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At least 271 records · Page 15

Multielectrode Array Sensors to Enable Long-Duration Corrosion Monitoring and Control of Concentrating Solar Power Systems

Molten mixtures of MgCl2-KCl-NaCl are promising heat transfer fluid (HTF) candidates for the next generation of concentrating solar power systems (Gen3 CSP), because of their low cost, high decomposition temperature, and favorable heat transfer characteristics. However, if the chemistry of the salts is not properly controlled, molten chlorides can cause corrosion of high-temperature metal alloys, such as Inconel (R), in CSP systems. Here we demonstrate a corrosion monitoring system that can be used to monitor the health of the structural alloys over long durations. The monitoring system includes a multielectrode array voltammetry sensor that measures the redox potential of molten MgCl2-KCl-NaCl mixture as well as the presence of corrosion products and impurities. The sensors have been successfully operated in static molten salt environments for long durations, and are capable of detecting corrosion products, such as Cr2+ and Fe2+, quantitatively at low concentrations (i.e., approximately 100 ppm) with less than 4% error.

Concentrated solar power↗

First-principles-derived transport properties of Molten chloride salts

Molten salts have many applications ranging from a heat transfer medium in both generation IV nuclear reactor designs and the solar industry to thermal storage systems. While molten salts show promising properties for these applications, there still exists a knowledge gap for the transport properties of molten salts at elevated temperatures. This work uses ab initio Molecular Dynamics to investigate the transport properties of KCl, LiCl, KCl-LiCl eutectic, NaCl, MgCl 2 , and NaCl-MgCl 2 eutectic molten salt systems. Further, the properties presented here are the diffusion coefficient, viscosity, and isochoric heat capacity. These properties are compared to experimental data where available and other computational work in cases where no experimental data is available. This is the first work to explore timescales over 100 ps via AIMD for the determination of transport properties in molten salts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Conducting thermal energy to the membrane/water interface for the enhanced desalination of hypersaline brines using membrane distillation

Membrane distillation (MD) is a membrane-based thermal desalination process capable of treating hypersaline brines. Standard MD systems rely on preheating the feed to drive the desalination process. However, relying on the feed to carry thermal energy is limited by a decline of the thermal driving force as the water moves across the membrane, and temperature polarization. In contrast, supplying heat directly into the feed channel, either through the membrane or other channel surfaces, has the potential of minimizing temperature polarization, increasing single-pass water recoveries, and decreasing the number of heat exchangers in the system. When solar thermal energy can be utilized, particularly if the solar heat is optimally delivered to enhance water evaporation and process performance, MD processes can potentially be improved in terms of energy efficiency, environmental sustainability, or operating costs. Here we describe an MD process using layered composite membranes that include a high-thermal-conductivity layer for supplying heat directly to the membrane-water interface and the flow channel. Here, the MD system showed stable performance with water flux up to 9 L/m 2 /hr, and salt rejection >99.9% over hours of desalinating hypersaline feed (100 g/L NaCl). In addition to bench-scale system, we developed a computational fluid dynamics model that successfully described the transport phenomena in the system.

42 ENGINEERING↗

Aqueous ion partitioning in Nafion: Applicability of Manning's counter-ion condensation theory

Nafion is a well-studied polymer of significant interest as a fuel cell membrane due to rapid transport of protons, which is often ascribed, at least in part, to its phase-separated morphology. The literature detailing ion sorption and transport in Nafion diverges considerably from that of water purification membranes, with contrasting analyses and models. To help bridge these gaps and facilitate comparisons of membranes with various structures, this study presents measurements of ion activity coefficients and sorption in Nafion 117 equilibrated with aqueous solutions of NaCl, MgCl 2 , and Na 2 SO 4 , which are relevant to water purification. The experimental data are compared to a theoretical framework based on Manning's counter-ion condensation theory and Donnan theory. Good agreement between the model and data is observed for NaCl and MgCl 2 , using no adjustable parameters. However, the model significantly underpredicts Na 2 SO 4 solubility, which is attributed to ion pairing effects. Furthermore, the results highlight the general applicability of counter-ion condensation theory to highly charged polymers, including those exhibiting nanoscale ordering, while revealing fundamental limitations related to ion pairing.

