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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Calorimetric Study of Functionalized Uranyl Peroxide Nanoclusters and Their Monomeric Building Block

The description of the energy landscape of polyoxometalates (POMs) enriches our understanding of their solution behavior through quantitative information that can be used to predict their existence, stability, and properties. Herein, we report thermodynamic values that describe the energy landscape of four uranyl peroxide nanoclusters (UPCs) (LiRb–U@U 24 , LiNa–U 24 Pp 12 , NaK–U 24 Pp 12 , and U 60 Ox 30 ) and a building block of UPCs, lithium uranyl triperoxide monomer (Li–UT). Furthermore, the results reveal relationships between the affinity of counter cations and the anionic uranyl peroxide units, enthalpy of dissolution, as well as enthalpy of crystallization and cluster solubility. Additionally, the calorimetric measurements of Li–UT allowed us to calculate a favorable enthalpy of formation of Li–U 24 and Li–U 28 from their monomeric units.

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

Synthetic Access to a Framework-Stabilized and Fully Sulfided Analogue of an Anderson Polyoxometalate that is Catalytically Competent for Reduction Reactions

Polyoxometalates (POMs) featuring 7, 12, 18, or more redox-accessible transition metal ions are ubiquitous as selective catalysts, especially for oxidation reactions. The corresponding synthetic and catalytic chemistry of stable, discrete, capping-ligand-free polythiometalates (PTMs), which could be especially attractive for reduction reactions, is much less well developed. Among the challenges are the propensity of PTMs to agglomerate and the tendency for agglomeration to block reactant access of catalyst active sites. Nevertheless, the pervasive presence of transition metal sulfur clusters metalloenzymes or cofactors that catalyze reduction reactions and the justifiable proliferation of studies of two-dimensional (2D) metal-chalcogenides as reduction catalysts point to the promise of well-defined and controllable PTMs as reduction catalysts. Here, we report the fabrication of agglomeration-immune, reactant-accessible, capping-ligand-free Co II Mo 6 IV S 24 n– clusters as periodic arrays in a water-stable, hierarchically porous Zr-metal–organic framework (MOF; NU1K) by first installing a disk-like Anderson polyoxometalate, Co III Mo 6 VI O 24 m– , in size-matched micropores where the siting is established via difference electron density (DED) X-ray diffraction (XRD) experiments. Flowing H 2 S, while heating, reduces molybdenum(VI) ions to Mo(IV) and quantitatively replaces oxygen anions with sulfur anions (S 2– , HS – , S 2 2– ). DED maps show that MOF-templated POM-to-PTM conversion leaves clusters individually isolated in open-channel-connected micropores. Importantly, the structure of the immobilized cluster as determined, in part, by X-ray photoelectron spectroscopy (XPS), X-ray absorption fine structure (XAFS) analysis, and pair distribution function (PDF) analysis of total X-ray scattering agrees well with the theoretically simulated structure. PTM@MOF displays both electrocatalytic and photocatalytic competency for hydrogen evolution. Nevertheless, the initially installed PTM appears to be a precatalyst, gaining competency only after the loss of ~3 to 6 sulfurs and exposure to hydride-forming metal ions.

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

Crystalline phase transitions and water-soluble complexes of copper(Ⅰ) 2-hydroxyethanethiolate

We report the coordination polymer copper(I) 2-hydroxyethanethiolate, (CuSCH 2 CH 2 OH) n , though insoluble in all common solvents, dissolved readily in basic aqueous solutions of the thiolate anion (HOCH 2 CH 2 S – ) of 2-mercaptoethanol to form a single species: the tetranuclear cluster [Cu 4 (μ-SCH 2 CH 2 OH) 6 ] 2– . From this solution were grown X-ray quality single crystals of copper(I) 2-hydroxyethanethiolate. This compound underwent a hitherto unknown crystal phase transition at ca. 6 °C, from point group P2 1 2 1 2 1 to Pna2 1 , with noticeable changes in the geometry of the Cu-S layer and in the orientation of the alkylthiolate side chains. When the bulky base tetrabutylammonium hydroxide was employed in the aqueous thiolate solution used to dissolve (CuSCH 2 CH 2 OH) n , the water-soluble polynuclear copper(I) complex bis(tetrabutylammonium) hexakis(μ-2-hydroxyethanethiolato) tetracuprate(I), [(C 4 H 9 ) 4 N] 2 [Cu 4 (μ-SCH 2 CH 2 OH) 6 ], could be isolated as X-ray quality crystals. Structural characterization of this complex revealed a tetrahedral arrangement of copper(I) centers with thiolates bridging the edges of the tetrahedra. On standing, this complex degraded to a larger polynuclear Cu(I) sulfide cluster.

