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At least 1,441 records · Page 80

Effect of Surface Stoichiometry on Blinking and Hole Trapping Dynamics in CdSe Nanocrystals

Here, we measure the photoinduced carrier dynamics as the surface composition of CdSe nanocrystals is systematically varied from metal rich (~80% surface Cd) to nearly stoichiometric (~50% surface Cd). Using time-resolved optical spectroscopy, we determine that the luminescence lifetime is controlled by the rate of hole trapping at the newly exposed surface selenium atoms. However, the increased rate of the photoluminescence decay is not sufficient to explain the decreased photoluminescence quantum yield, and requires a growing proportion of nanocrystals in a dark or “OFF” state to explain the data. A global kinetic model is proposed that relates the fraction of selenium sites to the rate of hole trapping. A linear relationship between the rate of hole trapping and the fraction of exposed Se sites (x Se ) is observed within the range of accessible stoichiometries (x Se = 0.5–0.2). Extrapolation to higher surface cadmium fractions suggests that not all Se sites serve as effective hole traps. These findings confirm the strong nonlinear dependence of the fluorescence yield on the nanocrystal stoichiometry.

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Solvent-Based Atomistic Theory for Doping Colloidal-Synthesized Quantum Dots via Cation Exchange

Electronic applications require the ability to dope a material with a controllable amount of impurities. However, current understanding of the doping mechanism in colloidal–synthesized quantum dots (QDs) is still limited. This is in contrast with bulk semiconductors for which first-principles-based theories have been well established. Using prototype CdSe as an example, in this report we propose an atomistic theory for the doping of colloidal-synthesized QDs. The key in our theory is the evaluation of atomic chemical potential inside the solution, whose range can deviate considerably from the bulk value due to the presence of solvent. This theory, coupled to first-principles calculations and ab initio molecular dynamics, is able to explain the difference of doping limit in Mn (or Co)-doped CdSe QDs and their bulk counterparts. It also explains the doping behavior of a number of other 3d transition-metal impurities in CdSe QDs in contrast with the solid case.

36 MATERIALS SCIENCE↗

Wide Band Gap CuGa(S,Se) 2 Thin Films on Transparent Conductive Fluorinated Tin Oxide Substrates as Photocathode Candidates for Tandem Water Splitting Devices

Theaim of this report was to explore the potential of CuGa(S,Se)2 thin films as wide-E G top cell absorbers for photoelectrochemical (PEC) water splitting. A synthesis was developed on fluorinated tin oxide (FTO) photocathodes by converting copper-rich co-evaporated CuGaSe2 into CuGa(S,Se)2 via a post-deposition annealing. We found it necessary to first anneal CuGaSe2 at low-temperature in sulfur then at high-temperature in nitrogen to preserve the transparency and conductivity of the FTO. Using this two-step synthesis, we fabricated a 1.72eV CuGa(S,Se) 2 photocathode with a saturation current density and photocurrent onset potential of 10mA/cm 2 and -0.20V vs. RHE, respectively. Yet we found that the PEC performance and sub-E G transmittance, worsened with increasing copper content. Using flatband potential measurements and the Gerischer model, we show that divergences in PEC performance of CuGa(S,Se) 2 photocathodes can be explained by differences in conduction band minimums and Fermi levels. We also explain that sub-E G transmittance is likely hampered by a defect band 100-400 meV below E C . Additional external quantum efficiency measurements of a high-efficiency 1.1 eV Cu(In,Ga)Se 2 photovoltaic driver, while shaded by the CuGa(S,Se) 2 photocathode, yielded a short-circuit current density of 4.14 mA/cm 2 revealing that CuGa(S,Se) 2 reflects promise as a top cell for PEC water splitting.

