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At least 19 records

Local composition activity coefficient model for mixed-gas adsorption equilibria

Taking into consideration the adsorbate–adsorbent interactions, a novel activity coefficient model is derived from the non-random two-liquid theory for mixed-gas adsorption equilibria. In contrast with the conventional activity coefficient models developed for bulk liquids, the new model correctly predicts negative deviations from ideality for adsorbed phase mixtures including azeotropic behavior exhibited by selected gas-adsorbent systems. Here, the requiring a single binary interaction parameter per adsorbate–adsorbate pair, the model successfully correlates wide varieties of binary adsorption isotherm data and it should be a powerful engineering thermodynamic tool in correlating and predicting mixed-gas adsorption equilibria.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Activity coefficient acquisition with thermodynamics–informed active learning for phase diagram construction

This work explores the use of thermodynamics-informed Gaussian processes (GPs) and active learning (AL) to model activity coefficients and construct phase diagrams. Relying on synthetic data generated from an excess Gibbs energy model, GPs were found to accurately describe the activity coefficients of several binary mixtures across large composition and temperature ranges. Moreover, GPs could estimate their own uncertainty and identify composition/temperature regions where activity coefficient data provide the most information to the models. This was leveraged to build AL algorithms targeted at modeling phase equilibria. In many cases, a single active-learning-acquired data point was sufficient to describe the phase diagrams studied. Lastly, the ability of AL to greatly reduce the amount of data needed to obtain accurate models was further verified on experimental case studies, namely individual ion activity coefficients, the solid–liquid and vapor–liquid equilibrium of deep eutectic solvents, and phase equilibria in ternary mixtures.

25 ENERGY STORAGE↗

Effect of Pressure on Trace Element Activity Coefficients in Metal-Silicate Systems

The partitioning of trace elements between metal and silicate melts serves as the foundation for understanding the differentiation of a planetary body into a metallic core and silicate mantle. Element activity influences metal-silicate partitioning behavior. Activity coefficients are directly dependent on composition and temperature, and can be indirectly dependent on oxygen fugacity and pressure. Distinguishing the effect of pressure from other variables on the activity coefficients and partitioning is important for understanding the chemical evolution of different planetary bodies during differentiation. In this study, we investigated the influence of pressure on the activity coefficients of Cu, Mo, Pd, Pt, As, Sb, and Bi in Fe-Si metallic liquids. All of these elements exhibit moderate to high activity coefficients in Fe-Si liquids at low pressure, which significantly controls their metal-silicate partitioning behavior. Identifying whether this strong dependence persists at higher pressures is critical to modeling and understanding the chemical consequences of core formation. New experiments at 10 GPa were used to derive activity coefficients for these metals which can be compared to activity coefficients determined at 1 GPa. Experiments were conducted at 10 GPa and 2373K using a 10/5 assembly in the 880-ton multi-anvil press at NASA Johnson Space Center. The standard 10/5 COMPRES assembly was slightly modified to accommodate a sample capsule machined from single-crystal MgO that minimizes melt percolation out of the sample volume during the experiment. Experiment starting materials were comprised of 70 wt.% Knippa basalt and 30 wt.% metal. The metal mixture (~85 wt.% Fe) was created by adding the elements of interest (Cu, Mo, Pd, Pt, As, Sb, Bi) to Fe metal powder. Varied amounts of Si metal (0-10 wt.% Si) were added to the metal-silicate mixtures to generate a systematic series of starting materials. For each element, an epsilon interaction parameter in Fe-Si liquid was derived from the results of our 0-10 wt.% Si metal series. To investigate whether pressure influences the trace element activity coefficients in the 1-10 GPa pressure range, we compared our results at 10 GPa to those at 1-4 GPa [1-3]. Our results can also be directly compared to interaction parameters for Au, P, V, Mn, Ga, Zn, Cd, Sn, W, Pb, and Nb previously determined at 10 GPa and 2373K following the same methods [4]. Combined, this suite of interaction parameters will directly inform metal-silicate partitioning between 1 and 10 GPa, and assess whether these values can be extrapolated to modeling differentiation processes at pressures >10 GPa.

