A continuum solvent model of ion-ion interactions in water

A Method for Efficiently Predicting the Radial Distribution Function and Osmotic Coefficients of Aqueous Electrolyte Solutions

The prediction of the structural and thermodynamic properties of electrolyte solutions is critical for a huge range of practical situations where these solutions play a vital role. Theoretical models, such as the continuum solvent model, attempt to explain the behavior of solutions using a coarse-grained description of the interactions of species in the solution, whereas molecular simulations aim to directly compute the behavior of the solution, including the interactions between all ions and molecules in the system. Both methods have limitations: theoretical models are generally less accurate because they rely on assumptions, while molecular simulations require significant computational resources, particularly if higher accuracy is desired. To address these issues, we propose an affordable and effective method that combines the advantages of the modified Poisson-Boltzmann equation (MPBE) with classical molecular dynamics (MD) simulations to predict the radial distribution functions and thermodynamic properties of electrolyte solutions. We demonstrate a method of using the MPBE to compute the short-range potential of mean force (PMF) from the radial distribution functions (RDFs) and vice versa. Furthermore, we provide insights into the relationship between the RDFs and the short-range PMF based on the MPBE. Our analysis reveals that the effective short-range PMFs can be approximately calculated using low concentration simulations but the short-range PMFs are slightly concentration-dependent in simulations at higher concentrations. Additionally, we demonstrate that for concentrated solutions, osmotic coefficients can be calculated in agreement with experiment using a virial approach. This is based on the effective short-range PMFs and RDFs obtained from the MPBE method. Our proposed MPBE can therefore accelerate the calculation of the structural and thermodynamic properties of electrolyte solutions.

Energy-Scaled Debye-Hückel Theory for the Electrostatic Solvation Free Energy in Size-Asymmetric Electrolyte Solutions

In this report, an energy-scaled Debye-Hückel theory is developed for fast and accurate evaluation of the electrostatic solvation free energy in size-asymmetric electrolyte solutions. A size-asymmetric electrolyte solution is mapped to a dielectric continuum medium with Debye-Hückel-like response. Based on the scaling relation of the electrostatic energy of a spherical ion in the small and large size limits, a Padé polynomial is used to interpolate the electrostatic energy at finite size. The Padé polynomial is further interpreted as the electrostatic energy of an effective Debye-Hückel mean field model, depicted by a modified Debye parameter and a surface charge density due to the size asymmetry of the solvent ions. This theory can distinguish the electrostatic energies and the electrostatic solvation free energies of solutes with the same size but opposite charges. Application to charged hard and charged soft spheres demonstrates the accuracy of our approach.

Perspectives on weak interactions in complex materials at different length scales

Nanocomposite materials consist of nanometer-sized quantum objects such as atoms, molecules, voids or nanoparticles embedded in a host material. These quantum objects can be exploited as a super-structure, which can be designed to create material properties targeted for specific applications. For electromagnetism, such targeted properties include field enhancements around the bandgap of a semiconductor used for solar cells, directional decay in topological insulators, high kinetic inductance in superconducting circuits, and many more. Despite very different application areas, all of these properties are united by the common aim of exploiting collective interaction effects between quantum objects. The literature on the topic spreads over very many different disciplines and scientific communities. In this review, we present a cross-disciplinary overview of different approaches for the creation, analysis and theoretical description of nanocomposites with applications related to electromagnetic properties.

Molecular-Based Description of the Osmotic Second Virial Coefficients of Electrolytes: Rigorous Formal Links to Solute-Solvent Interaction Asymmetry, Virial Expansion Paths, and Experimental Evidence

