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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 973 records · Page 54
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Cation-Dependent Multielectron Kinetics of Metal Oxide Splitting

We report direct electrolytic extraction of metals from metal oxides is a promising process for the sustainable production of metals. In this work, we elucidate the inherent thermodynamic driving forces behind the reduction of metal oxides to metals (M-OER). It is shown that the thermodynamics of M-OER can be systematically tuned via the interactions of oxygen with the participating metal cations as a function of metal–oxygen covalency, oxygen–oxygen covalency, and metal–oxygen ionicity. We screen both group 1 elements and metals that are able to exist in the +2 oxidation state for M-OER thermodynamics. Li, Fe, and Co are identified as having low thermodynamic overpotentials for electrolytic extraction from their metal oxides due to interactions between oxygen and these metals being neither too strong (covalent) nor too weak (ionic). We further show that the bulk formation energies are predictive of M-OER reaction energetics on surfaces by developing unified design principles for tuning the thermodynamics of these reduction reactions both in bulk oxides and on surfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Phantom Electrons in Mesoporous Nanocrystalline SnO 2 Thin Films with Cation-Dependent Reduction Onsets

Here, mesoporous thin films comprised of ~15 nm diameter SnO 2 nanocrystallites were synthesized and characterized in acetonitrile electrolytes by electrochemical and spectroscopic techniques. Spectroelectrochemical reduction of the thin films resulted in broad, non-superimposable UV/vis absorption changes. Simultaneous analysis of potential-dependent spectra, by a process termed “potential associated spectra”, resulted in the identification of three unique absorption spectra for reduced SnO 2 , while only one spectrum was identified for TiO 2 . Reduction of SnO 2 resulted in the appearance of (1) a broad absorption that spans across the visible and near-IR regions, (2) a blue-shifted fundamental absorption, and (3) an absorption band in the blue region. The absorption onsets were dependent on the electrolyte cation, present as the perchlorate salt of Li + , Na + , Mg 2+ , Ca 2+ , and TBA + , where TBA + is tetrabutylammonium. Correlations between the charge within the thin film and the absorbance intensity revealed that significant charge was transferred to SnO 2 films before significant visible color changes were observed. This suggested the presence of electrons within the SnO 2 thin films that did not absorb visible light and were termed “phantom electrons”.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Instability at the Electrode/Electrolyte Interface Induced by Hard Cation Chelation and Nucleophilic Attack

Electrochemistry is necessarily a science of interfacial processes, and understanding electrode/electrolyte interfaces is essential to controlling electrochemical performance and stability. Undesirable interfacial interactions hinder discovery and development of rational materials combinations. By example, we examine an electrolyte, magnesium(II) bis(trifluoromethanesulfonyl)imide (Mg(TFSI) 2 ) dissolved in diglyme, next to the Mg metal anode, which is purported to have a wide window of electrochemical stability. However, even in the absence of any bias, using in situ tender X-ray photoelectron spectroscopy, we discovered an intrinsic interfacial chemical instability of both the solvent and salt, further explained using first-principles calculations as driven by Mg 2+ dication chelation and nucleophilic attack by hydroxide ions. The proposed mechanism appears general to the chemistry near or on metal surfaces in hygroscopic environments with chelation of hard cations and indicates possible synthetic strategies to overcome chemical instability within this class of electrolytes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Hydroxylation and Cation Segregation in (La 0.5 Sr 0.5 )FeO 3-$δ$ Electrodes

