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DOE OSTI2024

Determination of the Diffusion Coefficients of Binary CH4 and C2H6 in a Supercritical CO2 Environment (500–2000 K and 100–1000 atm) by Molecular Dynamics Simulations

The self-diffusion coefficients of carbonaceous fuels in a supercritical CO2 environment provide transport information that can help us understand the Allam Cycle mechanism at a high pressure of 300 atm. The diffusion coefficients of pure CO2 and binary CO2/CH4 and CO2/C2H6 at high temperatures (500 K~2000 K) and high pressures (100 atm~1000 atm) are determined by molecular dynamics simulations in this study. Increasing the temperature leads to an increase in the diffusion coefficient, and increasing the pressure leads to a decrease in the diffusion coefficients for both methane and ethane. The diffusion coefficient of methane at 300 atm is approximately 0.012 cm2/s at 1000 K and 0.032 cm2/s at 1500 K. The diffusion coefficient of ethane at 300 atm is approximately 0.016 cm2/s at 1000 K and 0.045 cm2/s at 1500 K. The understanding of diffusion coefficients potentially leads to the reduction in fuel consumption and minimization of greenhouse gas emissions in the Allam Cycle.

Energy & Fuels↗

DOE OSTI2020

Isotope effects on the high pressure viscosity of liquid water measured by differential dynamic microscopy

In this paper, differential dynamic microscopy is performed in diamond anvil cells to measure the viscosity of water along the 24 °C isotherm to high-pressure by determination of the tracer diffusion coefficient of monodisperse silica spheres of known diameter and application of the Stokes-Einstein-Sutherland equation. This technique allows liquid samples to be compressed to greater pressure prior to freezing than with other viscometry methods. The highest-pressure measurement was made at 1.67 GPa, considerably deeper into the supercompressed regime than previously reported. The effect of isotopic composition is investigated with samples of normal water, heavy water, and partially deuterated water. When data below 0.25 GPa are excluded a free volume model fits the observed viscosities well yielding a theoretical glass transition density close to that observed in very-high-density amorphous ice. The improved fit above 0.25 GPa coincides with the loss of other anomalous behaviors in liquid water caused by hydrogen bonding and represents a transition to properties closer to those of a simple liquid.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2023

Investigation of desorption of hydrogen gas from polymer matrix using thermal desorption analysis and finite element modeling

Polymer materials are used widely as sealing materials and liners in hydrogen storage and transportation infrastructure. During operating conditions, polymers are exposed to high pressure hydrogen gas periodically. When in contact, the hydrogen gas diffuses through the polymer material with ease due to its smaller sized molecules compared to the polymer molecules. In the event of rapid decompression of outside hydrogen gas, the hydrogen molecules within the polymer diffuse out. This process is known as the desorption of polymer and can cause blisters or cracking causing permanent damage to the polymer. Here, we used a combined experimental and modeling approach to investigate the desorption of the hydrogen gas in the polymer. Thermal desorption analysis (TDA) experiments were performed on the polymer sample exposed to the high-pressure hydrogen gas to measure the diffusion coefficient and equilibrium hydrogen concentration. Experiments also provided the quantity of hydrogen within the polymer during the desorption process which followed Fick’s law. However, for higher pressurization values, some anomaly was observed in the quantity of hydrogen remaining in the polymer sample. A continuum mechanics based coupled diffusion–deformation-damage model was deployed to simulate the gas desorption process in the material using the finite element method to understand its effect on the material. It was found that the anomaly in TDA results were due to the blister formation on the polymer surface which resulted in longer hydrogen retention. Simulations also showed that blister formation can be affected by multiple parameters such as the addition of filler particles, and pre-existing cavity size.