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

Phosphate anion-quaternary ammonium ion pair coordinated polymer membranes

Ion exchange membranes materials according to the present disclosure exhibit improved conductivity at low and intermediate relative humidity without sacrificing mechanical strength. Polymers are provided that include a backbone with one or more aryl groups, a halocarbyl group, and a halocarbyl side chain attached to the backbone, wherein the halocarbyl side chain includes a halide separated from the backbone by a hydrocarbyl chain, a hydrocarbyl ring, or combinations thereof. The halide is substituted with a tertiary amine and halide anions are then exchanged with hydroxide anions. The polymers are then contacted with phosphoric acid, which is deprotonated by the hydroxide ions, forming anions which enhance interactions with adjacent quaternary ammonium groups and induce excess phosphoric acid molecules to cluster around those quaternary ammonium groups. The membranes exhibit negligible dopant leaching even at high relative humidity.

Bae, Chulsung↗
DOE OSTI2025

Ion Clusters in Multicomponent Solutions Determined from X-ray PDF and SAXS Analysis: The NaNO 2 –NaOH–H 2 O System

Here, this study explores ion cluster formation in the NaNO 2 –NaOH–H 2 O system to understand how ion cluster formation is influenced by the composition in multicomponent mixtures. X-ray pair distribution function (PDF) and small-angle X-ray scattering (SAXS) identified complex ion clusters in concentrated NaNO 2 and NaOH solutions as well as their mixtures. PDF analysis showed that the Na–O distance depended primarily on total Na + concentrations rather than anion composition, whereas the nitrite-water oxygen distance stayed the same regardless of concentration or composition. This result indicates that the nitrite ion hydration was relatively independent of composition. SAXS confirms local fluctuations and coherent clusters with notable size differences between NaOH and NaNO 2 solutions. SAXS analysis of mixed solutions shows that their clusters are an average of the individual solutions, indicating mixed clusters.

Reynolds, Jacob G. [Central Plateau Cleanup Compan↗
DOE OSTI2020

Building [U IV 70 (OH) 36 (O) 64 ] 4– oxocluster frameworks with sulfate, transition metals, and U V

Uranium (IV) oxide clusters, colloids, and materials are designed and studied for 1) nuclear materials applications, 2) understanding environmental fate and transport of actinides, and 3) exploring the complex bonding behavior of open-shell f-elements. U IV -oxyhydroxsulfate clusters are particularly relevant in industrial processes and in nature. Recent studies have shown that counter-cations to these polynuclear anions differentiate rich structural topologies in the solid-state. Here we present nine different structures with wheel-shaped [U 70 (OH) 36 (O) 64 (SO 4 ) 60 ] 4- (U 70 ) linked into 1-dimensional and 2-dimensional frameworks with sulfate, divalent transition metals (Cr II , Fe II , Co II , Ni II ) and U V . Here, the small-angle X-ray scattering of these phases dissolved in butylamine reveals differing supramolecular assembly of U 70 clusters, controlled primarily by sulfates. However, observed trends in transition metal linking guide future design of U 70 -materials with different topologies. Finally, U 70 linking via U IV -O-U V -O-U IV bridges presents a rare example of mixed oxidation state uranium oxides without disorder.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Computational study of the electrostatic potential and charges of multivalent ionic liquid molecules