36 MATERIALS SCIENCE↗

Cation–polymer interactions and local heterogeneity determine the relative order of alkali cation diffusion coefficients in PEGDA hydrogels

Current research efforts are focused on endowing polymer membranes with ion–ion selectivity by incorporating ion–polymer interactions into materials to bias the selective partitioning and or diffusivity of one species over another. However, little is known about the impact of such interactions on the mechanisms of ion transport. In this study, we probe the influence of cation–polymer interactions on cation, anion, and salt diffusivity in a model membrane material, poly(ethylene glycol) diacrylate (PEGDA) by modeling concentrated polyethylene oxide solutions via molecular dynamics simulations. These results are compared to published experimental data for LiCl, NaCl, and KCl diffusion in PEGDA. Experimentally, the order of salt and cation diffusion coefficients for LiCl, NaCl, and KCl deviate from the order in aqueous solutions. Here, simulations identify these deviations to arise from cation–polymer coordination in the membrane. Both the fraction of bound cations and the average binding lifetime increases with decreasing cation hydration free energy (moving down the alkali series), leading to different diffusivity trends in the membrane compared to solution. However, to recover the experimentally observed order of diffusivities cations and salt in our simulations, we needed to incorporate membrane heterogeneity explicitly via a polymer charge scaling procedure. Together, our results indicate that cation–polymer interactions, as well as spatial heterogeneity within the membrane, play a critical role in dictating the observed order of alkali cation and salt diffusion coefficients in membranes.

36 MATERIALS SCIENCE↗

Cellulose acetate membranes exhibit exceptional monovalent to divalent cation selectivities

Salt transport properties of cellulose acetate membranes are reported for a series of chloride salts with mono- valent and divalent cations (LiCl, NaCl, MgCl 2 , CaCl 2 ). Measurements include salt permeability and sorption, with diffusivity values calculated from the permeability and sorption results. We report an exceptionally high LiCl/MgCl 2 selectivity of 750:1. Salts with similar valence (LiCl and NaCl; MgCl 2 and CaCl 2 ) have similar transport properties. The high monovalent/divalent selectivity arises from differences in both sorption and diffusion, with a LiCl/MgCl 2 solubility selectivity of about 11 and a diffusivity selectivity of about 70. Atomistic molecular dynamics simulations show that ions tend to reside in isolated clusters of water. Increasing ion charge strengthens ion–water interactions relative to ion–polymer interactions, explaining the reduced sorption of divalent ions. Diffusion of ions through the membrane occurs via hop-like motion between water clusters. Lithium diffuses faster than magnesium due to weaker ion–water coordination for lithium, which allows for greater mobility within water clusters and more frequent hopping. Altogether, our atomistic simulations suggest that the high LiCl/MgCl 2 selectivity is linked to cellulose acetate’s high water/salt selectivity and is a consequence of low water content and relatively uniform water distribution.

36 MATERIALS SCIENCE↗

Actinides in complex reactive media: A combined ab initio molecular dynamics and machine learning analytics study of transuranic ions in molten salts

The predominant ionic chemistry and the similarity in ionic radius of actinides make it very difficult to structurally distinguish them in liquids. In this work, while ab initio molecular dynamics shows that the f-states clearly affects the electronic properties, their impact on structural properties is not obvious. For the series of trivalent actinides U 3+ , Pu 3+ , Cm 3+ , Cf 3+ , Fm 3+ in molten NaCl and FLiBe, actinide ligand bonds have a higher degree of covalency in NaCl (than in FLiBe), and a higher degree of ionicity in FLiBe. Furthermore, a machine learned classification model can distinguish atomic environments of chemically similar actinides, as long as atoms beyond the first solvation shells are considered. Our work shows that only two types of descriptors are necessary to account for all the fluctuations in heavy metal/molten salt mixtures: The first descriptor represents the electronic state of the heavy metal, while the second encompasses the local coordination environment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Structural coherence model for predicting molten salt thermal conductivity informed by the pair distribution function

