Ions interacting in solution: Moving from intrinsic to collective properties

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.

Chemical models for dense solutions

Here we examine the question of the chemical models widely used to describe dense solutions, particularly ionic solutions. First, a simple macroscopic analysis shows that, in the case of weak interactions, taking into account aggregated species amounts to modelling an effective attraction between solutes, although the stoichiometry used does not necessarily correspond to atomic reality. We then use a rigorous microscopic analysis to explain how, in the very general case, chemical models can be obtained from an atomic physical description. We show that there are no good or bad chemical models as long as we consider exact calculations. To obtain the simplest possible description, it is nevertheless advisable to take the speciation criterion that minimises the excess terms. Molecular simulations show that, very often, species can be defined simply by grouping ions which are in direct contact. In some cases, the appearance of macroscale clusters can be predicted.

To Pair or not to Pair? Machine-Learned Explicitly-Correlated Electronic Structure for NaCl in Water

The extent of ion pairing in solution is an important phenomenon to rationalize transport and thermodynamic properties of electrolytes. A fundamental measure of this pairing is the potential of mean force (PMF) between solvated ions. The relative stabilities of the paired and solvent shared states in the PMF and the barrier between them are highly sensitive to the underlying potential energy surface. However, direct application of accurate electronic structure methods is challenging, since long simulations are required. We develop wave function based machine learning potentials with the random phase approximation (RPA) and second order Møller-Plesset (MP2) perturbation theory for the prototypical system of Na and Cl ions in water. We show both methods in agreement, predicting the paired and solvent shared states to have similar energies (within 0.2 kcal/mol). We also provide the same benchmarks for different DFT functionals as well as insight into the PMF based on simple analyses of the interactions in the system.

Lysozyme aggregation and unfolding in ionic liquid solvents: Insights from small angle X-ray scattering and high throughput screening

Understanding protein behaviour is crucial for developing functional solvent systems. Ionic liquids (ILs) are designer salts with versatile ion combinations, where some suppress unfavourable protein behaviour. This work utilizes small angle X-ray scattering (SAXS) to investigate the size and shape changes of model protein hen egg white lysozyme (HEWL) in 137 IL and salt solutions. Guinier, Kratky, and pair distance distribution analysis were used to evaluate the protein size, shape, and aggregation changes in these solvents. At low IL and salt concentration (1 mol%), HEWL remained monodispersed and globular. Most ILs increased HEWL size compared to buffer, while the nitrate and mesylate anions induced the most significant size increases. IL cation branching, hydroxyl groups, and longer alkyl chains counteracted this size increase. Common salts exhibited specific ion effects, while the IL effect varied with concentration due to complex ion-pairing. Protein aggregation and unfolding occurred at 10 mol% IL, altering the protein shape, especially for ILs with multiple alkyl chains on the cation, or with a mesylate/nitrate anion. This study highlights the usefulness of adopting a high-throughput SAXS strategy for understanding IL effects on protein behaviour and provides insights on controlling protein aggregation and unfolding with ILs.

Binding of carboxylate and water to monovalent cations

The interactions of carboxylate anions with water and cations are important for a wide variety of systems, both biological and synthetic. To gain insight on properties of the local complexes, we apply density functional theory, to treat the complex electrostatic interactions, and investigate mixtures with varied numbers of carboxylate anions (acetate) and waters binding to monovalent cations, Li+, Na+ and K+. The optimal structure with overall lowest free energy contains two acetates and two waters such that the cation is four-fold coordinated, similar to structures found earlier for pure water or pure carboxylate ligands. More generally, the complexes with two acetates have the lowest free energy. In transitioning from the overall optimal state, exchanging an acetate for water has a lower free energy barrier than exchanging water for an acetate. In most cases, the carboxylates are monodentate and in the first solvation shell. As water is added to the system, hydrogen bonding between waters and carboxylate O atoms further stabilizes monodentate structures. These structures, which have strong electrostatic interactions that involve hydrogen bonds of varying strength, are significantly polarized, with ChelpG partial charges that vary substantially as the bonding geometry varies. Overall, these results emphasize the increasing importance of water as a component of binding sites as the number of ligands increases, thus affecting the preferential solvation of specific metal ions and clarifying Hofmeister effects. Finally, structural analysis correlated with free energy analysis supports the idea that binding to more than the preferred number of carboxylates under architectural constraints are a key to ion transport.