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Understanding Fragmentation of Organic Small Molecules in Atom Probe Tomography

In atom probe tomography of molecular organic materials, field ionization of either entire molecules or molecular fragments can occur, but the mechanism governing this behavior was not previously understood. This work explains when a doubly ionized small molecule organic material is expected to undergo fragmentation. Here, we find that multiple detection events arising from post-ionization fragmentation of a parent molecular dication into two daughter ions is well explained by the free energy and geometries of the molecules computed using density functional theory. Of the systems studied, exergonic free energies for formation of the daughter ions, smaller activation energies for dissociation, and increases in bond length are all found to be quantitative predictors for ion fragmentation. This work expands the applicability of atom probe tomography to organic materials by increasing the fundamental understanding of processes occurring during this analysis technique.

36 MATERIALS SCIENCE↗

Role of Local Conductivities in the Plasmon Reflections at the Edges and Stacking Domain Boundaries of Trilayer Graphene

Here, we employed infrared scattering-type scanning near-field optical microscopy (IR-sSNOM) to study surface plasmon polaritons (SPPs) in trilayer graphene (TLG). Our study reveals systematic differences in near-field IR spectra and SPP wavelengths between Bernal (ABA) and rhombohedral (ABC) TLG domains on SiO 2 , which can be explained by stacking-dependent intraband conductivities. We also observed that the SPP reflection profiles at ABA-ABC boundaries could be mostly accounted for by an idealized domain boundary defined by the conductivity discontinuity. However, we identified distinct shapes in the SPP profiles at the edges of the ABA and ABC TLG, which cannot be solely attributed to idealized edges with stacking-dependent conductivities. Instead, this can be explained by the presence of various edge structures with local conductivities differing from those of bulk TLGs. Our findings unveil a new structural element that can control SPP and provide insights into the structures and electronic states of the edges of few-layer graphene.

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X-ray Excitation Triggers Ytterbium Anomalous Emission in CaF 2 :Yb but Not in SrF 2 :Yb

Materials that luminesce after excitation with ionizing radiation are extensively applied in physics, medicine, security, and industry. Lanthanide dopants are known to trigger crystal scintillation through their fast d–f emissions; the same is true for other important applications as lasers or phosphors for lighting. However, this ability can be seriously compromised by unwanted anomalous emissions often found with the most common lanthanide activators. We report high-resolution X-ray-excited optical (IR to UV) luminescence spectra of CaF 2 :Yb and SrF 2 :Yb samples excited at 8949 eV and 80 K. Ionizing radiation excites the known anomalous emission of ytterbium in the CaF 2 host but not in the SrF 2 host. Wave function-based ab initio calculations of host-to-dopant electron transfer and Yb 2+ /Yb 3+ intervalence charge transfer explain the difference. Furthermore, the model also explains the lack of anomalous emission in Yb-doped SrF 2 excited by VUV radiation.

36 MATERIALS SCIENCE↗

Wetting Behavior of A -block- (B- random -C) Copolymers with Equal Block Surface Energies on Surfaces Functionalized with B- random -C Copolymers

To form nanopatterns with self-assembled block copolymers (BCPs), it is desirable to have through-film domains that are oriented perpendicular to the substrate. The domain orientation is determined by the interfacial interactions of the BCP domains with the substrate and with the free surface. Here, we use thin films of two different sets of BCPs with A-block-(B-random-C) architecture matched with a corresponding B-random-C copolymer nanocoating on the substrate to demonstrate two distinct wetting behaviors. The two sets of A-b-(B-r-C) BCPs are made by using thiol–epoxy click chemistry to functionalize polystyrene-block-poly(glycidyl methacrylate) with trifluoroethanethiol (TFET) and either 2-mercaptopyridine (2MP) or methyl thioglycolate (MTG). For each set of BCPs, the composition ratio of the two thiols in the BCP (φ 1 ) is found that results in the two blocks of the modified BCP having equal surface energies (Δγ air = 0). The corresponding B-r-C random copolymers were synthesized and used to modify the substrate, and the composition ratio (φ 2 ) values that resulted in the two blocks of the BCP having equal interfacial energy with the substrate (Δγ sub = 0) were determined with scanning electron microscopy. The correlation between each block’s γ sub value and the interaction parameter, χ, is employed to explain the different wetting behaviors of the two sets of BCPs. For the thiol pair 2MP and TFET, the values of φ 1 and φ 2 that lead to Δγ air = 0 and Δγ sub = 0, respectively, are significantly different. A similar difference was observed between the φ 1 and φ 2 values that lead to Δγ air = 0 and Δγ sub = 0 for the BCPs made with the thiol pair MTG and TFET. In the latter case, for Δγ sub = 0 two windows of φ 2 are identified, which can be explained by the thermodynamic interactions of the specific thiol pair and the A-b-(B-r-C) architecture.