To enable thermal behavior prediction and design optimization of molten salt reactors, thermal conductivity of molten salts must be characterized in terms of salt composition and temperature. Current theoretical models fail to provide consistent approximations for all halide mixtures, particularly actinide-bearing melts. This study aims to link the short-range order structure of molten salts to the mean free path of energy carriers through a simple structural coherence model informed by the partial pair distribution function. The proposed method is used to predict the thermal conductivity of 33 alkali and alkaline earth halide salts. Predictions approximate experimental measurements with a mean absolute error of 15.7% for dissociating, complexing, and actinide salts, including unary LiCl, NaCl, and MgCl 2 as well as mixtures LiF–NaF–KF (FLiNaK), LiF–BeF 2 (FLiBe), and NaCl–UCl 3 . The work provides evidence for the validity of energy carrier descriptions of molecular-level heat transfer in molten salts, with implications for improved theories of liquid energy transport in general.

Actinide mixtures↗

Effect of electrode rinse solutions on the electrodialysis of concentrated salts

The data presented indicate that modest attention to the chemistry of the electrode rinse solution can yield as much as 56% improvement in process efficiency. When operating electrodialysis (ED) with salt concentrations greater than 10,000 mg/l (as NaCl) the amperage can be relatively high even at low voltages. To maximize the overall rate of ion transport from diluate to concentrate, there is a need to minimize resistances in the electrode cells since these can represent as much as 30% of the total resistances in the entire process and in this particular ED unit, represented resistance roughly equivalent to that within the membrane stack. This work describes the performance of a 10-cell pair, 200 cm 2 (0.02 m 2 ) per membrane, pilot ED unit operated in batch mode at 5 V potential. The feedstock to the stack was varied from 0.5% to 6% NaCl. Results from Volt-amp profiles (2.0–15 V) were used as the rationale for choosing the preferred electrode rinse solution, 90 g/l (kg/m 3 ) disodium sulfate at pH 12.5. The recommended solution of 30 g/l (kg/m 3 ) disodium sulfate at neutral pH was tested against stronger solutions (60, 90, and 120 g/l (kg/m 3 ) disodium sulfate) at neutral pH and with 1 g/l (kg/m 3 ) sodium hydroxide added to yield solutions at pH 12.5. There were stark differences in the performance of the ED unit between the solutions at pH 7 and those at pH 12.5. The slopes of the Volt-amp profiles improved indicating less resistance to ion flow at pH 12.5. Most of the difference can be attributed to the greater conductivity of sodium hydroxide compared to disodium sulfate, where even a modest addition of 1 g/l (kg/m 3 ) sodium hydroxide increased the conductivity of the solution between 8 and 20% depending on the concentration of disodium sulfate. Most notably, the initiation voltage was 2.39 ± 0.08 V with solutions at pH 7 and 1.99 V ± 0.04 V when the rinse solutions were around pH 12.5, a difference of around 0.42 V. Since the full batch runs were performed at 5.0 V, this 0.42 V differential represented a loss of 8% in process efficiency. A series of tests showed a shift in initiation voltage occurred between pH 11.5 and 12.5. Nernst equations for water electrolysis are coupled with a simple flux model that estimates the concentration of hydroxide and hydronium ions at the electrode surfaces. This model indicates that the potential demanded by the electrodes is directly linked to the current. Furthermore, there is a steep drop in the potential demanded by the anode when there is sufficient hydroxide available to generate oxygen from hydroxide as opposed to generation from water. The voltage demand is minimal at pH 12.5 and reflective of the reference standard voltage (just over 1.23 V predicted at 0.1 amps). However, the flux model predicts that the voltage demanded by the electrodes at pH 7 is 1.61 V at 0.1 amps (the lowest amperage measurable with the power pack). In conclusion, comparing this result to the reference standard (E 0 = -1.23 V) yields a satisfactory explanation for the observed difference below reference standard of 0.42 V.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

In-situ thermophysical measurement of flowing molten chloride salt using modulated photothermal radiometry