Kelsey Prissel↗

Investigation into Na and Cs activity coefficients in high salt solutions to support Cs removal in Hanford tank waste

The treatment of Hanford tank waste is one of the most technically challenging environmental cleanup activities for the U.S. Department of Energy to date. To expedite the processing of liquid waste stored in underground tanks in southeastern Washington state, it is necessary to remove the significant dose contributor, 137 Cs. Toward this effort, ion exchange with crystalline silicotitanate (CST) has been employed as part of the Tank Side Cesium Removal system. The model used to predict Cs exchange onto CST was developed using activity coefficients calculated from the Bromley equation. A series of batch contact tests that varied in [Na] were conducted to look at the impact of Na concentration on Cs distribution. Experimental distribution ratios ( K d ) were compared to the distribution ratios predicted using three different activity coefficient models: (1) commercially available HSC software, (2) the Bromley equation, and (3) a simplified approach adapted from Marcos-Arroyo et al. Ultimately, the Bromley method underpredicted the effect of ionic strength on the Na activity coefficient ( γ Na+ ), HSC overestimated the impact of ionic strength on the expected performance due to the Cs activity coefficient ( γ Cs+ ), but the simplified approach predicted the experimental K d values quite well in a binary matrix. In conclusion, expansion of this approach in complex matrices is necessary for application to Hanford tank waste.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Effect of Pressure on the Activity Coefficients of Au and Other Siderophile Elements in Liquid Fe-Si Alloys

Light elements can alloy into the iron cores of terrestrial planetary bodies. It is estimated that the Earth’s core contains ~10% of a light element, most likely a combination of S, C, Si, and O with Si probably being the most abundant. Si dissolved into Fe metal liquids can have a significant influence on the activity coefficients of siderophile elements, and thus the partitioning behavior of those elements between the core and mantle. Many of these elements have been investigated extensively at ambient pressure, and studies up to 1 GPa are becoming more common, but few have been studied at pressures above this. The formation of the Earth’s core has been estimated to have formed at pressures between 40-60 GPa, so investigating the effect pressure has on Si’s influence on siderophile element partitioning is important for modeling core formation in the Earth and smaller planets. Pressure is well known to influence volumetric properties of metallic and silicate liquids, and oxygen fugacity (e.g., [10,11]), but less is known about its effect on activity coefficients (e.g., [12]). Some activity coefficients depend strongly upon the Si content of Fe liquids, and the concentration of siderophile elements such as P, Sb, and As in the terrestrial mantle is easily influenced by dissolved Si in the core. Thus, isolating the effect of pressure on activity coefficients in general is critical in quantitative analysis of core formation models. In this work, we investigate the effect variable Si content has on the partitioning of Au between Fe metal and silicate melt at 10 GPa and 2373 K, with the intention of comparing the behavior to that already investigated at lower pressures. In addition, P, V, Mn, Ga, Zn, Cd, Sn, W, Pb, and Nb were also measured and could thus be included in the assessment of potential pressure effects.

Righter, K.↗

Association‐based activity coefficient model for electrolyte solutions

Abstract This work presents an association‐based activity coefficient model that explicitly considers the solution nonideality due to associations among ions and solvent species. Built upon the electrolyte nonrandom two‐liquid (eNRTL) model, the model greatly improves the accuracy of eNRTL model for strongly associating electrolyte solutions due to presence of ionic species with high surface charge density. The model successfully correlates mean ionic activity coefficients of 46 aqueous single‐salt systems from 10 cations and 5 anions at 298.15 K up to their solubility limits. With the ion‐specific association parameters identified, the model accurately predicts activity and osmotic coefficients for aqueous mixed‐salt systems at 298.15 K. The temperature dependence of the model results has also been examined at 273–373 K. With superior accuracy over a wide range of concentration and temperature, the model represents a major advancement over eNRTL model and has a great potential to be a next‐generation model for electrolyte solutions.

Lin, Yu‐Jeng↗

Activity coefficients of siderophile elements in Fe-Si liquids at high pressure

Metallic core formation in differentiated bodies in the inner solar system can take place between low pressures (near 1 bar) to much higher pressures (up to 100 GPa). Most thermodynamic models of metal-silicate equilibria utilise activity coefficients for metallic tracers in Fe liquids, nearly all of which have been carried out at low pressures. This study focuses on the effect of pressure on activity coefficients for Au, P, V, Mn, Ga, Zn, Cd, Sn, W, Pb, and Nb in liquid Fe-Si alloys. From a series of experiments at 10 GPa, 2373 K containing variable Si content in a metallic liquid we have derived epsilon interaction parameters in Fe-Si liquids ($ε^{Si}_{M}$). Comparison of 1 GPa and 10 GPa data shows no difference except for Nb. Epsilon parameters derived from low pressure experiments can thus be used to calculate activity coefficients for application to higher pressure processes (at least to 10 GPa).

