A continuum model of solvation energies including electrostatic, dispersion, and cavity contributions

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.

Dispersion Interactions in Condensed Phases and inside Molecular Containers

ConspectusThe past decade has seen significant progress in the understanding and appreciation of the importance of London dispersion interactions (LDIs) in supramolecular systems and solutions. The Slater-Kirkwood formula relates LDIs to the molecular polarizabilities of the two interacting molecular species (α) and their interaction distance (a dependence of R-6). When advancing arguments related to intermolecular interactions, it is frequently assumed that molecules with larger molecular polarizabilities are more amenable to larger LDIs. However, arguments related to molecular polarizabilities are not always transferable to the condensed phase. In fact, the underlying bulk and molecular polarizabilities of common solvents show opposing trends. The intuitive concept that aromatic molecules are more polarizable than saturated hydrocarbons and that perfluorinated molecules are less polarizable than saturated hydrocarbons applies to the condensed phase only. When treating association phenomena in solution, where LDIs are generally very attenuated, the use of bulk polarizabilities is recommended, which are experimentally accessible through either refractive index measurements or suitable solvatochromic probes. Such probes can also be used to assess polarizabilities inside molecular container compounds, such as cucurbit[n]urils (CBn), cyclodextrins, calixarenes, and hemicarcerands. These macrocyclic cavities can have extreme microenvironments. For example, the inner concave phase of CB7 has been shown to be weakly polarizable, falling in between the gas phase and perfluorohexane; those of β-cyclodextrin and p-sulfonatocalix[4]arene have been found to be similarly polarizable as water and alkanes, respectively, and the inside of hemicarcerands displays a very large bulk polarizability, exceeding that of diiodomethane. CBn compounds are privileged molecular container compounds, which we exemplify in this Account through case studies. (1) CBn macrocycles are prime water-soluble receptors for hydrocarbons, allowing for the reduction of the binding free energies to two components: the hydrophobic effect and dispersion interactions. To understand hydrocarbon binding, we initiated the HYDROPHOBE challenge, which revealed the shortcomings of both quantum-chemical and molecular dynamics approaches. (2) The smallest CBn receptor, CB5, is uniquely suited to bind the entire noble gas series, where hydrophobic effects and dispersion interactions operate in opposite directions. CB5 was revaled to be a unique synthetic receptor for noble gases, with the dominant driving force being the recovery of the cavitation energies for the hydration of noble gases in aqueous solution. Computational methods that encounter challenges in predicting hydrocarbon affinities and trends for CB6 and CB7 perform well for noble gases binding to CB5. (3) The larger homologue, CB8, allows one to set up intermolecular interaction chambers by the encapsulation of a (first) aromatic guest, thereby tuning LDIs inside the receptor cavity. In this manner, CB8 can be modulated to preferentially bind unsaturated and aromatic rather than saturated hydrocarbons, while the unmodified cavities of the smaller macrocycles CB6 and CB7 show selective binding of saturated hydrocarbons. (4) The (charged) host-guest complexes of CBn hosts are sufficiently stable in the gas phase, allowing for the study of the influence of LDIs on inner-phase chemical reactions. These studies are particularly interesting for the theoretical analysis of isolated host-guest LDIs, as experimental and computational data are directly comparable in the gas phase due to the absence of the solvation effect.

Dielectric exclusion, an éminence grise

Dielectric exclusion has long been well-established as the key mechanism in membrane desalination, critical for delivering the required levels of salt rejection, also playing important role in electro-membrane processes, nanofluidics, and biomimetics. Unfortunately, its elusive nature and many features, such as dependence on the pore size, membrane hydration, and ion size and charge, make it deceivingly similar to the other ion exclusions mechanisms, steric and Donnan, which has led to much controversy and misconceptions. Starting from the Born model and the concept of self-energy, the present paper reviews and highlights the physical basis of dielectric exclusion, its main features and the ways it may be looked at. It discusses what makes the dielectric exclusion both similar and distinctly different from the other mechanism and its synergy and intimate connection with other phenomena, such as Donnan exclusion, permeability-selectivity upper-bound, and selectivity of charged membranes towards uncharged solutes. The paper also addresses subjects that still cause much controversy at present, such as appropriate measures of ionic radii and the subtle distinction between the dielectric exclusion and primary ion hydration. It also points to gaps that need to be bridged towards more complete theory. The points addressed here are important for understanding, modeling and development of various next-generation separation technologies including water purification, resource recovery and reuse, and green energy generation and storage.

