Solvation Thermodynamics: Theory and Applications

Ion-Size Dependent Adsorption Crossover on the Surface of a Water Droplet

The adsorption of ionic and neutral spherical solutes on the surface of a liquid water droplet are investigated using molecular dynamics simulations and theoretical analyses. The results reveal a crossover in the sign of the adsorption free energy as a function of ion size, with ions larger than iodide predicted to be increasingly surface active. Adsorption free energies are decomposed into competing energetic and entropic contributions arising from direct solute-water interaction energy and its fluctuations. The entropically driven surface activity of large ions is predicted to increase with ion size, while small ions are typically driven away from the interface by a more delicate balance of energetic and entropic contributions, with a nonmonotonic ion size dependence linked to the ion's hydration-shell structure and stability. The physical interpretation of the results is illuminated by comparisons with dielectric linear response and cavity formation predictions and implications to interfacial acidity and enhanced chemical reactivity are discussed.

Hydrophilic Versus Hydrophobic Coupling in the Pressure Dependence of the Chemical Potential of Alkali Metal and Halide Ions in Water

We computed the chemical potential for some alkali metal ions (K⁺, Rb⁺, and Cs⁺) and two halide ions (Br^- and I^-) in aqueous solution at ambient T and various pressures in the range 1-8000 atm. Results were obtained from classic Monte Carlo simulations in the NPT ensemble by means of the free energy perturbation method. Here, the chemical potential is computed as the sum of a term relative to a Lennard-Jones solute and a term relative to the process in which this solute is transformed into the ion. Hydrophobic and hydrophilic features of these two components of the chemical potential show opposite behaviors under isothermal compression. The increase in pressure determines an increase in the hydrophobic component, which becomes more positive with a stronger effect for larger ions. Correspondingly, the values of the hydrophilic component become more negative for alkali ions, whereas they are only slightly affected by compression for halide ions. Hydrophobic-hydrophilic quasi-compensation in the slopes is observed for Rb⁺. For a smaller ion, such as K⁺, the dependence on pressure of the hydrophilic component is slightly dominant. For a larger ion, as observed in the cases of Cs⁺, Br^-, and I^-, the hydrophobic component assumes the determinant role. Pressure dependence of the chemical potential is little affected by corrections introduced for molecular potential truncation. This view can change for possible boundary artifacts that could have affected the static electrostatic potential. Some inference is obtained from comparison with experimental data at 1 atm on the free energy of hydration. Discrepancies show the characteristic asymmetry between cations and anions. The further addition of a correction based on the static potential significantly reduces these discrepancies with important error cancellation on the sum of chemical potentials of ions of opposite charge. The correction is applied also at higher pressures, and results are compared with those obtained by adding an alternative correction that is based on the water number density. Regardless of the ion, changes of the chemical potential induced by an increase in pressure appear to be dominated by the hydrophobic component, in particular when using the alternative correction. For bromide and iodide electrolytes, the two corrections give chemical potentials in good agreement.

Anion-cation contrast of small molecule solvation in salt solutions

The contributions from anions and cations from salt are inseparable in their perturbation of molecular systems by experimental and computational methods, rendering it difficult to dissect the effects exerted by the anions and cations individually. Here we investigate the solvation of a small molecule, caffeine, and its perturbation by monovalent salts from various parts of the Hofmeister series. Using molecular dynamics and the energy-representation theory of solvation, we estimate the solvation free energy of caffeine and decompose it into the contributions from anions, cations, and water. We also decompose the contributions arising from the solute-solvent and solute-ions interactions and that from excluded volume, enabling us to pin-point the mechanism of salt. Anions and cations revealed high contrast in their perturbation of caffeine solvation, with the cations salting-in caffeine via binding to the polar ketone groups, while the anions were found to be salting-out via perturbations of water. In agreement with previous findings, the perturbation by salt is mostly anion dependent, with the magnitude of the excluded-volume effect found to be the governing mechanism. The free-energy decomposition as conducted in the present work can be useful to understand ion-specific effects and the associated Hofmeister series.