We introduce a molecular-based route to the evaluation of the osmotic second virial coefficients of dissociative solutes in dilute binary solutions, according to a general molecular thermodynamic solvation formalism of electrolyte solutions. We discuss the underlying solvation fundamentals and derive rigorous expressions leading to (i) the functional relationship among the osmotic second virial coefficients and the limiting composition behavior of the non-Coulombic contribution to the Kirkwood-Buff integral of the solute-solute interactions, the corresponding composition slope of the mean activity coefficient of the electrolyte solute, and a precisely defined solute-solvent intermolecular interaction asymmetry that characterizes unambiguously the solution non-ideality; (ii) the self-consistent calculation of the osmotic second virial coefficients of electrolytes as defined by the composition expansion along different thermodynamic paths and/or composition variables; (iii) the microstructural interpretation of Hill's isobaric-isothermal osmotic second virial coefficient in terms of Kirkwood-Buff correlation function integrals and its relationships to other osmotic coefficients from composition expansions along alternative thermodynamic paths; and (iv) the identification of drawbacks in the implementation of previous methods, originally intended for non-electrolyte systems, to systems involving dissociative solutes. The proposed formalism provides the fundamentally based foundations to the determination of the osmotic second virial coefficients of any type of electrolyte solute, whose thermodynamic expressions converge naturally to the non-electrolyte ones by setting to unity the solute stoichiometric coefficient ν. Following the formal results, we illustrate the formalism with the calculation of a variety of osmotic second virial coefficients involving a wide selection of aqueous solutions at ambient conditions and comprising a wide range of anion-cation type combinations characterized by 2 ≤ ν ≤ 6. Finally, we interpret the behavior of the resulting osmotic virial coefficients in terms of the solute-solvent intermolecular interaction asymmetry, discuss the experimental data requirements for the accurate evaluation of the osmotic second virial coefficients, and provide some observations as well as their modeling implications.

Salting-Up of Surfactants at the Surface of Saline Water as Detected by Tensiometry and SFG and Supported by Molecular Dynamics Simulation

Surfactant adsorption at the air-water interface is critical to many industrial processes but its dependence on salt ions is still poorly understood. Here, we investigate the adsorption of sodium dodecanoate onto the air-water interface using model saline waters of Li⁺ or Cs⁺ at pH values 8 and 11. Both cations enhance the surfactant adsorption, as expected, but their largest effects on the adsorption also depend on pH. Specifically, surface tension measurements, sum-frequency generation spectroscopy, and microelectrophoresis show that small (hard) Li⁺ enhances the surfactant adsorption more than large (soft) Cs⁺ at pH 11. This effect is fully reversed at pH 8. We argue that this salting-up (increasing adsorption) reversal is attributable to the conversion of the neutralized carboxylic (-COOH) headgroup at pH 8 into the charged carboxylate (-COO^-) headgroup at pH 11, which, respectively, interact with Cs⁺ and Li⁺ favorably. Molecular dynamics simulation shows that the affinity of Cs⁺ to the interface is decreased and eventually overtaken by Li⁺ as the carboxylic groups are deprotonated. This study highlights the importance of the charge and size of salt ions in selecting surfactants and electrolytes for industrial applications.

Effect of Gas Type and Its Pressure on Nanobubble Generation

The dependence of the volume number density of ion-stabilized gas nanobubbles (bubstons) on the type of gas and the pressure created by this gas in deionized water and saline solution has been investigated. The range of external pressures from the saturated water vapor (17 Torr) to 5 atm was studied. It turned out that the growth rate of the volume number density of bubstons is controlled by the magnitude of the molecular polarizability of dissolved gases. The highest densities of bubstons were obtained for gases whose molecules have a dipole moment. At fixed external pressure and the polarizability of gas molecules, the addition of external ions leads to a sharp increase in the content of bubstons.

From Surface Tension to Molecular Distribution: Modeling Surfactant Adsorption at the Air-Water Interface

Surfactants are centrally important in many scientific and engineering fields and are used for many purposes such as foaming agents and detergents. However, many challenges remain in providing a comprehensive understanding of their behavior. Here, we provide a brief historical overview of the study of surfactant adsorption at the air-water interface, followed by a discussion of some recent advances in this area from our group. The main focus is on incorporating an accurate description of the adsorption layer thickness of surfactant at the air-water interface. Surfactants have a wide distribution at the air-water interface, which can have a significant effect on important properties such as the surface excess, surface tension, and surface potential. We have developed a modified Poisson-Boltzmann (MPB) model to describe this effect, which we outline here. We also address the remaining challenges and future research directions in this area. We believe that experimental techniques, modeling, and simulation should be combined to form a holistic picture of surfactant adsorption at the air-water interface.

