Effects of ion solvation on phase equilibrium and interfacial tension of liquid mixtures

A Unified Description of Salt Effects on the Liquid-Liquid Phase Separation of Proteins

Protein aggregation via liquid-liquid phase separation (LLPS) is ubiquitous in nature and is intimately connected to many human diseases. Although it is widely known that the addition of salt has crucial impacts on the LLPS of proteins, full understanding of the salt effects remains an outstanding challenge. Here, we develop a molecular theory that systematically incorporates the self-consistent field theory for charged macromolecules into the solution thermodynamics. The electrostatic interaction, hydrophobicity, ion solvation, and translational entropy are included in a unified framework. Our theory fully captures the long-standing puzzles of the nonmonotonic salt concentration dependence and the specific ion effect. We find that proteins show salting-out at low salt concentrations due to ionic screening. The solubility follows the inverse Hofmeister series. In the high salt concentration regime, protein continues salting-out for small ions but turns to salting-in for larger ions, accompanied by the reversal of the Hofmeister series. We reveal that the solubility at high salt concentrations is determined by the competition between the solvation energy and translational entropy of the ion. Furthermore, we derive an analytical criterion for determining the boundary between the salting-in and salting-out regimes, which is in good agreement with experimental results for various proteins and salt ions.

Kinetic pathway and micromechanics of fusion/fission for polyelectrolyte vesicles

Despite the wide existence of vesicles in living cells as well as their important applications like drug delivery, the underlying mechanism of vesicle fusion/fission remains under debate. Classical models cannot fully explain recent observations in experiments and simulations. Here, we develop a constrained self-consistent field theory that allows tracking the shape evolution and free energy as a function of center-of-mass separation distance. Fusion and fission are described in a unified framework. Both the kinetic pathway and the mechanical response can be simultaneously captured. By taking vesicles formed by polyelectrolytes as a model system, we predict discontinuous transitions between the three morphologies: parent vesicle with a single cavity, hemifission/hemifusion, and two separated child vesicles, as a result of breaking topological isomorphism. With the increase in inter-vesicle repulsion, we observe a great reduction in the cleavage energy, indicating that vesicle fission can be achieved without hemifission, in good agreement with simulation results. The force-extension relationship elucidates typical plasticity for separating two vesicles. The super extensibility in the mechanical response of vesicle is in stark contrast to soft particles with other morphologies, such as cylinder and sphere. Our work elucidates the fundamental physical chemistry based on intrinsic topological features of vesicle fusion/fission, which provides insights into various phenomena observed in experiments and simulations.

Self-Consistent Description of Vapor-Liquid Interface in Ionic Fluids

Inhomogeneity of ion correlation widely exists in many physicochemical, soft matter, and biological systems. Here, we apply the modified Gaussian renormalized fluctuation theory to study the classic example of the vapor-liquid interface of ionic fluids. The ion correlation is decomposed into a short-range contribution associated with the local electrostatic environment and a long-range contribution accounting for the spatially varying ionic strength and dielectric permittivity. For symmetric salt, both the coexistence curve and the interfacial tension predicted by our theory are in quantitative agreement with simulation data reported in the literature. Furthermore, we provide the first theoretical prediction of interfacial structure for asymmetric salt, highlighting the importance of capturing local charge separation.

Association of two polyelectrolytes in salt solutions

The association of polyelectrolytes (PEs) in solution affects a wealth of structural and dynamic behaviors, and is also fundamentally important for an understanding of protein association and aggregation. Here, we theoretically study the association of two PE chains by addressing the stability and morphology of the non-spherical associates. Our theory predicts that an elongated pearl-necklace (PN) associate can be stable at high salt concentrations due to the screened electrostatic repulsion. This contradicts the implication of scaling theory. In addition, there is no one-to-one correspondence between the morphology of the associate and its constituting unimers, which is demonstrated by the existence of different association modes.

