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DOE OSTI2021

Mass accommodation and gas–particle partitioning in secondary organic aerosols: dependence on diffusivity, volatility, particle-phase reactions, and penetration depth

Abstract. Mass accommodation is an essential process for gas–particle partitioning of organic compounds in secondary organic aerosols (SOA). The mass accommodation coefficient is commonly described as the probability of a gas molecule colliding with the surface to enter the particle phase. It is often applied, however, without specifying if and how deep a molecule has to penetrate beneath the surface to be regarded as being incorporated into the condensed phase (adsorption vs. absorption). While this aspect is usually not critical for liquid particles with rapid surface–bulk exchange, it can be important for viscous semi-solid or glassy solid particles to distinguish and resolve the kinetics of accommodation at the surface, transfer across the gas–particle interface, and further transport into the particle bulk. For this purpose, we introduce a novel parameter: an effective mass accommodation coefficient αeff that depends on penetration depth and is a function of surface accommodation coefficient, volatility, bulk diffusivity, and particle-phase reaction rate coefficient. Application of αeff in the traditional Fuchs–Sutugin approximation of mass-transport kinetics at the gas–particle interface yields SOA partitioning results that are consistent with a detailed kinetic multilayer model (kinetic multilayer model of gas–particle interactions in aerosols and clouds, KM-GAP; Shiraiwa et al., 2012) and two-film model solutions (Model for Simulating Aerosol Interactions and Chemistry, MOSAIC; Zaveri et al., 2014) but deviate substantially from earlier modeling approaches not considering the influence of penetration depth and related parameters. For highly viscous or semi-solid particles, we show that the effective mass accommodation coefficient remains similar to the surface accommodation coefficient in the case of low-volatility compounds, whereas it can decrease by several orders of magnitude in the case of semi-volatile compounds. Such effects can explain apparent inconsistencies between earlier studies deriving mass accommodation coefficients from experimental data or from molecular dynamics simulations. Our findings challenge the approach of traditional SOA models using the Fuchs–Sutugin approximation of mass transfer kinetics with a fixed mass accommodation coefficient, regardless of particle phase state and penetration depth. The effective mass accommodation coefficient introduced in this study provides an efficient new way of accounting for the influence of volatility, diffusivity, and particle-phase reactions on SOA partitioning in process models as well as in regional and global air quality models. While kinetic limitations may not be critical for partitioning into liquid SOA particles in the planetary boundary layer (PBL), the effects are likely important for amorphous semi-solid or glassy SOA in the free and upper troposphere (FT–UT) as well as in the PBL at low relative humidity and low temperature.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Gallium isotopic constraints for the origin of the Earth-Moon system

Comparatively heavy isotopic compositions of moderately volatile elements (MVE) in lunar rocks have been advocated to reflect the loss of light isotopes during devolatilization processes from the Moon. In this study we present new gallium (Ga) isotope data for lunar highland rocks, with a focus on the Ferroan Anorthosite Suite (FAS). These are commonly thought to be direct crystallization products from the late lunar magma ocean (LMO) and should contain the majority of the Ga inventory of the Moon. As such, FAS rocks are crucial for identifying the processes that drove Ga isotope fractionation as well as for inferring the Ga isotopic composition of the bulk Moon. Our data reveal that FAS samples have a range in δ 71 Ga from -0.27 to 0.22‰ and are generally isotopically light in Ga compared to other lunar lithologies, but straddle values typical of terrestrial rocks. Although Ga is defined as an MVE, these Ga isotope variations do not correspond with concentrations of more volatile elements, indicating that Ga isotope variations in the FAS are not primarily controlled by devolatilization processes. Instead, the Ga isotopic compositions of bulk FAS rocks broadly correlate with the composition of plagioclase, with the calcium content of plagioclase decreasing as Ga becomes isotopically heavier. This suggests that fractionation of Ga isotopes in FAS rocks was caused by the preferential incorporation of isotopically light Ga into plagioclase during the later solidification stages of the LMO. The progressive crystallization and extraction of plagioclase forces the residual melt towards increasingly heavier Ga isotope ratios, corroborating similar conclusions derived from correlations between δ 71 and Eu* in the mare basalt suite. Using Ga isotope partitioning calculations, we demonstrate that an isotope fractionation coefficient between plagioclase and coexisting melt of -0.3 to -0.4‰ could explain the observed range of δ 71 values in FAS, mare basalt suite rocks, and KREEP. These calculations allow for a first order estimate of the Ga isotopic composition of the bulk silicate Moon prior to plagioclase fractionation and suggest it was close to the composition of the bulk silicate Earth. This would imply that the Moon did not lose a substantial fraction of its Ga inventory during accretion, consistent with new constraints from Rb-Sr isotope systematics that indicate the Moon's volatile deficit was primarily inherited from Theia. In conjunction with the overlap in non-mass-dependent isotope ratios, these collective observations could be reconciled if Theia and the proto-Earth formed in similar regions of the inner Solar System that were already volatile-depleted.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Enhanced reactivity at the oil–water interface accelerates the synthesis of zymonic acid in microemulsions