Expulsion of Hydroxide Ions from Methyl Hydration Shells

The affinity of hydroxide ions for methyl hydration shells is assessed using a combined experimental and theoretical analysis of tert-butyl alcohol (TBA) dissolved in pure water and aqueous NaOH and NaI. The experimental results are obtained using Raman multivariate curve resolution (Raman-MCR) and a new three-component total least squares (Raman-TLS) spectral decomposition strategy used to highlight vibrational perturbations resulting from interactions between TBA and aqueous ions. The experiments are interpreted and extended with the aid of effective fragment potential molecular dynamics (EFP-MD) simulations, as well as Kirkwood-Buff calculations and octanol/water partition measurements, to relate TBA-ion distribution functions to TBA solubility changes. The combined experimental and simulation results reveal that methyl group hydration shells more strongly expel hydroxide than iodide anions, whose populations near the methyl groups of TBA are predicted to be correlated with sodium counterion localization near the TBA hydroxyl group.

Surfactant aggregate size distributions above and below the critical micelle concentration

Aggregate size distributions in an aqueous solution containing either charged or neutral surfactants are investigated using Raman multivariate curve resolution (Raman-MCR) spectroscopy and analyzed with the aid of a multi-aggregation chemical potential surface (MCPS) modeling strategy. Total least squares decompositions of the concentration-dependent Raman-MCR spectra are used to quantify the free and micelle surfactant populations, and the surfactant's C-H stretch frequency is used as a measure of its average aggregation state. MCPS predictions relate the experimental measurements to the underlying surfactant aggregate size distribution by fitting either the component concentrations or the average C-H frequency to MCPS predictions, and thus determine the critical micelle concentration (CMC) and estimate the corresponding micelle size and polydispersity. The Raman-MCR spectra of aqueous 1,2-hexanediol, sodium octanoate, and sodium dodecyl sulfate, measured both below and above CMC, provide critical tests of the assumed functional form of the MCPS and the presence of low-order premicellar aggregates. Our results indicate that the low-order aggregate population gradually emerges as the CMC is approached and then remains nearly concentration-independent after the appearance of micelles.

Temperature, Pressure, and Length-Scale Dependence of Solvation in Water-like Solvents. II. Large Solvophovic Solutes

We use molecular simulation to determine solvation free energies, isochoric solvation energies and entropies, isobaric solvation enthalpies and entropies, partial molecular volumes, and isothermal density derivatives of the solvation free energy as a function of temperature and pressure for hard-sphere solutes with diameters ranging from 4 to 36 Å in TIP4P/2005 and Jagla water-like solvents exhibiting unusual thermodynamics. An important piece of our discussion focuses on the nanometer-sized solutes, for which simulation results are found to be accounted for by the most basic classical thermodynamic treatment contemplating bulk and interfacial contributions to the solvation free energy. Thus, since water's liquid-vapor surface tension is only special inasmuch as it takes unusually large values, solvent's water-like unusual thermodynamics manifests through a term proportional to the pressure in the solvation free energy. As a result, such solvent's unusual thermodynamics is found to be relevant to the temperature and pressure dependence of the isochoric solvation energy and entropy as well as to the isothermal density derivative of the solvation free energy. This sharply contrasts with the findings of the first part of this series indicating that the solvation free energy of small hard spheres responds to temperature and pressure changes as solvent's density does, with such a contrasting picture embodying a "pressure-density dichotomy." As for the length-scale dependence, we find the zero nominal pressure and the solvent's temperature of the maximum density as singular conditions for cavity surface-area size scaling of large solutes to occur for all solvation quantities. We finally argue that the overall study undertaken in this series suggests that water's unusual thermodynamics may be relevant to the thermodynamic stability of clusters of solvophobic units in the temperature-pressure plane. Some comments on the role of solute-solvent attractive interactions are also depicted.

Water-Mediated Interactions Determine Helix Formation of Peptides in Open Nanotubes

Water-mediated interactions (WMIs) play diverse roles in molecular biology. They are particularly relevant in geometrically confined spaces such as the interior of the chaperonin, at the interface between ligands and their binding partners, and in the ribosome tunnel. Inspired in part by the geometry of the ribosome tunnel, we consider confinement effects on the stability of peptides. We describe results from replica exchange molecular dynamics simulations of a system containing a 23-alanine or 23-serine polypeptide confined to nonpolar and polar nanotubes in the gas phase and when open to a water reservoir. We quantify the effect of water in determining the preferred conformational states of these polypeptides by calculating the difference in the solvation free energy for the helix and coil states in the open nanotube in the two phases. Our simulations reveal several possibilities. We find that nanoscopic confinement preferentially stabilizes the helical state of polypeptides with hydrophobic side chains, which is explained by the entropic stabilization mechanism proposed on the basis of polymer physics. Polypeptide chains with hydrophilic side chains can adopt helical structures within nanotubes, but helix formation is sensitive to the nature of the nanotube due to WMIs. We elaborate on the potential implications of our findings to the stability of peptides in the ribosome tunnel.