Ionosomes: Observation of Ionic Bilayer Water Clusters

Emulsification of immiscible two-phase fluids, i.e., one condensed phase dispersed homogeneously as tiny droplets in an outer continuous medium, plays a key role in medicine, food, chemical separations, cosmetics, fabrication of micro- and nanoparticles and capsules, and dynamic optics. Herein, we demonstrate that water clusters/droplets can be formed in an organic phase via the spontaneous assembling of ionic bilayers. We term these clusters ionosomes, by analogy with liposomes where water clusters are encapsulated in a bilayer of lipid molecules. The driving force for the generation of ionosomes is a unique asymmetrical electrostatic attraction at the water/oil interface: small and more mobile hydrated ions reside in the inner aqueous side, which correlate tightly with the lipophilic bulky counterions in the adjacent outer oil side. These ionosomes can be formed through electrochemical (using an external power source) or chemical (by salt distribution) polarization at the liquid-liquid interface. The charge density of the cations, the organic solvent, and the synergistic effects between tetraethylammonium and lithium cations, all affecting the formation of ionosomes, were investigated. These results clearly prove that a new emulsification strategy is developed providing an alternative and generic platform, besides the canonical emulsification procedure with either ionic or nonionic surfactants as emulsifiers. Finally, we also demonstrate the detection of individual ionosomes via single-entity electrochemistry.

Salt-Induced Liquid-Liquid Phase Separation: Combined Experimental and Theoretical Investigation of Water-Acetonitrile-Salt Mixtures

Salt-induced liquid-liquid phase separation in liquid mixtures is a common phenomenon in nature and in various applications, such as in separation and extraction of chemicals. Here, we present results of a systematic investigation of the phase behaviors in water-acetonitrile-salt mixtures using a combination of experiment and theory. We obtain complete ternary phase diagrams for nine representative salts in water-acetonitrile mixtures by cloud point and component analysis. We construct a thermodynamic free energy model by accounting for the nonideal mixing of the liquids, ion hydration, electrostatic interactions, and Born energy. Our theory yields phase diagrams in good agreement with the experimental data. By comparing the contributions due to the electrostatic interaction, Born energy, and hydration, we find that hydration is the main driving force for the liquid-liquid separation and is a major contributor to the specific ion effects. Our theory highlights the important role of entropy in the hydration driving force. We discuss the implications of our findings in the context of salting-out assisted liquid-liquid extraction and make suggestions for selecting salt ions to optimize the separation performance.

Electrostatic contribution to colloidal solvation in terms of the self-energy-modified Boltzmann distribution

Electrostatic interactions make a large contribution to solvation free energy in ionic fluids such as electrolytes and colloidal dispersions. The electrostatic contribution to solvation free energy has been ascribed to the self-energy of a charged particle. Here we apply a variational field theory based on lower bound inequality to the inhomogeneous fluids of one-component charged hard-spheres, thereby verifying that the self-energy is given by the difference between the total correlation function and direct correlation function. Based on the knowledge of the liquid state theory, the self-energy specified in this study not only relates a direct correlation function to the Gaussian smearing of each charged sphere, but also provides the electrostatic contribution to solvation free energy that shows good agreement with simulation results. Furthermore, the Ornstein-Zernike equation leads to a set of generalized Debye-Hückel equations reflecting the Gaussian distributed charges.

Interfacial properties of polymeric complex coacervates from simulation and theory

Polymeric complex coacervation occurs when two oppositely charged polyelectrolytes undergo an associative phase separation in aqueous salt solution, resulting in a polymer-dense coacervate phase and a polymer-dilute supernatant phase. This phase separation process represents a powerful way to tune polymer solutions using electrostatic attraction and is sensitive to environmental conditions such as salt concentration and valency. One area of particular research interest is using this to create nanoscale polymer assemblies, via (for example) block copolymers with coacervate-forming blocks. The key to understanding coacervate-driven assembly is the formation of the interface between the coacervate and supernatant phases and its corresponding thermodynamics. In this work, we use recent advances in coacervate simulation and theory to probe the nature of the coacervate-supernatant interface. First, we show that self-consistent field theory informed by either Monte-Carlo simulations or transfer matrix theories is capable of reproducing interfacial features present in large-scale molecular dynamics simulations. The quantitative agreement between all three methods gives us a way to efficiently explore interfacial thermodynamics. We show how salt affects the interface, and we find qualitative agreement with literature measurements of interfacial tension. We also explore the influence of neutral polymers, which we predict to drastically influence the phase behavior of coacervates. These neutral polymers can significantly alter the interfacial tension in coacervates; this has a profound effect on the design and understanding of coacervate-driven self-assembly, where the equilibrium structure is tied to interfacial properties.