36 MATERIALS SCIENCE↗

DOE OSTI2021

The mobility of small, over-pressurized helium bubbles in tungsten at 2000 K

Fusion reactor environments inevitably lead to the formation of high-pressure helium bubbles whose nucleation, growth, and diffusion strongly impact the performance of plasma-facing components. Here this research describes a diffusion mechanism of over-pressurized bubbles via a sequence of Frenkel pair nucleation, self-interstitial migration, and Frenkel pair annihilation. Molecular dynamics was used to simulate the diffusion of small bubbles in tungsten at 2000 K with helium-per-vacancy ratios in the range of 4.5 to 7. The diffusion coefficients are calculated and their dependence on helium content, number of vacancies, and number of attached self-interstitials is characterized. It is found that bubbles are most mobile when the nucleation/annihilation rates of Frenkel pairs are nearly equal and when the bubbles nucleate and annihilate a single self-interstitial. All bubbles experience a peak diffusivity, which can be as high as 10 -11 m 2 /s decreasing with bubble size. The calculated diffusion coefficients provide valuable insight into the mobility of small, high-pressure bubbles, and can be used as input parameters in mesoscale models to improve predictions of plasma-surface interactions. (LA-UR-21-21881)

36 MATERIALS SCIENCE↗

DOE OSTI2022

Droplet Evaporation-Based Approach for Microliter Fuel Property Measurements

Small-volume, high-throughput screening techniques are sought to enable downselection from a large candidate pool of bio-blendstocks to a select few, having physical properties consistent with requirements of downsized, turbo-boosted internal combustion engines. Herein, this work presents a droplet evaporation-based approach to predict heat of vaporization, vapor pressure, diffusion coefficient, and Lennard–Jones parameters for an unknown fuel. Two different schemes, considering the isothermal evaporation of a moving droplet in ambient air, are proposed, which combine droplet velocity and temperature measurements, with some known properties to predict unknown properties. The schemes utilize an inverse solution of a transient model of droplet evaporation solved in an iterative fashion. A baseline scheme, which only requires droplet size change measurements, is evaluated using test data for three liquid fuels, comprising of alkanes and alcohols, as obtained in a temperature-controlled chamber. Results yield temperature-dependent heat of vaporization and vapor pressure predictions within 10 % and 22 %, respectively, of reference values. The advanced scheme, which additionally requires droplet temperature measurement, is numerically evaluated in the current work and will be experimentally validated in future efforts. The advanced scheme is found to significantly improve prediction quality, with deviations less than 2 % and 1 % for heat of vaporization and vapor pressure, while also predicting diffusion coefficient and Lennard–Jones parameters within 5 % and 8 %, respectively. The combined set of approaches, which primarily track droplet evaporation, can be incorporated into a small-volume, high-throughput fuel screening process.

09 BIOMASS FUELS↗

DOE OSTI2023

The physics basis to integrate an MHD stable, high-power hybrid scenario to a cool divertor for steady-state reactor operation

Abstract Coupling a high-performance core to a low heat flux divertor is a crucial step for ITER and a Fusion Pilot Plant or DEMO. Experiments in DIII-D recently expanded the steady-state hybrid scenario to high density and divertor impurity injection to study the feasibility of a radiating mantle solution. This work presents the physics basis for trade-offs between density, current drive and stability to tearing modes (TMs) at high β. EC power is crucial to tailor the plasma profiles into a passively stable state, and to eject impurities from the core. Off-axis EC depositions decrease the heating efficiency, but calculated electron heat transport coefficients show that this effect is partially mitigated by improved confinement inside the EC deposition. Additionally, the reduction in pressure is recovered by increasing the density. This favourable scaling of confinement with density was observed in high power plasmas for years, and this work provides a comprehensive explanation. ELITE predictions indicate that a path in peeling-ballooning stability opens up for certain conditions of density, power, q 95 and shaping, allowing the edge pressure to continue increasing without encountering a limit. In the core, calculated anomalous fast-ion diffusion coefficients are consistent with density fluctuation measurements in the toroidicity-induced Alfvén eigenmode range, showing that smaller fast-ion losses contribute to the enhanced confinement at high density. The edge integration study shows that divertor heat loads can be reduced with Ne and Ar injection, but this eventually triggers a cascade of n = 1, 2, 3 core TMs. We can now show that impurity radiation in the core is small and it is not the cause for the drop in confinement at high Ar and Ne injection rates. The overlap between the core TMs is consistent with the loss of pressure as estimated by the Belt model for the coupled rational surfaces. Optimization of these trade-offs has achieved plasmas with sustained H 98y2 = 1.7, f GW = 0.7 and ∼85% mantle radiation. The scenario and its variations at higher density and on- vs off-axis EC heating has been studied as a candidate for an integrated solution for several reactor designs, such as ITER, ARC, and the ARIES-ACT1 case, showing promising results in terms of fusion power and gain.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Experimental Measurements of Ion Diffusion Coefficients and Heating in a Multi-Ion-Species Plasma Shock