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Nonlinear Shear Rheology of Entangled Polymer Rings

Steady-state shear viscosity η($\bar{γ}$) of unconcatenated ring polymer melts as a function of the shear rate $\bar{γ}$ is studied by a combination of experiments, simulations, and theory. Experiments using polystyrenes with Z ≈ 5 and Z ≈ 11 entanglements indicate weaker shear thinning for rings compared to linear polymers exhibiting power law scaling of shear viscosity η ~ $\bar{γ}$ –0.56 ± 0.02 , independent of chain length, for Weissenberg numbers up to about 10 2 . Nonequilibrium molecular dynamics simulations using the bead-spring model reveal a similar behavior with η ~ $\bar{γ}$ -0.57 ± 0.08 for 4 ≤ Z ≤ 57. Viscosity decreases with chain length for high $\bar{γ}$. In our experiments, we see the onset of this regime, and in simulations, which we extended to Wi ~ 10 4 , the nonuniversality is fully developed. In addition to a naive scaling theory yielding for the universal regime η ~ $\bar{γ}$ –0.57 , we developed a novel shear slit model explaining many details of observed conformations and dynamics as well as the chain length-dependent behavior of viscosity at large $\bar{γ}$. The signature feature of the model is the presence of two distinct length scales: the size of tension blobs and much larger thickness of a shear slit in which rings are self-consistently confined in the velocity gradient direction and which is dictated by the size of a chain section with relaxation time 1/$\bar{γ}$. These two length scales control the two normal stress differences. In this model, the chain length-dependent onset of nonuniversal behavior is set by tension blobs becoming as small as about one Kuhn segment. This model explains the approximate applicability of the Cox–Merz rule for ring polymers.

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Entropic Penalty Switches Li + Solvation Site Formation and Transport Mechanisms in Mixed Polarity Copolymer Electrolytes

Emerging solid polymer electrolyte (SPE) designs for efficient Li-ion (Li + ) conduction have relied on polarity and mobility contrast to improve conductivity. To further develop this concept, we employ simulations to examine Li + solvation and transport in poly(oligo ethylene methacrylate) (POEM) and its copolymers with poly(glycerol carbonate methacrylate) (PGCMA). We find that Li + is solvated by ether oxygens instead of the highly polar PGCMA, due to lower entropic penalties. The presence of PGCMA promotes single-chain solvation, thereby suppressing interchain Li + hopping. The conductivity difference between random copolymer PGCMA-r-POEM and block copolymer PGCMA-b-POEM is explained in terms of a hybrid solvation site mechanism. With diffuse microscopic interfaces between domains, PGCMA near the POEM contributes to Li + transport by forming hybrid solvation sites. The formation of such sites is hindered when PGCMA is locally concentrated. These findings help explain how thermodynamic driving forces govern Li + solvation and transport in mixed SPEs.