Towards single-species selectivity of membranes with subnanometre pores

Synthetic membranes with pores at the subnanometre scale are at the core of processes for separating solutes from water, such as water purification and desalination. While these membrane processes have achieved substantial industrial success, the capability of state-of-the-art membranes to selectively separate a single solute from a mixture of solutes is limited. Such high-precision separation would enable fit-for-purpose treatment, improving the sustainability of current water-treatment processes and opening doors for new applications of membrane technologies. Herein, we introduce the challenges of state-of-the-art membranes with subnanometre pores to achieve high selectivity between solutes. We then analyse experimental and theoretical literature to discuss the molecular-level mechanisms that contribute to energy barriers for solute transport through subnanometre pores. We conclude by providing principles and guidelines for designing next-generation single-species selective membranes that are inspired by ion-selective biological channels.

First-principles modeling of chemistry in mixed solvents: Where to go from here?

Mixed solvents (i.e., binary or higher order mixtures of ionic or nonionic liquids) play crucial roles in chemical syntheses, separations, and electrochemical devices because they can be tuned for specific reactions and applications. Apart from fully explicit solvation treatments that can be difficult to parameterize or computationally expensive, there is currently no well-established first-principles regimen for reliably modeling atomic-scale chemistry in mixed solvent environments. We offer our perspective on how this process could be achieved in the near future as mixed solvent systems become more explored using theoretical and computational chemistry. We first outline what makes mixed solvent systems far more complex compared to single-component solvents. An overview of current and promising techniques for modeling mixed solvent environments is provided. We focus on so-called hybrid solvation treatments such as the conductor-like screening model for real solvents and the reference interaction site model, which are far less computationally demanding than explicit simulations. We also propose that cluster-continuum approaches rooted in physically rigorous quasi-chemical theory provide a robust, yet practical, route for studying chemical processes in mixed solvents.

Decoding signatures of structure, bulk thermodynamics, and solvation in three-body angle distributions of rigid water models

A tetrahedral structure resulting from hydrogen bonding is a hallmark of liquid water and plays a significant role in determining its unique thermophysical properties. This water feature has helped understand anomalous properties and physically interpret and model hydrophobic solvation thermodynamics. Tetrahedrality is well described by the geometric relationship of any central water molecule with two of its nearest neighbors in the first coordination shell, as defined by the corresponding "three-body" angle. While order parameters and even full water models have been developed using specific or average features of the three-body angle distribution, here we examine the distribution holistically, tracking its response to changes in temperature, density, and the presence of model solutes. Surprisingly, we find that the three-body distribution responds by varying primarily along a single degree of freedom, suggesting a remarkably simplified view of water structure. We characterize three-body angle distributions across temperature and density space and identify principal components of the variations with state conditions. We show that these principal components embed physical significance and trace out transitions between tetrahedral and simple-fluid-like behavior. Moreover, we find that the ways three-body angles vary within the hydration shells of model colloids of different types and sizes are nearly identical to the variations seen in bulk water across density and temperature. Importantly, through the principal directions of these variations, we find that perturbations to the hydration-water distributions well predict the thermodynamics associated with colloid solvation, in particular, the relative entropy of this process that captures indirect, solvent-mediated contributions to the hydration free energy.

State of Oxygen Molecules in Aqueous Supersaturated Solutions

The state of oxygen in aqueous supersaturated solutions prepared by different methods was studied using high-resolution ultrasonic spectroscopy in combination with other techniques. This allowed for nondestructive evaluation of the properties of oxygen solute particles, composed of oxygen molecules and surrounding (coordinating) molecules of water, at equilibrium, supersaturated conditions, and different temperatures and concentrations of O₂. The results were compared with the behaviors of other types of solutes in water, including H₂O₂, which has similar molecular size and mass to O₂ but is characterized by a significantly different type of interaction with water molecules. Additionally, theoretical modeling was performed to assess the ultrasonic characteristics of dispersions of oxygen nanobubbles stabilized by a surface electrical charge. The obtained data indicate a clathrate-like organization of water in the coordination shells of single molecules of O₂. We did not find any signs of formation of clusters of oxygen molecules in supersaturated solutions. No quantifiable presence of oxygen nanobubbles in the solutions was detected. The state of O₂ molecules was not affected by supersaturation within the analyzed concentration range of oxygen. The results also demonstrated the potential of the ultrasonic technique in precision real-time nondestructive monitoring of oxygen solubilization and outgassing processes.

