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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Nanoparticle Diffusion in Miscible Polymer Nanocomposite Melts

X-ray photon correlation spectroscopy measurements were used to quantify the dynamics of bare and bimodal grafted silica nanoparticles mixed with PEO melts of different molecular weights. In dilute polymer nanocomposite (PNC) samples, we find diffusive NP behavior as described by the Stokes–Einstein relationship so long as the adsorbed PEO polymer layer is taken into account in determining both the effective NP size and its role on composite viscosity. The size of this bound layer was found to be approximately 2R g , where R g is the chain radius of gyration. We also expanded our system to investigate how the dynamics of grafted NPs differ from bare NPs with an adsorbed layer. We showed that the dynamics again can be determined by an effective NP radius at a scale smaller than the effective interparticle spacing; however, at larger length scales, the morphology and grafting parameters play a major role in the system dynamics. These results allow us to quantify NP ordering driven by polymer crystallization. It has previously been speculated that behavior is controlled by the relative ratio of time scale of crystal growth and the diffusive time scale of the NPs, a Peclet number. When the former time scale is longer, then the NPs are expected to be segregated into the interlamellar amorphous zones, while the NPs are too slow to be reorganized in the opposite case. We show here that this conjecture is quantitatively correct and the demarcation in behavior occurs for Pe = 1. Thus, we provide a way to estimate a critical spherulite growth rate for any semicrystalline PNC, at which a given NP can be ordered. Together, the results of this study permit us to tunably design PNCs through directed dispersion of NPs in a polymer matrix.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2023

Morphology–Diffusivity Relationships in Fluorine-Free Random Terpolymers for Proton-Exchange Membranes

Here, using atomistic molecular dynamics simulations, we investigate the morphology and transport properties of a new family of fluorine-free terpolymers designed as proton-exchange membranes. Simulated random terpolymers consist of three monomers with a 5-carbon backbone with a phenylsulfonate, phenyl, or no pendant group and have ion exchange capacities (IECs) ranging from 1.06–4.14 mmol/g. At a hydration level of 9, cluster analysis reveals macrophase separation between water and terpolymers with IEC < 2.1 mmol/g and continuous, percolated hydrophilic and hydrophobic nanoscale domains at higher IECs. Channel width distribution analysis of the percolated morphologies revealed that more hydrophobic units produce less uniform channels. Decreasing the surface area per sulfonate group and increasing the fractal dimension of the hydrophilic domains correlate with increased water diffusivity, due to a more acidic interface and more isotropic water channels. Relative to the previously studied phenylsulfonate homopolymer, these terpolymers with lower IECs have only modestly lower water diffusion, and we anticipate other advantages related to processability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Evidence for Enhanced Tracer Diffusion in Densely Packed Interfacial Assemblies of Hairy Nanoparticles

Nearly monodisperse nanoparticle (NP) spheres attached to a nonvolatile ionic liquid surface were tracked by in situ scanning electron microscopy to obtain the tracer diffusion coefficient D tr as a function of the areal fraction Φ. The in situ technique resolved both tracer (gold) and background (silica) particles for ~1–2 min, highlighting their mechanisms of diffusion, which were strongly dependent on Φ. Structure and dynamics at low and moderate Φ paralleled those reported for larger colloidal spheres, showing an increase in order and a decrease in D tr by over 4 orders of magnitude. However, ligand interactions were more important near jamming, leading to different caging and jamming dynamics for smaller NPs. Finally, the normalized D tr at ultrahigh Φ depended on particle diameter and ligand molecular weight. Increasing the PEG molecular weight by a factor of 4 increased D tr by 2 orders of magnitude at ultrahigh Φ, indicating stronger ligand lubrication for smaller particles.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2025

Self-Diffusivity Measurement of Eutectic F 7 LiNaK with and without Additives Using Quasi-Elastic Neutron Scattering