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Effect of Water on Molecular Mobility and Physical Stability of Amorphous Pharmaceuticals

In this work, we investigated the influence of sorbed water concentration on the molecular mobility and crystallization behavior in a model amorphous drug and a solid dispersion. The temperature scaling ($T_g/T$) allowed us to simultaneously evaluate the effects of water content and temperature on the relaxation time. In the supercooled dispersions, once scaled, the relaxation times of the systems with different water content overlapped. Thus, the observed increase in mobility could be explained by the “plasticization” effect of water. This effect also explained the decrease in crystallization onset temperature brought about by water. That is, plasticization is the underlying mechanism governing the observed increase in mobility and physical instability in the supercooled state. Similar results were observed in the glassy drug substance. A single linear relationship was observed between crystallization time (time for 0.5% crystallization) and $T_g/T$ in both dry and water containing systems. Since fragility is unaffected by modest amounts of water, much like crystallization time, the mobility in the glass is expected to scale with $T_g$.

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Mechanistic Advantages of Organotin Molecular EUV Photoresists

Here, extreme ultraviolet (EUV)-induced radiation exposure chemistry in organotin-oxo systems, represented by the archetypal [(R-Sn) 12 O 14 (OH) 6 ](A) 2 cage, has been investigated with density functional theory. Upholding existing experimental evidence of Sn-C cleavage-dominant chemistry, computations have revealed that either electron attachment or ionization can single-handedly trigger tin-carbon bond cleavage, partially explaining the current EUV sensitivity advantage of metal oxide systems. We have revealed that tin atoms at different parts of the molecule react differently to ionization and electron attachment and have identified such selectivity as a result of local coordination chemistry instead of the macro geometry of the molecule. An ionization-deprotonation pathway has also been identified to explain the observed evolution of an anion conjugate acid upon exposure and anion mass dependence in resist sensitivity.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

The Role of Protons and Hydrides in the Catalytic Hydrogenolysis of Guaiacol at the Ruthenium Nanoparticle-water Interface

The mechanistic roles of free hydronium ions, surface hydrides, and interfacial protons during guaiacol hydrodeoxygenation (HDO) on ruthenium nanoparticles are established. As guaiacol adsorbs on Ru, it loses its strong aromaticity and undergoes a rapid H-shift from its hydroxyl to meta carbons (in relation to its hydroxyl group), leading enol and keto surface isomers to exist in chemical equilibrium. HDO occurs via a hydridic H-adatom (H*) attack to the enol, followed by a kinetically relevant C-O bond rupture step, during which water shuttles the hydroxyl proton, enabling its intramolecular attack to the methoxy, evolving a high charged [Ru(s)-(C6H5O-)…(H+)…OCH3]† transition state. The competing HYD begins with a rapid H* attack to the keto, before a second, kinetically relevant H* attack, without proton involvement. Water, despite shifting the thermodynamics towards the more polar surface keto, promotes HDO to a much greater extent than HYD, because of its dual catalytic roles—it mobilizes hydroxyl proton (Brønsted acid) to cleave the strong C-O bond, synchronizing with the Ru metal surface (base) function that stabilizes the resulting [Ru(s)-(C6H5O-)…(H+)…OCH3]† transition state, and the water layers solvate this charged transition state, further reducing its free energy. Free hydronium ions do catalyze a separate homogeneous enol-keto isomerization, but this reaction is kinetically unrelated to HDO catalysis. This mechanistic picture explains the strong effects of polar protic solvent in hydrodeoxygenation, highlighting (i) the requirements of surface hydrides and interfacial protons acting in tandem to complete a HDO turnover and (ii) the cooperative role of protic solvent and metal surface in breaking the aromaticity and stabilizing charged reactive precursors and transition states.

Shangguan, Junnan↗

Unraveling the Intermediate Reaction Complexes and Critical Role of Support-Derived Oxygen Atoms in CO Oxidation on Single-Atom Pt/CeO 2

