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DOE OSTI2023

Correlating the Viscosity and Rate of Water Diffusion in Semisolid Gel-Forming Aerosol Particles

Aerosol particles are known to exist in highly viscous amorphous states at a low relative humidity and temperature. The slow diffusion of molecules in viscous particles impacts the uptake and loss of volatile and semivolatile species and the rate of heterogeneous chemistry. Recent work has demonstrated that in particles containing organic molecules and salts, the formation of two-phase gel states is possible, leading to observations of rigid particles that resist coalescence. The way that molecules diffuse and transport in gel systems is not well-characterized. In this work, we use an electrodynamic balance to levitate sample particles containing a range of organic compounds in mixtures with calcium chloride and measure the rate of water diffusion. Particles of the pure organics have been shown to form viscous amorphous states, while in mixtures with divalent salts, coalescence measurements have revealed the apparent solidification of particles, consistent with the formation of a gel state facilitated by ion–molecule interactions. We report in several cases that water transport can actually be increased in the rigid gel state relative to the pure compound that forms a viscous state under similar conditions. These measurements reveal the limitations of using viscosity as a metric for predicting molecular diffusion and that the gel structure that forms is a much stronger controlling factor in the rate of diffusion. In conclusion, this underscores the need for diffusion measurements as well as a deeper understanding of noncovalent molecular assembly that leads to supramolecular structures in aerosol particles.

organic-inorganic mixtures↗

DOE OSTI2025

Experimental Characterization of Hydrogen Diffusion in Shale Rocks for Geologic Storage Applications

As global energy systems undergo a transition to cleaner alternatives, geologic hydrogen storage has emerged as a promising solution for large-scale energy storage. A critical factor in determining the feasibility of this approach is the effectiveness of caprock formations, such as shale, in preventing hydrogen migration. This study investigates the diffusion behavior of hydrogen through shale to assess its suitability as a caprock for geologic hydrogen storage. Using a novel double-seal core holder design and a through-diffusion apparatus, hydrogen diffusion was measured through shale rock from the Eagle Ford and Wolfcamp Formations under dry conditions. These measurements were complemented by microstructural and mineralogical analyses using low-pressure nitrogen adsorption and X-ray diffraction. The effective diffusion coefficient of hydrogen in these shale caprocks ranged from 2.51 × 10 –8 to 9.85 × 10 –8 m 2 /s. Notably, we observed that the diffusion behavior was more related to the pore network structure and could not be attributed to differences in the total pore volume between shale types alone. Here, to further understand the role of pore network complexity, a fractal pore model was developed to correlate tortuosity with the fractal dimension of the pore structure (a measure of pore network complexity). The proposed model closely matched tortuosity values obtained from diffusion experiments, outperforming existing theoretical tortuosity–porosity correlations. These findings provide key quantitative parameters needed to assess the feasibility of geologic hydrogen storage as well as insights that can be applied to hydrogen storage in a range of geologic formations.

08 HYDROGEN↗

DOE OSTI2025

Defect-Mediated Diffusion Pathways in Spodumene Accelerate Lithium Transport

Lithium extraction from naturally occurring α-spodumene is hindered by poor lithium diffusivity, necessitating high-temperature phase transformation to a low-density β polymorph. Although β spodumene exhibits up to 5 orders of magnitude higher lithium-ion diffusivity, both phases have diffusion activation energies between 0.8 and 1 eV, indicating that polymorph density is not the controlling factor over diffusivity. We show that aluminum vacancies facilitate lithium-ion diffusion in α-spodumene by reducing the migration barrier from 2.4 to 0.9 eV. Bond valence site energy and nudged elastic band calculations show a new lithium local minimum site which promotes a one-dimensional percolation network by reducing the lithium intersite distance from 4.5 Å to 2.9 Å. However, aluminum vacancies are energetically unfavorable to percolate through the whole structure, resulting in very low net lithium diffusivity and highlighting the critical role of nonstoichiometric defects in facilitating lithium transport in rigid aluminosilicate structures.