Contrasting the hydration thermodynamics of methane and methanol

The hydration thermodynamics of methane and methanol depend on the cavity creation work and energy of van der Waals and H-bonding attractions.

Thermodynamics of Reactions Affected by Medium Reorganization

We present a thermodynamic analysis of the activation barrier for reactions which can be monitored through the difference in the energies of reactants and products defined as the reaction coordinate (electron and atom transfer, enzyme catalysis, etc.). The free-energy surfaces along the reaction coordinate are separated into the enthalpy and entropy surfaces. For the Gaussian statistics of the reaction coordinate, the free-energy surfaces are parabolas, and the entropy surface is an inverted parabola. Its maximum coincides with the transition state for reactions with zero value of the reaction free energy. Maximum entropic depression of the activation barrier, anticipated by the concept of transition-state ensembles, can be achieved for such reactions. From Onsager's reversibility, the entropy of equilibrium fluctuations encodes the entropic component of the activation barrier. The reorganization entropy thus becomes the critical parameter of the theory reducing the problem of activation entropy to the problem of reorganization entropy. Standard solvation theories do not allow reorganization entropy sufficient for the barrier depression. Complex media, characterized by many relaxation processes, need to be involved. Proteins provide several routes for achieving large entropic effects through incomplete (nonergodic) sampling of the complex energy landscape and by facilitating an active role of water in the reaction mechanism.

Interfacial structural crossover and hydration thermodynamics of charged C60 in water

Classical molecular dynamics simulations of the hydration thermodynamics, structure, and dynamics of water in hydration shells of charged buckminsterfullerenes are presented in this study. Charging of fullerenes leads to a structural transition in the hydration shell, accompanied by creation of a significant population of dangling O-H bonds pointing toward the solute. In contrast to the well accepted structure-function paradigm, this interfacial structural transition causes nearly no effect on either the dynamics of hydration water or on the solvation thermodynamics. Linear response to the solute charge is maintained despite significant structural changes in the hydration shell, and solvation thermodynamic potentials are nearly insensitive to the altering structure. Only solvation heat capacities, which are higher thermodynamic derivatives of the solvation free energy, indicate some sensitivity to the local hydration structure. We have separated the solvation thermodynamic potentials into direct solute-solvent interactions and restructuring of the hydration shell and analyzed the relative contributions of electrostatic and nonpolar interactions to the solvation thermodynamics.

Simple Entropy Terms for End-Point Binding Free Energy Calculations

We introduce a number of computationally inexpensive modifications to the MM/PBSA and MM/GBSA estimators for binding free energies, which are based on average receptor-ligand interaction energies in simulations of a noncovalent complex, to improve the treatment of entropy: second- and higher-order terms in a cumulant expansion and a confining potential on ligand external degrees of freedom. We also consider a filter for snapshots where ligands have drifted from the initial binding pose. The variations were tested on six sets of systems for which binding modes and free energies have previously been experimentally determined. For some data sets, none of the tested estimators led to results significantly correlated with measured free energies. In data sets with nontrivial correlation, a ligand RMSD cutoff of 3 Å and a second-order truncation of the cumulant expansion was found to be comparable or better than the average interaction energy by several statistical metrics.

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.

The Excess Chemical Potential of Water at the Interface with a Protein from End Point Simulations

We use end point simulations to estimate the excess chemical potential of water in the homogeneous liquid and at the interface with a protein in solution. When the pure liquid is taken as the reference, the excess chemical potential of interfacial water is the difference between the solvation free energy of a water molecule at the interface and in the bulk. Using the homogeneous liquid as an example, we show that the solvation free energy for growing a water molecule can be estimated by applying UWHAM to the simulation data generated from the initial and final states (i.e., "the end points") instead of multistate free energy perturbation simulations because of the possible overlaps of the configurations sampled at the end points. Then end point simulations are used to estimate the solvation free energy of water at the interface with a protein in solution. The estimate of the solvation free energy at the interface from two simulations at the end points agrees with the benchmark using 32 states within a 95% confidence interval for most interfacial locations. The ability to accurately estimate the excess chemical potential of water from end point simulations facilitates the statistical thermodynamic analysis of diverse interfacial phenomena. Our focus is on analyzing the excess chemical potential of water at protein receptor binding sites with the goal of using this information to assist in the design of tight binding ligands.