CeO 2 -supported Pt single-atom catalysts have been extensively studied due to their relevance in automobile emission control and for the fundamental understanding of CeO 2 -based catalysts. Though CeO 2 -supported Pt nanoparticles are often more active than their single-atom counterparts, the former could easily redisperse to Pt single atom under oxidizing diesel conditions. Therefore, to maximize the reactivity of every Pt atom, it is important to fully understand the reaction mechanism of CeO 2 -supported Pt single atoms. Here, we report a CO oxidation study on a Pt/CeO 2 single-atom catalyst, where we can account for all of the neighbors using in situ and operando spectroscopy techniques and microcalorimetric measurements. Coupled with density functional theory calculations, we present a comprehensive picture of the dynamics of the surface species, the role of surface intermediates, and explain the observed reaction kinetics. We started with a catalyst containing exclusively single atoms and used in situ/operando spectroscopy to provide evidence for their stability during the reaction and to identify the Pt 1 complexes before and during the reaction and their binding to CO. The results reveal that in the precatalyst, Pt is present as Pt(O) 4 on the CeO 2 (111) step edge sites, but during CO oxidation, we find that two Pt 1 complexes coexist, representing two states of the same active site in the reaction cycle. The dominant state/complex remains Pt(O) 4 , which adsorbs CO very weakly as shown by CO microcalorimetry. The second, minority state/complex, Pt(CO)(O) 3 is generated through the reaction of Pt(O) 4 with CO, and CO is bound strongly to Pt 1 . Labile oxygen adatoms from the CeO 2 surface play a major role in the regeneration of Pt(O) 4 either directly from Pt(O) 3 or by reaction with the strongly adsorbed CO in Pt(CO)(O) 3 . We show that the formation of an oxygen vacancy and generation of a labile O* are not barrierless, which explains the long lifetime of Pt(CO)(O) 3 and its detectability despite being a minority complex. The results help to develop a comprehensive view of the dynamic evolution of Pt 1 complexes along the reaction cycle and provide mechanistic insights to guide the design of Pt-based single-atom catalysts.

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Electrochemical CO2 Reduction over Metal-/Nitrogen-Doped Graphene Single-Atom Catalysts Modeled Using the Grand-Canonical Density Functional Theory

Renewably driven, electrochemical conversion of carbon dioxide into value-added products is expected to be a critical tool in global decarbonization. However, theoretical studies based on the computational hydrogen electrode largely ignore the nonlinear effects of the applied potential on the calculated results, leading to inaccurate predictions of catalytic behavior or mechanistic pathways. Here, we use grand canonical density functional theory (GC-DFT) to model electrochemical CO2 reduction (CO2R) over metal- and nitrogen-doped graphene catalysts (MNCs) and explicitly include the effects of the applied potential. We used GC-DFT to compute the CO2 to CO reaction intermediate energies at -0.3, -0.7, and -1.2 VSHE catalyzed by MNCs each doped with 1 of the 10 3d block metals coordinated by four pyridinic nitrogen atoms. Our results predict that Sc-, Ti-, Co-, Cu-, and Zn-N4Cs effectively catalyze CO2R at moderate to large reducing potentials (-0.7 to -1.2 VSHE). ZnN4C is a particularly promising electrocatalyst for CO2R to CO both at low and moderate applied potentials based on our thermodynamic analysis. Our findings also explain the observed pH independence of CO production over FeN4C and predict that the rate-determining step of CO2R over FeN4C is not *CO2- formation but rather *CO desorption. Additionally, the GC-DFT-computed density of states analysis illustrates how the electronic states of MNCs and adsorbates change non-uniformly with applied potential, resulting in a significantly increased *CO2- stability relative to other intermediates and demonstrating that the formation of the adsorbed *CO2- anion is critical to CO2R activation. This work demonstrates how GC-DFT paves the way for physically realistic and accurate theoretical simulations of reacting electrochemical systems.