The atomic scale relaxation dynamics of eutectic F 7 LiNaK (46.5 LiF–11.5 NaF–42 KF mol %, Li-7 enriched) were measured using quasi-elastic neutron scattering (QENS) over a temperature range of 500–750 °C. Here, the effect of adding 0.988 mol % cerium, 0.499 mol % cesium, and 1.21 mol % zirconium individually to the dynamics of F 7 LiNaK was also investigated. The relaxation process in both pure and doped F 7 LiNaK molten salts was fit with a stretched exponential function and the temperature dependence follows an Arrhenius behavior over a wavevector transfer range of 0.4 Å –1 < Q < 0.9 Å –1 . The measured activation energy for self-diffusion is E a = 0.77 ± 0.02 eV/atom for pure molten F 7 LiNaK. The QENS response with additives added to F 7 LiNaK was also fit with a stretched exponential and the associated Arrhenius behavior was characterized with activation energies of E a = 0.88 ± 0.01 eV/atom for zirconium (1.21 mol %), E a = 1.02 ± 0.02 eV/atom for cerium (0.988 mol %), and E a = 0.71 ± 0.03 eV/atom for cesium (0.499 mol %). The measured diffusivities are compared to those simulated with a neural network force field model by Lee et al. [Lee, S.-C. Comparative Studies of the Structural and Transport Properties of Molten Salt FLiNaK Using the Machine-Learned Neural Network and Reparametrized Classical Forcefields. J. Phys. Chem. B 2021, 125(37), 10562–10570].

FLiNaK↗
DOE OSTI2025

A Transferable Force Field for Predicting Adsorption and Diffusion of Water in Cationic Zeolites with Coupled Cluster Accuracy

We present a transferable force field for water in proton-exchanged, alkali (Li, Na, K, Rb, and Cs) metal-exchanged, and alkaline-earth (Mg, Ca, Sr, and Ba) metal-exchanged zeolites. The fitting methodology is based on adsorbate–adsorbent interaction energies obtained from periodic density functional theory calculations and corrected using the coupled-cluster method applied to small model clusters. To ensure an accurate prediction of both adsorption and diffusion properties of water, sets of configurations that sample both adsorption sites and intracrystalline hopping transition states were used in the fitting. The quality of the force field is assessed for a wide range of zeolites with different topologies and chemical compositions, demonstrating good agreement between theoretical predictions and experimental measurements of water adsorption and diffusion.

Adsorption↗
DOE OSTI2025

Diffusion Model-Guided Inverse Design of Bimetallic Catalysts for Ammonia Decomposition

In the past decade, artificial intelligence and deep learning have played increasingly prominent roles in materials design and discovery. Among these, generative AI models, known for their ability to create unique and complex structures, have emerged as state-of-the-art tools for materials screening due to their high efficiency and low computational cost. In catalysis, one of the major challenges is identifying promising material candidates within an immense chemical space. This challenge can be addressed using generative approaches, such as diffusion-based inverse design models. In this study, we present a machine learning-guided workflow that employed a diffusion model for the inverse design of bimetallic alloy catalysts for low-carbon ammonia decomposition, a key reaction for ammonia emission control and sustainable hydrogen production. Catalyst candidates were evaluated using nitrogen adsorption energy as the key descriptor, inspired by multiscale modeling. The proposed workflow identified low-cost, environmentally friendly catalysts with excellent catalytic performance, which have been validated theoretically and experimentally. Our framework decoupled the generative and property-prediction components, enhancing both flexibility and accuracy in the catalytic material design process.