Collisional plasma shocks generated from supersonic flows are an important feature in many astrophysical and laboratory high-energy-density plasmas. Compared to single-ion-species plasma shocks, plasma shock fronts with multiple ion species contain additional structure, including interspecies ion separation driven by gradients in species concentration, temperature, pressure, and electric potential. We present time-resolved density and temperature measurements of two ion species in collisional plasma shocks produced by head-on merging of supersonic plasma jets, allowing determination of the ion diffusion coefficients. Here our results provide the first experimental validation of the fundamental inter-ion-species transport theory. The temperature separation, a higher-order effect reported here, is valuable for advancements in modeling HED and ICF experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Kinetics and transport of hydrogen in graphite at high temperature and the effects of oxidation, irradiation and isotopics

The kinetics of uptake and desorption impact the performance of graphite as a vector for tritium in high-temperature fission reactors and in the blanket of fusion reactors. Graphite components in these reactors are exposed to temperatures > 500 °C and H 2 partial pressures of few Pa and desorption temperatures are limited to < 1600 °C; limited data is available at these conditions. Here we review the mechanisms for uptake in, transport and desorption of hydrogen from graphite at high temperature, compiling data on uptake rates, diffusion coefficients and activation energies and providing a discussion of the impact of irradiation, pre-oxidation and isotope. At FHR conditions, trapping impacts uptake rates, leading to a reduction in apparent diffusivity by 35 to 80% compared to higher partial-pressure uptake. Timelines for desorption are not clearly defined; extrapolating from available data, at 1150 °C desorbing 80% of tritium uptaken at FHR conditions may take from 100 to 10,000 h.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Xe Recovery from Nuclear Power Plants Off-Gas Streams: Molecular Simulations of Gas Permeation through DD3R Zeolite Membrane

Recent experimental work has shown zeolite membrane-based separation as a promising potential technology for Kr/Xe gas mixtures due to its much lower energy requirements in comparison to cryogenic distillation, the conventional separation method for such mixtures. Such a separation is also economically rewarding because Xe is in high demand, as a valuable product for many applications/processes. In this work, we have used Molecular Dynamics (MD) simulations to study the effects of different conditions, i.e., temperature, pressure, and gas feed composition, on Kr/Xe separation performance via DD3R zeolite membranes. We provide a comprehensive study of the permeation of the different gas species, density profiles, and diffusion coefficients. Molecular simulations show that if the feed is changed from pure Kr/Xe to an equimolar mixture, the Kr/Xe separation factor increases, which agrees with experiments. In addition, when Ar is introduced as a sweep gas, the adsorption of both Kr and Xe increases, while the permeation of pure Kr increases. A similar behavior is observed with equimolar mixtures of Kr/Xe with Ar as the sweep gas. High-separation Kr/Xe selectivity is observed at 50 atm and 425 K but with low total permeation rates. Changing pressure and temperature are found to have profound effects on optimizing the separation selectivity and the permeation throughput.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

In situ investigation of high-pressure hydrogen-induced swelling in elastomers and its correlation with material properties

The resistance of elastomeric materials to high-pressure hydrogen-induced damage is essential for ensuring the reliability of hydrogen infrastructure. Here, in this study, we systematically investigated the swelling behavior and hydrogen transport properties of four elastomer types – EPDM, NBR, FKM, and HNBR – using a custom in-situ view cell system capable of real-time monitoring during decompression from pressures up to 96.5 MPa. Each elastomer was formulated with and without fillers and plasticizers to assess the effects of formulation on swelling response. Thermal desorption analysis (TDA) was employed to determine equilibrium hydrogen content and diffusion coefficients, providing insight into gas uptake and mobility within each material. Correlation analyses using Pearson and Spearman coefficients revealed that the diffusion coefficient showed a stronger relationship with swelling behavior than hydrogen content, highlighting the dominant role of hydrogen mobility. Filled elastomers, particularly those with carbon black, consistently showed reduced swelling due to enhanced stiffness and reduced diffusivity. These results deepen our understanding of diffuso-mechanical interactions in elastomers and support the rational design of sealing materials for high-pressure hydrogen systems.

