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At least 1,585 records · Page 88

Comparing Experimental Phase Behavior of Ion-Doped Block Copolymers with Theoretical Predictions Based on Selective Ion Solvation

The effects of salt-doping on the morphological behavior of block copolymers are well established but remain poorly understood, partially because of the challenge of resolving electrostatics in a heterogeneous medium with low average permittivity. By employing a recently developed field theory, we analyze the phase behavior of polystyrene-b-poly(ethylene oxide) (SEO) copolymers doped with lithium bis(trifluoromethanesulfonyl)imide salts (LiTFSI). Using a single fitting parameter, the ionic solvation radius, we obtain qualitative agreement between our theory and experimental data over a range of polymer molecular weights and copolymer compositions. Such agreement supports and highlights the need of solvation free energy to accurately describe the self-assembly of ion-doped block copolymers and demonstrates that experimentally observed dependence on molecular weight, not present in neutral block copolymers, can be rationalized by solvation effects. Overall, morphological variations are stronger than those predicted by the leading, linear order theory but can be captured by the full model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Unraveling the Ion Adsorption Kinetics in Microporous Carbon Electrodes: A Multiscale Quantum-Continuum Simulation and Experimental Approach

With the understanding that sorption in porous carbon electrodes is crucial to many environmental and energy technologies, such as capacitive deionization (CDI), supercapacitor energy storage, and activated carbon filters. In each of these examples, a practical model that can describe ion electrosorption kinetics is highly desirable for accelerating material design. Here, we proposed a multiscale model to study the ion electrosorption kinetics in porous carbon electrodes by combining quantum mechanical simulations with continuum approaches. Our model integrates the Butler-Volmer (BV) equation for sorption kinetics and a continuously stirred tank reactor (CSTR) formulation with atomistic calculations of ion hydration and ion-pore interactions based on density functional theory (DFT). We validated our model experimentally by using ion mixtures in a flow-through electrode CDI device and developed an in-line UV absorption system to provide unprecedented resolution of individual ions in the separation process. We showed that the multiscale model captures unexpected experimental phenomena that cannot be explained by the traditional ion electrosorption theory. The proposed multiscale framework provides a viable approach for modeling separation processes in systems where pore sizes and ion hydration effects strongly influence the sorption kinetics, which can be leveraged to explore possible strategies for improving carbon-based and, more broadly, pore-based technologies

36 MATERIALS SCIENCE↗

Assessing the Effects of Temperature and Oxygen Vacancy on Band Gap Renormalization in LaCrO 3-δ : First-Principles and Experimental Corroboration [plus supplemental information]

Understanding the temperature dependence of functional properties in high-temperature gas sensors is vital for applications in combustion environments. Temperature effect on the electronic structure due to electron-phonon coupling is a key property of interest as this influences other responses of sensors. In this work, we assess the impact of temperature on band gap renormalization of pristine and oxygen-vacant LaCrO 3–δ perovskite employing Allen–Heine–Cardona theory with first-principles simulations and corroborate with experimental observation. Antiferromagnetic cubic LaCrO 3 shows a direct ground-state band gap of 2.62 eV that is reduced by over 1 eV due to the presence of oxygen vacancies, which can form endothermically. We find excellent agreement in temperature-dependent band gap shift in LaCrO 3 between theory and an in-house experiment, proving that the theory can adequately predict renormalization on the band gap in a magnetic system. Band gaps in cubic LaCrO 3–δ are found to monotonically narrow by 1.13 eV in pristine and by around 0.62 eV in oxygen-vacant structures as temperature increases from 0 to 1500 K. The predicted band gap variations are rationalized using an analytical model. Furthermore, the experimental zero-temperature band gaps are extracted from the model fits that can provide useful insights on the simulated band gaps.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Coupled Experimental–Theoretical Characterization of a Carbon Electrode in Vanadium Redox Flow Batteries using X-ray Absorption Spectroscopy