Unlocking the potential of polymeric desalination membranes by understanding molecular-level interactions and transport mechanisms

Polyamide reverse osmosis (PA-RO) membranes achieve remarkably high water permeability and salt rejection, making them a key technology for addressing water shortages through processes including seawater desalination and wastewater reuse. However, current state-of-the-art membranes suffer from challenges related to inadequate selectivity, fouling, and a poor ability of existing models to predict performance. In this Perspective, we assert that a molecular understanding of the mechanisms that govern selectivity and transport of PA-RO and other polymer membranes is crucial to both guide future membrane development efforts and improve the predictive capability of transport models. We summarize the current understanding of ion, water, and polymer interactions in PA-RO membranes, drawing insights from nanofiltration and ion exchange membranes. Building on this knowledge, we explore how these interactions impact the transport properties of membranes, highlighting assumptions of transport models that warrant further investigation to improve predictive capabilities and elucidate underlying transport mechanisms. We then underscore recent advances in in situ characterization techniques that allow for direct measurements of previously difficult-to-obtain information on hydrated polymer membrane properties, hydrated ion properties, and ion-water-membrane interactions as well as powerful computational and electrochemical methods that facilitate systematic studies of transport phenomena.

Physical insight into the entropy-driven ion association

The ion association is widely believed to be dominated by the favorable entropy change arising from the release of water molecules from ion hydration shells. However, no direct thermodynamic evidence exists to validate the reliability and suitability of this view. Herein, we employ complicated free energy calculations to rigorously split the free energy including its entropic and enthalpic components into the water-induced contributions and ion-ion interaction terms for several ion pairs from monatomic to polyatomic ions, spanning the size range from small kosmotropes to large chaotropes (Na⁺ , Cs⁺ , Ca²⁺ , F^- , I^- , CO₃ ^2- , and HPO₄ ^2- ). Our results successfully reveal that though ion associations are indeed determined by a delicate balance between the favorable entropy variation and the repulsive enthalpy change, the entropy gain dominated by the solvent occurs only for the monatomic ion pairing. The water-induced entropic contribution significantly goes against the ion pairing between polyatomic anion and cation, which is, alternatively, dominated by the favorable entropy from the ion-ion interaction term, due to the configurational arrangement of polyatomic anions involved in ion association. The structural and dynamic analysis demonstrates that the entropy penalty from the water phase is primarily ascribed to the enhanced stability of water molecules around the cation imposed by the incoming anion. Our study successfully provides a fundamental understanding of water-mediated ion associations and highlights disparate lengthscale dependencies of the dehydration thermodynamics on the specific types of ions.

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.

Toward a First-Principles Framework for Predicting Collective Properties of Electrolytes