EPDM↗

DOE OSTI2025

Measurement of turbulent velocity and bounds for thermal diffusivity in laser shock compressed foams by x-ray photon correlation spectroscopy

Experimental benchmarking of transport coefficients under extreme conditions is required for validation of differing theoretical models. To date, measurement of transport properties of dynamically compressed samples remains a challenge with only a limited number of studies able to quantify transport in high pressure and temperature matter. x-ray photon correlation spectroscopy utilizes coherent x-ray sources to measure time correlations of density fluctuations, thus providing measurements of length and timescale-dependent transport properties. Here, we present a first-of-a-kind experiment to conduct x-ray photon correlation spectroscopy in laser shock compression experiments. We report measurement of the turbulent velocity in the wake of a laser driven supersonic shock and place an upper bound on thermal diffusivity in a solid density plasma on nanosecond timescales.

High-energy-density plasmas↗

DOE OSTI2023

Structure and dynamics of $\mathrm{Fe_{90}}$$\mathrm{Si_3}$$\mathrm{O_7}$ liquids close to Earth's liquid core conditions

Using an artificial neural-network machine learning interatomic potential, we have performed molecular dynamics simulations to study the structure and dynamics of $\mathrm{Fe_{90}}$$\mathrm{Si_3}$$\mathrm{O_7}$ liquid close to the Earth's liquid core conditions. Here, the simulation results reveal that the short-range structural order (SRO) in the $\mathrm{Fe_{90}}$$\mathrm{Si_3}$$\mathrm{O_7}$ liquid is very strong. About 80% of the atoms are arranged in crystallinelike SRO motifs. In particular, ~ $70$% of Fe-centered clusters can be classified as either hexagonal-close-packed-like or icosahedrallike SRO motifs. The SRO clusters centered on Fe, Si, or O atoms are strongly intermixed and homogenously distributed throughout the liquid. The atomic structure of the liquid and the fractions of dominant SRO clusters are not sensitive to pressure/temperature used in the simulations except that the SRO of the O-centered clusters is enhanced close to inner core pressures. The O-diffusion coefficient is about two to three times larger than the Fe and Si ions and increases more rapidly in the deeper core regions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Experimental investigation of elemental and isotopic evaporation processes by laser heating in an aerodynamic levitation furnace

In this report we carried out evaporation experiments on a B-type calcium–aluminium-rich inclusion (CAI) melt in a gas-mixing aerodynamic levitation laser furnace, at 1873 K and an oxygen partial pressure of 10 -9.1 atm, for durations ranging from 60 to 600 s. Evaporation of SiO 2 and MgO follow the same trend as those observed in vacuum furnace experiments at the same temperature and starting composition, showing that their evaporation relative to one another from the melt is independent of pressure, oxygen fugacity, and hydrodynamical regime specific to the furnace. Isotopic ratios of Mg and Si in evaporation residues are used to derive fractionation factors of α 26/24 Mg vap-liq = 0.9906± 0.0004 and α 30/28 Si vap-lip = 0.9943±0.0003, which are both significantly closer to unity than those found for evaporation in a vacuum, which translates to less isotope fractionation. The residues are also less isotopically fractionated than expected for cases in which transport of the gas species away from the melt is diffusion-controlled at 1-atm. By analysing the flow regimes in our furnace, we find that advection by the levitating gas is the primary mode of mass transport away from the melt surface, as opposed to diffusion-limited transport in a vacuum or 1-atm tube furnace. A modified Hertz–Knudsen–Langmuir formulation accounts for this process, and shows that isotopic fractionation of both Si and Mg reflect a saturation factor (ratio of the pressure of the evaporating species to vapour saturation pressure) equal to 0.75. This is in perfect accord with recent measurements of Cu isotopic fractionation using a similar furnace. The fact that three elements (Mg, Si, Cu) with varying equilibrium vapour pressures, activity coefficients in the liquid, and diffusion coefficients in the gas have the same scaling behaviour to saturation pressure is a strong indication that the mechanism controlling evaporation is driven by the hydrodynamical regime imposed in the furnace. Therefore, this class of experiments can be used to constrain processes in which advection dominates over diffusion, such as (but not limited to) planetary ejecta, tektites, giant impacts, nebular condensation in a turbulent flow, or nuclear fallout material. Finally, the possibility to reach high temperatures (in excess of 3500 K) in this furnace allows it to be used to evaluate the activity coefficients of melt components in extreme conditions relevant to molten planetary interiors (i.e., magma oceans), with a specific focus on refractory elements.