Molten salts are leading candidates for high-temperature heat transfer fluids (HTFs) for thermal energy storage and conversion systems in concentrated solar power (CSP) and nuclear energy power plants. The ability to probe molten salt thermal transport properties in both stationary and flowing status is important for the evaluation of their heat transfer performance under realistic operational conditions, including the temperature range and potential degradation due to corrosion and contamination. However, accurate thermal transport properties are usually challenging to obtain even for stagnant molten salts due to different sources of errors from convection, radiation, and corrosion, let alone at flowing status. To the best of authors’ knowledge, there is no available in-situ technique for measuring flowing molten salt thermal conductivity. Here, we report the first in-situ flowing molten salt thermal conductivity measurement using modulated photothermal radiometry (MPR). We could successfully perform the first in-situ thermal conductivity measurement of flowing molten NaCl-KCl-MgCl 2 in the typical operating temperature (520 and 580 °C) with flow velocities ranging from around 0.3 to 1.0 m s -1 . The relative change of the molten salt thermal conductivity was measured. Gnielinski’s correlation was also used to estimate the heat transfer coefficient h of the flowing NaCl-KCl-MgCl 2 in the given experimental condition. Furthermore, the work showed the potential of the MPR technique serving as an in-situ diagnostics tool to evaluate the heat transfer performance of flowing molten salts and other high-temperature HTFs.

14 SOLAR ENERGY↗

Desalinating a Real Hyper-Saline Pre-Treated Produced Water via Direct-Heat Vacuum Membrane Distillation

Membrane distillation (MD) is an emerging thermal desalination technology capable of desalinating waters of any salinity. During typical MD processes, the saline feedwater is heated and acts as the thermal energy carrier; however, temperature polarization (as well as thermal energy loss) contributes to low distillate fluxes, low single-pass water recovery and poor thermal efficiency. An alternative approach is to integrate an extra thermal energy carrier as part of the membrane and/or module assembly, which can channel externally provided heat directly to the membrane-feedwater interface and/or along the feed channel length. This direct-heat delivery has been demonstrated to increase single-pass water recovery and enhance the overall thermal efficiency. We developed a bench-scale direct-heated vacuum MD (DHVMD) process to desalinate pre-treated oil and gas "produced water" with an initial total dissolved solids of 115,500 ppm at a feed temperature ranging between 24 and 32 degrees C. We evaluated both water flux and specific energy consumption (SEC) as a function of water recovery. The system achieved a 50% water recovery without significant scaling, with an average flux >6 kg m-2 hr-1 and a SEC as low as 2,530 kJ kg-1. The major species of mineral scales (i.e., NaCl, CaSO4, and SrSO4) that limited the water recovery to 68% were modeled in terms of thermodynamics and identified by scanning electron microscopy and energy-dispersive X-ray spectroscopy. In addition, we further developed and employed a physics-based process model to estimate temperature, salinity, water transport and energy flows for full-scale vacuum MD and DHVMD modules. Model results show that a direct-heat input rate of 3,600 W can increase single-pass water recovery from 2.1% to 3.1% while lowering the thermal SEC from 7,800 kJ kg-1 to 6,517 kJ kg-1 in an unoptimized module. Finally, the scaling up potential of DHVMD process is briefly discussed.

brine↗

High-Pressure Phase Transition of Metastable Wurtzite-Like CuInSe 2 Nanocrystals

Ternary I–III–VI 2 semiconductors, such as CuInSe 2 , exhibit diverse polymorphs with unique structural characteristics and optoelectronic properties. This study investigates the pressure-induced phase transitions of metastable wurtzite-like CuInSe 2 nanocrystals. Using a combination of synchrotron X-ray diffraction, pair distribution function analysis, and density functional theory calculations, we reveal a transition from cation-ordered wurtzite-like (Pmc2 1 ) to cation-disordered NaCl-like (Fm3̅m) structures at 7.7 GPa. The cation-disordered NaCl-like phase persists upon decompression. Bulk modulus calculations highlight size-dependent deviations from bulk material behavior. These findings deepen our understanding of phase stability in colloidal I–III–VI 2 semiconductor nanocrystals, with implications for tailoring functional materials under extreme conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Mineral Scaling in 3D Interfacial Solar Evaporators–A Challenge for Brine Treatment and Lithium Recovery