The electrostatic interactions in ionic liquids (ILs) can be difficult to quantify, but this information is very valuable for improving intermolecular potentials for performing molecular-level simulations. Although polarizable forcefields can provide improved accuracy, the computational efficiency of fixed charge molecular models is often preferred for larger systems. Here, we propose a multi-scale screening approach for analyzing the charge scaling behavior and other electrostatic properties of ILs, which is more attainable than previous analysis methods that rely on the IL crystalline structures. Based on isolated molecules and small clusters, we study the electrostatic potential properties and charges of multivalent IL molecules using density-functional theory calculations and ab initio molecular dynamics simulations. The charges of the IL molecules are calculated and compared using several different charge estimation techniques. Although there are some differences among the estimated partial charges on the atoms, the total anion and cation charges are very similar. In conclusion, the charge scaling factors are substantial, and they are only slightly affected by the IL cluster size model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Effects of nanoconfinement and surface charge on iron adsorption on mesoporous silica

Here, we present a combined molecular dynamics (MD) simulation and X-ray absorption fine structure (XAFS) spectroscopic investigation of aqueous iron adsorption on nanoconfined amorphous silica surfaces. The simulation models examine the effects of pore size, pH (surface charge), iron valency, and counter-ion (chloride or hydroxide). The simulation methods were validated by comparing the coordination environment of adsorbed iron with coordination numbers and bond lengths derived from XAFS. In the MD models, nanoconfinement effects on local iron coordination were investigated by comparing results for unconfined silica surfaces and in confined domains within 2 nm, 4 nm, and 8 nm pores. Experimentally, coordination environments of iron adsorbed onto mesoporous silica with 4 nm and 8 nm pores at pH 7.5 were investigated. The effect of pH in the MD models was included by simulating Fe(II) adsorption onto negatively charged SiO 2 surfaces and Fe(III) adsorption on neutral surfaces. The simulation results show that iron adsorption depends significantly on silica surface charge, as expected based on electrostatic interactions. Adsorption on a negatively charged surface is an order of magnitude greater than on the neutral surface, and simulated surface coverages are consistent with experimental results. Pore size effects from the MD simulations were most notable in the adsorption of Fe(II) at deprotonated surface sites (SiO - ), but adsorption trends varied with concentration and aqueous Fe speciation. The coordination environment of adsorbed iron varied significantly with the type of anion. Considerable ion pairing with hydroxide anions led to the formation of oligomeric surface complexes and aqueous species, resulting in larger iron hydroxide clusters at higher surface loadings.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Elucidating the geometric and electronic structure of a fully sulfided analog of an Anderson polyoxomolybdate cluster

The catalytic activity of transition metal sulfide (TMS) clusters in small molecule activation, redox transformations, and charge transfer has inspired the design of novel TMS-based materials for energy-related catalysis and chemical applications. Polyoxometalates (POMs), known for their structural diversity, can in principle be transformed into TMS clusters; however, fully sulfided analogs are rarely isolated, likely due to the strong tendency of uncapped TMS clusters to agglomerate. Here, we report the geometric and electronic structure of a capping ligand-free fully sulfided analog of heptamolybdate Anderson POM [Mo VI 7 O 24 ] 6− , synthesized through the sulfidation of a nanoconfined POM secured within a porous Zr-metal organic framework (NU-1000). A combined computational and experimental analysis indicates that the sulfided counterpart of the Anderson POM is geometrically and electronically more sophisticated than the parent POM. Comparison of experimental pair distribution function (PDF) data with computational simulations confirms that, unlike the oxygen-only [Mo VI 7 O 24 ] 6− cluster, the [Mo IV 7 (μ 3 -S) 6 (μ 2 -SH) 6 (S 2 ) 6 ] 2− polythiometalate (PTM) exhibits diverse sulfur anions (S 2− , HS − , S 2 2− ). DFT calculations indicate that H 2 S acts as a reducing agent, and together with terminal disulfide (S 2 2− ) ligands in the PTM structure, facilitates the complete reduction of all seven Mo VI centers in the parent POM to Mo IV . These findings are supported by X-ray photoelectron spectroscopy (XPS), which confirms exclusive Mo IV , and elemental analysis, which shows quantitative sulfur incorporation. Difference envelope density (DED) mapping further reveals that the PTM clusters are spatially confined within the MOF pores, preventing agglomeration and preserving molecular integrity.