Nanoscale Resolution of Electric-field Induced Motion in Ionic Diblock Copolymer Thin Films

Understanding the responses of ionic block copolymers to applied electric fields is crucial when targeting applications in areas such as energy storage, microelectronics, and transducers. This work shows that the identity of counterions in ionic diblock copolymers substantially affects their responses to electric fields, demonstrating the importance of ionic species for materials design. In situ neutron reflectometry measurements revealed that thin films containing imidazolium based cationic diblock copolymers, tetrafluoroborate counteranions led to film contraction under applied electric fields, while bromide counteranions drove expansion under similar field strengths. Coarse-grained molecular dynamics simulations were used to develop a fundamental understanding of these responses, uncovering a nonmonotonic trend in thickness change as a function of field strength. This behavior was attributed to elastic responses of microphase separated diblock copolymer chains resulting from variations in interfacial tension of polymer-polymer interfaces due to the redistribution of counteranions in the presence of electric fields.

Inhomogeneous screening near the dielectric interface

Screening is one of the most important concepts in the study of charged systems. Near a dielectric interface, the ion distribution in a salt solution can be highly nonuniform. Here, we develop a theory that self-consistently treats the inhomogeneous screening effects. At higher concentrations when the bulk Debye screening length is comparable to the Bjerrum length, the double layer structure and interfacial properties are significantly affected by the inhomogeneous screening. In particular, the depletion zone is considerably wider than that predicted by the bulk screening approximation or the WKB approximation. The characteristic length of the depletion layer in this regime scales with the Bjerrum length, resulting in a linear increase of the negative adsorption of ions with concentration, in agreement with experiments. For asymmetric salts, inhomogeneous screening leads to enhanced charge separation and surface potential.

Efficient field-theoretic simulation of polymer solutions

We present several developments that facilitate the efficient field-theoretic simulation of polymers by complex Langevin sampling. A regularization scheme using finite Gaussian excluded volume interactions is used to derive a polymer solution model that appears free of ultraviolet divergences and hence is well-suited for lattice-discretized field theoretic simulation. We show that such models can exhibit ultraviolet sensitivity, a numerical pathology that dramatically increases sampling error in the continuum lattice limit, and further show that this pathology can be eliminated by appropriate model reformulation by variable transformation. We present an exponential time differencing algorithm for integrating complex Langevin equations for field theoretic simulation, and show that the algorithm exhibits excellent accuracy and stability properties for our regularized polymer model. These developments collectively enable substantially more efficient field-theoretic simulation of polymers, and illustrate the importance of simultaneously addressing analytical and numerical pathologies when implementing such computations.

On the theoretical description of weakly charged surfaces

It is widely accepted that the Poisson-Boltzmann (PB) theory provides a valid description for charged surfaces in the so-called weak coupling limit. Here, we show that the image charge repulsion creates a depletion boundary layer that cannot be captured by a regular perturbation approach. The correct weak-coupling theory must include the self-energy of the ion due to the image charge interaction. The image force qualitatively alters the double layer structure and properties, and gives rise to many non-PB effects, such as nonmonotonic dependence of the surface energy on concentration and charge inversion. In the presence of dielectric discontinuity, there is no limiting condition for which the PB theory is valid.

The distribution of homogeneously grafted nanoparticles in polymer thin films and blends