Visual demonstration and prediction of the Hofmeister series based on a poly(ionic liquid) photonic array

The Hofmeister effect and associated Hofmeister series (HS) are ubiquitous in physicochemical phenomena and have demonstrated fundamental importance in a myriad of fields ranging from chemistry to biology. Visualization of the HS not only helps to straightforwardly understand the underpinning mechanism, but also enables the prediction of new ion positions in the HS and directs the applications of the Hofmeister effect. Owing to the difficulties of sensing and reporting complete multiple and subtle inter- and intramolecular interactions involved in the Hofmeister effect, facile and accurate visual demonstration and prediction of the HS remain highly challenging. Herein, a poly(ionic liquid) (PIL)-based photonic array containing 6 inverse opal microspheres was rationally constructed to efficiently sense and report the ion effects of the HS. The PILs can not only directly conjugate with HS ions due to their ion-exchange properties, but also provide sufficient noncovalent binding diversity with these ions. Meanwhile, subtle PIL-ion interactions can be sensitively amplified to optical signals owing to their photonic structures. Therefore, synergistic integration of PILs and photonic structures gives rise to accurate visualization of the ion effect of the HS, as demonstrated by correctly ranking 7 common anions. More importantly, assisted by principal component analysis (PCA), the developed PIL photonic array can serve as a general platform to facilely, accurately, and robustly predict the HS positions of an unprecedented amount of important and useful anions and cations. These findings indicate that the PIL photonic platform is very promising for addressing challenges in the visual demonstration and prediction of HS and promoting a molecular-level understanding of the Hoffmeister effect.

Cucurbiturils mimicked by low polarizability solvents with pre-formed cavities: an empirical model to predict hydrocarbon selectivity

Relative binding affinities of a series of nine rigid hydrocarbons towards the cavity formed by a portion of the inner wall of cucurbit[8]uril (CB[8]) and a positive auxiliary guest were determined by competitive ¹⁹F NMR titrations in deuterium oxide. The corresponding free binding energies were corrected by the hydrocarbon computed solvation energies to obtain their free energies of transfer from the gas phase to the CB[8]/auxiliary guest cavity. These energies correlate linearly with the hydrocarbon static polarizabilities, thereby suggesting that the selectivity is driven, perhaps exclusively, by dispersive interactions between the hydrocarbons and the tailor-made cavity, regardless of the degree of unsaturation of the guests. The free energies of transfer also correlate linearly with the energy released upon introduction of the hydrocarbon into a pre-formed cavity extruded from a solvent (benzene) selected to mimic the polarity and polarizability of the CB[8]/auxiliary probe cavity – and this, with a unity slope. Among other features, this empirical model also accurately predicts the relative binding affinities of various rigid hydrocarbons to CB[6] and CB[7], as well as noble gases to CB[5], when the macrocycles are mimicked with pre-formed cavities in perfluorohexane or perfluorohexane/benzene mixtures, both being notoriously non-polar and non-polarizable environments.

Mimicking cucurbiturils with low polarizability solvents and pre-formed cavities allows the in silico prediction of their selectivities towards hydrocarbons and noble gases in aqueous solution.

Buffer-specific effects arise from ionic dispersion forces

Buffer solutions do not simply regulate pH, but also change the properties of protein molecules. The zeta potential of lysozyme varies significantly at the same buffer concentration, in the order...