CO2 reduction↗

Hydrogen Dissociation Controls 1-Hexyne Selective Hydrogenation on Dilute Pd-in-Au Catalysts

Increasing the selectivity of the catalytic hydrogenation of alkynes to alkenes is of major importance for the processing of petrochemicals and the production of fine chemicals. Achieving high selectivity for alkene formation at high conversions, however, remains a long-standing challenge in heterogeneous catalysis. Here, the mechanism and origin of the high selectivity of dilute Pd-in-Au catalysts has been studied by a combination of first-principles calculations, microkinetic simulations, and isotopic exchange hydrogenation experiments using Pd 0.04 Au 0.96 nanoparticles embedded in raspberry colloid-templated silica. The Pd is predominantly in the form of isolated atoms, only surrounded by Au atoms, based on prior studies. The simulations indicate that the rate-limiting process for 1-hexyne hydrogenation on Pd monomers in Au(111) is H 2 dissociation, which has a large free energy barrier of 0.86 eV at 363 K and 0.2 bar of H 2 . The C–H bond formation steps, on the other hand, proceed with lower barriers, which contrasts with previous studies of extended Pd catalysts. The microkinetic simulations identify the sizable H 2 dissociation barrier and the small barrier for the hydrogenation of 1-hexyne as key factors that lead to a high selectivity for the production of 1-hexene from 1-hexyne, even at high conversion. The unconventional H 2 dissociation limiting process in combination with the low coverage of weakly bound hydrocarbon intermediates explains the near-zero order of 1-hexyne found experimentally. Furthermore, the partial hydrogenation of 1-hexyne to form 1-hexene is shown to be an irreversible process from our isotopic exchange hydrogenation experiments and is explained by the strongly exothermic nature of the reaction. Diluting active species, like Pd, in a less active host metal, like Au, hence appears promising as a means of tuning the binding energy of reactants and altering reaction profiles, leading to distinct kinetic behavior for an optimal catalytic activity and selectivity. Furthermore, the combination of microkinetic modeling, density functional theory calculations, and isotopic exchange experiments is thus demonstrated to be an effective approach to modeling important catalytic phenomena.

1-hexyne↗

Ripening of Rh Nanoparticle Catalysts in Reverse Water–Gas Shift via a Data-Driven Model Combining Physics, Theory, and Experiment

Degradation via sintering is an ongoing challenge that impedes the broad commercial success of supported metallic nanoparticle catalysts. To mitigate degradation via informed catalyst design and process operations, here we aim to disambiguate the underlying mechanisms of sintering by combining theory and experiment in a quantitative framework. While mechanistic sintering models exist, they only model a single sintering pathway, even though multiple sintering mechanisms can occur simultaneously or dominate at different stages of the process. Data-driven machine learning models have emerged as a means to represent complex processes through data regression. However, machine learning models have very large data needs and lack mechanistic insights due to their black-box encoding. To develop an interpretive model of catalyst degradation via sintering, we constructed a hybrid model combining mechanistic “physics-based” models and data-driven methods to obtain both reliable predictions and mechanistic insights regarding experimentally observed sintering phenomena. Focusing on nanoparticle sintering in the Rh–TiO 2 catalyst for the reverse water–gas shift (RWGS) reaction, the hybrid model couples a mechanistic term for Ostwald ripening with energy values calculated via density functional theory (DFT) with a parametric, data-driven discrepancy function term for unmodeled mechanisms. The hybrid model is trained using Bayesian inference with data collected from small-angle X-ray scattering (SAXS) in situ experiments wherein average nanoparticle diameter versus time was measured at three relevant operating temperatures. The calibrated hybrid model results show that an Ostwald ripening-only model parameterized with fixed DFT energies does not fully capture the time and temperature dependence of the SAXS-observed sintering kinetics, and that an additional functional contribution, or DFT energy calibration, is required to reconcile simulation and experiment. Analysis of the hybrid-model error confirms that the hybrid model outperforms both the purely mechanistic and purely data-driven alternatives in terms of expected predictive accuracy for time-evolving average particle sizes. Furthermore, the results support the hypothesis that the Ostwald ripening mechanism is less important for explaining the sintering phenomena as operating temperature increases under an assumed fixed DFT parameterization. This could be explained in one of two ways: either latent, unmodeled sintering mechanisms dominate at higher temperatures, or the DFT uncertainty increases with temperature. The proposed modeling approach directly links theory to experiments and simulations via a statistical hybrid modeling framework and can be extended to other catalytic systems to improve predictive models and mechanistic understanding.