In this work, we analyzed the effects of mineral scaling on the performance of a 3D interfacial solar evaporator, with a focus on the cations relevant to lithium recovery from brackish water. The field has been rapidly moving toward resource recovery applications from brines with higher cation concentrations. However, the potential complications caused by common minerals in these brines other than NaCl have been largely overlooked. Therefore, in this study, we thoroughly examined the effects of two common cations (calcium and magnesium) on the long-term solar evaporation performance of a 3D graphene oxide stalk. The 3D stalk can achieve an evaporation flux as high as 17.8 kg m –2 h –1 under one-sun illumination, and accumulation of NaCl on the stalk surface has no impact. However, the presence of CaCl 2 and MgCl 2 significantly reduces the evaporative flux even in solutions lacking scale-forming anions. A close examination of scale formation during long-term evaporation experiments revealed that CaCl 2 and MgCl 2 tend to precipitate out within the stalk, thus blocking water transport through the stalk and significantly dropping the evaporation rates. These findings imply that research attention is needed to modify and optimize the internal water transport channels for 3D evaporators. Additionally, we emphasize the importance of testing realistic mixtures–including prominent divalent cations– and testing long-term operations in interfacial solar evaporation research and investigating approaches to mitigate the negative impacts of divalent cations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Electrically Powered High-Salinity Brine Separation Using Dimethyl Ether

Dewatering highly saline aqueous streams, from mining and geothermal leachates to industrial wastewater, is essential for effective resource recovery and safe disposal. Membraneless water extraction (MWE) uses a low-polarity solvent to separate water from concentrated aqueous solutions. In this study, we design a new MWE that uses dimethyl ether (DME) to selectively extract water from high-salinity brines, leveraging the volatility of DME to achieve rapid solvent recovery. By separating water and dissolved salts at a liquid–liquid interface, MWE minimizes the deleterious effects of scaling on vulnerable membrane and heat exchanger surfaces, reducing the need for extensive pretreatment and expensive materials. We begin by developing a computational framework for a multistage counterflow liquid–liquid contactor, which extracts water into DME, coupled with a multistage solvent regenerator that uses vapor compression to efficiently separate the desalinated water from the DME extractant. Excess Gibbs free energy and equation of state frameworks are used to model fluid phase equilibria in water–DME–sodium chloride (NaCl) mixtures, with interaction parameters estimated from experimental data. Incorporating equilibrium calculations into a system-scale computational model, we examine the performance of MWE using DME for the first time. Our analysis demonstrates that MWE can concentrate seawater desalination brine (>1.0 mol NaCl kg –1 ) to zero-liquid discharge salinities, with an energy consumption of under 50 kW h per m 3 of water extracted with a solvent recovery ratio greater than 99.9%. We highlight the importance of staging the vapor compression process to simultaneously minimize energy consumption while enabling brine concentration and product water solvent contamination. Finally, the thermodynamic framework developed here allows for the robust evaluation of new MWE solvents and systems for critical brine concentration and fractional precipitation applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

High-Voltage, Intermediate-Temperature, Fe- and Al-Mixed Metal Halide Molten Salt for Molten Sodium Battery Energy Storage

An inorganic Fe and Al halide-based, low-temperature molten salt catholyte is described, which, when paired with a molten sodium anode, has high operating potentials rivaling those of Li ion batteries. The newly developed catholyte consists of metal halides FeCl 3 /FeCl 2 –AlCl 3 –NaCl and is intended to cycle between Fe 3+ /Fe 2+ redox couples in the molten salt. The multicomponent molten salt was initially evaluated for phase behavior and basic electrochemical behavior before full battery testing. The assembled battery, utilizing a 20:35:45 (FeCl 3 :AlCl 3 :NaCl) composition, with a 50.83 Ah/kg theoretical gravimetric capacity and a specific energy of 176.95 Wh/kg, was cycled at variable depths of discharge (DoD) and current densities to determine its cycling efficiencies and limitations. In conclusion, preliminary cycling tests showed two operational potential regimes, with higher potential, 3.91 V (vs Na/Na + ), at low DoD and lower potential, 3.39 V (vs Na/Na + ), at high DoD with excellent energy efficiencies and cycling behavior under both regimes.