58 GEOSCIENCES↗

DOE OSTI2022

Microsized Pore Structure Determination in EPDM Rubbers Using High-Pressure 129 Xe NMR Techniques

Microsized pore parameters, such as pore size and distance between pores in a series of model EPDM rubbers, were determined in situ under the pressure of 500 psi using 129 Xe nuclear magnetic resonance (NMR) techniques: spin–lattice (T 1 ) and spin–spin (T 2 ) relaxation measurements, pulsed-field gradient (PFG) NMR, and two-dimensional exchange spectroscopy (2D EXSY). The T 1 /T 2 (>>1) ratio for the xenon confined in the pores is larger than that for nonconfined free xenon. This suggests that almost the entire pore surface interacts with xenon atoms like a closed pore. While these pores still connect each other through very narrow diffusion/exchange channels, it is possible to observe the echo decay in PFG-NMR and cross-peaks in 2D EXSY. The results show that both diffusion (D pore ≈ 2.1 × 10 –10 m 2 /s) and exchange (exchange rate, τ exch = a few tens of milliseconds) of xenon between a pore within the material and outer surface are prolonged. The exchange distances (l), which correspond to the xenon gas penetration depth, were estimated to be 70–100 μm based on the measured diffusion coefficients and exchange rate (1/τ exch ). NMR diffraction analysis reveals that pore size (a) and pore distance (b) are on the order of magnitude of micrometers and tens of micrometers, while the diffusion coefficients of xenon gas in the diffusion channels (D eff ) are about 10 –8 m 2 /s. Overall, this study suggests that the pores with a few micrometers connected through very narrow flowing channels with the length of several tens of micrometers are developed 70 to 100 μm below the rubber surface. Furthermore, the overall steady-state diffusion of xenon is slower, approximately 2 orders of magnitudes, than the diffusion in the channel between the pores. Finally, the pore and exchange distances correlated with the composition of rubbers showed that the properties of EPDM rubber as a high-pressure gas barrier could be improved by reducing the size of cracks and the depth of gas penetration by the addition of both carbon black and silica fillers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Europium diffusion in IG-110 nuclear graphite

Europium diffusion in graphite has been recognized to be of interest in high-temperature gas reactor safety analysis, particularly as an indicator of strontium diffusion. However, no measurements of europium diffusion coefficients have been reported in the literature. In this work, the effective diffusion coefficient of europium was measured using a time-release method. Natural europium was loaded into pre-milled unirradiated IG-110 graphite spheres using a pressurized acid digestion vessel. The time-release experiments were performed in the temperature range 1823 K – 1973 K using a SiC diffusion cell connected to an inductively-coupled plasma mass spectrometer (ICP-MS) via a He gas line. Finally, the results of this work are: D Eu, IG-110 = (1.5 x 10 -3 m 2 /s) exp $(\frac{-2.87\mathrm{x}10^{5} J/mol}{RT})$ This effective diffusion coefficient can be used to aid in predictive modelling of europium transport in HTGRs.