Simultaneously achieving high activity and stability is the primary challenge when engineering (electro)catalysts. Transition metal perovskite oxides are employed as air electrodes for solid-oxide fuel cells and electrolyzers. However, degradation of oxygen exchange kinetics at the solid–gas interface, often linked to alkaline-earth cation segregation and precipitation, limits widespread commercialization. Here, we systematically investigated the surface degradation mechanism induced by gas-phase impurities in La 0.5 Sr 0.5 )FeO 3-$δ$ (LSF55) thin-film electrodes by varying the concentration of H 2 O, SO 2 , and CO 2 . Degradation of the area-specific resistance in ambient and humidified synthetic air is significantly greater than in dry ambient and dry synthetic air, pointing to the importance of water vapor. Time-resolved, in situ ambient pressure X-ray photoelectron spectroscopy performed in O 2 showed that nonbulk Sr is present on the surface before the exposure to water vapor. Upon introduction of water vapor, neither additional Sr segregation nor precipitation driven by water vapor is a necessary condition for degradation. Rather, hydroxylation of the surface induces irreversible and significant degradation. At the same time, we show that Sr migration driven by water vapor is partially reversible. These fundamental insights can be used for the rational design of electrodes with improved catalytic stability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Intramolecular Electrostatic Effects on O 2 , CO 2 , and Acetate Binding to a Cationic Iron Porphyrin

Noncovalent electrostatic interactions are important in many biological and chemical reactions, especially those that involve charged intermediates. There has been a growing interest in using electrostatic ligand designs—placing charges in the second coordination sphere—to improve molecular reactivity, catalysis, and electrocatalysis. For instance, an iron porphyrin bearing four cationic ortho -trimethylanilinium groups, Fe( o -TMA), has been reported to be an exceptional electrocatalyst for both the carbon dioxide reduction reaction (CO 2 RR) and the oxygen reduction reaction (ORR). These reactions involve many different steps, and it is not evident which steps are affected by the four positive charges, or why. By comparing Fe( o -TMA) with the related iron-tetraphenylporphyrin, this work examines how covalently positioned charged groups affect substrate binding and other key pre-equilibria of both the ORR and CO 2 RR, specifically acetate, dioxygen, and carbon dioxide binding. This study is among the first to directly measure the effects of electrostatics on ligand-binding. The results show that adding electrostatic groups to a catalyst design often results in a complex interplay of multiple effects, including changes in pre-equilibria prior to substrate binding, combinations of through-space and inductive contributions, and effects of ionic strength and solution dielectric. The inverse half-order dependence of binding constant on ionic strength is proposed as a clear marker for an electrostatic effect. Overall, the conclusions provide guidance for the increasingly popular electrostatic ligand designs in catalysis and other reactivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Activation of CO 2 by Actinide Cations (Th + , U + , Pu + , and Am + ) as Studied by Guided Ion Beam and Triple Quadrupole Mass Spectrometry

Reactions of CO 2 with Th+ have been studied using guided ion beam tandem mass spectrometry (GIBMS) and with An + (An + = Th + , U + , Pu + , and Am + ) using triple quadrupole inductively coupled plasma mass spectrometry (QQQ-ICP-MS). Additionally, the reactions ThO + + CO and ThO + + CO 2 were examined using GIBMS. Modeling the kinetic energy dependent GIBMS data allowed determination of bond dissociation energies (BDEs) for D o (Th + -O) and D o (OTh + -O) that are in reasonable agreement with previous GIBMS measurements. The QQQ-ICP-MS reactions were studied at higher pressures where multiple collisions between An + and the neutral CO 2 occur. As a consequence, both AnO + and AnO 2 + products were observed for all An + except Am + , where only AmO + was observed. Here, the relative abundances of the observed monoxides compared to the dioxides are consistent with previous reports of the AnO n + (n = 1, 2) BDEs. Comparison of the periodic trends of the group 4 transition metal, lanthanide (Ln), and actinide atomic cations in reactions with CO 2 (a formally spin-forbidden reaction for most M + ground states), and O 2 (a spin unrestricted reaction) indicate that spin conservation plays a minor role, if any, for the heavier An + metals. Further correlation of Ln + and An + + CO 2 reaction efficiencies with the promotion energy (E p ) to the first electronic state with two valence d-electrons (E p (5d 2 ) for Ln + and E p (6d 2 ) for An + ) indicates that the primary limitation in the activation of CO 2 is the energetic cost to promote from the electronic ground state of the atomic metal ion to a reactive state.

