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At least 19 records

Effect of stoichiometry and hydration level on water domain size and transport in poly(aryl piperidinium) alkaline anion-exchange membranes

Alkaline water electrolysis holds promise in decarbonizing the global economy by enabling renewable hydrogen production with non-precious group metal catalysts. Anion exchange membranes are an important component of alkaline water electrolyzers and would ideally be durable while allowing for high hydroxide conductivity. The poly(aryl piperidinium) (PAP) class of polymers has attracted recent interest due to their good mechanical robustness and high ionic conductivity. Here, in this work, we perform atomistic molecular dynamics (MD) simulations of several PAP polymers at experimentally relevant hydration levels and polymer ion exchange capacities (IECs) to gain nanoscale insight into their properties and to help elucidate the trade-offs that result from tuning the IECs through the polymer stoichiometry. Our MD-predicted macroscopic polymer properties were found to be in good agreement with experimentally available polymer swelling ratios, water-occupied volumes, X-ray scattering, and ionic conductivities. The models show that for hydration levels greater than 8H 2 O per cation a single water cluster will form that percolates through the system. The growth in water cluster size results in large polymer swelling, the creation of larger channels with widths of 7 Å or larger, and nanophase separation between the hydrophilic domains and the polymer with characteristic length scales of approximately 20–30 Å. The experimentally observed lack of a strong X-ray scattering peak at low wavevectors can be explained by a cancellation between the polymer-polymer/water-water and polymer-water correlations and not a loss in nanophase separation. The overlap in coordination environments of the hydroxide oxygen and polymer nitrogen atoms implies that vehicular diffusion between cationic groups could play a role in hydroxide transport. The polymers' hydroxide and water diffusion constants increase by approximately an order of magnitude between hydration levels of 8 and 20H 2 O per cation. However, there are diminishing returns in hydroxide diffusion constant once the IEC exceeds 2.4 meq/g.

08 HYDROGEN↗

The effect of ion pairing on speciation and transport in ion exchange membranes at varying hydration levels: A four-state model

Understanding ion pairing in ion exchange membranes (IEMs) is essential for advancing IEM applications in energy and environmental technologies. Here, this study introduces a four-state molecular dynamics model to quantify speciation and transport within Nafion-117, specifically examining the role of ion pairing in monovalent and divalent counterions (NaCl, Na 2 SO 4 , and MgSO 4 ). By analyzing radial distribution functions (RDFs) and molecular snapshots, we distinguish ion pairing modes and classify counterions into four states: condensed counterion, condensed ion pair, free ion pair, and free counterion. A key finding is that while divalent counterions (e. g., Mg 2+ ) maintain stable speciation across hydration levels, monovalent counterions (e.g., Na + ) show notable speciation shifts with hydration. Both monovalent and divalent counterions are not diffusive when condensed onto the polymer (sorbed to membrane functional groups). In contrast, free counterions are diffusive across all hydration levels. To evaluate the overall diffusivity of counterions, four-state fractions and diffusivities are computed, each contributing to counterion transport. The condensed/free ion speciation for multivalent sulfate salts aligns with previous revisions to the Donnan-Manning framework that include ion pairing, thereby validating its relevance to established membrane theories. The four-state model's diffusivity results support several current ion exchange assumptions, including that the condensed counterions are immobile, while uncondensed counterions are mobile. The four-state model offers insights into contact ion pairing within IEMs, highlighting its potential even when undetected in aqueous solution experiments. This work advances the theoretical understanding of counterion speciation in IEMs while identifying model limitations that suggest avenues for refinement, such as distinguishing water-mediated ion pairs between fully hydrated ions.