Interfacial Adsorption of Neutral and Ionic Solutes in a Water Droplet

Direct (solute-water) and indirect (water-water) contributions to adsorption at an air-water interface are identified using the Widom potential distribution theorem and quantified using molecular dynamics simulations of a liquid water droplet containing either neopentane or iodide-like solutes with charges of 0 or ±1. The results are used to quantitatively compare direct and indirect energetic and entropic contributions to adsorption, as well as to critically test surface capillary wave, linear response (LR), and mean field (MF) predictions. The negative signs of the total adsorption energies and entropies of both the anionic and cationic solutes are found to result from indirect adsorption induced changes in water-water interactions, rather than from surface capillary wave perturbations, which are found to be asymmetric with respect to solute charge. The LR and MF approximations both accurately describe the adsorption of neutral (hydrophobic) solutes, while for ionic solutes the MF approximation is entirely inappropriate and LR predictions are qualitatively (but not quantitatively) accurate.

Excess Volumes from the Pressure Derivative of the Excess Chemical Potential: Testing Simple Models for Cavity Formation in Water

Excess volumes and excess compressibilities for hard spheres in water were computed by pressure derivatives of the excess chemical potential, which is equivalent to the work of cavity formation. This is relevant to the application of continuum solvation methods at various pressures. The excess chemical potential was modeled within phenomenological expressions for curved surfaces plus a pressure-volume term, for which two approaches were adopted, differing for the radius of the spherical volume. This implies a different dependence on pressure of parameters. In all cases, in the surface term, for the pressure derivative of parameters of the curvature function, use was made of the previously proposed expressions for the first two moments obtained from the density and radial distribution of oxygens in liquid water. Only for the parameter which has the dimension of surface tension (γ̃) was explicit dependence on pressure considered and results are affected by the specific polynomial used. In agreement with what inferred from simulation results obtained for cavities in TIP4P water, negative and positive adsorptions at the contact radius were extrapolated for a very large cavity at 1 and 8000 atm, respectively. The expressions here employed for the excess chemical potential predict the zero value of asymptotic adsorption to be at a pressure between 500 and 800 atm, which can be compared to results from the revised scaled particle theory. In the same range, for a nanometer-sized cavity, a change of behavior occurs regarding the ratio between the excess Helmholtz free energy and the product between pressure and excess volume.

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.

Interfacial solvation thermodynamics

Previous studies have reached conflicting conclusions regarding the interplay of cavity formation, polarizability, desolvation, and surface capillary waves in driving the interfacial adsorptions of ions and molecules at air-water interfaces. Here we revisit these questions by combining exact potential distribution results with linear response theory and other physically motivated approximations. The results highlight both exact and approximate compensation relations pertaining to direct (solute-solvent) and indirect (solvent-solvent) contributions to adsorption thermodynamics, of relevance to solvation at air-water interfaces, as well as a broader class of processes linked to the mean force potential between ions, molecules, nanoparticles, proteins, and biological assemblies.

Hydration thermodynamics beyond the linear response approximation

The solvation energetics associated with the transformation of a solute molecule at infinite dilution in water from an initial state A to a final state B is reconsidered. The two solute states have different potentials energies of interaction, [Formula: see text] and [Formula: see text], with the solvent environment. Throughout the A [Formula: see text] B transformation of the solute, the solvation system is described by a Hamiltonian [Formula: see text] that changes linearly with the coupling parameter ξ. By focusing on the characterization of the probability density [Formula: see text] that the dimensionless perturbational solute-solvent interaction energy [Formula: see text] has numerical value y when the coupling parameter is ξ, we derive a hierarchy of differential equation relations between the ξ-dependent cumulant functions of various orders in the expansion of the appropriate cumulant generating function. On the basis of this theoretical framework we then introduce an inherently nonlinear solvation model for which we are able to find analytical results for both [Formula: see text] and for the solvation thermodynamic functions. The solvation model is based on the premise that there is an upper or a lower bound (depending on the nature of the interactions considered) to the amplitude of the fluctuations of Y in the solution system at equilibrium. The results reveal essential differences in behavior for the model when compared with the linear response approximation to solvation, particularly with regards to the probability density [Formula: see text]. The analytical expressions for the solvation properties show, however, that the linear response behavior is recovered from the new model when the room for the thermal fluctuations in Y is not restricted by the existence of a nearby bound. We compare the predictions of the model with the results from molecular dynamics computer simulations for aqueous solvation, in which either (1) the solute-solvent electrostatic interactions, or (2) the shorter-range attractive interactions are switched-on in the A [Formula: see text] B process.