Chemical structure↗

DOE OSTI2020

Long-Range Exciton Diffusion in Two-Dimensional Assemblies of Cesium Lead Bromide Perovskite Nanocrystals

Förster resonant energy transfer (FRET)-mediated exciton diffusion through artificial nanoscale building block assemblies could be used as an optoelectronic design element to transport energy. However, so far, nanocrystal (NC) systems supported only diffusion lengths of 30 nm, which are too small to be useful in devices. In this work, we demonstrate a FRET-mediated exciton diffusion length of 200 nm with 0.5 cm 2 /s diffusivity through an ordered, two-dimensional assembly of cesium lead bromide perovskite nanocrystals (CsPbBr 3 PNCs). Exciton diffusion was directly measured via steady-state and time-resolved photoluminescence (PL) microscopy, with physical modeling providing deeper insight into the transport process. This exceptionally efficient exciton transport is facilitated by PNCs' high PL quantum yield, large absorption cross section, and high polarizability, together with minimal energetic and geometric disorder of the assembly. This FRET-mediated exciton diffusion length matches perovskites' optical absorption depth, thus enabling the design of device architectures with improved performances and providing insight into the high conversion efficiencies of PNC-based optoelectronic devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Diffusion of Hydrophilic to Hydrophobic Forms of Nile Red in Aqueous C 12 EO 10 Gels by Variable Area Fluorescence Correlation Spectroscopy

In this work, solute diffusion within lyotropic liquid crystal gels prepared from a series of water and decaethylene glycol monododecyl ether (C 12 EO 10 ) mixtures was explored by variable area fluorescence correlation spectroscopy. Aqueous C 12 EO 10 gels were prepared in concentrations ranging from 55:45 to 70:30 wt% of surfactant and water. Small angle X-ray scattering revealed that these gels comprise hexagonal mesophases of cylindrical micelles. Micelle spacing was found to decrease with increasing C 12 EO 10 concentration. Three different Nile red (NR) dyes were employed as model solutes and were separately doped into the gels at nanomolar levels. These include a hydrophilic form of NR incorporating an anionic sulfonate group (NRSO 3 - ), a hydrophobic form incorporating a fourteen-carbon alkane tail (NRC 14 ), and commercial NR as an intermediate case. FCS data acquired from the gels revealed that NRSO 3 - diffused primarily in 3D. Its diffusion coefficient exhibited a monotonic decrease with increasing gel concentration and micelle packing density, consistent with confinement of its motions as a result of its exclusion from the micelle cores. NRC 14 exhibited the smallest diffusion coefficient, most likely due to its larger size and enhanced interactions with the micelle cores. NR yielded an intermediate diffusion coefficient and the most anomalous behavior of the three dyes, attributable to its facile partitioning between core and corona regions, and greater participation by 1D diffusion. The results of these studies afford an improved understanding of molecular mass transport through soft-matter nanomaterials like those being developed for use in drug delivery and membrane based chemical separations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Observation and interpretation of energy efficient, diffuse direct current glow discharge at atmospheric pressure

A diffuse direct-current glow discharge was realized with low energy consumption and high energy utilization efficiency at atmospheric pressure. The formation of diffuse discharge was demonstrated by examining and comparing the electrical properties and optical emissions of plasmas. In combination with theoretical derivation and calculation, we draw guidelines that appearance of nitrogen ions at low electron density is crucial to enhance the ambipolar diffusion for the expansion of discharge channel and the increasing ambipolar diffusion near the cathode plays a key role in the onset of diffuse discharge. An individual-discharge-channel expansion model is proposed to explain the diffuse discharge formation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Observation of silicon self-diffusion enhanced by the strain originated from end-of-range defects using isotope multilayers

