Deconstructing Free Energies in the Law of Matching Water Affinities

Effects of Ionic Interferents on Electrocatalytic Nitrate Reduction: Mechanistic Insight

Nitrate, a prevalent water pollutant, poses substantial public health concerns and environmental risks. Electrochemical reduction of nitrate (eNO3RR) has emerged as an effective alternative to conventional biological treatments. While extensive lab work has focused on designing efficient electrocatalysts, implementation of eNO3RR in practical wastewater settings requires careful consideration of the effects of various constituents in real wastewater. In this critical review, we examine the interference of ionic species commonly encountered in electrocatalytic systems and universally present in wastewater, such as halogen ions, alkali metal cations, and other divalent/trivalent ions (Ca2+, Mg2+, HCO3-/CO32-, SO42-, and PO43-). Notably, we categorize and discuss the interfering mechanisms into four groups: (1) loss of active catalytic sites caused by competitive adsorption and precipitation, (2) electrostatic interactions in the electric double layer (EDL), including ion pairs and the shielding effect, (3) effects on the selectivity of N intermediates and final products (N2 or NH3), and (4) complications by the hydrogen evolution reaction (HER) and localized pH on the cathode surface. Finally, we summarize the competition among different mechanisms and propose future directions for a deeper mechanistic understanding of ionic impacts on eNO3RR.

Polarizability Plays a Decisive Role in Modulating Association between Molecular Cations and Anions

Electrostatic interactions involving proteins depend on not only the ionic charges involved but also their chemical identities. Here we examine the origins of incompletely understood differences in the strength of association of different pairs of monovalent molecular ions that are relevant to protein-protein and protein-ligand interactions. Cationic analogues of the basic amino acid side chains are simulated, along with oxyanionic analogues of cation-exchange ligands and acidic amino acids. Experimentally observed association trends with respect to the cations, but not anions, are captured by a nonpolarizable model. An effective continuum correction to account for electronic polarizability can capture both trends better but at the expense of fidelity to the underlying free energy landscape for ion-pair association. A polarizable model proves decisive in capturing experimentally suggested trends with respect to both cations and anions; critically, the free energy landscape for ion-pair association is itself altered, thus altering configurational sampling.

Deep neural network based quantum simulations and quasichemical theory for accurate modeling of molten salt thermodynamics

With dual goals of efficient and accurate modeling of solvation thermodynamics in molten salt liquids, we employ ab initio molecular dynamics (AIMD) simulations, deep neural network interatomic potentials (NNIP), and quasichemical theory (QCT) to calculate the excess chemical potentials for the solute ions Na+ and Cl- in the molten NaCl liquid. NNIP-based molecular dynamics simulations accelerate the calculations by 3 orders of magnitude and reduce the uncertainty to 1 kcal mol-1. Using the Density Functional Theory (DFT) level of theory, the predicted excess chemical potential for the solute ion pair is -178.5 ± 1.1 kcal mol-1. A quantum correction of 13.7 ± 1.9 kcal mol-1 is estimated via higher-level quantum chemistry calculations, leading to a final predicted ion pair excess chemical potential of -164.8 ± 2.2 kcal mol-1. The result is in good agreement with a value of -163.5 kcal mol-1 obtained from thermo-chemical tables. This study validates the application of QCT and NNIP simulations to the molten salt liquids, allowing for significant insights into the solvation thermodynamics crucial for numerous molten salt applications.

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.

Understanding specific ion effects and the Hofmeister series

Specific ion effects (SIE), encompassing the Hofmeister Series, have been known for more than 130 years since Hofmeister and Lewith's foundational work. SIEs are ubiquitous and are observed across the medical, biological, chemical and industrial sciences. Nevertheless, no general predictive theory has yet been able to explain ion specificity across these fields; it remains impossible to predict when, how, and to what magnitude, a SIE will be observed. In part, this is due to the complexity of real systems in which ions, counterions, solvents and cosolutes all play varying roles, which give rise to anomalies and reversals in anticipated SIEs. Herein we review the historical explanations for SIE in water and the key ion properties that have been attributed to them. Systems where the Hofmeister series is perturbed or reversed are explored, as is the behaviour of ions at the liquid-vapour interface. We discuss SIEs in mixed electrolytes, nonaqueous solvents, and in highly concentrated electrolyte solutions - exciting frontiers in this field with particular relevance to biological and electrochemical applications. We conclude the perspective by summarising the challenges and opportunities facing this SIE research that highlight potential pathways towards a general predictive theory of SIE.

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.

The behavior of ions in water is controlled by their water affinity

The strong, long-range electrostatic forces described by Coulomb's law disappear for ions in water, and the behavior of these ions is instead controlled by their water affinity – a weak, short-range force which arises from their charge density. This was established experimentally in the mid-1980s by size-exclusion chromatography on carefully calibrated Sephadex®G-10 (which measures the effective volume and thus the water affinity of an ion) and by neutron diffraction with isotopic substitution (which measures the density and orientation of water molecules near the diffracting ion and thus its water affinity). These conclusions have been confirmed more recently by molecular dynamics simulations, which explicitly model each individual water molecule. This surprising change in force regime occurs because the oppositely charged ions in aqueous salt solutions exist functionally as ion pairs (separated by 0, 1 or 2 water molecules) as has now been shown by dielectric relaxation spectroscopy; this cancels out the strong long-range electrostatic forces and allows the weak, short-range water affinity effects to come to the fore. This microscopic structure of aqueous salt solutions is not captured by models utilizing a macroscopic dielectric constant. Additionally, the Law of Matching Water Affinity, first described in 1997 and 2004, establishes that contact ion pair formation is controlled by water affinity and is a major determinant of the solubility of charged species since only a net neutral species can change phases.

Physical origin underlying the prenucleation-cluster-mediated nonclassical nucleation pathways for calcium phosphate

The involvement of prenucleation clusters (PNCs) in crystallization from a supersaturated solution has been recently admitted within the framework of nonclassical nucleation theory; however, little is known about PNCs, at the quantitative level, for their formation mechanism and stability, the new phase formed by them, as well as their impact on nucleation barriers. Herein, using the sophisticated free energy calculations with a cumulative simulation time of over 5 μs, we identify a thermodynamically favored pathway of the PNC-mediated nucleation for calcium phosphate, starting with the ion pair association in solution. We demonstrate that such an ion association occurs not only between cations and anions, but also for the polyatomic species with charges of the same sign, which, in fact, leads to PNC formation via the consecutive coordination of the phosphate ions to calcium. The free energy decomposition calculations illustrate that the water phase is capable to either hinder or promote ion association for the abovementioned processes, and its specific role is intricately related to the characteristics of the hydration shell around calcium ions. The favorable interactions between the highly charged species play a crucial role in stabilizing the PNC complexes and the aggregates formed by PNCs. Furthermore, our present work reveals that the uptake of an extra calcium ion is the first and mandatory step to trigger PNC aggregation into amorphous calcium phosphate (ACP) by eliminating the related free energy barriers. Our theoretical study successfully provides quantitative explanations to a large set of experimental data in the field, which is currently under intense discussions associated with the nonclassical nucleation mechanism. The combination of computational methods developed in our present work offers a feasible and general solution to quantitatively and systematically study ion associations and crystal nucleation/growth in an aqueous solution at the atomic level, which are normally inaccessible to most of the existing experimental acquisitions.

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.