Vanadium redox flow batteries (VRFBs) have emerged as promising solutions for stationary grid energy storage due to their high efficiency, scalability, safety, near room-temperature operation conditions, and the ability to independently size power and energy capacities. The performance of VRFBs heavily relies on the redox couple reactions of V 2+ /V 3+ and VO 2+ /VO 2 + on carbon electrodes. Therefore, a thorough understanding of the surface functionality of carbon electrodes and their propensity for degradation during electrochemical cycles is crucial for designing VRFBs with extended lifespans. In this study, we present a coupled experimental–theoretical approach based on carbon K edge X-ray absorption spectroscopy (XAS) to characterize carbon electrodes prepared under different conditions and identify relevant functional groups that contribute to unique spectroscopic features. Atomic models were created to represent functional groups, such as hydroxyl, carboxyl, methyl, and aldehyde, bonded to carbon atoms in either sp 2 or sp 3 environments. The interactions between functionalized carbon and various solvated vanadium complexes were modeled using density functional theory. A library of carbon K-edge XAS spectra was generated for distinct carbon atoms in different functional groups, both before and after interacting with solvated vanadium complexes. Here we demonstrate how these simulated spectra can be used to deconvolve ex situ experimental spectra measured from carbon electrodes and to track changes in the electrode composition following immersion in different electrolytes or extended cycling within a functional VRFB. By doing so, we identify the active species present on the carbon electrodes, which play a crucial role in determining their electrochemical performance.

25 ENERGY STORAGE↗

Multiscale Modeling and Experimental Insights into High-Temperature Soil Biodegradation Dynamics of Semi-Crystalline Poly(Lactic Acid) Nonwoven Fabrics

This study investigates the biodegradation of semi-crystalline poly(lactic acid) (PLA) nonwovens (NWs) in soil at 58 °C using both experimental and mathematical modeling approaches. The model utilizes a system of parabolic diffusion-reaction partial differential equations (PDEs) to elucidate chemical transformations over time and in space. It accounts for phenomena such as the diffusion of water and lactic acid monomers through the polymer matrix and into the surrounding soil, along with their microbial breakdown. It also accounts for the initial PLA crystallinity and predicts its evolution in time. The model is solved numerically for a single filament, and the results were used to shed light on PLA NW transformations observed in soil over a 180-day incubation period. Various characterization techniques, including scanning electron microscopy (SEM), differential scanning calorimetry (DSC), and Raman spectroscopy, were employed to assess morphological changes, crystallinity, and molecular changes in the NWs throughout the experiment. By comparing the experimental data with the model predictions, the hydrolysis rate coefficient was found to be 3.37 × 10 -7 s -1 , while the rate of microbial degradation of lactic acid monomers was faster, of the order of 9.63 × 10 -7 s -1 . The findings highlight the significant role of crystallinity in the biodegradation process. The PLA degradation ceases when no amorphous material remains, and the crystallinity reaches 0.8, as observed in the experiments by day 120. Furthermore, this research contributes to a deeper understanding of PLA biodegradation dynamics and offers insights for effectively managing biodegradable materials in environmental settings.

Diffusion−reaction modeling↗

Catalytic Resonance Theory: Experimental and Kinetic Interpretation of Programmable Catalysis

The complexity of programmable catalysts that change in the physical or electronic state on the time scale of a catalytic turnover results in uncertainty in the kinetic outcome of common measurements with dynamic catalyst experiments. To provide an interpretation of utility to experimentalists, a general programmable catalytic reaction exhibiting high turnover efficiency was simulated to understand the kinetic behavior of catalysts with varying frequency, binding energy, oscillation amplitude, and minimum oscillation binding energy at different temperatures and reactant gas pressures. The time-averaged catalytic rate for varying temperature in the form of an Arrhenius plot exhibited three distinct kinetic regimes, with the intermediate temperatures or applied frequencies exhibiting zero slope, indicative of barrier-free kinetic control. Transitions in experimentally measurable kinetic regimes with both temperature and applied catalyst oscillation frequency were associated with transitions in the sensitivity of reaction rate constants and degrees of rate control. Furthermore, these distinct kinetic macroscopic features specific to programmable catalysts were identified for observation in experimental dynamic kinetic measurements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Systematic computational and experimental investigation of lithium-ion transport mechanisms in polyester-based polymer electrolytes

Understanding the mechanisms of lithium-ion transport in polymers is crucial for the design of polymer electrolytes. We combine modular synthesis, electrochemical characterization, and molecular simulation to investigate lithium-ion transport in a new family of polyester-based polymers and in poly(ethylene oxide) (PEO). Theoretical predictions of glass-transition temperatures and ionic conductivities in the polymers agree well with experimental measurements. Interestingly, both the experiments and simulations indicate that the ionic conductivity of PEO, relative to the polyesters, is far higher than would be expected from its relative glass-transition temperature. The simulations reveal that diffusion of the lithium cations in the polyesters proceeds via a different mechanism than in PEO, and analysis of the distribution of available cation solvation sites in the various polymers provides a novel and intuitive way to explain the experimentally observed ionic conductivities. This work provides a platform for the evaluation and prediction of ionic conductivities in polymer electrolyte materials.