Si self-diffusion in the presence of end-of-range (EOR) defects is investigated using {sup nat}Si/{sup 28}Si isotope multilayers. The isotope multilayers were amorphized by Ge ion implantation, and then annealed at 800–950 °C. The behavior of Si self-interstitials is investigated through the {sup 30}Si self-diffusion. The experimental {sup 30}Si profiles show further enhancement of Si self-diffusion at the EOR defect region, in addition to the transient enhanced diffusion via excess Si self-interstitials by EOR defects. To explain this additional enhanced diffusion, we propose a model which takes into account enhanced diffusion by tensile strain originated from EOR defects. The calculation results based on this model have well reproduced the experimental {sup 30}Si profiles.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Mutual diffusion of binary liquid mixtures containing methanol, ethanol, acetone, benzene, cyclohexane, toluene, and carbon tetrachloride

Mutual diffusion coefficients of all 20 binary liquid mixtures that can be formed out of methanol, ethanol, acetone, benzene, cyclohexane, toluene, and carbon tetrachloride without a miscibility gap are studied at ambient conditions of temperature and pressure in the entire composition range. The considered mixtures show a varying mixing behavior from almost ideal to strongly non-ideal. Predictive molecular dynamics simulations employing the Green-Kubo formalism are carried out. Radial distribution functions are analyzed to gain an understanding of the liquid structure influencing the diffusion processes. It is shown that cluster formation in mixtures containing one alcoholic component has a significant impact on the diffusion process. The estimation of the thermodynamic factor from experimental vapor-liquid equilibrium data is investigated, considering three excess Gibbs energy models, i.e., Wilson, NRTL, and UNIQUAC. It is found that the Wilson model yields the thermodynamic factor that best suits the simulation results for the prediction of the Fick diffusion coefficient. Four semi-empirical methods for the prediction of the self-diffusion coefficients and nine predictive equations for the Fick diffusion coefficient are assessed and it is found that methods based on local composition models are more reliable. Finally, the shear viscosity and thermal conductivity are predicted and in most cases favorably compared with experimental literature values.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

Analysis of Al diffusion processes in TiN barrier layers for the application in silicon solar cell metallization

An evaporated Al layer is known as an excellent rear metallization for highly efficient solar cells, but suffers from incompatibility with a common solder process. To enable solar cell-interconnection and module integration, in this work the Al layer is complemented with a solder stack of TiN/Ti/Ag or TiN/NiV/Ag, in which the TiN layer acts as an Al diffusion barrier. X-ray photoelectron spectroscopy measurements prove that diffusion of Al through the stack and the formation of an Al{sub 2}O{sub 3} layer on the stack's surface are responsible for a loss of solderability after a strong post-metallization anneal, which is often mandatory to improve contact resistance and passivation quality. An optimization of the reactive TiN sputter process results in a densification of the TiN layer, which improves its barrier quality against Al diffusion. However, measurements with X-ray diffraction and scanning electron microscopy show that small grains with vertical grain boundaries persist, which still offer fast diffusion paths. Therefore, the concept of stuffing is introduced. By incorporating oxygen into the grain boundaries of the sputtered TiN layer, Al diffusion is strongly reduced as confirmed by secondary ion mass spectroscopy profiles. A quantitative analysis reveals a one order of magnitude lower Al diffusion coefficient for stuffed TiN layers. This metallization system maintains its solderability even after strong post-metallization annealing at 425 °C for 15 min. This paper thus presents an industrially feasible, conventionally solderable, and long-term stable metallization scheme for highly efficient silicon solar cells.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2017

Diffusion of copolymers composed of monomers with drastically different friction factors in copolymer/homopolymer blends