Given the universal importance of electrolyte solutions, it is natural to expect that we have a nearly complete understanding of the fundamental properties of these solutions (e.g., the chemical potential) and that we can therefore explain, predict, and control the phenomena occurring in them. In fact, reality falls short of these expectations. But, recent advances in the simulation and modeling of electrolyte solutions indicate that it should soon be possible to make progress toward these goals. In this Account, we will discuss the use of first-principles interaction potentials based in quantum mechanics (QM) to enhance our understanding of electrolyte solutions. Specifically, we will focus on the use of quantum density functional theory (DFT) combined with molecular dynamics simulation (DFT-MD) as the foundation for our approach. The overarching concept is to understand and accurately reproduce the balance between local or short-ranged (SR) structural details and long-range (LR) correlations, allowing the prediction of the thermodynamics of both single ions in solution as well as the collective interactions characterized by activity/osmotic coefficients. In doing so, relevant collective motions and driving forces characterized by chemical potentials can be determined.In this Account, we will make the case that understanding electrolyte solutions requires a faithful QM representation of the SR nature of the ion-ion, ion-water, and water-water interactions. However, the number of molecules that is required for collective behavior makes the direct application of high-level QM methods that contain the best SR physics untenable, making methods that balance accuracy and efficiency a practical goal. Alternatives such as continuum solvent models (CSMs) and empirically based classical molecular dynamics have been extensively employed to resolve this problem but without yet overcoming the fundamental issue of SR accuracy. We will demonstrate that accurately describing the SR interaction is imperative for predicting both intrinsic properties, namely, at infinite dilution, and collective properties of electrolyte solutions.DFT has played an important role in our understanding of condensed phase systems, e.g., bulk liquid water, the air-water interface, ions in bulk, and at the air-water interface. This approach holds huge promise to provide benchmark calculations of electrolyte solution properties that will allow for the development and improvement of more efficient methods, as well as an enhanced understanding of fundamental phenomena. However, the standard protocol using the generalized gradient approximation with van der Waals (vdW) correction requires improvement in order to achieve a high level of quantitative accuracy. Simply simulating with higher level DFT functionals may not be the best route considering the significant computational cost. Alternative methods of incorporating information from higher levels of QM should be explored; e.g., using force matching techniques on small clusters, where high level benchmark calculations are possible, to develop ideal correction terms to the DFT functional is a promising possibility. We argue that DFT with statistical mechanics is becoming an increasingly useful framework enabling the prediction of collective electrolyte properties.

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.

Hofmeister Effect in Self-Organized Chemical Systems

We studied the effect of spectator ions in the prototype of far-from-equilibrium self-organized chemical systems, the Belousov-Zhabotinsky (BZ) reaction. In particular, we investigated the specific ion effect of alkali metal cations, connoted for their kosmotropic and chaotropic properties. By means of combined experimental and numerical approaches, we could show a neat and robust evidence for the Hofmeister effect in this system. Spectator cations induce a marked increment of the induction period that preludes regular oscillations and decrease the oscillation amplitude following the sequence Li⁺ < Na⁺ ≪ K⁺ ∼ Cs⁺. These ions affect the system kinetics by interfering in the interaction between the oxidized form of the catalyst and the organic substrate, responsible for resetting the BZ system to pre-autocatalytic (reduced) conditions. The specific ion effect on these key reactive steps is systematically characterized and correlated with different parameters which describe the interaction of the cations with the solvent.

Dissociation of salts in water under pressure

The investigation of salts in water at extreme conditions is crucial to understanding the properties of aqueous fluids in the Earth. We report first principles (FP) and classical molecular dynamics simulations of NaCl in the dilute limit, at temperatures and pressures relevant to the Earth’s upper mantle. Similar to ambient conditions, we observe two metastable states of the salt: the contact (CIP) and the solvent-shared ion-pair (SIP), which are entropically and enthalpically favored, respectively. We find that the free energy barrier between the CIP and SIP minima increases at extreme conditions, and that the stability of the CIP is enhanced in FP simulations, consistent with the decrease of the dielectric constant of water. The minimum free energy path between the CIP and SIP becomes smoother at high pressure, and the relative stability of the two configurations is affected by water self-dissociation, which can only be described properly by FP simulations.

Salts in water at extreme conditions play a fundamental role in determining the properties of the Earthʼs mantle constituents. Here the authors shed light on ion-water and ion-ion interactions for NaCl dissolved in water at conditions relevant to the Earthʼs upper mantle by molecular dynamics simulations.

Quantifying the hydration structure of sodium and potassium ions: taking additional steps on Jacob's Ladder

The ability to reproduce the experimental structure of water around the sodium and potassium ions is a key test of the quality of interaction potentials due to the central importance of these ions in a wide range of important phenomena.

Ion at Air-Water Interface Enhances Capillary Wave Fluctuations: Energetics of Ion Adsorption

Recent simulations provide the energetics of ion adsorption at the air-water (a/w) interface: The presence of the ion at the interface suppresses the fluctuations of the capillary waves (CWs) reducing the entropy and displaces the weakly interacting water molecules to the bulk causing a reduction in the enthalpy. Here, we provide atomistic simulation-based evidence that the inferences of the existing studies stem from considering a small simulation volume that pins the CWs. For an appropriate size of the simulation system, an ion at the a/w interface enhances the CW fluctuations. Furthermore, we discover that the characteristics of the waves governing these enhanced CW fluctuations ensure a significant decrease in the pressure-volume work causing the enthalpy decrease, while the same wave characteristics of the CWs become responsible for an entropy decrease. Overall, the paper revisits the free energy picture of this fundamental problem of ion adsorption at the a/w interface.