Quantifying the Counterion-Specific Effect on Surfactant Adsorption Using Modeling, Simulation, and Experiments

Ionic surfactants behave differently in the presence of various counterions, which plays an important role in many scientific and engineering processes. Previous work has shown that the counterion-specific surface tension can be reproduced with classical adsorption models, but the underlying origin of this effect has not been explained. In this paper, we extend our previously developed adsorption model to account for the specific counterion adsorption. This model can accurately predict the surface tension of surfactant solutions like sodium dodecyl sulfate (SDS) in the presence of the monovalent salts LiCl, NaCl, KCl, and CsCl. The predicted surface excess and surface potential are validated by corresponding sum-frequency generation (SFG) spectroscopy experiments. We also used molecular dynamic (MD) simulation to explain the origin of the counterion-specific effect for surfactant behavior. Our study shows that for SDS, binding of the counterion to both the headgroup and a few CH₂ fragments close to the surfactant head contributes to the counterion-specific effect. In general, SDS behaves like a large ion, and it prefers to bind with large counterions such as Cs⁺, which is consistent with Collins's law of matching water affinity. Therefore, large counterions enhance the surface adsorption and lower the surface tension the most.

Theory of electrolytes including steric, attractive, and hydration interactions

We present a continuum theory of electrolytes composed of a waterlike solvent and univalent ions. First, we start with a density functional F for the coarse-grained solvent, cation, and anion densities, including the Debye-Hückel free energy, the Coulombic interaction, and the direct interactions among these three components. These densities fluctuate obeying the distribution ∝exp(-F/k_BT). Eliminating the solvent density deviation in F, we obtain the effective non-Coulombic interactions among the ions, which consist of the direct ones and the solvent-mediated ones. We then derive general expressions for the ion correlation, the apparent partial volume, and the activity and osmotic coefficients up to linear order in the average salt density n_s. Second, we perform numerical analysis using the Mansoori-Carnahan-Starling-Leland model [J. Chem. Phys. 54, 1523 (1971)] for three-component hardspheres. The effective interactions sensitively depend on the cation and anion sizes due to competition between the steric and hydration effects, which are repulsive between small-large ion pairs and attractive between symmetric pairs. These agree with previous experiments and Collins' rule [Biophys. J. 72, 65 (1997)]. We also give simple approximate expressions for the ionic interaction coefficients valid for any ion sizes.

The Born model can accurately describe electrostatic ion solvation

The solvation free energies of ions in water are consistent with the Born linear response model if the centre on which the ion–water repulsion force acts is moved from the oxygen atom towards the hydrogens.

The Hofmeister series: Specific ion effects in aqueous polymer solutions

Specific ion effects in aqueous polymer solutions have been under active investigation over the past few decades. The current state-of-the-art research is primarily focused on the understanding of the mechanisms through which ions interact with macromolecules and affect their solution stability. Hence, we herein first present the current opinion on the sources of ion-specific effects and review the relevant studies. This includes a summary of the molecular mechanisms through which ions can interact with polymers, quantification of the affinity of ions for the polymer surface, a thermodynamic description of the effects of salts on polymer stability, as well as a discussion on the different forces that contribute to ion-polymer interplay. Finally, we also highlight future research issues that call for further scrutiny. These include fundamental questions on the mechanisms of ion-specific effects and their correlation with polymer properties as well as a discussion on the specific ion effects in more complex systems such as mixed electrolyte solutions.

Understanding the scale of the single ion free energy: A critical test of the tetra-phenyl arsonium and tetra-phenyl borate assumption

The tetra-phenyl arsonium and tetra-phenyl borate (TATB) assumption is a commonly used extra-thermodynamic assumption that allows single ion free energies to be split into cationic and anionic contributions. The assumption is that the values for the TATB salt can be divided equally. This is justified by arguing that these large hydrophobic ions will cause a symmetric response in water. Experimental and classical simulation work has raised potential flaws with this assumption, indicating that hydrogen bonding with the phenyl ring may favor the solvation of the TB^- anion. Here, we perform ab initio molecular dynamics simulations of these ions in bulk water demonstrating that there are significant structural differences. We quantify our findings by reproducing the experimentally observed vibrational shift for the TB^- anion and confirm that this is associated with hydrogen bonding with the phenyl rings. Finally, we demonstrate that this results in a substantial energetic preference of the water to solvate the anion. Our results suggest that the validity of the TATB assumption, which is still widely used today, should be reconsidered experimentally in order to properly reference single ion solvation free energy, enthalpy, and entropy.