Polymer nanocomposites are an important and growing class of materials where nanoparticles are mixed in a polymer matrix. Much of the interest in polymer nanocomposites is derived from the nanoparticles' ability to impart properties to the polymer not commonly found in polymer materials, such as tunable optical, electrical, and mechanical properties. Grafting polymer chains to the surface of a nanoparticle is one of the most common routes towards promoting dispersion of nanoparticles in a polymer matrix. However, we only understand the thermodynamics of grafted nanoparticles in a polymer matrix in the simplest of cases, and this problem is exacerbated by the lack of theoretical and computational tools capable of efficiently predicting the structure of phase separated grafted nanoparticle/polymer blends. In this work, we extend a recently developed field theoretic framework to study the distribution of homogeneously grafted nanoparticles in homopolymer thin films and blends. We demonstrate that our method reproduces trends observed experimentally in homopolymer thin films, and then we examine how the nanoparticle size, grafting density, and the length of the grafted chains relative to the matrix chains affects the distribution of the grafted nanoparticles in phase separated polymer blends. We find that position of the nanoparticles relative to the interface in the blends is sensitive to the brush conformation, even when the nanoparticles are miscible in one of the two homopolymer phases.

Mesoscale models of dispersions stabilized by surfactants and colloids

In this paper we discuss and give an outlook on numerical models describing dispersions, stabilized by surfactants and colloidal particles. Examples of these dispersions are foams and emulsions. In particular, we focus on the potential of the diffuse interface models based on a free energy approach, which describe dispersions with the surface-active agent soluble in one of the bulk phases. The free energy approach renders thermodynamic consistent models with realistic sorption isotherms and adsorption kinetics. The free energy approach is attractive because of its ability to describe highly complex dispersions, such as emulsions stabilized by ionic surfactants, or surfactant mixtures and dispersions with surfactant micelles. We have classified existing numerical methods into classes, using either a Eulerian or a Lagrangian representation for fluid and for the surfactant/colloid. A Eulerian representation gives a more coarse-grained, mean field description of the surface-active agent, while a Lagrangian representation can deal with steric effects and larger complexity concerning geometry and (amphiphilic) wetting properties of colloids and surfactants. However, the similarity between the description of wetting properties of both Eulerian and Lagrangian models allows for the development of hybrid Eulerian/Lagrangian models having advantages of both representations.

Effects of image charges on double layer structure and forces

The study of the electrical double layer lies at the heart of soft matter physics and biophysics. Here, we address the effects of the image charges on the double layer structure and forces. For electrolyte solutions between two neutral plates, we show that depletion of the salt ions by the image charge repulsion results in short-range attractive and long-range repulsive forces. If cations and anions are of different valency, the asymmetric depletion leads to the formation of an induced electrical double layer. In comparison to a 1:1 electrolyte solution, both the attractive and the repulsive parts of the interaction are stronger for the 2:1 electrolyte solution. For two charged plates, the competition between the surface charge and the image charge effect can give rise to like-charge attraction and charge inversion. These results are in stark contrast with predictions from the Poisson-Boltzmann theory.

Continuous self-energy of ions at the dielectric interface

By treating both the short-range (solvation) and long-range (image force) electrostatic forces as well as charge polarization induced by these forces in a consistent manner, we obtain a simple theory for the self-energy of an ion that is continuous across the interface. Along with nonelectrostatic contributions, our theory enables a unified description of ions on both sides of the interface. Using intrinsic parameters of the ions, we predict the specific ion effect on the interfacial affinity of halogen anions at the water-air interface, and the strong adsorption of hydrophobic ions at the water-oil interface, in agreement with experiments and atomistic simulations.

Chromatography and the hundred year mystery of inorganic ions at aqueous interfaces: adsorption of inorganic ions at the Porous Graphitic Carbon Aqueous Interface follows the Hofmeister series

Many physical phenomena are affected by the structure of water interfaces, yet it remains an active and controversial subject. A great deal of recent theoretical endeavour and computer simulations question the validity of the Onsager Samaras theory of the ion-free interface between an electrolyte solution and an hydrophobic surface. Experimental results play a crucial role in assessing the legitimacy of the theories. Experimental data are scarce, while simulation results suggest an increasing surface affinity of ions with increasing chaotropic character, in dramatic contradiction to the classical view. Chromatography is a powerful separative technique, but we originally used it as a tool to detect the adsorption of chloride electrolytes and sodium electrolytes, strongly expected to shun any dielectric boundary, onto an hydrophobic surface, and to rank ions according to their adsorbophilicities. Frontal analysis gave unequivocal experimental evidence to this unexpected phenomenon and it was used to quantify it. The infinite dilution equilibrium constants for adsorption of kosmotropes and chaotropes onto the interface were obtained and contrasted to the Jones-Dole B viscosity coefficients, that is a common quantifier of the Hofmeister effect. It is clear that (i) the more chaotropic the ion is, the more it contributes to the global adsorbophilicity of the electrolyte; (ii) the influence of the variable anion is more than twofold that of the variable cation, thereby confirming a robust observation in many other physical systems. Standard free energy of adsorption for each electrolyte was calculated and its reliability was commented upon. The central issue in this paper is the effective and ascertained adsorption of electrolytes onto an hydrophobic surface and the fact that the adsorbophilicity of an electrolyte may be inferred from its position in the Hofmeister series.