25 ENERGY STORAGE↗

Thermal Stability of π-Conjugated n -Ethylene-Glycol-Terminated Quaterthiophene Oligomers: A Computational and Experimental Study

This work represents a joint computational and experimental study on a series of $\textit{n}$-ethylene glycol (PEO$\textit{n}$)-terminated quaterthiophene (4T) oligomers for 1 < $\textit{n}$ < 10 to elucidate their self-assembly behavior into a smectic-like lamellar phase. This study builds on an earlier study for $\textit{n}$ = 4 that showed that our model predictions were consistent with experimental data on the melting behavior and structure of the lamellar phase, with the latter consisting of crystal-like 4T domains and liquid-like PEO4 domains. The present study aims to understand how the length of the terminal PEO$\textit{n}$ chains modulates the disordering temperature of the lamellar phase and hence the relative stability of the ordered structure. In this work, a simplified bilayer model, where the 4T domains are not explicitly described, is put forward to efficiently estimate the disordering effect of the PEO domains with increasing n; this method is first validated by correctly predicting that layers of alkyl (PE)-capped 4T oligomers (for 1 < $\textit{n}$ < 10) stay ordered at room temperature. Both 4T-domain implicit and explicit model simulations reveal that the order-disorder temperature decreases with the length of the PEO capping chains, as the associated increase in conformational entropy drives a tendency toward disorder that overtakes the cohesive energy, keeping the ordered packing of the 4T domains.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Necessary Experimental Conditions for Single-Shot Diffraction Imaging of DNA-Based Structures with X-ray Free-Electron Lasers

It has been proposed that the radiation damage to biological particles and soft condensed matter can be overcome by ultrafast and ultraintense X-ray free-electron lasers (FELs) with short pulse durations. The successful demonstration of the “diffraction-before-destruction” concept has made single-shot diffraction imaging a promising tool to achieve high resolutions under the native states of samples. However, the resolution is still limited because of the low signal-to-noise ratio, especially for biological specimens such as cells, viruses, and macromolecular particles. Here, we present a demonstration single-shot diffraction imaging experiment of DNA-based structures at SPring-8 Angstrom Compact Free Electron Laser (SACLA), Japan. Through quantitative analysis of the reconstructed images, the scattering abilities of gold and DNA were demonstrated. Suggestions for extracting valid DNA signals from noisy diffraction patterns were also explained and outlined. To sketch out the necessary experimental conditions for the 3D imaging of DNA origami or DNA macromolecular particles, we carried out numerical simulations with practical detector noise and experimental geometry using the Linac Coherent Light Source (LCLS) at the SLAC National Accelerator Laboratory, USA. In conclusion, the simulated results demonstrate that it is possible to capture images of DNA-based structures at high resolutions with the technique development of current and next-generation X-ray FEL facilities.

59 BASIC BIOLOGICAL SCIENCES↗

Exploring Microphase Separation in Semi-Fluorinated Diblock Copolymers: A Combined Experimental and Modeling Investigation