bond activation↗
DOE OSTI2023

Influencing Bonding Interactions of the Neptunyl (V, VI) Cations with Electron-donating and -withdrawing Groups

Neptunium makes up the largest percentage of minor actinides found in spent nuclear fuel, yet separations of this element have proven difficult due to its rich redox chemistry. Developing new reprocessing techniques should rely on understanding how to control the Np oxidation state and its interactions with different ligands. Designing new ligands for separations requires understanding how to properly tune a system toward a desired trait through functionalization. Emerging technologies for minor actinide separations focus on ligands containing carboxylate or pyridine functional groups, which are desirable due to their high degree of functionalization. So we use DFT calculations to study the interactions of carboxylate and polypyridine ligands with the neptunyl cation [Np(V/VI)O2] +/2+ . A systematic study is performed by varying the electronic properties of the carboxylate and polypyridine ligands through the inclusion of different electron-withdrawing and electron-donating R groups. We focus on how these groups can affect geometric properties, electronic structure, and bonding characterization as a function of the metal oxidation state and ligand character and discuss how these factors can play a role in neptunium ligand design principles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Electronic and Thermal Properties of the Cation Substitution-Derived Quaternary Chalcogenide CuInSnSe 4

Quaternary chalcogenides continue to be of interest for a variety of technological applications, with physical properties stemming from their structural complexity and stoichiometric variation. In certain structure types, partial vacancies on specific lattice positions present an opportunity to investigate electrical and thermal properties in light of these lattice defects. In this work, we investigated the structural, thermal, and electronic properties of CuInSnSe 4 , a material that belongs to a relatively unexplored class of quaternary chalcogenides with a defect adamantine crystal structure. First-principles calculations together with experimental measurements revealed a chalcopyrite-like structure with inherent vacancies and characteristic s–p and p–d orbital hybridizations in the electronic structure of the material. Cation disorder and lattice anharmonicity result in very low thermal conductivity with values significantly lower than those for related compositions. In conclusion, this work reveals the fundamental physical properties of a previously uninvestigated quaternary chalcogenide and may aid investigations of similar as well as other quaternary chalcogenide compositions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Interplay of Cation Ordering and Ferroelectricity in Perovskite Tin Iodides: Designing a Polar Halide Perovskite for Photovoltaic Applications

Owing to its ideal semiconducting band gap and good carrier transport properties, the fully inorganic perovskite CsSnI 3 has been proposed as a visible-light absorber for photovoltaic (PV) applications. However, compared to the organic inorganic lead halide perovskite CH 3 NH 3 PbI 3 , CsSnI 3 solar cells display very low energy conversion efficiency. In this work, we propose a potential route to improve the PV properties of CsSnI 3 . Using first-principles calculations, we examine the crystal structures and electronic properties of CsSnI 3 , including its structural polymorphs. Next, we purposefully order Cs and Rb cations on the A site to create the double perovskite (CsRb)Sn 2 I 6 . We find that a stable ferroelectric polarization arises from the nontrivial coupling between polar displacements and octahedral rotations of the SnI 6 network. These ferroelectric double perovskites are predicted to have energy band gaps and carrier effective masses similar to those of CsSnI 3 . More importantly, unlike nonpolar CsSnI 3 , the electric polarization present in ferroelectric (CsRb)Sn 2 I 6 can effectively separate the photoexcited carriers, leading to novel ferroelectric PV materials with,potentially enhanced energy conversion efficiency.