Rabbani, S. M. Gulam [The Ohio State University, C↗
DOE OSTI2022

Photoelectron spectroscopy of cryogenically cooled NiO 2 – via slow photoelectron velocity-map imaging

In this work, high-resolution anion photoelectron spectra of cryogenically cooled NiO 2 – anions, obtained using slow photoelectron velocity-map imaging (cryo-SEVI), are presented in tandem with coupled cluster electronic structure calculations including relativistic effects. The experimental spectra encompass the $\tilde{\text{X}}^1Σ_{\text{g}}^+ ← \tilde{\text{X}}^2Π_{\text{g}}, ã^3Π{\text{g}} ← \tilde{\text{X}}^2Π_{\text{g}}$, and $\tilde{\text{A}}^1Π_{\text{g}} ← \tilde{\text{X}}^2Π_{\text{g}}$ photodetachment transitions of linear ONiO 0/– , revealing previously unobserved vibrational structure in all three electronic bands. The high-resolution afforded by cryo-SEVI allows for the extraction of vibrational frequencies for each state, consistent with those previously measured in the ground state and in good agreement with scalar-relativistic coupled-cluster calculations. Previously unobserved vibrational structure is observed in the $ã^3Π_{\text{g}}$ and $Ã^1Π_{\text{g}}$ states and is tentatively assigned. Further, a refined electron affinity of 3.0464(7) eV for NiO 2 is obtained as well as precise term energies for the ã and à states of NiO 2 of 0.3982(7) and 0.7422(10) eV, respectively. Numerous Franck–Condon forbidden transitions involving the doubly degenerate $ν_2$ bending mode are observed and ascribed to Herzberg-Teller coupling to an excited electronic state.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Using Density-Corrected DFT to Understand Density-Driven and Functional-Dependent Errors in Ab Initio Simulations of the Hydrated Electron

The hydrated electron, an excess electron in liquid water, plays a crucial role in a plethora of chemical processes, motivating extensive research efforts to characterize its structure, dynamics, and reactivity in solution. Recent theoretical approaches to understanding this intriguing object have involved ab initio simulations based on density functional theory (DFT). Although DFT allows for the study of hydrated electron reactivity and quantum mechanical behavior, it is well-known that anionic systems can suffer from significant density-driven errors (DDEs). Density-corrected DFT (DC-DFT) provides a framework to mitigate such errors; the method reduces DDEs by replacing the self-consistent (SC) density associated with a given density functional with the Hartree–Fock (HF) density. Since HF densities tend to be more localized than DFT SC densities, the DC-DFT scheme significantly improves errors in calculations where the SC density is spuriously delocalized. Here, we investigate how the use of density correction affects the calculated properties of the DFT-simulated (PBEh) hydrated electron, a particularly challenging diffuse anionic system to simulate. First, we analyze charge delocalization in a system consisting of a model octahedral hydrated electron water cluster (the so-called Kevan structure) along with a spatially separated sulfur atom. We show that the use of density correction indeed reduces DDEs in comparison to a standard DFT global hybrid functional. We then propagate molecular dynamics trajectories of the hydrated electron using DC-DFT, where we find that DC further localizes electron density in the cavity region, a signature of reduced charge delocalization. Unfortunately, the decreased radius of gyration of the spin density and corresponding tightening of the local solvation structure from density correction causes predicted observables to deviate further from experimental measurements than when density correction is not employed. Here, we argue that DC’s worse agreement with experiment results from the removal of a fortuitous cancellation of errors that is intrinsic to the PBEh functional. This indicates that the difficulties with DFT to simulate hydrated electrons are primarily due to the inherent approximations in DFT rather than to density-driven errors.