Model-free test of local-density mean-field behavior in electric double layers

We derive a self-similarity criterion that must hold if a planar electric double layer (EDL) can be captured by a local-density approximation (LDA), without specifying any specific LDA. Our procedure generates a similarity coordinate from EDL profiles (measured or computed), and all LDA EDL profiles for a given electrolyte must collapse onto a master curve when plotted against this similarity coordinate. Noncollapsing profiles imply the inability of any LDA theory to capture EDLs in that electrolyte. We demonstrate our approach with molecular simulations, which reveal dilute electrolytes to collapse onto a single curve, and semidilute ions to collapse onto curves specific to each electrolyte, except where size-induced correlations arise.

Ion solvation in liquid mixtures: effects of solvent reorganization

Using field-theoretic techniques, we study the solvation of salt ions in liquid mixtures, accounting for the permanent and induced dipole moments, as well as the molecular volume of the species. With no adjustable parameters, we predict solvation energies in both single-component liquids and binary liquid mixtures that are in excellent agreement with experimental data. Our study shows that the solvation energy of an ion is largely determined by the local response of the permanent and induced dipoles, as well as the local solvent composition in the case of mixtures, and does not simply correlate with the bulk dielectric constant. In particular, we show that, in a binary mixture, it is possible for the component with the lower bulk dielectric constant but larger molecular polarizability to be enriched near the ion.

Influence of specific anions on the orientational ordering of thermotropic liquid crystals at aqueous interfaces

We report that specific anions (of sodium salts) added to aqueous phases at molar concentrations can trigger rapid, orientational ordering transitions in water-immiscible, thermotropic liquid crystals (LCs; e.g., nematic phase of 4'-pentyl-4-cyanobiphenyl, 5CB) contacting the aqueous phases. Anions classified as chaotropic, specifically iodide, perchlorate, and thiocyanate, cause 5CB to undergo continuous, concentration-dependent transitions from planar to homeotropic (perpendicular) orientations at LC-aqueous interfaces within 20 s of addition of the anions. In contrast, anions classified as relatively more kosmotropic in nature (fluoride, sulfate, phosphate, acetate, chloride, nitrate, bromide, and chlorate) do not perturb the LC orientation from that observed without added salts (i.e., planar orientation). Surface pressure-area isotherms of Langmuir films of 5CB supported on aqueous salt solutions reveal ion-specific effects ranking in a manner similar to the LC ordering transitions. Specifically, chaotropic salts stabilized monolayers of 5CB to higher surface pressures and areal densities (12.6 mN/m at 27 Å(2)/molecule for NaClO(4)) and thus smaller molecular tilt angles (30° from the surface normal for NaClO(4)) than kosmotropic salts (5.0 mN/m at 38 Å(2)/molecule with a corresponding tilt angle of 53° for NaCl). These results and others reported herein suggest that anion-specific interactions with 5CB monolayers lead to bulk LC ordering transitions. Support for the proposition that these ion-specific interactions involve the nitrile group was obtained by using a second LC with nitrile groups (E7; ion-specific effects similar to 5CB were observed) and a third LC with fluorine-substituted aromatic groups (TL205; weak dipole and no ion-specific effects were measured). Finally, we also establish that anion-induced orientational transitions in micrometer-thick LC films involve a change in the easy axis of the LC. Overall, these results provide new insights into ionic phenomena occurring at LC-aqueous interfaces, and reveal that the long-range ordering of LC oils can amplify ion-specific interactions at these interfaces into macroscopic ordering transitions.