14 SOLAR ENERGY↗
DOE OSTI2018

Unusual Coexistence of Nickel(II) and Nickel(IV) in the Quadruple Perovskite Ba 4 Ni 2 Ir 2 O 12 Containing Ir 2 NiO 12 Mixed-Metal-Cation Trimers

In this paper, the crystal chemistry and magnetic properties of two hexagonal nickel(IV)-containing perovskites, Ba 4 Ni 1.94 Ir 2.06 O 12 and BaNiO 3 , are reported. The 12R perovskite, Ba 4 Ni 1.94 Ir 2.06 O 12 , possesses an unexpected coexistence of nickel(II) and nickel(IV). This quadruple perovskite structure contains Ir 2 NiO 12 mixed-metal-cation units in which direct metal–metal bonding between nickel(IV) and iridium(V) is inferred. Finally, X-ray absorption near-edge spectroscopy and X-ray photoelectron spectroscopy measurements were conducted to confirm the simultaneous presence of nickel(II) and nickel(IV).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Activation of Water by Pentavalent Actinide Dioxide Cations: Characteristic Curium Revealed by a Reactivity Turn after Americium

Swapping of an oxygen atom of water with that of a pentavalent actinide dioxide cation, AnO 2 + also called an “actinyl”, requires activation of an An–O bond. It was previously found that such oxo exchange in the gas phase occurs for the first two actinyls, PaO 2 + and UO 2 + , but not the next two, NpO 2 + and PuO 2 + . The An–O bond dissociation energies (BDEs) decrease from PaO 2 + to PuO 2 + , such that the observation of a parallel decrease in the An–O bond reactivity is intriguing. To elucidate oxo exchange, we here extend experimental studies to AmO 2 + , americyl(V), and CmO 2 + , curyl(V), which were produced in remarkable abundance by electrospray ionization of Am 3+ and Cm 3+ solutions. Like other AnO 2 + , americyl(V) and curyl(V) adsorb up to four H 2 O molecules to form tetrahydrates AnO 2 (H 2 O) 4 + with the actinide hexacoordinated by oxygen atoms. It was found that AmO 2 + does not oxo-exchange, whereas CmO 2 + does, establishing a “turn” to increasing the reactivity from americyl to curyl, which validates computational predictions. Because oxo exchange occurs via conversion of an actinyl(V) hydrate, AnO 2 (H 2 O) + , to an actinide(V) hydroxide, AnO(OH) 2 + , it reflects the propensity for actinyl(V) hydrolysis: PaO 2 + hydrolyzes and oxo-exchanges most easily, despite the fact that it has the highest BDE of all AnO 2 + . We note a reexamination of the computational results for actinyl(V) oxo exchange reveals distinctive properties and chemistry of curyl(V) species, particularly CmO(OH) 2 + .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Energy Decomposition Analysis for Interactions of Radicals: Theory and Implementation at the MP2 Level with Application to Hydration of Halogenated Benzene Cations and Complexes between CO 2 -· and Pyridine and Imidazole

To study intermolecular interactions involving radicals at the correlated level, the energy decomposition analysis scheme for second-order Møller-Plesset perturbation theory based on absolutely localized molecular orbitals (ALMO-MP2-EDA) is generalized to unrestricted and restricted open-shell MP2. The benefit of restricted open-shell MP2 is that it can provide accurate binding energies for radical complexes where density functional theory can be error-prone due to delocalization errors. As a model application, the open-shell ALMO-MP2-EDA is applied to study the first solvation step of halogenated benzene radical cations, where both halogen- and hydrogen-bonded isomers are possible. We determine that the lighter halogens favor the hydrogen-bonded form, while the iodine-substituted species prefers halogen bonding due to larger polarizability and charge transfer at the halogen. As a second application, relevant to the activation of CO 2 in photoelectrocatalysis, complexes of CO 2 -· interacting with both pyridine and imidazole are analyzed with ALMO-MP2-EDA. The results reveal the importance of charge transfer into the π* orbital of the heterocycle in controlling the stability of the carbamate binding mode, which is favored for pyridine but not for imidazole.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

The Role of the Solvent in the Condensed-Phase Dynamics and Identity of Chemical Bonds: The Case of the Sodium Dimer Cation in THF