Fast Calculation of Electrostatic Solvation Free Energy in Simple Ionic Fluids Using an Energy-Scaled Debye-Hückel Theory

Continuum theories are useful to compute the solvation free energy in ionic fluids. Herein, the electrostatic solvation free energy (ESFE) in simple ionic fluids is studied with an energy-scaled Debye-Hückel (ESDH) theory. Given the ESFEs of simple spherical ions as input, the ESDH theory is applicable to molecules with various complex geometries and charge distributions. Specifically, the ESDH theory is applied to molecules in a molten salt system, where the predicted ESFEs are in good agreement with molecular dynamics simulation results. Our study sheds light on accurately predicting the ESFE in ionic fluids with phenomenological continuum theories.

Allosteric Signal Amplification Sensing Using a Bisthiourea-Binaphthyl-Polythiophene Conjugate: A Positive Homotropic Allosterim Case

The development of signal amplification systems has attracted much attention and presents a highly challenging objective. Herein, we reveal the amplification processes using a newly synthesized bisthiourea-binaphthyl-polythiophene conjugate. The spectral data, behavior of supramolecular complexation, and thermodynamic parameters with calculation support comprehensively elucidated the factors that control the outcomes of the signal amplification. The present work provides a new perspective on functional chemosensors and an attractive alternative to conventional amplification systems.

Specific Ion Effects on the Colloidal Stability of Layered Double Hydroxide Single-layer Nanosheets

The surface charge properties and aggregation behavior of positively charged Mg-Al-NO₃ layered double hydroxide (LDH) single-layer nanosheets dispersed in water were investigated in the presence of K⁺ salts with different mono-, di-, and trivalent anions, using electrophoresis and dynamic light scattering techniques. An increase in the salt concentration can significantly decrease the effective surface charge density (σ_eff) of LDHs, leading to the aggregation of nanosheets. The critical coagulation concentration (CCC) or ionic strength (CCIS) of salts for nanosheets significantly decreases with an increase in the valence of anions. Specific ion effects, with a partially reverse Hofmeister series, are observed. On the basis of the Stern model and the DLVO theory, the relationship of CCC with σ_eff and the ionic valences of salts (z_i) is theoretically analyzed, which can accurately describe the dependence of CCC on the σ_eff and z_i but cannot explain the origin of specific ion effects. To explore the origin of specific ion effects, a correlation between CCIS and the specific adsorption energy (E_sc) of anions within the Stern layer is developed. Especially, an empirical relationship of E_sc with the characteristic physical parameters of anions is proposed. Our model can accurately predict the CCISs of at least monovalent anions and divalent anions (CO₃^2- and SO₄^2-), demonstrating that the specific ion effects observed can be attributed to the differences in ionic size, polarizability, and hydration free energy (or the formation capacity of anion-cation pairs) of different anions. This work not only deepens the understanding of specific ion effects on the colloidal stability but also provides useful information for the potential applications of LDH single-layer nanosheets.

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.

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.

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.

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.

Pair correlations that link the hydrophobic and Hofmeister effects

The Hofmeister effect describes how different ions make solutes more or less hydrophobic. The effect is thought to occur due to structural changes in the solvent induced by the ion's presence, particularly in water. In this study, the structural changes in water due to the presence of ions are investigated by molecular dynamics simulations of various monatomic ions in the SPC/E water model. Structural analyses reveal specific orientations of solvating waters around each of the ions studied. Using a new method, these orientations are quantified by a set of pair correlation functions that describe dipole-ion correlations in structure. These correlations are shown to contribute to the potential of mean force between waters and the ion of interest, and therefore to the free energy of the system. The magnitude of this free energy is found to result in a Hofmeister series for the various ions studied, therefore demonstrating a Hofmeister effect with respect to water's structure that is quantified by pair correlation functions. Most crucially, the pair correlations that lead to this Hofmeister effect also contribute to the hydrophobic effect (the entropy of hydrophobic solvation) [Liu et al., J. Chem. Phys., 2015, 142, 114117], and those which dominate the hydrophobic effect are modulated by an ion's presence, therefore demonstrating a mechanistic link between the two effects.