Ion exchange membranes↗

Structural and thermodynamic effects of hydration in Na-zeolite A (LTA) from low-temperature heat capacity

Zeolite A (Linde Type A; LTA) is an industrially important porous mineral that has recently been shown to exhibit framework flexibility upon changes in hydration level. Here, to investigate the flexibility transition from a thermodynamic perspective, we have performed heat capacity measurements on sodium zeolite A at seven incremental hydration levels ranging from zero to equilibrium with ambient air. Excess low-frequency vibrations beyond the predictions of the Debye model are found in all samples, and the frequency of these vibrations increases as a function of hydration level. This suggests that an increase in hydration causes a decrease in at least one type of framework flexibility for sodium zeolite A. In addition, a subtle excess heat capacity contribution from 150 to 280 K is observed only for low and intermediate hydration levels, which may arise from a transformation tied to framework flexibility previously observed in zeolite A via gas absorption calorimetry. Values of the standard thermodynamic functions C p,m °, Δ 0 T S m °, Δ 0 T H m °, and Φ m ° are also reported.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Improving Proton Conductivity by Navigating Proton Trapping in High Scandium-Doped Barium Zirconate Electrolytes

Proton-conducting oxides are used in intermediate-temperature (300 °C < T < 700 °C) applications of fuel cells, electrolyzers, membrane reactors, hydrogen pumps, and sensors. The proton conductivity of doped ABO 3 perovskites is partly dependent on the proton concentration and hence on the level of material hydration. However, how the material hydration ability is affected by differences in doping is not fully understood. Here, we show the prospect of proton trapping and detrapping that influences material hydration and dehydration. The proton-trapping influence is significant for Sc-doped BaZrO 3 compared to Y-doped BaZrO 3 . Here, our work offers a perspective to understand how defect interaction/associations influence the hydration ability of proton-conducting oxides. Furthermore, positron annihilation lifetime spectroscopy was revealed to be a valuable technique for studying the proton-trapping phenomena and the defect chemistry of dense proton conductors. Density functional theory calculations also showed that a high hydration level in Sc-doped BaZrO 3 boosts proton migration. In contrast, the effect of boosting the proton migration due to increased hydration is limited for Y-doped BaZrO 3 . This effect, in turn, might explain the trend of conductivity with dopant concentration in doped BaZrO 3 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Structural water in amorphous carbonate minerals: ab initio molecular dynamics simulations of X-ray pair distribution experiments

Water is known to play a controlling role in directing mineralization pathways and stabilizing metastable amorphous intermediates in hydrous carbonate mineral MCO 3 ·nH 2 O systems, where M 2+ is a divalent metal cation. Despite this recognition, the nature of the controls on crystallization is poorly understood, largely owing to the difficulty in characterizing the dynamically disordered structures of amorphous intermediates at the atomic scale. Here, we present a series of atomistic models, derived from ab initio molecular dynamics simulation, across a range of experimentally relevant cations (M = Ca, Mg, Sr) and hydration levels (0 ≤ n ≤ 2). Theoretical simulations of the dependence of the X-ray pair distribution function on the hydration level n show good agreement with available experimental data and thus provide further evidence for a lack of significant nanoscale structure in amorphous carbonates. Upon dehydration, the metal coordination number does not change significantly, but the relative extent of water dissociation increases, indicating that a thermodynamic driving force exists for water dissociation to accompany dehydration. Mg strongly favors monodentate conformation of carbonate ligands and shows a marked preference to exchange monodentate carbonate O for water O upon hydration, whereas Ca and Sr exchange mono- and bidentate carbonate ligands with comparable frequency. Finally, water forms an extensive hydrogen bond network among both water and carbonate groups that exhibits frequent proton transfers for all three cations considered suggesting that proton mobility is likely predominantly due to water dissociation and proton transfer reactions rather than molecular water diffusion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Protonation Dynamics of Confined Ethanol–Water Mixtures in H-ZSM-5 from Machine Learning-Driven Metadynamics

Zeolites are indispensable heterogeneous catalysts in industrial chemical processes, valued for their strong Brønsted acidity, well-defined microporous frameworks, and tunable pore structures. Their catalytic activity arises primarily from Brønsted acid sites (BAS), typically present as bridging hydroxyl groups (Si–OH–Al). Under aqueous reaction conditions, these protons interact dynamically with water and alcohol molecules, leading to complex solvation and protonation behavior within confined pores. In this study, we investigate the protonation equilibrium occurring between ethanol and water at the BAS of acidic zeolites under varying hydration levels, i.e., C2H5OH–(H2O)n, n=1–4. Local structure was analyzed through an adaptive-learning global optimization algorithm, while enhanced sampling molecular dynamics simulations with Well-Tempered Metadynamics (WMetaD) and machine learning interatomic potentials (MLPs) provide free-energy surfaces (FES) at variable hydration levels. The results reveal a strong dependence of proton localization on the degree of hydration. At low hydration (1 water molecule), the proton resides predominantly on ethanol; with 2 water molecules, it shifts toward water, and at higher hydration (3 or more water molecules), it becomes extensively delocalized over the water cluster. These findings underscore the critical role of solvation in modulating acid site behavior and suggest that a minimum of three water molecules is necessary to fully stabilize the proton on water within the zeolite framework. This solvation threshold has significant implications for catalytic processes, particularly in biomass conversion reactions where alcohol protonation is a key step in dehydration mechanisms.