When a solute molecule is placed in solution, is it acceptable to presume that its electronic structure is essentially the same as in the gas phase? In this paper, we address this question from a simulation perspective for the case of the sodium dimer cation (Na 2 + ) molecule in both liquid Ar and liquid tetrahydrofuran (THF). In previous work, we showed that when local specific interactions between a solute and solvent are energetically on the order of a hydrogen bond, the solvent can become part of the chemical identity of the solute. Here, using mixed quantum/classical molecular dynamics simulations, we see that for the Na 2 + molecule, solute--solvent interactions lead to two stable, chemically-distinct coordination states (Na(THF) 4 -Na(THF) 5 + and Na(THF) 5 -Na(THF) 5 + ) that are not only stable themselves as gas-phase molecules but that also have a completely new electronic structure with important implications for the excited-state photodissociation of this molecule in the condensed phase. Furthermore, we show through a set of comparative classical simulations that treating the solute's bonding electron explicitly quantum mechanically is necessary to understand both the ground-state dynamics and chemical identity of this simple diatomic molecule; even use of the quantum-derived potential of mean force is insufficient to describe the behavior of the molecule classically. Lastly, we calculate the results of a proposed transient hole-burning experiment that could be used to spectroscopically disentangle the presence of the different coordination states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Hydrophilic and Apolar Hydration in Densely Grafted Cationic Brushes and Counterions with Large Mobilities

We employ all-atom molecular dynamics (MD) simulation framework to unravel water microstructure and ion properties for cationic [Poly(2-(methacryloyloxy)ethyl trimethylammonium chloride] (PMETAC) brushes with chloride ions as counterions. First, we identify locally separate water domains (or first hydration shells) each around the {N(CH 3 ) 3 } + and the C=O functional groups of the PMETAC chain and one around the Cl - ion. These first hydration shells around the respective moieties overlap and the extent of the overlap depends on the nature of the species triggering it. Second, despite the overlap, the water molecules in these domains demonstrate disparate properties dictated by the properties of the atoms/groups around which they are located. For example, the presence of the methyl groups make the {N(CH 3 ) 3 } + group trigger apolar hydration as evidenced by the corresponding orientation of the dipole of the water molecules around the {N(CH 3 ) 3 } + moiety. These water molecules around the N(CH 3 ) 3 } + group also have enhanced tetrahedrality as compared to the water molecules constituting the hydration layer around the C=O group and the Cl - counterion. Our simulations also identify that there is an intervening water layer between the Cl - ion and {N(CH 3 ) 3 } + group: this layer prevents the Cl - ion from coming very close to the {N(CH 3 ) 3 } + group. As a consequence, there is a significantly large mobility of the Cl - ions inside the PMETAC brush layer. Furthermore, the C=O group of the PE chain, due to the partial negative charge on the oxygen atom and the specific structure of the PMETAC brush system, demonstrates strongly hydrophilic behavior and enforces a specific dipole response of water molecules analogous to that experienced by water around anionic species of high charge density. As a result, our findings confirm that PMETAC brushes undergo hydrophilic hydration at one site, apolar hydration at another site, and ensures large mobility of the supported Cl- counterions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Computer simulation of methanol exchange dynamics around cations and anions

In this paper, we present the first computer simulation of methanol exchange dynamics between the first and second solvation shells around different cations and anions. After water, methanol is the most frequently used solvent for ions. Methanol has different structural and dynamical properties than water, so its ion solvation process is different. To this end, we performed molecular dynamics simulations using polarizable potential models to describe methanol-methanol and ion-methanol interactions. In particular, we computed methanol exchange rates by employing the transition state theory, the Impey-Madden-McDonald method, the reactive flux approach, and the Grote-Hynes theory. We observed that methanol exchange occurs at a nanosecond time scale for Na+ and at a picosecond time scale for other ions. We also observed a trend in which, for like charges, the exchange rate is slower for smaller ions because they are more strongly bound to methanol. This work was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences. The calculations were carried out using computer resources provided by the Office of Basic Energy Sciences.