Experimental Binding Energies in Supramolecular Complexes

On the basis of many literature measurements, a critical overview is given on essential noncovalent interactions in synthetic supramolecular complexes, accompanied by analyses with selected proteins. The methods, which can be applied to derive binding increments for single noncovalent interactions, start with the evaluation of consistency and additivity with a sufficiently large number of different host-guest complexes by applying linear free energy relations. Other strategies involve the use of double mutant cycles, of molecular balances, of dynamic combinatorial libraries, and of crystal structures. Promises and limitations of these strategies are discussed. Most of the analyses stem from solution studies, but a few also from gas phase. The empirically derived interactions are then presented on the basis of selected complexes with respect to ion pairing, hydrogen bonding, electrostatic contributions, halogen bonding, π-π-stacking, dispersive forces, cation-π and anion-π interactions, and contributions from the hydrophobic effect. Cooperativity in host-guest complexes as well as in self-assembly, and entropy factors are briefly highlighted. Tables with typical values for single noncovalent free energies and polarity parameters are in the Supporting Information.

A continuum solvent model of ion-ion interactions in water

The calculation of ion-ion interactions in water is a problem of long standing importance. Modelling these interactions is a prerequisite to explaining Hofmeister (specific ion) effects. We here generalize our solvation model of ions to calculate the free energy of two ions in water as a function of separation. The same procedure has previously been applied to calculate ion interactions with the air-water interface successfully. The Conductor like Screening Model (COSMO) is used. This treats the ions on a quantum mechanical level and calculates numerically the electrostatic response of the surrounding solvent. Estimates of the change in the cavity formation energy and the change in the ion-water dispersion energy as the ions approach are included separately. The calculated interaction potentials are too attractive and this is a significant issue. However, they do reproduce the affinity of similarly sized ions for each other, which is a crucial property of these potentials. They are also oscillatory, another important property. We normalize the potentials to reduce the over-attraction, and good correlation with experimental values is achieved. We identify the driving contributions to this like-prefers-like behaviour. We then put forward a plausible hypothesis for the over-attraction of the potentials. An agreeable feature of our approach is that it does not rely on salt specific parameters deliberately adjusted to reproduce experimental values.

Accurate evaluation of charge asymmetry in aqueous solvation

Charge hydration asymmetry (CHA)-a characteristic dependence of hydration free energy on the sign of the solute charge-quantifies the asymmetric response of water to electric field at microscopic level. Accurate estimates of CHA are critical for understanding hydration effects ubiquitous in chemistry and biology. However, measuring hydration energies of charged species is fraught with significant difficulties, which lead to unacceptably large (up to 300%) variation in the available estimates of the CHA effect. We circumvent these difficulties by developing a framework which allows us to extract and accurately estimate the intrinsic propensity of water to exhibit CHA from accurate experimental hydration free energies of neutral polar molecules. Specifically, from a set of 504 small molecules we identify two pairs that are analogous, with respect to CHA, to the K(+) /F(-) pair-a classical probe for the effect. We use these "CHA-conjugate" molecule pairs to quantify the intrinsic charge-asymmetric response of water to the microscopic charge perturbations: the asymmetry of the response is strong, ∼50% of the average hydration free energy of these molecules. The ability of widely used classical water models to predict hydration energies of small molecules correlates with their ability to predict CHA.

Extended Debye-Hückel theory for studying the electrostatic solvation energy

The electrostatic part of the solvation energy has been studied by using extended Debye-Hückel (DH) theories. Specifically, our molecular Debye-Hückel theory [J. Chem. Phys. 2011, 135, 104104] and its simplified version, an energy-scaled Debye-Hückel theory, were applied to electrolytes with strong electrostatic coupling. Our theories provide a practical methodology for calculating the electrostatic solvation free energies, and the accuracy was verified for atomic and diatomic charged solutes.