machine learning↗

Molecular level insight into non-bilayer structure formation in thylakoid membranes: a molecular dynamics study

In oxygenic photosynthetic organisms, the light reactions are performed by protein complexes embedded in the lipid bilayer of thylakoid membranes (TMs). The organization of the bulk lipid molecules into bilayer structures provide optimal conditions for the build-up of the proton motive force (pmf) and its utilization for ATP synthesis. However, the lipid composition of TMs is dominated by the non-bilayer lipid species monogalactosyl diacylglycerol (MGDG), and functional plant TMs, besides the bilayer, contain large amounts of non-bilayer lipid phases. Bulk lipids have been shown to be associated with lumenal, stromal-side and marginal-region proteins and proposed to play roles in the self-assembly and photoprotection of the photosynthetic machinery. Furthermore, it has recently been pointed out that the generation and utilization of pmf for ATP synthesis according to the ‘protet’ or protonic charge transfer model Kell (Biochim Biophys Acta Bioenerg 1865(4):149504, 2024), requires high MGDG content Garab (Physiol Plant 177(2):e70230, 2025). In this study, to gain better insight into the structural and functional roles of MGDG, we employed all atom and coarse-grained molecular dynamics simulations to explore how temperature, hydration levels and varying MGDG concentrations affect the structural and dynamic properties of bilayer membranes constituted of plant thylakoid lipids. Our findings reveal that MGDG promotes increased membrane fluidity and dynamic fluctuations in membrane thickness. MGDG-rich stacked bilayers spontaneously formed inverted hexagonal phases; these transitions were enhanced at low hydration levels and at elevated but physiologically relevant temperatures. It can thus be inferred that MGDG plays important roles in heat and drought stress mechanisms.

59 BASIC BIOLOGICAL SCIENCES↗

Unexpected Hydroxide Ion Structure and Properties at Low Hydration

Understanding the behavior of hydroxide ions in aqueous and non-aqueous media is fundamental to many chemical, biological, and electrochemical processes. Research has primarily focused on a single fully solvated hydroxide ion, either as an isolated cluster or in bulk. This work presents the first computational study to consider hydroxide under low hydration levels in detail, where the anion may not be fully solvated. Under such conditions, we find that the anions are predominantly present as unique water-bridged hydroxide pair complexes, distinct from previously reported structures under fully hydrated conditions. Although similar hydroxide pair structures were previously reported, we analyze these structures for the first time in the disordered liquid state where they are found to be unusually stable in the presence of bulky quaternary ammonium cations. Our findings help explain the unusual diffusion behavior as well as the higher reactivity of hydroxide anions observed under low hydration conditions.

computational studies↗

Consequences of Convex Nanopore Chemistry on Confined Water Dynamics

A basic understanding of confined water is crucial for developing selective ion transport and water purification membranes, yet the roles of nanopore geometry and functionality on confined water dynamics remain unresolved. We discuss the synthesis of perdeuterated ionic alkylsulfonate amphiphiles and their water-induced self-assembly into lyotropic liquid crystal (LLC) mesophases with well-defined, convex, sulfonate-lined nanopores. Quasielastic neutron scattering (QENS) measurements demonstrate that the water self-diffusion coefficients within these sulfonate-lined convex nanopores depend on the hydration level and amphiphile counterion identity (H + , K + , NMe 4 + ). The consistency of the observed counterion-dependent water dynamics trends with those of carboxylate LLCs is rationalized on the basis of similarities in the counterion spatial distributions in the water-filled channels, which we deduce from electron density maps derived from small-angle X-ray scattering (SAXS) analyses. These findings indicate that water diffusion is systematically faster in sulfonate-lined nanopores as compared to carboxylate-lined pores due to weaker water interactions with the softer and more hydrophobic–SO 3 – functionalities. These molecular-level insights into the relationships between convex pore wall chemical functionalities, hydrated counterions, and confined water diffusion may inform future development of new nanoporous media.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