Chemical reactions in microscale compartments, such as aerosols and emulsions, can exhibit significantly faster reaction rates relative to macroscale containers. This enhancement in chemistry is often due to the elevated importance of surfaces as reaction vessels are reduced to picoliter volumes. While most studies have focused on the air-water interface of droplets, there are comparably fewer studies of reactions in micron-scale aqueous solutions encapsulated by oil. Here we investigate the condensation reaction of pyruvic acid (PA) to form zymonic acid (ZA) and water. Using microfluidics and optical trapping, chemical kinetics are measured in monodisperse micron-sized emulsion droplets in situ via Raman spectroscopy. Relative to a macroscopic bulk solution, which exhibits little to no reaction over many days, we find efficient production of ZA over the same time period. A kinetic model is developed to elucidate the role of the interface in accelerating the microdroplet reaction kinetics. After quantifying the surface partitioning of PA from interfacial tension measurements, the rate coefficient for the condensation reaction at the oil-water interface is determined to be 1.8 × 10-2 M-1 s-1. This rate coefficient is estimated to be 105 larger than the reaction rate in bulk aqueous solutions. Compared to previous studies of accelerated ZA formation at the air-water interface on nanodroplets, we find that the reaction at the oil-water interface is 20 times more efficient. Despite this difference, the overall ZA formation rate in emulsions is significantly slower than in the same-sized aerosols, which arises from the weaker partitioning of PA to the oil-aqueous relative to air-water interface. These results highlight the interplay between interfacial partitioning and reactivity in accelerating chemistry in microcompartments and provides new insights into how interfacial composition influences condensation reactions.

Wallace, Brandon J↗

NASA NTRS1987

Partitioning of flight data for aerodynamic modeling of aircraft at high angles of attack

It is sometimes necessary to determine aerodynamic model structure and estimate associated stability and control derivatives for airplanes from flight data that cover a large range of angle of attack or sideslip. One method of dealing with that problem is through data partitioning. The main purpose of this paper is to provide an explanation of a data partitioning procedure and its application and to discuss both the power and limitations of that procedure for the analysis of large maneuvers of aircraft. The partitioning methodology is shown to provide estimates for coefficients of those regressors that are well excited in the aircraft motion. In particular, primary lateral stability and damping derivatives are identified throughout the maneuver ranges.

Batterson, James G.↗

NASA NTRS2018

Effect of Silicon on the Activity Coefficient of Rhenium in Fe-Si Liquids: Implications for HSE and Os Isotopes in Planetary Mantles

Metallic cores contain light alloying elements that can be a combination of S, C, Si, and O, all of which have important chemical and physical influences. For Earth, Si may be the most abundant light element in the core. Si dissolved into Fe liquids can have a large effect on the magnitude of the activity coefficient of siderophile elements (SE), and thus the partitioning behavior of those elements between core and mantle. The effect of Si on the highly siderophile elements is only beginning to be studied and the effects on Au, Pd and Pt are significant. Here we report new experiments designed to quantify the effect of Si on the partitioning of Re between metal and silicate melt. A solid understanding of Re partitioning is required for a complete understanding of the Re-Os isotopic systems. The results will be applied to understanding the HSEs and Os isotopic data for planetary mantles, and especially Earth.