Copolymers are commonly used as interface modifiers that allow for the compatibilization of polymer components in a blend. For copolymers to function as a compatibilizer, they must diffuse through the matrix of the blend to the interface between the two blend components. The diffusivity of a copolymer in a blend matrix therefore becomes important in determining good candidates for use as compatibilizers. In this paper, coarse-grained Monte Carlo simulations using the bond fluctuation model modified with an overlap penalty have been developed to study the diffusive behavior of PS/PMMA random copolymers in a PMMA homopolymer blend. The simulations vary the connectivity between different monomers, the thermodynamic interactions between the monomers which manifest within a chain, and between copolymer and homopolymer matrix and define the monomer friction coefficient of each component independently, allowing for the determination of the combined effect of these parameters on copolymer chain diffusion. Finally, the results of this work indicate that PS-r-PMMA copolymer diffusion is not linearly dependent on the copolymer composition on a logarithmic scale, but its diffusion is a balance of the kinetics governed by the dominant motion of the faster styrene monomers and thermodynamics, which are governed by the concentration of styrene monomer within a given monomer’s local volume.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Diffusive tunneling in an isobaric but non-isothermal fuel-pusher mixture

The hydrodynamic mix of fusion fuel and inert pusher can simultaneously generate smaller fuel pockets and finer pusher layers that separate them. Smaller fuel pockets have greater local Knudsen numbers, which tend to exacerbate the Knudsen layer reactivity reduction. A thinner pusher layer separating the neighboring fuel pockets, on the other hand, can enable the diffusive tunneling of Gamow fuel ions through the pusher layer and hence alleviate the Knudsen layer reactivity degradation. Here in this paper, the diffusive tunneling phenomenon describes a random walk process by which the Gamow fuel ions from one fuel pocket can traverse the inert pusher layer to join a neighboring fuel pocket without losing much of their energy. This is made possible by the much slower collisional slowing down rate compared with the pitch angle scattering rate of light fuel ions with heavier pusher ions. In an isobaric target mixture where fuel and pusher segments can have distinct temperatures, due to their different compressibilities, the temperature effect on the critical pusher layer areal density below which diffusive tunneling can occur, which is a property of the hydrodynamic mix, is understood by computing the ion charge state distribution using a collisional radiative model. This information is fed into the collisionality evaluation, enabling a parametric scan of the diffusive tunneling physics in terms of the target pressure, fuel, and pusher temperatures. It is found that when the gold pusher layer has a temperature above 1 keV, the variation of the pusher temperature has little effect on the critical areal mass density below which diffusive tunneling can occur. If the pusher layer is 1 keV or below, the critical areal mass density rises sharply, indicating that for a stronger fuel-pusher temperature disparity, the onset of diffusive tunneling will be at an earlier stage of the hydrodynamic mix when the fuel-pusher mixing structures are of less reduced size.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Multiscale modeling of solute diffusion in triblock copolymer membranes

We develop a multiscale simulation model for diffusion of solutes through porous triblock copolymer membranes. The approach combines two techniques: self-consistent field theory (SCFT) to predict the structure of the self-assembled, solvated membrane and on-lattice kinetic Monte Carlo (kMC) simulations to model diffusion of solutes. Solvation is simulated in SCFT by constraining the glassy membrane matrix while relaxing the brush-like membrane pore coating against the solvent. The kMC simulations capture the resulting solute spatial distribution and concentration-dependent local diffusivity in the polymer-coated pores; we parameterize the latter using particle-based simulations. We apply our approach to simulate solute diffusion through nonequilibrium morphologies of a model triblock copolymer, and we correlate diffusivity with structural descriptors of the morphologies. We also compare the model’s predictions to alternative approaches based on simple lattice random walks and find our multiscale model to be more robust and systematic to parameterize. Furthermore, our multiscale modeling approach is general and can be readily extended in the future to other chemistries, morphologies, and models for the local solute diffusivity and interactions with the membrane.