58 GEOSCIENCES↗

Measurement of the Activity Coefficients of P and Mn in Carbon-Saturated Fe-P-Mn-C Alloy

The thermodynamic properties of the Fe-P-Mn-C(sat.) alloy, which is obtained following the reduction of steelmaking slag or manganese ore, are not adequately clarified. Thus, the current study involved measuring the activity coefficients of both Mn and P in the alloy system. The Fe-P-Mn-C (sat.) alloy (2.5 to 15.2 mass pct of P and 2.9 to 12.8 mass pct of Mn) was equilibrated with Ag in a graphite crucible at 1673 K, and thus several thermodynamic data were obtained as follows: Interaction parameters: ε{sub Mn (C sat.)}{sup P}=− 4.72±0.27,(X{sub Mn}<0.06, X{sub P}<0.25, 1673K), ε{sub C (C sat.)}{sup P}=6.09 ± 0.15, (X{sub Mn}<0.06, X{sub P}<0.25, 1673K). C solubility: X{sub C[in Fe-P-Mn-C(sat.)]}=0.19e{sup −(6.09X{sub P}− 0.47X{sub M}{sub n})}. Activity coefficient: lnγ{sub Mn [in Fe-P-Mn-C(sat.)]}=− 4.72X{sub P}−0.47X{sub C}−0.87, lnγ{sub P [in Fe-P-Mn-C(sat.)]}{sup H}−lnγ{sub P [in Fe-P-C]}{sup H}=ε{sub P}{sup Mn}X{sub Mn}=−4.72X{sub Mn}, and lnγ{sub P [in Fe-P-Mn-C (sat.)]}{sup H}=−4.72X{sub Mn}+4.26X{sub P}+6.09X{sub C}. In addition, a comparison with the results obtained by previous studies on the selective reduction of steelmaking slag indicated that the activity coefficients of P and Mn obtained in the study were applicable.

36 MATERIALS SCIENCE↗

Thermodynamic modeling of aqueous lithium salt solutions with association electrolyte nonrandom two-liquid activity coefficient model

The high charge density of lithium ion and the resulting strong association phenomena make thermodynamic modeling of aqueous lithium electrolyte solutions extremely challenging. In this study, the association electrolyte nonrandom two-liquid activity coefficient model of Lin et al. (AIChE J. 2022, 68(2), e17422) is utilized to correlate and predict thermodynamic properties and solubility behavior of aqueous single electrolyte solutions of LiCl, LiBr, LiI, and LiNO 3 , and their mixed electrolyte solutions. Capturing self-association of water, cross-association of ion and water for hydration, and cross-association of cation and anion for ion-pairing, the association model accurately represents the literature experimental data up to saturation concentrations and at the temperature ranging from 263 K to 523 K. Here, this study further investigated the effect of anions of the lithium salts, and re-confirmed that the order of solution non-ideality as LiI > LiBr > LiCl > LiNO 3 because the anions with stronger association strengths are more likely to form ion pairs and thus lower the mean ionic activity coefficients.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Activity Coefficients of Siderophile Elements in Fe-Si Liquids at High Pressure

Metallic core formation in differentiated bodies in the inner solar system can takeplace between low pressures (near 1 bar) to much higher pressures (up to 100 GPa). Mostthermodynamic models of metal-silicate equilibria utilize activity coefficients for metallic tracersin Fe liquids, nearly all of which have been carried out at low pressures. This study focuses onthe effect of pressure on activity coefficients for Au, P, V, Mn, Ga, Zn, Cd, Sn, W, Pb, and Nb inliquid Fe-Si alloys. From a series of experiments at 10 GPa, 2373 K containing variable Sicontent in a metallic liquid we have derived epsilon interaction parametersin FeSi liquids (εMSi). Comparison of 1 GPa and 10 GPa data shows no difference except for Nb. Epsilonparameters derived from low pressure experiments can thus be used to calculate activitycoefficients for application to higher pressure processes (at least to 10 GPa).