Volcano Plots Emerge from a Sea of Nonaqueous Solvents: The Law of Matching Water Affinities Extends to All Solvents

The properties of all electrolyte solutions, whether the solvent is aqueous or nonaqueous, are strongly dependent on the nature of the ions in solution. The consequences of these specific-ion effects are significant and manifest from biochemistry to battery technology. The "law of matching water affinities" (LMWA) has proven to be a powerful concept for understanding and predicting specific-ion effects in a wide range of systems, including the stability of proteins and colloids, solubility, the behavior of lipids, surfactants, and polyelectrolytes, and catalysis in water and ionic liquids. It provides a framework for considering how the ions of an electrolyte interact in manifestations of ion specificity and therefore represents a considerable conceptual advance on the Hofmeister or lyotropic series in understanding specific-ion effects. Underpinning the development of the law of matching water affinities were efforts to interpret the so-called "volcano plots". Volcano plots exhibit a stark inverted "V" shape trend for a range of electrolyte dependent solution properties when plotted against the difference in solvation energies of the ions that constitute the electrolyte. Here we test the hypothesis that volcano plots are also manifest in nonaqueous solvents in order to investigate whether the LMWA can be extended to nonaqueous solvents. First we examine the standard solvation energies of electrolytes in nonaqueous solvents for evidence of volcano trends and then extend this to include the solubility and the activity/osmotic coefficients of electrolytes, in order to explore real electrolyte concentrations. We find that with respect to the solvent volcano trends are universal, which brings into question the role of solvent affinity in the manifestation of specific-ion effects. We also show that the volcano trends are maintained when the ionic radii are used in place of the absolute solvation energies as the abscissa, thus showing that ion sizes, rather than the solvent affinities, fundamentally determine the manifestation of ion specificity. This leads us to propose that specific-ion effects across all solvents including water can be understood by considering the relative sizes of the anion and cation, provided the ions are spherical or tetrahedral. This is an extension of the LMWA to all solvents in which the "water affinity" is replaced with the relative size of the anion and cation.

Experimentally quantifying anion polarizability at the air/water interface

The adsorption of large, polarizable anions from aqueous solution on the air/water interface controls important atmospheric chemistry and is thought to resemble anion adsorption at hydrophobic interfaces generally. While the favourability of adsorption of such ions is clear, quantifying adsorption thermodynamics has proven challenging because it requires accurate description of the structure of the anion and its solvation shell at the interface. In principle anion polarizability offers a structural window, but to the best of our knowledge there has so far been no experimental technique that allowed its characterization with interfacial specificity. Here, we meet this challenge using interface-specific vibrational spectroscopy of Cl–O vibrations of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{ClO}}_4^ -$$\end{document}ClO4- anion at the air/water interface and report that the interface breaks the symmetry of the anion, the anisotropy of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{ClO}}_4^ -$$\end{document}ClO4-’s polarizability tensor is more than two times larger than in bulk water and concentration dependent, and concentration-dependent polarizability changes are consistent with correlated changes in surface tension.

Understanding anion-specific interactions with hydrophobic interfaces is challenging due to an absence of local structural probes. Here, the authors experimentally quantify the anisotropy of perchlorate’s polarizability at the air/water interface, a window into anion and solvation shell structure.

Supersaturated calcium carbonate solutions are classical

Mechanisms of CaCO₃ nucleation from solutions that depend on multistage pathways and the existence of species far more complex than simple ions or ion pairs have recently been proposed. Herein, we provide a tightly coupled theoretical and experimental study on the pathways that precede the initial stages of CaCO₃ nucleation. Starting from molecular simulations, we succeed in correctly predicting bulk thermodynamic quantities and experimental data, including equilibrium constants, titration curves, and detailed x-ray absorption spectra taken from the supersaturated CaCO₃ solutions. The picture that emerges is in complete agreement with classical views of cluster populations in which ions and ion pairs dominate, with the concomitant free energy landscapes following classical nucleation theory.