36 MATERIALS SCIENCE↗

DOE OSTI2015

SPECTRA OF COSMIC RAY ELECTRONS AND DIFFUSE GAMMA RAYS WITH THE CONSTRAINTS OF AMS-02 AND HESS DATA

Recently, AMS-02 reported their results of cosmic ray (CR) observations. In addition to the AMS-02 data, we add HESS data to estimate the spectra of CR electrons and the diffuse gamma rays above TeV. In the conventional diffusion model, a global analysis is performed on the spectral features of CR electrons and the diffuse gamma rays by the GALRPOP package. The results show that the spectrum structure of the primary component of CR electrons cannot be fully reproduced by a simple power law and that the relevant break is around 100 GeV. At the 99% confidence level (C.L.) the injection indices above the break decrease from 2.54 to 2.35, but the ones below the break are only in the range of 2.746–2.751. The spectrum of CR electrons does not need to add TeV cutoff to also match the features of the HESS data. Based on the difference between the fluxes of CR electrons and their primary components, the predicted excess of CR positrons is consistent with the interpretation that these positrons originate from a pulsar or dark matter. In the analysis of the Galactic diffuse gamma rays with the indirect constraint of AMS-02 and HESS data, it is found that the fluxes of Galactic diffuse gamma rays are consistent with the GeV data of the Fermi-Large Area Telescope (LAT) in the high-latitude regions. The results indicate that inverse Compton scattering is the dominant component in the range of hundreds of GeV to tens of TeV, respectively from the high-latitude regions to the low ones, and in all of the regions of the Galaxy the flux of diffuse gamma rays is less than that of CR electrons at the energy scale of 20 TeV.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Se diffusion in CdTe thin films for photovoltaics

Manipulating CdSeTe bandgrading to enhance photocurrent and carrier lifetime is an essential part of high-performance CdTe photovoltaics (PVs). Here, we examine Se diffusion kinetics in single-crystal and polycrystalline CdTe during deposition, thermal annealing, and CdCl 2 treatments. Se distributions are determined by dynamic secondary-ion-mass spectroscopy and Auger electron spectroscopy depth profiling and coupled with electron backscatter diffraction images of the crystalline structure. Effective bulk and grain boundary diffusion coefficients are determined by analytical models and discussed in the context of processing and film morphology. Se is found to diffuse in CdTe at much higher rates during CdCl 2 treatments than with thermal processing alone. GB diffusion also occurs at a significantly faster rate than bulk diffusion. As a result of these two effects, the near interface bulk and GB Se diffusion during CdCl 2 treatments dominates the bandgrading profiles in CdTe PVs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Self-learning kinetic Monte Carlo simulations of diffusion in ferromagnetic α -Fe–Si alloys

Diffusion in α-Fe-Si alloys is studied using AKSOME, an on-lattice self-learning KMC code, in the ferromagnetic state. Si diffusivity in the α-Fe matrix were obtained with and without the magnetic disorder in various temperature ranges. In addition we studied vacancy diffusivity in ferromagnetic α-Fe at various Si concentrations up to 12.5at.% in the temperature range of 350–550 K. The results were compared with available experimental and theoretical values in the literature. Local Si-atom dependent activation energies for vacancy hops were calculated using a broken-model and were stored in a database. The migration barrier and prefactors for Si-diffusivity were found to be in reasonable agreement with available modeling results in the literature. Magnetic disorder has a larger effect on the prefactor than on the migration barrier. Prefactor was approximately an order of magnitude and the migration barrier a tenth of an electron-volt higher with magnetic disorder when compared to a fully ferromagnetic ordered state. In addition, the correlation between various have a larger effect on the Si-diffusivity extracted in various temperature range than the magnetic disorder. In the case of vacancy diffusivity, the migration barrier more or less remained constant while the prefactor decreased with increasing Si concentration in the disordered or A2-phase of Fe-Si alloy. Important vacancy-Si/Fe atom exchange processes and their activation barriers were also identified and discuss the effect of energetics on the formation of ordered phases in Fe-Si alloys.