36 MATERIALS SCIENCE↗

DOE OSTI2023

The stability of FeH x and hydrogen transport at Earth’s core mantle boundary

Iron hydride in Earth’s interior can be formed by the reaction between hydrous minerals (water) and iron. Studying iron hydride improves our understanding of hydrogen transportation in Earth’s interior. Our high-pressure experiments found that face-centered cubic (fcc) FeH x (x≤1) is stable up to 165 GPa, and our ab initio molecular dynamics simulations predicted that fcc FeH x transforms to a superionic state under lower mantle conditions. In the superionic state, H-ions in fcc FeH become highly diffusive-like fluids with a high diffusion coefficient of ~3.7 × 10 -4 cm 2 s -1 , which is comparable to that in the liquid Fe-H phase. The densities and melting temperatures of fcc FeH x were systematically calculated. Similar to superionic ice, the extra entropy of diffusive H-ions increases the melting temperature of fcc FeH. Further, the wide stability field of fcc FeH enables hydrogen transport into the outer core to create a potential hydrogen reservoir in Earth’s interior, leaving oxygen-rich patches (ORP) above the core mantle boundary (CMB).

58 GEOSCIENCES↗

DOE OSTI2025

Explosive Soot Challenge (Final Report)

This project assembled a broad ensemble of modeling and experimentation tools to study the morphological and optical properties of detonation soots in explosive fireballs. A gram-scale hemispherical high explosive was studied in a low-pressure controlled environment using in-situ experimentation with diffusely illuminated visible absorption spectroscopy, particle sizing through light scattering techniques, and post-test collections with subsequent morphological analysis. Hydrocode modeling was performed to replicate the detonation flow observations, and subsequent aerosol kinetics models provided particle size distributions and extinction coefficients from the hydrocode results. Experimentally observed soot morphologies agreed with expectation from the literature - a bimodal distribution was found, brought upon by the particles growing to a size where their inertia and fluid wakes are non-negligible. The aerosol kinetics model did not replicate the observed bimodal size distribution for lack of a coagulation kernel to represent the behavior. To recover particulate optical properties, a spectrally resolved absorption spectroscopy method termed Spectral diffuse back-illuminated extinction imaging (SBI-EI) was developed and implemented on two explosive types. Inverting the absorption spectra using a Kramers-Kronig consistent method yielded the complex index of refraction for the soots produced by the explosives. This method resulted in an unrealistic index of refraction for one of the two explosives, and this is suspected to be due to the model neglecting scattering brought upon by the large particle sizes observed. In addition to the core work, three additional studies were performed in parallel. These investigated the impact of scattering on diffuse absorption spectroscopy, studied how soots oxidate and sublimate in a well-controlled shock tube, and laid the theoretical groundwork for a new collision kernel to replicate the bimodal size distribution from the observations. Summaries of these efforts are included at the end of this report.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2022

The effect of stress on the migration of He gas bubbles under a thermal gradient in Fe by phase-field modeling

Here a phase-field model is parameterized to study the effect of elastic stresses on the migration of He gas bubbles in Fe under a temperature gradient. Stresses caused by the gas bubble pressure and residual stress in the Fe matrix are considered. The dependence of He bubble migration velocity on the magnitude of the residual stress, average temperature, temperature gradient, and bubble size is measured. In agreement with a theoretical model based on surface diffusion, simulation results demonstrate that He bubbles move towards the high temperature region with velocities in Fe that are orders of magnitude faster than previously reported in UO 2 . It is found that local stresses in the matrix caused by the He bubble have negligible effect on the bubble migration process; however, residual stresses in the Fe matrix, potentially caused by processing or irradiation, can modestly modify bubble kinetics through pressure dependence of the He diffusion coefficients. Compressive residual stress decreases diffusion coefficients for bulk and surface diffusion mechanisms, thus reducing the migration velocity of the gas bubble. In contrast, tensile residual stress increases the diffusion coefficients, resulting in an increase in the gas bubble migration velocity. This pressure dependence is also consistent with a theoretical model. This phase field model lays the foundation for analysis of bubble coalescence-induced fracture in He bubble-containing steels.

36 MATERIALS SCIENCE↗