Using Grand Canonical Monte Carlo Simulations to Understand the Role of Interfacial Fluctuations on Solvation at the Water-Vapor Interface

The present work investigates the effect of interfacial fluctuations (predominantly capillary wave-like fluctuations) on the solvation free energy (Δμ) of a monatomic solute at the water-vapor interface. We introduce a grand-canonical-ensemble-based simulation approach that quantifies the contribution of interfacial fluctuations to Δμ. This approach is used to understand how the above contribution depends on the strength of dispersive and electrostatic solute-water interactions at the temperature of 400 K. At this temperature, we observe that interfacial fluctuations do play a role in the variation of Δμ with the strength of the electrostatic solute-water interaction. We also use grand canonical simulations to further investigate how interfacial fluctuations affect the propensity of the solute toward the water-vapor interface. To this end, we track a quantity called the interface potential (surface excess free energy) with the number of water molecules. With increasing number of water molecules, the liquid-vapor interface moves across a solute, which is kept at a fixed position in the simulation. Hence, the dependence of the interface potential on the number of waters models the process of moving the solute through the water-vapor interface. We analyze the change of the interface potential with the number of water molecules to explain that solute-induced changes in the interfacial fluctuations, like the pinning of capillary-wave-like undulations, do not play any role in the propensity of solutes toward water-vapor interfaces. The above analysis also shows that the dampening of interfacial fluctuations accompanies the adsorption of any solute at the liquid-vapor interface, irrespective of the chemical nature of the solute and solvent. However, such a correlation does not imply that dampening of fluctuations causes adsorption.

Solvation thermodynamics of amino acid side chains on a short peptide backbone

The hydration process of side chain analogue molecules differs from that of the actual amino acid side chains in peptides and proteins owing to the effects of the peptide backbone on the aqueous solvent environment. A recent molecular simulation study has provided evidence that all nonpolar side chains, attached to a short peptide backbone, are considerably less hydrophobic than the free side chain analogue molecules. In contrast to this, the hydrophilicity of the polar side chains is hardly affected by the backbone. To analyze the origin of these observations, we here present a molecular simulation study on temperature dependent solvation free energies of nonpolar and polar side chains attached to a short peptide backbone. The estimated solvation entropies and enthalpies of the various amino acid side chains are compared with existing side chain analogue data. The solvation entropies and enthalpies of the polar side chains are negative, but in absolute magnitude smaller compared with the corresponding analogue data. The observed differences are large; however, owing to a nearly perfect enthalpy-entropy compensation, the solvation free energies of polar side chains remain largely unaffected by the peptide backbone. We find that a similar compensation does not apply to the nonpolar side chains; while the backbone greatly reduces the unfavorable solvation entropies, the solvation enthalpies are either more favorable or only marginally affected. This results in a very small unfavorable free energy cost, or even free energy gain, of solvating the nonpolar side chains in strong contrast to solvation of small hydrophobic or nonpolar molecules in bulk water. The solvation free energies of nonpolar side chains have been furthermore decomposed into a repulsive cavity formation contribution and an attractive dispersion free energy contribution. We find that cavity formation next to the peptide backbone is entropically favored over formation of similar sized nonpolar side chain cavities in bulk water, in agreement with earlier work in the literature on analysis of cavity fluctuations at nonpolar molecular surfaces. The cavity and dispersion interaction contributions correlate quite well with the solvent accessible surface area of the nonpolar side chains attached to the backbone. This correlation however is weak for the overall solvation free energies owing to the fact that the cavity and dispersion free energy contributions are almost exactly cancelling each other.