Righter, K.↗

DOE OSTI2025

Lectures on statistical mechanics

Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman’s graduate statistical mechanics course Physics 212A and 212B at the University of California Berkeley from the 1972–1973 academic year. 212A addressed equilibrium statistical mechanics with topics: fundamentals (micro-canonical and sub-canonical ensembles, adiabatic law and action conservation, fluctuations, pressure, and virial theorem), classical fluids and other systems (equation of state, deviations from ideality, virial coefficients and van der Waals potential, canonical ensemble and partition function, quasistatic evolution, grand-canonical ensemble and partition function, chemical potential, simple model of a phase transition, quantum virial expansion, numerical simulation of equations of state, and phase transition), chemical equilibrium (systems with multiple species and chemical reactions, law of mass action, Saha equation, chemical equilibrium including ionization and excited states), and long-range interactions (including Coulomb, dipole, and gravitational interactions, Debye–Hückel theory, and shielding). 212B addressed nonequilibrium statistical mechanics with topics: fundamentals (definitions: realizations, moments, characteristic function, and discrete variables), Brownian motion (Langevin equation, fluctuation–dissipation theorem, spatial diffusion, Boltzmann’s H-theorem), Liouville and Klimontovich equations, Landau equation (derivation, elaboration, and H-theorem, and irreversibility), Markov processes and Fokker–Planck equation (derivations of the Fokker–Planck equation and a master equation), linear response and transport theory (linear Boltzmann equation, linear response theory of Kubo and Mori, relation of entropy production to electrical conductivity, transport relations and coefficients, normal mode solutions of the transport equations, sketch of a generalized Langevin equation method for transport theory), and an introduction to nonequilibrium quantum statistical mechanics.

plasma dynamics↗

DOE OSTI2021

On the feasibility of using physics-informed machine learning for underground reservoir pressure management

In this work, we evaluate the feasibility of using physics-informed machine learning (PIML) for underground energy-related pressure management. To this end, we develop a PIML framework to manage underground reservoir pressures by training neural networks to determine fluid extraction rates for dedicated extraction wells during fluid injection operations given a range of reservoir conditions (e.g., transmissivity and storativity). We implement an automatically-differentiable analytical physics model of fluid flow in porous media within the PIML framework as a proxy for more complicated models. This allows us to execute a sufficient number of training scenarios to fully evaluate the feasibility of using PIML to support pressure management activities. We quantify the number of physics-model parameters required for automatic differentiation to become more efficient than finite-difference gradient calculations. We use a simple scenario with a single injector, extractor, and critical location for our feasibility analysis. We evaluate the effect of the size of the training dataset (i.e., the number of reservoir condition samples) on the accuracy and efficiency of the PIML framework. For an equivalent number of model evaluations, the larger training dataset took less time to train and produced a neural network that was able to more accurately manage reservoir pressures. We also evaluate the effect of the training dataset batch size (i.e., number of reservoir condition samples used to update the neural network coefficients during training; i.e., how the training dataset is partitioned). While training ran faster with larger batch sizes, they produced neural networks that managed pressures less accurately. We demonstrate the approach on a more complex scenario involving 10 injectors, 10 extractors, and 4 critical locations (a relatively high well density of 20 wells/km2). We provide the number of forward and adjoint model evaluations required in each case as an indication of the feasibility of using PIML for pressure management when more complicated physics models with longer execution times are used.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRSDate not supplied

Metal-silicate Partitioning of Re, Ru, Pt, Os, Ti, Nb, and Ta in Reduced Differentiated Planetary Bodies

Siderophile (iron-loving) elements are strongly fractionated during differentiation of planetary bodies into core and mantle [1]. Because the fractionation is controlled by the pressure, temperature, redox conditions, and composition, this group of elements can provide important constraints on the conditions of accretion and core formation in early solar system bodies (planetesimals) and planets (Earth, Mercury, Venus)[2]. At the reducing conditions thought to prevail in the early solar system, Si is known to alloy with FeNi metallic liquids (e.g., [3]) affecting the activity coefficients of siderophile elements in FeNi liquids and thus ultimately their detailed partitioning between metal and silicate melt. The effect of Si can be significant for some siderophile elements, as demonstrated previously by (e.g., [4]: Ni, Co; [5,6]: Ge, As, Sb, Pd, Pt, Au). The effect of Si has not yet been determined for several key groups of siderophile elements including the highly siderophile Re, Ru and Os, and the weakly siderophile Ta, Nb, and Ti. Here, we report new experiments designed to quantify the effect of Si on the partitioning of Re, Pt, Os, Ru, Ti, Ta and Nb between metal and silicate melts. The results will be used to evaluate metal/silicate equilibrium for Nb, Ta, Ti and Nb/Ta ratios in planetary mantles, mantle concentrations of Ru, Re, Pt, Os during accretion, the evolution of Re/Os, Pt/Os ratios in magma oceans, and the role of late veneer in establishing Re and Ru abundances in the terrestrial mantle.

core formation↗

NASA NTRS2004

Three-Dimensional High-Order Spectral Volume Method for Solving Maxwell's Equations on Unstructured Grids