What is the fundamental ion-specific series for anions and cations? Ion specificity in standard partial molar volumes of electrolytes and electrostriction in water and non-aqueous solvents

The importance of electrolyte solutions cannot be overstated. Beyond the ionic strength of electrolyte solutions the specific nature of the ions present is vital in controlling a host of properties. Therefore ion specificity is fundamentally important in physical chemistry, engineering and biology. The observation that the strengths of the effect of ions often follows well established series suggests that a single predictive and quantitative description of specific-ion effects covering a wide range of systems is possible. Such a theory would revolutionise applications of physical chemistry from polymer precipitation to drug design. Current approaches to understanding specific-ion effects involve consideration of the ions themselves, the solvent and relevant interfaces and the interactions between them. Here we investigate the specific-ion effects trends of standard partial molar volumes and electrostrictive volumes of electrolytes in water and eleven non-aqueous solvents. We choose these measures as they relate to bulk properties at infinite dilution, therefore they are the simplest electrolyte systems. This is done to test the hypothesis that the ions alone exhibit a specific-ion effect series that is independent of the solvent and unrelated to surface properties. The specific-ion effects trends of standard partial molar volumes and normalised electrostrictive volumes examined in this work show a fundamental ion-specific series that is reproduced across the solvents, which is the Hofmeister series for anions and the reverse lyotropic series for cations, supporting the hypothesis. This outcome is important in demonstrating that ion specificity is observed at infinite dilution and demonstrates that the complexity observed in the manifestation of specific-ion effects in a very wide range of systems is due to perturbations of solvent, surfaces and concentration on the underlying fundamental series. This knowledge will guide a general understanding of specific-ion effects and assist in the development of a quantitative predictive theory of ion specificity.

Ion-induced alterations of the local hydration environment elucidate Hofmeister effect in a simple classical model of Trp-cage miniprotein

Protein stability is known to be influenced by the presence of Hofmeister active ions in the solution. In addition to direct ion-protein interactions, this influence manifests through the local alterations of the interfacial water structure induced by the anions and cations present in this region. In our earlier works it was pointed out that the effects of Hofmeister active salts on the stability of Trp-cage miniprotein can be modeled qualitatively using non-polarizable force fields. These simulations reproduced the structure-stabilization and structure-destabilization effects of selected kosmotropic and chaotropic salts, respectively. In the present study we use the same model system to elucidate atomic processes behind the chaotropic destabilization and kosmotropic stabilization of the miniprotein. We focus on changes of the local hydration environment of the miniprotein upon addition of NaClO₄ and NaF salts to the solution. The process is separated into two parts. In the first, 'promotion' phase, the protein structure is fixed, and the local hydration properties induced by the simultaneous presence of protein and ions are investigated, with a special focus on the interaction of Hofmeister active anions with the charged and polar sites. In the second, 'rearrangement' phase we follow changes of the hydration of ions and the protein, accompanying the conformational relaxation of the protein. We identify significant factors of an enthalpic and entropic nature behind the ion-induced free energy changes of the protein-water system, and also propose a possible atomic mechanism consistent with the Collins's rule, for the chaotropic destabilization and kosmotropic stabilization of protein conformation.

Real single ion solvation free energies with quantum mechanical simulation

Single ion solvation free energies are one of the most important properties of electrolyte solutions and yet there is ongoing debate about what these values are. Only the values for neutral ion pairs are known. Here, we use DFT interaction potentials with molecular dynamics simulation (DFT-MD) combined with a modified version of the quasi-chemical theory (QCT) to calculate these energies for the lithium and fluoride ions. A method to correct for the error in the DFT functional is developed and very good agreement with the experimental value for the lithium fluoride pair is obtained. Moreover, this method partitions the energies into physically intuitive terms such as surface potential, cavity and charging energies which are amenable to descriptions with reduced models. Our research suggests that lithium's solvation free energy is dominated by the free energetics of a charged hard sphere, whereas fluoride exhibits significant quantum mechanical behavior that cannot be simply described with a reduced model.

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⁺.

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).