Dissolution and ionization of sodium superoxide in sodium-oxygen batteries

With the demand for high-energy-storage devices, the rechargeable metal–oxygen battery has attracted attention recently. Sodium–oxygen batteries have been regarded as the most promising candidates because of their lower-charge overpotential compared with that of lithium–oxygen system. However, conflicting observations with different discharge products have inhibited the understanding of precise reactions in the battery. Here we demonstrate that the competition between the electrochemical and chemical reactions in sodium–oxygen batteries leads to the dissolution and ionization of sodium superoxide, liberating superoxide anion and triggering the formation of sodium peroxide dihydrate (Na₂O₂·2H₂O). On the formation of Na₂O₂·2H₂O, the charge overpotential of sodium–oxygen cells significantly increases. This verification addresses the origin of conflicting discharge products and overpotentials observed in sodium–oxygen systems. Our proposed model provides guidelines to help direct the reactions in sodium–oxygen batteries to achieve high efficiency and rechargeability.

Sodium-oxygen batteries are promising energy storage devices but the nature of their discharge products remains unresolved. Here, the authors reveal that the dissolution and ionization of sodium superoxide leads to the formation of other phases, which increases the charge overpotential of the cell.

Mechanism of Polymer Collapse in Miscible Good Solvents

We propose a physical mechanism for co-nonsolvency of a stimulus-responsive polymer in water/methanol mixed solution based on results obtained with molecular simulations. Even though the phenomenon is well known, the mechanism behind co-nonsolvency is still under debate. Herein, we study co-nonsolvency of poly(N-isopropylacrylamide) (PNiPAM) in methanol aqueous solutions, the most widely studied and experimentally well-characterized system. Our results show that at low alcohol content of the solution methanol preferentially binds to the PNiPAM globule and drives polymer collapse. The energetics of electrostatic, hydrogen bonding, or bridging-type interactions with the globule is found to play no role. Instead, preferential methanol binding results in a significant increase in the globule's configurational entropy, stabilizing methanol-enriched globular structures over wet globular structures in neat water. This mechanism drives the reduction of the lower critical solution temperature with increasing methanol content in the co-nonsolvency regime and eventually leads to polymer collapse. The globule-to-coil re-entrance at high methanol concentrations is instead driven by changes in solvent-excluded volume of the coil and globular states imparted by a decrease in solvent density with increasing methanol content of the solution: with increasing proportion of larger solvent particles (methanol), the entropic (cavity formation) cost of redistributing solvent molecules upon polymer re-entrance becomes smaller. This effect provides a natural explanation for the experimentally observed dependence of the re-entrance transition on chain molecular weight.

On the urea induced hydrophobic collapse of a water soluble polymer

Polymer collapse despite cosolvent binding: solvation of extended coil conformations is entropically penalized, therefore stabilizing compact globular conformations in the coil-globule equilibrium of poly(N-isopropylacrylamide) in aqueous urea solution.

A nucleation-based method to study hydrophobic interactions under confinement: enhanced hydrophobic association driven by energetic contributions

A novel simulation approach was developed and applied to the study of hydrophobic interactions for a small hydrophobic solute pair under confinement. In this method, the aggregation-volume-bias Monte Carlo algorithm, developed originally for nucleation studies, is used to evaluate the association free energy with water molecules for a methane pair through the gradual addition of water molecules into a nanometer-sized sphere. Through a thermodynamic cycle, this method allows for a convenient examination of the free energy difference between two different solvated configurations without sampling any of the configurations in between. The potential of mean force (PMF) for a methane pair under confinement obtained from this method reveals that the stability of the contact pair configuration can be enhanced compared to that in bulk water, which is in agreement with previous studies. Also, constraining the center of this methane pair at the center of this confined volume yields a PMF with a metastable solvent separated configuration, resembling more closely the PMF from the bulk-phase system compared to previous studies in which this solvent-separated minimum was found to be completely absent. A combination with histogram reweighting enables the study of this association behavior at different thermodynamic conditions without additional simulations. From a comprehensive thermodynamic analysis, it is evident that such hydrophobic association, known to be entropically driven in the bulk-phase system at ambient conditions, is entropically favorable only when a suitable range of solvent molecules is added to the confined system. More importantly, the energetic contributions are a favorable factor that explains the enhanced hydrophobic association toward the high number of solvent molecules.