Roy, Santanu↗
DOE OSTI2020

Atomistic Insight into Cation Effects on Binding Energies in Cu-Catalyzed Carbon Dioxide Reduction

Electrolyte properties in general and electrolyte ions in particular have been shown to have significant effects on the kinetics of electrochemical CO 2 and CO reduction at metal electrodes, but these effects have not yet been fully understood. Here, we investigate the effects of cations at the aqueous electrolyte–Cu(211) interface on adsorbate binding energies and the electrolyte structure using density functional theory (DFT). Charging the interface via explicit Na + has systematic effects on adsorbate–electrolyte interactions and conformations. We describe specific local adsorbate–ion interactions, including direct alkali ion–adsorbate coordination and hydrogen bonding via ion-coordinated water molecules. The relative importance of these specific interactions and purely electrostatic field–adsorbate interactions is investigated by comparing the DFT-calculated ion effects to those predicted by purely electrostatic models of the interface and the adsorbates. We find that the trend in ion effects among different adsorbates at constant surface charge density is well explained by a purely electrostatic interaction model. The binding energy of OCCHO is found to depend strongly on the surface charge density as well as the spatial distribution of ions at constant surface charge density. These effects are also explained by a purely electrostatic local electrostatic field–adsorbate model. This indicates that alkali ion effects can be mainly attributed to purely electrostatic field interactions and that the local field at ion-stabilized active sites can depend significantly on both the overall charge density and on the spatial distribution of ions at constant charge density. This work provides new insight on alkali ion effects on a variety of adsorbates relevant to the CO 2 and CO reduction reactions by describing specific local ion–adsorbate interactions, systematic changes in adsorbate–electrolyte interactions induced by explicit surface charge, and comparisons of the calculated effects on binding energies to simple electrostatic field–adsorbate models to explain trends among various adsorbates and at varying surface charge densities and supercell configurations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Machine Learning and IAST-Aided High-Throughput Screening of Cationic and Silica Zeolites for Alkane Capture, Storage, and Separations

We present an approach for quantitatively predicting the temperature-dependent single-component adsorption behavior of linear alkanes in silica and Na-exchanged cationic zeolites using machine learning (ML) models trained from extensive molecular simulations based on force fields with coupled cluster accuracy. A high-performing classification model was developed to distinguish between instances with negligible and non-negligible adsorption. Subsequently, two ML models were trained to predict the single-component adsorption loading and the heat of adsorption at any pressure at 300 K for any zeolite topology and silicon-to-aluminum ratio. The ML models were trained on International Zeolite Association (IZA) zeolites, and their transferability to hypothetical zeolites was successfully validated. We then expand the power of these predictions to adsorbed mixtures at arbitrary temperatures by integrating them with the Clausius–Clapeyron equation and ideal adsorbed solution theory (IAST). This approach was validated and then applied to a temperature swing adsorption separation process to demonstrate its practical utility. We demonstrate how predictions from this ML-enabled approach can allow the selection of high-performing materials that are then validated using detailed molecular simulations based on quantitatively accurate force fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Swelling properties of montmorillonite and beidellite clay minerals from molecular simulation: Comparison of temperature interlayer cation, and charge location effects

In this study, the swelling properties of smectite clay minerals are relevant to many engineering applications including environmental remediation, repository design for nuclear waste disposal, borehole stability in drilling operations, and additives for numerous industrial processes and commercial products. We used molecular dynamics and grand canonical Monte Carlo simulations to study the effects of layer charge location, interlayer cation, and temperature on intracrystalline swelling of montmorillonite and beidellite clay minerals. For a beidellite model with layer charge exclusively in the tetrahedral sheet, strong ion–surface interactions shift the onset of the two-layer hydrate to higher water contents. In contrast, for a montmorillonite model with layer charge exclusively in the octahedral sheet, weaker ion–surface interactions result in the formation of fully hydrated ions (two-layer hydrate) at much lower water contents. Clay hydration enthalpies and interlayer atomic density profiles are consistent with the swelling results. Water adsorption isotherms from grand canonical Monte Carlo simulations are used to relate interlayer hydration states to relative humidity, in good agreement with experimental findings.

36 MATERIALS SCIENCE↗