CO 2 Capture Characteristics of Hyperbranched Poly(alkylene imine): A Molecular Dynamics Simulation Approach

This study explores the CO 2 capture characteristics of hyperbranched poly(ethylenimine) (HB-PEI) and poly- (propyleneimine) (HB-PPI) through molecular dynamics simulations using density functional theory-calibrated force fields. Key features such as density, free volume, glass transition temperature, CO 2 /H 2 O distribution, and molecular diffusion are systematically investigated to elucidate structure−function relationships under dry and hydrated conditions. HB-PEI demonstrates a slightly higher density and lower free volume compared to HB-PPI yet shows superior CO 2 capture due to the high amine concentration. Glass transition analysis indicates a higher thermal mobility in HBPEI, enhancing the CO 2 diffusivity. Pair correlation and coordination analyses confirm a stronger affinity of CO 2 with primary and secondary amines, particularly in hydrated environments where water competes with CO 2 for binding sites. Despite its more compact structure, HB-PEI outperformed HB-PPI in CO 2 and H 2 O transport, as confirmed by higher diffusion coefficients across all hydration levels. These findings highlight a critical balance among polymer architecture, amine accessibility, and hydration in designing next-generation solid amine sorbents for efficient direct air capture applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Investigating Morphology and Diffusion in Simulations of Precise Anion-Conducting Polymers

Using atomistic molecular dynamics simulations, we investigate the morphology and transport properties of a new class of polymers which are functionalized with quaternary ammonium groups for use as anion exchange membranes. The polymers are precision polyolefins with either a trimethylammonium (p5CNMe3) or a dimethyl-hexyl ammonium (p5CNMe2Hx) pendant group at every fifth carbon along a polyethylene backbone. Simulations are performed at hydration levels of 5, 10, 15, and 20 water molecules per ammonium group. The hydrated polymers form nanoscale, percolated hydrophilic domains (water channels) in the hydrophobic polymer matrix that become wider with increasing water content. Water and hydroxide anion diffusion coefficients also increase with increasing water content. The morphology of the water domains is similar in both polymers, while the diffusion coefficients are somewhat lower in p5CNMe2Hx at fixed water content. Furthermore, the diffusion coefficients in both polymers fall on the same curve as a function of the fractal dimension of the percolated water channels, which appears to be a useful scalar measure of the effects of the nanoscale morphology on water and hydroxide anion transport.

Anion exchange membrane↗

Pore-scale observations of natural hydrate-bearing sediments via pressure core sub-coring and micro-CT scanning

Abstract Both intra-pore hydrate morphology and inter-pore hydrate distribution influence the physical properties of hydrate-bearing sediments, yet there has been no pore-scale observations of hydrate habit under pressure in preserved pressure core samples so far. We present for the first time a pore-scale micro-CT study of natural hydrate-bearing cores that were acquired from Green Canyon Block 955 in UT-GOM2-1 Expedition and preserved within hydrate pressure–temperature stability conditions throughout sub-sampling and imaging processes. Measured hydrate saturation in the sub-samples, taken from units expected to have in-situ saturation of 80% or more, ranges from 3 ± 1% to 56 ± 11% as interpreted from micro-CT images. Pore-scale observations of gas hydrate in the sub-samples suggest that hydrate in silty sediments at the Gulf of Mexico is pore-invasive rather than particle displacive, and hydrate particles in these natural water-saturated samples are pore-filling with no evidence of grain-coating. Hydrate can form a connected 3D network and provide mechanical support for the sediments even without cementation. The technical breakthrough to directly visualize particle-level hydrate pore habits in natural sediments reported here sheds light on future investigations of pressure- and temperature-sensitive processes including hydrate-bearing sediments, dissolved gases, and other biochemical processes in the deep-sea environment.

