies regarding the thermodynamic driving force in polyelectrolyte complex coacervation: experiments find the free energy change to be dominated by entropy, while simulations using coarse-grained models with implicit solvent usually report a large, even dominant energetic contribution in systems with weak to intermediate electrostatic strength. Here, using coarse-grained, implicit-solvent molecular dynamics simulation combined with thermodynamic analysis, we study the potential of mean force (PMF) in the two key stages on the coacervation pathway for symmetric polyelectrolyte mixtures: polycation-polyanion complexation and polyion pair-pair condensation. We show that the temperature dependence in the dielectric constant of water gives rise to a substantial entropic contribution in the electrostatic interaction. By accounting for this electrostatic entropy, which is due to solvent reorganization, we find that under common conditions (monovalent ions, room temperature) for aqueous systems, both stages are strongly entropy-driven with negligible or even unfavorable energetic contributions, consistent with experimental results. Furthermore, for weak to intermediate electrostatic strengths, this electrostatic entropy, rather than the counterion-release entropy, is the primary entropy contribution. From the calculated PMF, we find that the supernatant phase consists predominantly of polyion pairs with vanishingly small concentration of bare polyelectrolytes, and we provide an estimate of the spinodal of the supernatant phase. Finally, we show that prior to contact, two neutral polyion pairs weakly attract each other by mutually induced polarization, providing the initial driving force for the fusion of the pairs.

Wetting behavior of polyelectrolyte complex coacervates on solid surfaces

The wetting behavior of complex coacervates underpins their use in many emerging applications of surface science, particularly wet adhesives and coatings. Many factors dictate if a coacervate phase will condense on a solid surface, including solution conditions, the nature of the polymer-substrate interaction, and the underlying supernatant-coacervate bulk phase behavior. In this work, we use a simple inhomogeneous mean-field theory to study the wetting behavior of complex coacervates on solid surfaces both off-coexistence (wetting transitions) and on-coexistence (contact angles). We focus on the effects of salt concentration, the polycation/polyanion surface affinity, and the applied electrostatic potential on the wettability. We find that the coacervate generally wets the surface via a first order wetting transition with second order transitions possible above a surface critical point. Applying an electrostatic potential to a solid surface always improves the surface wettability when the polycation/polyanion-substrate interaction is symmetric. For asymmetric surface affinity, the wettability has a nonmonotonic dependence with the applied potential. We use simple scaling and thermodynamic arguments to explain our results.

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

Self-consistent field theory is used to systematically study the characteristics and electrostatic energy storage of electric double layers in confined polyelectrolyte solutions for salt-free and low salt concentration systems.