Bayesian hybrid modeling↗

Understanding the Role of Metal and Molecular Structure on the Electrocatalytic Hydrogenation of Oxygenated Organic Compounds

Electrocatalytic hydrogenation is increasingly studied as an alternative to integrate the utilization of recycled carbon feedstocks with renewable energy sources. However, the abundant empiric observations available have not been correlated with fundamental properties of substrates and catalysts. In this paper, we investigated the electrocatalytic hydrogenation of homologues series of carboxylic acids, ketones, phenolics, and aldehydes on a variety of metals (Pd, Rh, Ru, Cu, Ni, Zn, and Co). We found that the rates of carbonyl reduction in aldehydes correlate with the corresponding binding energies between the aldehydes and the metals according to the Sabatier principle. That is, the highest rates are obtained at intermediate binding energies. The rates of H 2 evolution, occurring in parallel to hydrogenation, also correlate with the H-metal binding energies, following the same Volcano-type behavior. Within the boundaries of this model (e.g., compounds reactive at room temperature and without important steric effects over the carbonyl group), the reported correlations help to explain the complex trends derived from the experimental observations, allowing for the correlation of rates with binding energies and the differentiation of mechanistic routes.

Sabatier principle↗

Loss and Isotopic Fractionation of Alkali Elements during Diffusion-Limited Evaporation from Molten Silicate: Theory and Experiments

Moderately volatile elements (MVEs) are variably depleted in planetary bodies, reflecting the imprints of nebular and planetary processes. Among MVEs, Na, K, and Rb are excellent tracers for unraveling the history of MVE depletion in planetary bodies because they have similar geochemical behaviors but can be chemically fractionated by evaporation and condensation processes. Furthermore, K and Rb are amenable to high-precision isotopic analyses, which can help constrain the conditions of evaporation and condensation. To quantitatively understand why Na, K, and Rb are depleted in planetary bodies, we have carried out vacuum evaporation experiments from basaltic melt at 1200 and 1400 °C to study their evaporation kinetics and isotopic fractionations. We chose this composition because it is relevant to evaporation from small differentiated planetesimals. The Rb isotopic compositions of the evaporation residues were measured by multicollector inductively coupled plasma mass spectrometry (MC-ICPMS), and the K isotopic compositions were measured along profiles across the residues by secondary ion mass spectrometry (SIMS). In the 1400 °C run products, we found that the concentrations of both K and Rb in the run products decreased from core to rim, which was accompanied by a heavy K isotope enrichment near the surface. This indicates that, in this run, evaporation was limited by diffusion. To use those data quantitatively, we derive analytical equations that describe the evaporation rate and isotopic fractionation associated with diffusion-limited evaporation from a sphere, slab, and cylinder in transient and quasi-steady state regimes. This model is used to tease out the roles that diffusive transport in the melt and evaporation at the melt/gas interface play in setting the elemental depletion and isotopic composition of the residue. Under our experimental conditions, volatility decreases in the order of Na, Rb, and K. Using our experimental results in a thermodynamic model, we have estimated the product γΓ of activity coefficients × evaporation coefficients of Na, Rb, and K. The measured isotopic compositions of the residues are well explained using Rayleigh distillations, whereby the relative volatilities of K and Rb isotopes are given by the square root of their masses. We use our results and previously published data to predict how K and Rb could have been lost as a function of temperature, melt composition, oxygen fugacity, and saturation degree relevant to Vesta’s building blocks. We find that the K and Rb depletions, K/Rb elemental fractionation, and δ 41 K and δ 87 Rb isotopic fractionations of Vesta (as sampled by howardite-eucrite-diogenite (HED) meteorites) are best explained by evaporation of submillimeter size objects for 0.1-10 years at moderate temperatures (~1050 °C) in a medium ~98.8% saturated.

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