We report the combined experimental and theoretical study of the bulk self-assembly behavior of polystyrene-blockpoly( 2,3,4,5,6-pentafluorostyrene) diblock copolymers. These block copolymers were designed to create highly antagonistic blocks (with a high Flory−Huggins interaction parameter, χ) with minimum disruption to the molecular construct (i.e., only replacing five hydrogen atoms with five fluorine atoms). A large library of diblock copolymers (41 samples) was synthesized by reversible addition− fragmentation chain transfer (RAFT) polymerization to map out a major portion of the phase space. All block copolymers exhibited narrow molecular weight distributions with dispersity (D) values between 1.07 and 1.32, and subsequent thermal annealing revealed phase separation into well-defined nanoscale morphologies depending on their molecular composition, as determined from small-angle X-ray scattering and transmission electron microscopy analyses, with an experimental phase diagram being constructed. The χ value at 25 °C for this block copolymer was estimated to be 0.2 using strong segregation theory, based on trends in phase-separated domain spacing and interfacial width. When applying theoretical approaches, the majority of the domain spacing data trends were captured by a coil−coil diblock copolymer model; however, a better fit to the data for samples with shorter fluorinated blocks was obtained with a rod−coil model, indicating that the chains in these fluorinated blocks likely have a higher inherent stiffness and were thus rod-like. This observation demonstrates that, due to the very high value of χ, a transition from coil−coil to rod−coil behavior can be obtained purely by reducing the length of the stiffer of the two blocks and without varying temperature or the chemical composition of the polymers. Here, this work showcases the presence of strong microphase separation within AB diblock copolymers despite the relatively similar chemical composition of the constituent “A” and “B” units, with a clear transition from rod−coil to coil−coil segregation behavior.

RAFT polymerization↗

Accelerating Technology Development through Integrated Computation and Experimentation

This special section of Energy & Fuels comprises a selection of papers presented at the topical conference “Accelerating Technology Development through Integrated Computation and Experimentation”, sponsored and organized by the United States Department of Energy’s National Energy Technology Laboratory (NETL) as part of the 2012 American Institute of Chemical Engineers (AIChE) Annual Meeting held in Pittsburgh, PA, Oct 28-Nov 2, 2012. That topical conference focused on the latest research and development efforts in five main areas related to fossil energy, with each area focusing on the utilization of both experimental and computational approaches: (1) gas separations (membranes, sorbents, and solvents for CO{sub 2}, H{sub 2}, and O{sub 2} production), (2) CO{sub 2} utilization (enhanced oil recovery, chemical production, mineralization, etc.), (3) carbon sequestration (flow in natural systems), (4) advanced power cycles (oxy-combustion, chemical looping, gasification, etc.), and (5) fuel processing (H{sub 2} production for fuel cells).

08 HYDROGEN↗

Computational and Experimental Characterization of the Ligand Environment of a Ni-Oxo Catalyst Supported in the Metal–Organic Framework NU-1000

Heterogeneous catalysts exhibit significant changes in composition due to the influence of operating conditions, and these compositional changes can have dramatic effects on catalytic performance. For traditional bulk metal heterogeneous catalysts, relationships between composition and catalytic operating conditions are well documented. However, the influence of operating conditions on the compositions of single-site heterogeneous catalysts remains largely unresolved. To address this, we report a combined computational and experimental characterization of a Ni oxo catalyst under catalytic hydrogenation conditions. Specifically, pair distribution function (PDF) analysis is combined with ab initio thermodynamic modeling to investigate ligand environments present on a Ni oxo cluster supported in the metal–organic framework NU-1000. Comparisons of the experimentally observed and simulated Ni–O coordination numbers and Ni–O, Ni···Ni, and Ni···Zr distances provide insight into the Ni ligand environment under H 2 (g). These comparisons suggest significant OH and H 2 O content and, further, that different Ni ions within the cluster and/or NU-1000 structure may comprise subtly different numbers of these ligands. Further, the observation of significant H 2 O content under H 2 (g) suggests that the NU-1000 support supplies H 2 O to the cluster. Examples of ligand environments that could lead to the observed PDFs are provided. Furthermore, the combination of simulations and experiments provides new insights into the ligand environment for Ni-NU-1000 catalysts that will be useful for understanding the ligand environments of other single-site Ni catalysts as well.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Theoretical Prediction and Experimental Verification of IrO x Supported on Titanium Nitride for Acidic Oxygen Evolution Reaction