Crystal nucleation initiated by transient ion-surface interactions at aerosol interfaces

Particle collisions are a common occurrence in the atmosphere, but no empirical observations exist to fully predict the potential effects of these collisions on air quality and climate projections. The current consensus of heterogeneous crystal nucleation pathways relevant to the atmosphere dictates that collisions with amorphous particles have no effect on the crystallization relative humidity (RH) of aqueous inorganic aerosols because there is no stabilizing ion-surface interaction to facilitate the formation of crystal nuclei. In contrast to this view of heterogeneous nucleation, we report laboratory observations demonstrating that collisions with hydrophobic amorphous organic aerosols induced crystallization of aqueous inorganic microdroplets at high RH, the effect of which was correlated with destabilizing water-mediated ion-specific surface interactions. These same organic aerosols did not induce crystallization once internally mixed in the droplet, pointing toward a previously unconsidered transient ion-specific crystal nucleation pathway that can promote aerosol crystallization via particle collisions.

Cation effects on haemoglobin aggregation: balance of chemisorption against physisorption of ions

A theoretical model of haemoglobin is presented to explain an anomalous cationic Hofmeister effect observed in protein aggregation. The model quantifies competing proposed mechanisms of non-electrostatic physisorption and chemisorption. Non-electrostatic physisorption is stronger for larger, more polarizable ions with a Hofmeister series Li⁺< K⁺< Cs⁺. Chemisorption at carboxylate groups is stronger for smaller kosmotropic ions, with the reverse series Li⁺ > K⁺ > Cs⁺. We assess aggregation using second virial coefficients calculated from theoretical protein-protein interaction energies. Taking Cs⁺ to not chemisorb, comparison with experiment yields mildly repulsive cation-carboxylate binding energies of 0.48 k_BT for Li⁺ and 3.0 k_BT for K⁺. Aggregation behaviour is predominantly controlled by short-range protein interactions. Overall, adsorption of the K⁺ ion in the middle of the Hofmeister series is stronger than ions at either extreme since it includes contributions from both physisorption and chemisorption. This results in stronger attractive forces and greater aggregation with K⁺, leading to the non-conventional Hofmeister series K⁺ > Cs⁺ ≈ Li⁺.

Investigations of the Hofmeister series and other specific ion effects using lipid model systems

From the ion point-of-view specific ion effects (SIE) arise as an interplay of ionic size and shape and charge distribution. However in aqueous systems SIE invariably involve water, and at surfaces they involve both interacting surface groups and local fields emanating from the surface. In this review we highlight the fundamental importance of ionic size and hydration on SIE, properties which encompass all types of interacting forces and ion-pairing phenomena and make the Hofmeister or lyotropic series of ions pertinent to a broad range of systems and phenomena. On the other hand ionic hydrophobicity and complexation capacity also determine ionic behavior in a variety of contexts. Over the years we have carried out carefully designed experiments on a few selected soft matter model systems, most involving zwitterionic phospholipids, to assess the importance of fundamental ionic and interfacial properties on ion specific effects. By tuning down direct Coulomb interactions, working with different interfacial geometries, and carefully tuning ion-lipid headgroup interactions it is possible to assess the importance of different parameters contributing to ion specific behavior. We argue that the majority of specific ion effects involving relatively simple soft matter systems can be at least qualitatively understood and demystified.