K Righter↗

Simultaneous Absorption and Desorption Isotherms of Various Hydrogen and Deuterium Mixtures between 20 and 120 °C Are Used to Determine the Activity Coefficients for Palladium-Hydride Solutions

A test bed was constructed to measure the absorption and desorption isotherms for palladium hydride using H 2 , D 2 , and various H 2 /D 2 mixtures for temperatures in the range 20 °C ≤ T ≤ 120 °C. The pressure–composition–temperature isotherms were measured. The pressures obtained with mixtures between each pure isotope were monotonic, yet nonlinear. This nonlinear dependence of total pressure with feed gas protium concentration reveals the mixed isotope hydride system behaves nonideally. A thermodynamic model was adapted from the literature, which accounts for the nonideal nature of the mixed-isotope system. The measured data were used as constraints in this model in order to calculate the protium mole fractions in the hydride phase and the protium activity coefficients for palladium hydride at various temperatures and protium concentrations in the system. Knowing the protium mole fraction and activity coefficients allows for a priori calculation of the isotopologue distribution in the gas phase and the isotope distribution in the hydride phase, given a palladium temperature and equilibrium pressure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Osmotic and activity coefficients for five lithium salts in three non–aqueous solvents

To obtain osmotic coefficients, a classic static–view apparatus was used to measure the difference between the vapor pressure of a solvent and that of its salt solution at 25 °C. Vapor–pressure lowering was measured for solutions containing a lithium salt (LiCl, LiBr, LiNO 3 , LiPF 6 and LITFSI) dissolved in a non–aqueous solvent (dimethyl carbonate, dimethyl sulfoxide and acetonitrile) that may be used in a lithium–ion battery. The osmotic–coefficient data are represented by Archer's extended Pitzer equation. As a result, mean ionic activity coefficients for the salts are calculated from the osmotic–coefficient data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Determining Activity Coefficients of SOA from Isothermal Evaporation in a Laboratory Chamber

Nonideal molecular interactions in aerosol particles influence the partitioning of semivolatile organic compounds (SVOCs). However, few direct measurements exist that determine activity coefficients (γ), which quantify nonideality, for individual organic compounds in different atmospheric mixtures. By measuring the isothermal evaporation of SOA formed from multifunctional SVOCs in an environmental chamber, this study determines the mole-fraction-based γ of the bulk SOA in a variety of pre-existing chemically complex particles, approximated as if the bulk SOA behaved like a single SVOC. These multicomponent mixtures contain molecular structures commonly found in the atmosphere. When treated as a single liquid phase, γ of the bulk SOA tends to increase from ~1 to ~5 as the organic seeds and the SOA have more differing polarities. A high computed γ value of 74 for a wet ammonium sulfate-SOA system indicates phase separation. The γ for some individual species was also quantified based on gas-phase measurements and AIOMFAC model predictions. However, the bulk SOA γ cannot be explained by the simplified speciated SVOC–seed interactions, suggesting incomplete compositional understanding of the bulk SOA. In this work, these results demonstrate a method to quantify nonideal behavior and show that it can occur in multicomponent mixtures and therefore influence OA formation, evolution, and lifetimes.

54 ENVIRONMENTAL SCIENCES↗

Effect of Silicon on Activity Coefficients of Platinum in Liquid Fe-Si, With Application to Core Formation

Earth's core contains approximately 10% of a light element that is likely a combination of S, C, Si, and O, with Si possibly being the most abundant light element. Si dissolved into Fe liquids can have a large effect on the magnitude of the activity coefficient of siderophile elements (SE) in Fe liquids, and thus the partitioning behavior of those elements between core and mantle. The effect of Si can be small such as for Ni and Co, or large such as for Mo, Ge, Sb, As. The effect of Si on many siderophile elements is unknown yet could be an important, and as yet unquantified, influence on the core-mantle partitioning of SE. Here we report new experiments designed to quantify the effect of Si on the partitioning of Pt (with Re and Ru in progress or planned) between metal and silicate melt. The results will be applied to Earth, for which we have excellent constraints on the mantle Pt concentrations.

Righter, K.↗