A three-dimensional, high-order, conservative, and efficient discontinuous spectral volume (SV) method for the solutions of Maxwell's equations on unstructured grids is presented. The concept of discontinuous 2nd high-order loca1 representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) method, but instead of using a Galerkin finite-element formulation, the SV method is based on a finite-volume approach to attain a simpler formulation. Conventional unstructured finite-volume methods require data reconstruction based on the least-squares formulation using neighboring cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In the SV method, one starts with a relatively coarse grid of triangles or tetrahedra, called spectral volumes (SVs), and partition each SV into a number of structured subcells, called control volumes (CVs), that support a polynomial expansion of a desired degree of precision. The unknowns are cell averages over CVs. If all the SVs are partitioned in a geometrically similar manner, the reconstruction becomes universal as a weighted sum of unknowns, and only a few universal coefficients need to be stored for the surface integrals over CV faces. Since the solution is discontinuous across the SV boundaries, a Riemann solver is thus necessary to maintain conservation. In the paper, multi-parameter and symmetric SV partitions, up to quartic for triangle and cubic for tetrahedron, are first presented. The corresponding weight coefficients for CV face integrals in terms of CV cell averages for each partition are analytically determined. These discretization formulas are then applied to the integral form of the Maxwell equations. All numerical procedures for outer boundary, material interface, zonal interface, and interior SV face are unified with a single characteristic formulation. The load balancing in a massive parallel computing environment is therefore easier to achieve. A parameter is introduced in the Riemann solver to control the strength of the smoothing term. Important aspects of the data structure and its effects to communication and the optimum use of cache memory are discussed. Results will be presented for plane TE and TM waves incident on a perfectly conducting cylinder for up to fifth order of accuracy, and a plane wave incident on a perfectly conducting sphere for up to fourth order of accuracy. Comparisons are made with exact solutions for these cases.

Liu, Yen↗

NASA NTRS1978

Partitioning of Ni/2+/ between basaltic and synthetic melts and olivines An experimental study

Olivine/liquid distribution coefficients for Ni in basaltic and simple synthetic melts are found in the 1400-1070 C temperature range. The results suggest that: (1) the Ni distribution coefficients and NiO activity coefficients are strongly temperature dependent, (2) the Ni distribution coefficients are functions of melt composition and structure at a constant temperature although the dependence is small for most basaltic magmas, (3) differences in melt composition do not significantly influence generally 'basaltic' melts, (4) the Ni distribution coefficients may be used as geothermometers to predict the olivine crystallization temperatures of basaltic magmas to within plus or minus 50 C, (5) the Ni distribution coefficients are greater than one at all natural magmatic temperatures, and (6) the Ni distribution coefficients do not significantly vary as functions of the Ni content of the melt to at least one mole percent.

Leeman, W. P.↗

DOE OSTI2021

Duality defect of the monster CFT

Abstract We show that the fermionization of the Monster CFT with respect to Z 2 A is the tensor product of a free fermion and the Baby Monster CFT. The chiral fermion parity of the free fermion implies that the Monster CFT is self-dual under the Z 2 A orbifold, i.e. it enjoys the Kramers–Wannier duality. The Kramers–Wannier duality defect extends the Monster group to a larger category of topological defect lines that contains an Ising subcategory. We introduce the defect McKay – Thompson series defined as the Monster partition function twisted by the duality defect, and find that the coefficients can be decomposed into the dimensions of the (projective) irreducible representations of the Baby Monster group. We further prove that the defect McKay–Thompson series is invariant under the genus-zero congruence subgroup 16 D 0 of P S L ( 2 , Z ) .

Physics↗

NASA NTRS1983

Kinetic effects on trace element partitioning

A potential difficulty regarding the application of trace element abundance data to problems in igneous petrogenesis is related to the possibility that partitioning of trace elements among minerals and melt may not be an equilibrium process. It may rather be controlled by kinetic processes, specifically the interplay between crystal growth and diffusion of the trace elements in crystals and melt. The present investigation has the objective to quantify kinetic effects on trace element partitioning. Crystals of olivine, pyroxene, and plagioclase were grown rapidly from synthetic melts resembling naturally-occurring mafic melts and doped with La, Sm, and Lu to quantify the magnitude of the effect of crystal growth rate on concentration of excluded trace elements. Olivine melt partitioning failed to show any appreciable kinetic effects, while diopside/melt distribution coefficients increased by 70 percent when the crystals grew very rapidly.

Lindstrom, D. J.↗

NASA NTRS2016

Effect of Silicon on Activity Coefficients of Siderophile Elements (P, Au, Pd, As, Ge, Sb, and In) in Liquid Fe, with Application to Core Formation

Earth's core contains approximately 10 percent light elements that are likely a combination of S, C, Si, and O, with Si possibly being the most abundant. 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 P, Au, Pd, and many other SE between metal and silicate melt. The results will be applied to Earth, for which we have excellent constraints on the mantle siderophile element concentrations.