Two sides of the coin. Part 1. Lipid and surfactant self-assembly revisited

Hofmeister, specific ion effects, hydration and van der Waals forces at and between interfaces are factors that determine curvature and microstructure in self assembled aggregates of surfactants and lipids; and in microemulsions. Lipid and surfactant head group interactions and between aggregates vary enormously and are highly specific. They act on the hydrophilic side of a bilayer, micelle or other self assembled aggregate. It is only over the last three decades that the origin of Hofmeister effects has become generally understood. Knowledge of their systematics now provides much flexibility in designing nanostructured fluids. The other side of the coin involves equally specific forces. These (opposing) forces work on the hydrophobic side of amphiphilic interfaces. They are due to the interaction of hydrocarbons and other "oils" with hydrophobic tails of surfactants and lipids. The specificity of oleophilic solutes in microemulsions and lipid membranes provides a counterpoint to Hofmeister effects and hydration. Together with global packing constraints these effects determine microstructure. Another factor that has hardly been recognised is the role of dissolved gas. This introduces further, qualitative changes in forces that prescribe microstructure. The systematics of these effects and their interplay are elucidated. Awareness of these competing factors facilitates formulation of self assembled nanostructured fluids. New and predictable geometries that emerge naturally provide insights into a variety of biological phenomena like anaesthetic and pheromone action and transmission of the nervous impulse (see Part 2).

Ion-Specific and Thermal Effects in the Stabilization of the Gas Nanobubble Phase in Bulk Aqueous Electrolyte Solutions

Ion-stabilized nanobubbles in bulk aqueous solutions of various electrolytes were investigated. To understand the ion-specific mechanism of nanobubble stabilization, an approach based on the Poisson--Boltzmann equation at the nanobubble interface and in the near-surface layer was developed. It has been shown that the stabilization of nanobubbles is realized by the adsorption of chaotropic anions at the interface, whereas the influence of cosmotropic cations is weak. With increasing temperature, it should be accounted for by blurring the interface due to thermal fluctuations. As a result, the adsorbed state of ions becomes unstable: the nanobubble loses its stability and vanishes. This prediction was proven in our experiments. It turned out that in the case of liquid samples being kept in hermetically sealed ampules, where the phase equilibrium at the liquid-gas interface is fulfilled for any temperature, the volume number density of nanobubbles decreases with increasing temperature and this decrease is irreversible.

Emergence of a Stern Layer from the Incorporation of Hydration Interactions into the Gouy-Chapman Model of the Electrical Double Layer

In one of the most commonly used phenomenological descriptions of the electrical double layer, a charged solid surface and a diffuse region of mobile ions are separated from each other by a thin charge-depleted Stern layer. The Stern layer acts as a capacitor that improves the classical Gouy-Chapman model by increasing the magnitude of the surface potential and limiting the maximal counterion concentration. We show that very similar Stern-like properties of the diffuse double layer emerge naturally from adding a nonelectrostatic hydration repulsion to the electrostatic Coulomb potential. The interplay of electrostatic attraction and hydration repulsion of the counterions and the surface leads to the formation of a diffuse counterion layer that remains well separated from the surface. In addition, hydration repulsions between the ions limit and control the maximal ion concentration and widen the width of the diffuse double layer. Our mean-field model, which we express in terms of electrostatic and hydration potentials, is physically consistent and conceptually similar to the classical Gouy-Chapman model. It allows the incorporation of ion specificity, accounts for hydration properties of charged surfaces, and predicts Stern layer properties, which we analyze in terms of the effective size of the hydrated counterions.

Hofmeister effect of anions on calcium translocation by sarcoplasmic reticulum Ca(2+)-ATPase

The occurrence of Hofmeister (specific ion) effects in various membrane-related physiological processes is well documented. For example the effect of anions on the transport activity of the ion pump Na⁺, K⁺-ATPase has been investigated. Here we report on specific anion effects on the ATP-dependent Ca²⁺ translocation by the sarcoplasmic reticulum Ca²⁺-ATPase (SERCA). Current measurements following ATP concentration jumps on SERCA-containing vesicles adsorbed on solid supported membranes were carried out in the presence of different potassium salts. We found that monovalent anions strongly interfere with ATP-induced Ca²⁺ translocation by SERCA, according to their increasing chaotropicity in the Hofmeister series. On the contrary, a significant increase in Ca²⁺ translocation was observed in the presence of sulphate. We suggest that the anions can affect the conformational transition between the phosphorylated intermediates E₁P and E₂P of the SERCA cycle. In particular, the stabilization of the E₁P conformation by chaotropic anions seems to be related to their adsorption at the enzyme/water and/or at the membrane/water interface, while the more kosmotropic species affect SERCA conformation and functionality by modifying the hydration layers of the enzyme.