AKSOME↗

DOE OSTI2018

Validation study of GENE on ASDEX Upgrade using perturbative thermal diffusivity measured with partial sawtooth heat pulses

Perturbative thermal diffusivity is measured with partial sawtooth-generated heat pulses on ASDEX Upgrade for the first time, and these measurements are used to validate the first nonlinear ion-scale gyrokinetic simulation that agrees with experimentally measured perturbative diffusivity. Recent work on Alcator C-Mod and DIII-D has shown that ion-scale gyrokinetics cannot adequately describe certain plasma conditions, and that in these instances multi-scale simulations may resolve the observed discrepancies. This work presents the first measurements of electron perturbative thermal diffusivity with partial sawteeth on ASDEX Upgrade (measuring values between 2 and 9 m 2 s -1 ), and compares these measurements to those made with more established modulated electron cyclotron heating measurements, finding good agreement within experimental uncertainty. Perturbative diffusivity is found to scale inversely with collisionality across ASDEX Upgrade and Alcator C-Mod plasmas. Finally, perturbative diffusivity is used as a validation constraint in a study with the gyrokinetic code GENE, showing the first instance where an ion-scale gyrokinetic simulation can simultaneously match the experimental ion and electron heat fluxes and the perturbative thermal diffusivity. Here these results indicate that multi-scale effects may only be important in some plasmas, and the collisionality and ratio of high to low wavenumber linear growth rates may distinguish these cases.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Maximum CO 2 diffusion inside leaves is limited by the scaling of cell size and genome size

Maintaining high rates of photosynthesis in leaves requires efficient movement of CO 2 from the atmosphere to the mesophyll cells inside the leaf where CO 2 is converted into sugar. CO 2 diffusion inside the leaf depends directly on the structure of the mesophyll cells and their surrounding airspace, which have been difficult to characterize because of their inherently three-dimensional organization. Yet faster CO 2 diffusion inside the leaf was probably critical in elevating rates of photosynthesis that occurred among angiosperm lineages. Here we characterize the three-dimensional surface area of the leaf mesophyll across vascular plants. We show that genome size determines the sizes and packing densities of cells in all leaf tissues and that smaller cells enable more mesophyll surface area to be packed into the leaf volume, facilitating higher CO 2 diffusion. Measurements and modelling revealed that the spongy mesophyll layer better facilitates gaseous phase diffusion while the palisade mesophyll layer better facilitates liquid-phase diffusion. Our results demonstrate that genome downsizing among the angiosperms was critical to restructuring the entire pathway of CO 2 diffusion into and through the leaf, maintaining high rates of CO 2 supply to the leaf mesophyll despite declining atmospheric CO 2 levels during the Cretaceous.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

Explainable machine learning for hydrogen diffusion in metals and random binary alloys

Hydrogen diffusion in metals and alloys plays an important role in the discovery of new materials for fuel cell and energy storage technology. While analytic models use hand-selected features that have clear physical ties to hydrogen diffusion, they often lack accuracy when making quantitative predictions. Machine learning models are capable of making accurate predictions, but their inner workings are obscured, rendering it unclear which physical features are truly important. To develop interpretable machine learning models to predict the activation energies of hydrogen diffusion in metals and random binary alloys, we create a database for physical and chemical properties of the species and use it to fit six machine learning models. Our models achieve root-mean-squared errors between 98–119 meV on the testing data and accurately predict that elemental Ru has a large activation energy, while elemental Cr and Fe have small activation energies. By analyzing the feature importances of these fitted models, we identify relevant physical properties for predicting hydrogen diffusivity. While metrics for measuring the individual feature importances for machine learning models exist, correlations between the features lead to disagreement between models and limit the conclusions that can be drawn. Instead grouped feature importance, formed by combining the features via their correlations, agree across the six models and reveal that the two groups containing the packing factor and electronic specific heat are particularly significant for predicting hydrogen diffusion in metals and random binary alloys. In conclusion, this framework allows us to interpret machine learning models and enables rapid screening of new materials with the desired rates of hydrogen diffusion.

36 MATERIALS SCIENCE↗