Reducing iridium (Ir) catalyst loading for acidic oxygen evolution reaction (OER) is a critical strategy for large-scale hydrogen production via proton exchange membrane (PEM) water electrolysis. However, simultaneously achieving high activity, long-term stability, and reduced material cost remains challenging. To address this challenge, we develop a frame-work by combining density functional theory (DFT) prediction using model surfaces and proof-of-concept experimental ver-ification using thin films and nanoparticles. DFT results predict that oxidized Ir monolayers over titanium nitride (IrO x /TiN) should display higher OER activity than IrO x while reducing Ir loading. Further, this prediction is verified by depositing Ir monolayers over TiN thin films via physical vapor deposition. The promising thin film results are then extended to commercially viable powder IrO x /TiN catalysts, which demonstrate a lower overpotential and higher mass activity than commercial IrO 2 , and a long-term stability of 250 hours to maintain a current density of 10 mA cm -2 . The superior OER performance of IrO x /TiN is further confirmed using proton exchange membrane water electrolyzer (PEMWE), which shows a lower cell voltage than commercial IrO 2 to achieve a current density of 1 A cm -2 . Both DFT and in situ X-ray absorption spectroscopy reveal that the high OER performance of IrO x /TiN strongly depends on the IrO x - TiN interaction via direct Ir-Ti bonding. This study highlights the importance of close interaction between theoretical prediction based on mechanistic understanding and experimental verification based on thin film model catalysts to facilitate the development of more practical powder IrO x /TiN catalysts with high activity and stability for acidic OER.

08 HYDROGEN↗

Symmetrization of Strong Hydrogen Bond under High Pressure in Bihydroxide-Ion-Containing NaCu 2 (SO 4 ) 2 ·H 3 O 2 Revealed by Experimental Charge Density, Single-Crystal Electron Diffraction, and Neutron Diffraction Studies

In minerals and inorganic compounds, strong hydrogen bonding can lead to the formation of complex ionic species such as the H 3 O 2 – bihydroxide anion and Zundel cation H 5 O 2 + . We studied [NaCu 2 (SO 4 ) 2 ·H 3 O 2 ] natrochalcite, which contains bihydroxide anions and undergoes hydrogen bond symmetrization at the lowest pressure reported so far among inorganic compounds. Hydrogen bond symmetrization leads to changes in the bulk modulus, seismic wave velocities, and proton mobility and plays a primary role in high-temperature superconductivity, but its characteristics are not well understood due to a lack of systematic studies and limitations of experimental methods sensitive to this subtle change. In this work, we applied experimental charge density analysis based on in situ single-crystal X-ray diffraction data, along with the single-crystal neutron and electron diffraction experiments, to probe the behavior of hydrogen atoms during the hydrogen bond symmetrization process under high-pressure conditions. On the way to the symmetrical H-bonding, natrochalcite undergoes a series of complex redistributions of electron density, which we trace with multipole refinement and detailed analysis of changes in the Laplacian of electron density values. Additionally, we deconvoluted the equation of state (volume of the unit cell vs pressure relation) into the atomic equation of states describing dependencies of atomic charges or volumes vs pressure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Acidity of the amidoxime functional group in aqueous solution. A combined experimental and computational study

Poly(acrylamidoxime) adsorbents are often invoked in discussions of mining uranium from seawater. It has been demonstrated repeatedly in the literature that the success of these materials is due to the amidoxime functional group. While the amidoxime-uranyl chelation mode has been established, a number of essential binding constants remain unclear. This is largely due to the wide range of conflicting pK a values that have been reported for the amidoxime functional group in the literature. To resolve this existing controversy we investigated the pK a values of the amidoxime functional group using a combination of experimental and computational methods. Experimentally, we used spectroscopic titrations to measure the pK a values of representative amidoximes, acetamidoxime and benzamidoxime. Computationally, we report on the performance of several protocols for predicting the pK a values of aqueous oxoacids. Calculations carried out at the MP2 or M06-2X levels of theory combined with solvent effects calculated using the SMD model provide the best overall performance with a mean absolute error of 0.33 pK a units and 0.35 pK a units, respectively, and a root mean square deviation of 0.46 pK a units and 0.45 pK a units, respectively. Finally, we employ our two best methods to predict the pK a values of promising, uncharacterized amidoxime ligands. Hence, our study provides a convenient means for screening suitable amidoxime monomers for future generations of poly(acrylamidoxime) adsorbents used to mine uranium from seawater.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Experimental and Modeling Study of Methane Adsorption onto Partially Saturated Shales