Adsorption↗
DOE OSTI2020

Unified Entrainment and Detrainment Closures for Extended Eddy-Diffusivity Mass-Flux Schemes

The extended Eddy Diffusivity Mass Flux (EDMF) scheme is used as a unied parameterization that simulates subgrid-scale dynamics across a range of regimes.This work presents unied entrainment and detrainment closures that allow this scheme to simulate the dry convective boundary layer, shallow convection and deep convection , while adjacent works present other necessary closures for this unied scheme and test its performance for stable, stratocumulus topped and convective boundary layers. Entrainment and detrainment are modeled as a combination of turbulent and dynamical processes. The turbulent component is taken as downgradient diffusion between subdomains. The dynamical component is based on a ratio of buoyancy and vertical velocity that ensures consistent treatment of the ratio of mass-flux at vanishing area fraction. Dynamical detrainment is controlled by the difference in relative humidity between subdomains when liquid water is present. These closures are rst evaluated with entrainment and detrainment diagnosed from Large Eddy Simulations where decaying tracers are used to identify the different subdomains and mass exchanges between them. When implemented in a single column model (SCM), these closures are tested in simulations of several observationally motivated cases of dry convective boundary layer, shallow convection and deep convection. Results show good agreement between the SCM and Large Eddy Simulations in key properties for climate models and profiles of first, second and third moments. The development of diurnal cycles and the onset of and precipitation (with simplified microphysics) are well predicted by the SCM.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Evidence for the 3D Radiative Effects of Boundary-Layer Clouds From Observations of Direct and Diffuse Surface Solar Fluxes

Numerical experiments have revealed the importance of horizontal transport of light in the presence of clouds (“3D effects”), with consequences for climate, weather, and solar resource availability predictions. Yet, analysis of 3D effects from observations remain sparse because of the difficulty to isolate the effect of horizontal transport in radiation measurements. In this study, we provide observational evidence for 3D effects based on the direct-diffuse partition of surface solar fluxes. It is compared to outputs from the ecRad radiative transfer scheme run on retrieved cloud profiles. Furthermore, the direct-beam calculation takes careful account of the field-of-view of the pyrheliometer to ensure consistency between observed and modeled direct fluxes. Only the solver that accounts for 3D effects is able to reproduce the observed mean direct-diffuse partition as a function of solar zenith angle and cloud cover, in particular at large solar zenith angles where cloud sides intercept most of the direct beam.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Probabilistic Diffusion Models Advance Extreme Flood Forecasting

Extreme floods pose escalating risks in a changing climate, yet forecasting remains challenging due to peak flow underestimation and high uncertainty. We introduce diffusion-based runoff model (DRUM), a probabilistic deep learning (DL) approach that advances extreme flood forecasting across representative basins in the contiguous United States. DRUM outperforms state-of-the-art benchmarks, enhancing nowcasting skill for the top 1‰ of flows in 72.3% of studied basins. Under operational scenarios, DRUM extends reliable lead times by nearly a full day for 20- and 50-year floods. When evaluated with measured precipitation, an ideal condition, recall improves by 0.3–0.4 and the early warning window extends by 2.3 days for 50-year floods. The enhancement potential varies regionally, with precipitation-driven flood zones in the eastern and northwestern US benefiting most, gaining 3–7 days in lead time. These findings highlight the transformative potential of diffusion models as a cutting-edge generative AI technique for advancing hydrology and broader Earth system sciences.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Stratification of polymer mixtures in drying droplets: Hydrodynamics and diffusion

In this work, we study the evaporation-induced stratification of a mixture of short and long polymer chains in a drying droplet using molecular simulations. We systematically investigate the effects of hydrodynamic interactions (HI) on this process by comparing hybrid simulations accounting for HI between polymers through the multiparticle collision dynamics technique with free-draining Langevin dynamics simulations neglecting the same. We find that the dried supraparticle morphologies are homogeneous when HI are included but are stratified in core–shell structures (with the short polymers forming the shell) when HI are neglected. The simulation methodology unambiguously attributes this difference to the treatment of the solvent in the two models. We rationalize the presence (or absence) of stratification by measuring phenomenological multicomponent diffusion coefficients for the polymer mixtures. The diffusion coefficients show the importance of not only solvent backflow but also HI between polymers in controlling the dried supraparticle morphology.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Calculation of self-diffusion coefficients in supercritical carbon dioxide using mean force kinetic theory