Density functional theory↗
DOE OSTI2025

Ionic Associations and Hydration in the Electrical Double Layer of Water-in-Salt Electrolytes

Water-in-Salt-Electrolytes (WiSEs) are an exciting class of concentrated electrolytes finding applications in energy storage devices because of their expanded electrochemical stability window, good conductivity and cation transference number, and fire-extinguishing properties. These distinct properties are thought to originate from the presence of an anion-dominated ionic network and interpenetrating water channels for cation transport, which indicates that associations in WiSEs are crucial to understanding their properties. Currently, associations have mainly been investigated in the bulk, while little attention has been given to the electrolyte structure near electrified interfaces. Here, we develop a theory for the electrical double layer (EDL) of WiSEs, where we consistently account for the thermoreversible associations of species into Cayley tree aggregates. The theory predicts an asymmetric structure of the EDL. At negative voltages, hydrated Li + dominates, and cluster aggregation is initially slightly enhanced before disintegration at larger voltages. At positive voltages, when compared to the bulk, clusters are strictly diminished. Performing atomistic molecular dynamics (MD) simulations of the EDL of WiSE provides EDL data for validation and bulk data for parametrization of our theory. Validating the predictions of our theory against MD showed good qualitative agreement. Furthermore, we performed electrochemical impedance measurements to determine the differential capacitance of the studied LiTFSI WiSE and also found reasonable agreement with our theory. Overall, the developed approach can be used to investigate ionic aggregation and solvation effects in the EDL, which, among other properties, can be used to understand the precursors for solid-electrolyte interphase formation.

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

Time-Resolved Radioluminescence of the Polynuclear Copper(I) Phosphor Cu4I6²–. Different Temporal responses to Photo, X-Ray, β-Ray and α-Particle Excitation

Described for the first time are the time-resolved radioluminescence (TRRL) properties of the highly luminescent copper(I) cluster Cu4I62– using X-ray, b-ray and a-particle excitation. The copper(I) phosphors are two crystalline salts of this anion, [Na2(18-crown-6)2(H2O)3][Cu4I6] (I) and [Li(benzo-15-crown-5)2(H2O)]2[Cu4I6] (II), that had been shown to display strong photoluminescence (PL) when excited with ultraviolet light. The integrated radioluminescence (RL) spectra observed when pulsed X-rays were used as the excitation source are virtually the same as the PL spectra under comparable conditions. These temporal RL spectra are invariant at all observation times indicating that the observed scintillation occurs from a common excited state (or set of excited states). When the TRRL is collected from excitation with a pulsed X-ray source, b-ray decay from 90Sr or a-decay from 244Cm, the longer components (>2 μs) of the TRRL displayed (in each case) lifetimes comparable to those of the strictly exponential PL decays recorded under pulsed laser UV excitation. However, at shorter observation times (< 500 ns), the RL decay deviated from the exponential model, indicating a markedly different temporal luminescence behavior when these materials were excited with pulsed high energy radiation. Furthermore, this effect was the most pronounced for the a-particle excitation. These results suggest that the absorption of a very high energy X-ray photon, b-ray or a-particle at a site within the crystalline solid leads to a high local density of electronic excited states and that coupling between these states provides an alternative channel for excited state decay. Given that the patterns observed

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2022

ThAu 2 – , ThAu 2 O – , and ThAuOH – anions: Photoelectron spectroscopic and theoretical characterization

The thorium–gold negative ions ThAu 2 – , ThAu 2 O – , and ThAuOH – have been observed and experimentally characterized by anion photoelectron spectroscopy. These experiments are accompanied by extensive ab initio electronic structure calculations using a relativistic composite methodology based primarily on coupled cluster singles and doubles with perturbative triples calculations. The theoretical electron affinities (EAs) at 0 K agree with the experimental adiabatic EAs to within 0.02 eV for all species. Two separate isomers were located in the calculations for ThAuOH – , and detachment from both of these appears to be present in the photoelectron spectrum. Excited electronic states of the neutral molecules are reported at the equation of motion-coupled cluster singles and doubles level of theory. Atomization energies and heats of formation are also calculated for each neutral species and have expected uncertainties of 3 and 4 kcal/mol, respectively. The σ bonds between Th and Au are determined by natural bond orbital analysis to consist of predominately sd hybrids on Th bonding with the Au 6s orbital. In order to investigate the correspondence between the bonding in Th–Au and Th–F molecules, a limited number of calculations were also carried out on most of the F-analogs of this study. These results demonstrate that Au does behave like F in these cases, although the Th–F σ bonds are much more ionic compared to Th–Au. This results in an EA for ThF 2 that is 10 kcal/mol smaller than that of ThAu 2 . The EA values for the Th(IV) species, i.e., ThX 2 O and ThXOH, only differed, however, by 3–4 kcal/mol.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Solvation governs cation transference in glyme-based lithium battery electrolytes