Shale gas equilibrates through gas-liquid-solid interactions in reservoirs, but the role of moisture is rarely investigated. To determine how adsorbed water influences methane behavior, three carboniferous shale samples from the Qaidam Basin, China, were humidified at five levels up to a relative humidity of 89%, and their methane capacities at pressures up to 12 MPa were studied. The experimental results indicate that two water-related mechanisms, “water blocking for methane transport” and “surface competition for gas-solid interaction,” are primarily responsible for the methane capacity variations. A compositional comparison suggests that a high abundance of clay minerals plays a favorable role in methane migration by retaining water in interlayer pores. Based on the experimental data, an optimized method for calculating the adsorption amount based on an approximation of density distribution is proposed. The model predicts the average thickness of the adsorption layer and the adsorbed methane density distribution on the surface at a given pressure. Here, the methane adsorption layer “thins” in a stepped pattern by up to 45% in the presence of water, with little further change observed at relative humidities greater than 75% in the studied samples.

58 GEOSCIENCES↗

Changes in Sedimentary Phosphorus Burial Following Artificial Eutrophication of Lake 227, Experimental Lakes Area, Ontario, Canada

Lake 227 of the Experimental Lakes Area (ELA) in Ontario, Canada has been fertilized with phosphorus (P) since 1969, which resulted in a rapid transition from oligotrophic to eutrophic conditions. Sediment cores collected from the oxygenated epilimnion and the mostly anoxic hypolimnion of this unique lake contain a historical record of the changes in sediment P speciation and burial rates across the trophic transition. To elucidate these changes, results of chemical extractions were combined with 210 Pb sediment dating, and with 31 P NMR, Mössbauer and XANES spectroscopies. Prior to 1969, organic P (P Org ) was the major sedimentary P sink in Lake 227. Eutrophication of the lake coincided with marked increases in the burial rate of total P (TP), as well as in the relative contribution of the NaHCO 3 -extractable P pool (humic-bound P, P Hum ). Together, P Hum and P Org account for ≥70% of total P burial in the sediments deposited since artificial fertilization started. The P Hum fraction likely comprises phosphate complexes with humic substances. The strong linear correlation between P and iron (Fe) extracted by NaHCO 3 implies a close association of the two elements in the humic fraction. Mössbauer and XANES spectra further indicate that most Fe in the post-1969 sediments remained in the Fe(III) oxidation state, which is attributed to the stabilization of reducible Fe by organic matter, in part via the formation of phosphate-Fe(III)-humic complexes. Importantly, our results show that the eutrophication experimentation of Lake 227 caused the accumulation of a large reservoir of reactive sediment P, which may continue to fuel internal P loading to the water column once artificial fertilization is terminated.

54 ENVIRONMENTAL SCIENCES↗

Experimental Investigation of Mercury's Magma Ocean Viscosity: Implications for the Formation of Mercury's Cumulate Mantle, Its Subsequent Dynamic Evolution, and Crustal Petrogenesis

Mercury has a compositionally heterogeneous surface that was produced by different periods of igneous activity during Mercury’s history, perhaps suggesting heterogeneous mantle sources. Furthermore, understanding the structure of Mercury’s mantle formed during the planet’s magma ocean stage could help in developing a petrologic model for Mercury, and thus, its dynamic history in the context of crustal petrogenesis. We present results of falling sphere viscometry experiments on late stage Mercurian magma ocean analogue compositions. Owing to the presence of sulfur on the surface of Mercury, two compositions were tested, one with sulfur and one without. The liquids have viscosities of 0.6-3.9 (sulfur-bearing) and 0.6-10.9 Pa·s (sulfur-free), similar to an andesite at the tested experimental conditions (1.4-6.2 GPa, 1600-2000°C). We present new viscosity models that enable extrapolation beyond the experimental conditions and evaluate grain growth and the potential for crystal entrainment in a cooling, convecting magma ocean. We consider scenarios with and without a graphite flotation crust, which suggests two possible endmember outcomes for Mercury’s mantle structure. With a graphite flotation crust, crystallization of the mantle would be fractional with negatively buoyant minerals sinking to form a stratified cumulate pile according to the crystallization sequence. Without a flotation crust, crystals would largely remain entrained in the convecting liquid during solidification, producing a homogeneous mantle. In the context of these endmember models, the chemically heterogeneous surface could result from dynamical stirring or mixing of a mantle that was initially compositionally stratified, or from different extents of melting of a homogeneous mantle.

58 GEOSCIENCES↗