Righter, K.↗

NASA NTRS2017

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.↗

NASA NTRS1972

Reflection and transmission of acoustic waves from a moving layer

The refraction of acoustic waves by a moving medium layer is theoretically treated and the expressions for reflection and transmission coefficients are determined. The moving medium layer velocity is assumed to have a space dependence in one direction. A partitioning of the moving medium layer into constant-velocity sublayers is introduced and the number of sublayers is allowed to increase until the reflection and transmission coefficients converage to their respective values. Numerical results for several sublayer approximations of Poiseuille's flow are presented as functions of the moving layer velocity for several angles of incidence of the acoustic wave. The degenerate case of single constant-velocity layer is also treated, both theoretically and by a numerical analysis.

Steinmetz, G. G.↗

NASA NTRS1986

Crystal/liquid partitioning of REE in basaltic systems Extreme fractionation of REE in olivine

The calculation of partial coefficients for Nd, Sm, Gd, and Yb between olivine and synthetic basaltic melts using the percent level doping technique and microprobe analytical techniques is examined. The experimental and analytical procedures are described. The relationship between rare earth elements (REEs) concentrations and crystal margins caused by Rees X-rays from surrounding glass is discussed. Average olivine/liquid distribution coefficients for Nd, Sm, Gd, and Yb for mare and highlands basaltic melts are presented. The data reveal that the distribution coefficients for light REEs are lower than those obtained in previous studies, and the slope of the olivine/liquid distribution coefficient pattern is steeper; potential sources of error in the previous and present studies which could explain the differences in distribution coefficients and slope are investigated.

Mckay, G. A.↗

NASA NTRS2016

Apatite-Melt Partitioning at 1 Bar: An Assessment of Apatite-Melt Exchange Equilibria Resulting from Non-Ideal Mixing of F and Cl in Apatite

The mineral apatite [Ca5(PO4)3(F,Cl,OH)] is present in a wide range of planetary materials. Due to the presence of volatiles within its crystal structure (X-site), many recent studies have attempted to use apatite to constrain the volatile contents of planetary magmas and mantle sources. In order to use the volatile contents of apatite to precisely determine the abundances of volatiles in coexisting silicate melt or fluids, thermodynamic models for the apatite solid solution and for the apatite components in multi-component silicate melts and fluids are required. Although some thermodynamic models for apatite have been developed, they are incomplete. Furthermore, no mixing model is available for all of the apatite components in silicate melts or fluids, especially for F and Cl components. Several experimental studies have investigated the apatite-melt and apatite-fluid partitioning behavior of F, Cl, and OH in terrestrial and planetary systems, which have determined that apatite-melt partitioning of volatiles are best described as exchange equilibria similar to Fe-Mg partitioning between olivine and silicate melt. However, McCubbin et al. recently reported that the exchange coefficients may vary in portions of apatite compositional space where F, Cl, and OH do not mix ideally in apatite. In particular, solution calorimetry data of apatite compositions along the F-Cl join exhibit substantial excess enthalpies of mixing. In the present study, we conducted apatite-melt partitioning experiments in evacuated, sealed silica-glass tubes at approximately 1 bar and 950-1050 degrees Centigrade on a synthetic Martian basalt composition equivalent to the basaltic shergottite Queen Alexandria Range (QUE) 94201. These experiments were conducted dry, at low pressure, to assess the effects of temperature and apatite composition on the partitioning behavior of F and Cl between apatite and basaltic melt along the F-Cl apatite binary join, where there is non-ideal mixing of F and Cl in apatite.

McCubbin, F. M.↗

DOE OSTI2020

Thermodynamics of rotating quantum matter in the virial expansion

We characterize the high-temperature thermodynamics of rotating bosons and fermions in two-dimensional (2D) and three-dimensional (3D) isotropic harmonic trapping potentials. In this work, we begin by calculating analytically the conventional virial coefficients $b_n$ for all $\textit{n}$ in the noninteracting case, as functions of the trapping and rotational frequencies. We also report on the virial coefficients for the angular momentum and associated moment of inertia. Using the $b_n$ coefficients, we analyze the deconfined limit (in which the angular frequency matches the trapping frequency) and derive explicitly the limiting form of the partition function, showing from the thermodynamic standpoint how both the 2D and 3D cases become effectively homogeneous 2D systems. To tackle the virial coefficients in the presence of weak interactions, we implement a coarse temporal lattice approximation and obtain virial coefficients up to third order.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