Aluminum↗

Modeling Equilibrium Solid–Liquid Interfaces under Effective Constant Chemical Potential Using Machine Learning Interatomic Potentials

The chemical potential (μ) of species in solution is essential for understanding various chemical processes at interfaces. Molecular dynamics (MD) simulations, constrained by fixed compositions, cannot maintain constant chemical potential with reference to a targeted concentration or chemical potential under nonequilibrium or dynamic conditions, as solute species can migrate to the interface and deplete (or enrich) the bulk due to solute-interface interactions. In this study, we introduce a simple and computationally efficient approach named iterative quasi-constant chemical potential molecular dynamics (iqCμMD) simulation, which helps simulate targeted molar concentrations of species in solution. iqCμMD overcomes the limitations of conventional MD by adjusting the number of species in the solution to reach a target bulk concentration (chemical potential), which allows simulation of the interface under the bulk conditions comparable to experiment. We demonstrate our approach using machine learning interatomic potential (MLIP)-based MD simulations of the Na 2 SO 4,aq –graphene interface, and to show the transferability of our approach, we also perform classical force field-based MD simulations of NaCl aq –air and NaCl aq –graphite interfaces, which produce comparable results to previous CμMD simulations. Our results also show that the iqCμMD approach efficiently achieves the desired bulk ion concentration within two iterations, and by utilizing MLIPs, we can achieve converged results using relatively small-scale simulations compared to previous CμMD simulations. By combining iqCμMD with MLIP-driven simulations, solid–liquid interfaces can be modeled under an effective constant chemical potential with DFT-level accuracy. Here, we show that iqCμMD offers a robust and simple computational framework for constant chemical potential simulations, as its only requirement is to be able to converge interfacial simulations with a measurable bulk region.

Chemical structure↗

Strong Enhancement of Nanoconfined Water Mobility by a Structure Breaking Salt

For the majority of the water present on earth, the two most important factors influencing its behavior are confinement, in either inorganic or organic matrixes, and the presence of solutes. Here, we investigate the effect of confinement in 3 nm pores on water diffusivity in aqueous solutions with archetypical solutes, a structure making (kosmotrope) NaCl and a structure breaking (chaotrope) KCl, up to 1.0 M in concentration. The water diffusivity in bulk aqueous solutions in such a concentration range is known to decrease very slightly in the presence of NaCl and increase very slightly in the presence of KCl. However, here we observe the water diffusivity in confined H 2 O–KCl increases by a factor of 2 compared to the pure water diffusivity in the same confinement. This unusually strong cumulative effect of confinement and a structure breaking additive may have profound implications for the mobility and transport of aqueous species in nature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ion-Specific Effects on PuO 2 Nanoparticle Aggregation and Dissolution in Concentrated Electrolytes

Hydrolytic PuO 2 nanoparticles (NPs) are a dominant aqueous Pu-bearing phase in high ionic strength nuclear wastes, yet their reactivity in nonideal brines remains poorly constrained. We quantify how electrolyte identity and concentration control PuO 2 NP aggregation and ligand-assisted dissolution in acidic, high salinity solutions (NaCl, NaNO 3 , NaClO 4 , Na 2 SO 4 , Na 2 C 2 O 4 up to 5 M). A multitechnique workflow combining liquid scintillation counting (operationally defined aqueous [Pu]), scattering/electrokinetic measurements (aggregate size and zeta potential), and spectroscopy (UV–vis, XPS, Raman) resolves electrolyte-dependent partitioning between colloidal and molecular Pu species. Weakly coordinating anions (ClO 4 – , Cl – , NO 3 – ) largely preserve the (aggregated) nanoparticulate fraction but generate distinct dissolved species at high concentration, i.e., Pu(IV)–nitrato complexes in NaNO 3 and Pu(VI)–chloro complexes in NaCl. In contrast, stronger ligands substantially perturb PuO 2 NP stability: sulfate promotes partial dissolution to Pu(IV)–sulfate complexes at low concentration but reduces aqueous [Pu] at higher sulfate levels via secondary Pu(IV) sulfate formation, whereas oxalate drives strong dissolution to aqueous Pu–oxalate complexes. Aged NPs show similar trends with reduced aqueous fractions and more dominant aggregation mechanisms. In conclusion, these spectroscopically constrained speciation data provide a foundation for incorporating PuO 2 NP reactivity into thermodynamic and reactive transport models for high salinity waste and brine environments.

Aggregation↗