This paper presents an application of mean force kinetic theory (MFT) to the calculation of the self-diffusivity of CO 2 in the supercritical fluid regime. Two modifications to the typical application of MFT are employed to allow its application to a system of molecular species. Therefore, the first is the assumption that the inter-particle potential of mean force can be obtained from the molecule center-of-mass pair correlation function, which in the case of CO 2 is the C–C pair correlation function. The second is a new definition of the Enskog factor that describes the effect of correlations at the surface of the collision volume. The new definition retains the physical picture that this quantity represents a local density increase, resulting from particle correlations, relative to that in the zero density homogeneous fluid limit. These calculations are facilitated by the calculation of pair correlation functions from molecular dynamics (MD) simulations using the FEPM2 molecular CO2 model. The self-diffusivity calculated from theory is in good agreement with that from MD simulations up to and slightly beyond the density at the location of the Frenkel line. The calculation is compared with and is found to perform similarly well to other commonly used models but has a greater potential for application to systems of mixed species and to systems of particles with long range interatomic potentials due to electrostatic interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Oxide dissolution and oxygen diffusion scenarios in niobium and implications on the Bean–Livingston barrier in superconducting cavities

We generalize a native Nb 2 O 5 dissolution model [G. Ciovati, Appl. Phys. Lett. 89, 022507 (2006)] to sequential overlayer dissolutions, multilayer dissolution, and realistic temperature profiles, which may be applicable to other materials. The model is applied to secondary ion mass spectrometry depth profile measurements for varying temperature profiles and two-step oxide dissolution in Nb and found to agree well. In the context of the Meissner screening response due to impurity profiles on the length scale of the London penetration depth, the shallow diffusion of O impurities results in a substantial decrease in the peak supercurrent density near the surface. In this framework, oxide dissolution and oxygen diffusion can account for a rise in peak supportable magnetic field in SRF cavities with baking time and a suppression after the optimal baking time is reached, in good agreement with peak-field baking temperatures and times as well as recent quench field measurements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Femtosecond temperature measurements of laser-shocked copper deduced from the intensity of the x-ray thermal diffuse scattering

We present 50-fs, single-shot measurements of the x-ray thermal diffuse scattering (TDS) from copper foils that have been shocked via nanosecond laser ablation up to pressures above ∼135 GPa. We hence deduce the x-ray Debye–Waller factor, providing a temperature measurement. The targets were laser-shocked with the DiPOLE 100-X laser at the High Energy Density endstation of the European X-ray Free-Electron Laser. Single x-ray pulses, with a photon energy of 18 keV, were scattered from the samples and recorded on Varex detectors. Despite the targets being highly textured (as evinced by large variations in the elastic scattering) and with such texture changing upon compression, the absolute intensity of the azimuthally averaged inelastic TDS between the Bragg peaks is largely insensitive to these changes, and allowing for both Compton scattering and the low-level scattering from a sacrificial ablator layer provides a reliable measurement of $T/Θ^2_D$, where Θ D is the Debye temperature. We compare our results with the predictions of the SESAME 3336 and LEOS 290 equations of state for copper and find good agreement within experimental errors. We, thus, demonstrate that single-shot temperature measurements of dynamically compressed materials can be made via thermal diffuse scattering of XFEL radiation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Experimental Investigation of FCCI Using Diffusion Couple Test Between UZr Fuel with Sb Additive and Cladding

Alloying additions are introduced into U-Zr fuel in order to bind lanthanides (e.g., cerium) and prevent their migration to the fuel-cladding interface. Antimony (Sb) is being investigated as a candidate additive. The present study focuses on the diffusion couple behavior of U-10Zr (wt%) alloy with Sb against cladding (iron or HT9) at 640°C. The diffusion cross sections were analyzed using a scanning electron microscope and X-ray diffraction. Zr-rind was found at the interface of the fuel alloy, Sb was found to be bound in Sb-Zr precipitates or Sb-Ce precipitates, and no reaction was found between Sb precipitates and the cladding materials.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Diffusion Limit–Preserving Lumped DFEMs on AMR Meshes