58 GEOSCIENCES↗

Proton Dissociation and Delocalization under Stepwise Hydration of Zeolite HZSM-5

The protonation behavior of zeolite Brønsted acid sites (BAS) in the presence of water is important for the performance of these widely used catalysts. Despite extensive study, the number of water molecules necessary for deprotonation is not well understood, in large part because experiments have been unable to access this information. In this work, we report experimental evidence for full deprotonation of the BAS in the presence of two or more water molecules, with a deprotonation energy of 1.6 kcal/mol. Linear IR absorption and 2D IR spectra were measured over a wide range of controlled hydration levels from 0.5 to 8.0 equivalents of H 2 O/Al at a constant temperature. Distinct spectral signatures of the protonated BAS and excess proton are identified, and their hydration dependence is analyzed quantitatively. Using the experiment as a benchmark, ab initio molecular dynamics simulations are reported that reproduce the experimental trends in the protonation state and IR spectra. The proton charge position and delocalization are quantified in clusters of 1–8 H 2 O molecules using the recently developed rCEC method. This analysis provides insight into the proton structure in confined water clusters, showing that the excess charge remains relatively localized between two oxygen atoms across the hydration range.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Determination of Ce 3+ , Co 2+ , Mn 2+ and Fe 2+ diffusion coefficients in Nafion® membrane

Concentration gradient diffusion coefficients for Ce 3+ , Co 2+ , Mn 2+ and Fe 2+ cations are determined in Nafion®211 membranes over a wide range of environmental conditions. Measurements are made using finite-width cation-rich bands introduced to NR211 via a hot-pressing procedure. A robust method of accurate diffusion coefficient determination of the finite-width deposits is developed using a Fick's second law of diffusion solution for one-dimensional systems. The transition metal dications are found to have nearly identical NR211 diffusion coefficients under water saturated conditions over the 22–80 °C range. The powerful chemical mitigant, Ce 3+ , is about one-half as diffusive as the dications under identical conditions. Derived diffusion coefficients for Ce 3+ and Co 2+ are found to be independent of initial cation concentration over the range of 12.5–70 mol% exchange level. The diffusion behavior of Ce 3+ in 80 °C liquid water and saturated water vapor is identical. The diffusion coefficients of Ce 3+ are shown to have a strong dependence on membrane hydration level varying by a factor of more than 30 over the range of 95 to 40% RH. Finally, the implications of these new diffusion findings are applied to a discussion of potential guidelines for the development of highly durable fuel cell systems, which employ mobile metal cations as lifetime-extending redox stabilizers.

08 HYDROGEN↗

Heat capacity and thermodynamic functions of partially dehydrated sodium and zinc zeolite A (LTA)

Zeolite A (LTA) is an industrially important zeolite that exhibits sorption-induced framework flexibility, the thermodynamics of which are poorly understood. In this work, we report heat capacity measurements on zinc and sodium zeolite A from 1.8 to 300 K and compare the heat capacity of water in sodium zeolite A with that of water in other zeolites. The heat capacity of zeolitic water varies significantly depending on the hydration level and identity of the host zeolite, and more tightly bound water exhibits strong inflections in its heat capacity curve. This suggests a combination of effects, including differences in water-framework binding strength and hydration-dependent flexibility transitions. We also report fits of the heat capacity data using theoretical functions, and we report values for $C_{P,m}^°$,$Δ_0^TS_m^°$,$Δ_0^TH_m^°$, and $Φ_m^°$ from 0 to 300 K. These results contribute to a systematic thermodynamic understanding of the effects of cation exchange, guest molecule confinement, and sorbate-dependent flexibility transitions in zeolites.

Geochemistry & Geophysics↗

Effect of reacting gas flowrates and hydration on the carbonation of anion exchange membrane fuel cells in the presence of CO 2

Anion exchange membrane fuel cells (AEMFCs) have been widely touted as a low-cost alternative to existing proton exchange membrane fuel cells. However, one of the limitations of this technology has been the severe performance penalty related to the introduction of CO 2 to the cell – typically in the air cathode feed. Introduction of CO 2 into AEMFCs results in cell carbonation, which imparts thermodynamic, kinetic and Ohmic overpotentials that can add up to hundreds of millivolts. Therefore, it is important to find strategies and operational protocols for AEMFCs that minimize these overpotentials. In this paper, we reserach the impacts of the anode and cathode flowrate, as well as the cell hydration level, on the extent of cell carbonation and cell polarization. Key findings include: (1) decreasing the cathode flowrate generally decreases the total CO 2 -related voltage loss while changing the anode flowrate has a minimal effect; (2) increasing cell hydration helps to mitigate the performance loss in the presence of CO 2 ; and (3) operational combinations are found that significantly reduce the CO 2 penalty compared to the present literature.