The efficacy of electrochemical systems is governed by the cation transference number, which represents the fraction of current carried by the working ion. Energy is wasted when field-induced motion also drives anions and solvent molecules, decreasing the transference number to near-zero. We present a systematic study of cation transference in a series of electrolytes: tetraglyme (TG), octaglyme (OG), and poly(ethylene oxide) (PEO) mixed with lithium bis(trifluoromethanesulfonyl)imide. In all three electrolytes, starting from the dilute salt concentration limit, the experimentally measured cation transference number decreases with increasing concentration, reaching a minimum between -0.1 and -0.2, before rising back to positive values. Explicit measurements of field-induced species' velocities by electrophoretic nuclear magnetic resonance indicate that negative cation transference numbers in TG and OG electrolytes are dictated by solvation interactions with minimal contribution from anion-cation interactions. Simulation-based solvation structures indicate that OG serves as a bridge between TG and PEO. Multi-charge positive clusters, which are negligible in TG, become increasingly important at higher chain lengths (OG and PEO). As migrating cations drag their solvation shells, this solvation-induced motion is amplified in glyme electrolytes because of covalent interactions between solvating glyme molecules and free glyme molecules.

Im, Julia↗
DOE OSTI2020

Ion-specific clustering of metal-amphiphile complexes in rare earth separations

The nanoscale structure of a complex fluid can play a major role in the selective adsorption of ions at the nanometric interfaces, which is crucial in industrial and technological applications. Here we study the effect of anions and lanthanide ions on the nanoscale structure of a complex fluid formed by metal-amphiphile complexes, using small angle X-ray scattering. The nano- and mesoscale structures we observed can be directly connected to the preferential transfer of light (La and Nd) or heavy (Er and Lu) lanthanides into the complex fluid from an aqueous solution. While toluene-based complex fluids containing trioctylmethylammonium-nitrate (TOMA-nitrate) always show the same mesoscale hierarchical structure regardless of lanthanide loading and prefer light lanthanides, those containing TOMA-thiocyanate show an evolution of the mesoscale structure as a function of the lanthanide loading and prefer heavy lanthanides. The hierarchical structure indicates the presence of attractive interactions between ion-amphiphile aggregates, causing them to form clusters. A clustering model that accounts for the hard sphere repulsions and short-range attractions between the aggregates has been adapted to model the X-ray scattering results. The new model successfully describes the nanoscale structure and helps in understanding the mechanisms responsible for amphiphile assisted ion transport between immiscible liquids. Accordingly, our results imply different mechanisms of lanthanide transport depending on the anion present in the complex fluid and correspond with anion-dependent trends in rare earth separations.

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

Ion Conductivity and Correlations in Model Salt-Doped Polymers: Effects of Interaction Strength and Concentration

Correlated anion and cation motion can greatly reduce the overall ion conductivity in electrolytes versus the ideal conductivity calculated based on the diffusion constants alone. Using coarse-grained molecular dynamics simulations, we calculate conductivity and the degree of uncorrelated ion motion in salt-doped homopolymers and block copolymers as a function of concentration and interaction strengths. Calculating conductivity from ion mobility under an applied electric field increases accuracy versus the typical use of fluctuation dissipation relationships in equilibrium simulations. In typical electrolytes, correlation in cation-anion motion is often expected to be reduced at low ion concentrations. Yet, for these polymer electrolytes with strong ion-polymer and ion-ion interactions, we find cation-anion motion is more correlated at lower concentrations when other variables are held constant. We show this phenomenon is related to the slower ion cluster relaxation rate at low concentrations rather than the static spatial state of ion aggregation or the fraction of free ions.

36 MATERIALS SCIENCE↗