Here, we present sweep-compatible, novel upwinding recipes for the bilinear discontinuous (BLD) finite element method (FEM) that allows lumped BLD to be used on adaptive mesh refinement (AMR) meshes for thick transport applications without adding additional degrees of freedom at hanging nodes that exist on refinement boundaries. We analyze the properties of the upwinding and lumping that are needed for BLD to get the thick diffusion limit on such meshes, present results demonstrating locking with the wrong recipe, and present results showing error convergence and robustness properties for two diffusive problems on a variety of AMR meshes.

42 ENGINEERING↗
DOE OSTI2024

On how structures convey non-diffusive turbulence spreading

Abstract We report on comprehensive experimental studies of turbulence spreading in edge plasmas. These studies demonstrate the relation of turbulence spreading and entrainment to intermittent convective density fluctuation events or bursts (i.e. blobs and holes). The non-diffusive character of turbulence spreading is thus elucidated. The turbulence spreading velocity (or mean jet velocity) manifests a linear correlation with the skewness of density fluctuations, and increases with the auto-correlation time of density fluctuations. Turbulence spreading by positive density fluctuations is outward, while spreading by negative density fluctuations is inward. The degree of symmetry breaking between outward propagating blobs and inward propagating holes increases with the amplitude of density fluctuations. Thus, blob-hole asymmetry emerges as crucial to turbulence spreading. These results highlight the important role of intermittent convective events in conveying the spreading of turbulence, and constitute a fundamental challenge to existing diffusive models of spreading.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Technological diffusion trends suggest a more equitable future for rooftop solar in the United States

Abstract Equity has become central in the academic and regulatory discourse shaping the future of residential-scale clean energy technologies in the United States, particularly rooftop solar. Here, we develop a holistic perspective on these issues by analyzing rooftop solar adoption trends using two alternative forecasting methods: an inside-view forecast based on historical solar adoption data, and an outside-view forecast based on adoption data for other emerging consumer technologies. We show how rooftop solar, like other emerging consumer technologies, has become more equitably adopted over time. We show that solar diffusion patterns are largely consistent with those of other technologies. Both forecasting methods suggest that clean energy technologies should be expected to become more equitably adopted over time. Policy could accelerate this process by supporting low-income adoption without unduly curbing overall diffusion.

14 SOLAR ENERGY↗
DOE OSTI2025

Resolving turbulent magnetohydrodynamics: a hybrid operator-diffusion framework

We present a hybrid machine learning framework that combines physics-informed neural operators (PINOs) with score-based generative diffusion models to simulate the full spatio-temporal evolution of two-dimensional, incompressible, resistive magnetohydrodynamic turbulence across a broad range of Reynolds numbers (Re). The framework leverages the equation-constrained generalization capabilities of PINOs to predict coherent, low-frequency dynamics, while a conditional diffusion model stochastically corrects high-frequency residuals, enabling accurate modeling of fully developed turbulence. Trained on a comprehensive ensemble of high-fidelity simulations with Re ϵ {100, 250, 500, 750, 1000, 3000, 10000}, the approach achieves state-of-the-art accuracy in regimes previously inaccessible to deterministic surrogates. At Re = 1000 and 3000, the model faithfully reconstructs the full spectral energy distributions of both velocity and magnetic fields late into the simulation, capturing non-Gaussian statistics, intermittent structures, and cross-field correlations with high fidelity. At extreme turbulence levels (Re = 10 000), it remains the first surrogate capable of recovering the high-wavenumber evolution of the magnetic field, preserving large-scale morphology and enabling statistically meaningful predictions.

Diffusion-Integrated Neural Operators↗