25 ENERGY STORAGE↗

Controlling the Structure of MoS 2 Membranes via Covalent Functionalization with Molecular Spacers

Restacked two-dimensional (2D) materials represent a new class of membranes for water-ion separations. Understanding the interplay between the 2D membrane’s structure and the constituent material’s surface chemistry to its ion sieving properties is crucial for further membrane development. In this paper, we reveal, and tune via covalent functionalization, the structure of MoS 2 -based membranes. We find features on both the ~1 nm (interlayer spacing) and ~100 nm (mesoporous voids between layers) length scales that evolve with the hydration level. The functional groups act as permanent molecular spacers, preventing local impermeability caused by irreversible restacking and promoting the uniform rehydration of the membrane. Molecular dynamics simulations show that the choice of functional group tunes the structure of water within the MoS 2 channel and consequently determines the hydrated interlayer spacing. We demonstrate that MoS 2 membranes functionalized with acetic acid have consistently ~92% rejection of Na 2 SO 4 with a flux of ~1.5 lm -2 hr -1 bar -1 .

2D channel↗

Decoding Zeolite Crystallization and Stage III in Nuclear Waste Glasses by Coupled Modeling and Experiments

Under specific conditions of pH and temperature, nuclear waste immobilization borosilicate glasses may exhibit a sudden acceleration in their corrosion kinetics (stage III)—a behavior that has been associated with the formation of zeolite crystals. Such accelerated dissolution may compromise the integrity of nuclear wasteforms placed in geological depositories. However, thus far, none of the available models is able to predict the thermodynamic propensity and kinetics of zeolite precipitation as a function of the solution conditions due to (i) a lack of fundamental knowledge regarding the nucleation & growth mechanisms of zeolitic phases, (ii) uncertainty regarding the compositions (types) of zeolites that may form and the rate-limiting step in their precipitation as a function of the solution conditions, and (iii) the complexities that arise due to the vast parametric space (i.e., solution chemistry, temperature, number of secondary phases, etc.) that encompass these systems under conditions of environmental exposure. To resolve these challenges, this project aimed to unambiguously identify the thermodynamic propensity for zeolite precipitation and the kinetics thereof as a function of the solution conditions (composition, pH, and temperature). To achieve this goal: 1) We identified the solution conditions and zeolite phases relevant to nuclear glass dissolution. 2) We performed a series of ab initio molecular dynamics (AIMD) simulations to compute the thermodynamic properties of a group of characteristic zeolites that features a large range of compositions, various hydration levels, a wide range of framework structures, and partial atomic site occupancies. 3) We released a first-of-a-kind self-consistent thermodynamic database that can be used to assess the kinetics and the stability fields of zeolitic phases within a Gibbs energy minimization (GEM) framework. 4) We developed a robust geochemical modeling method allowing us to predict the stability of secondary phases (including zeolites, calcium–silicate–hydrate gels, and clays) upon the dissolution of nuclear waste immobilization glasses. 5) We introduced a model that predicts the dissolution kinetics of a series of borosilicate nuclear waste immobilization glasses in terms of the topology of their atomic network. 6) We investigated the roles of the solution composition on the crystallization kinetics of phillipsite zeolites and tobermorite silicate hydrates. Via PNNL’s collaboration and engagement, this project directly supports DOE’s nuclear waste immobilization activities by offering a technical, science-based foundation that will (i) facilitate predictions of the long-term corrosion rates and extents of existing nuclear waste immobilization glasses to help ensure safe and successful vitrification operations, (ii) inform the development of advanced glass formulations with enhanced durability, and, (iii) enable cost-savings that result from making more decisive and hence less conservative predictions while offering higher levels of nuclear waste embedment in smaller, more compact glass volumes.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