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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

Effect of Sulfonation Level on the Percolated Morphology and Proton Conductivity of Hydrated Fluorine-Free Copolymers: Experiments and Simulations

Using all-atom molecular dynamics simulations and a variety of experimental methods, we previously reported on a linear polyethylene with pendant phenyl sulfonated groups precisely on every fifth carbon along the backbone. With increasing relative humidity this fluorine-free polymer self-assembled to form nanoscale water channels and exhibited exceptional proton conductivity. Expanding upon those findings, here we explore partially sulfonated random copolymers, referred to as p 5PhSH-Y. Using either acetyl sulfate or sulfuric acid, a wide range of sulfonation levels were prepared ( Y = 34−98%) corresponding to ion-exchange capacities (IEC) of 2.0−4.4 mmol/g. Combining experimental techniques and all-atom molecular dynamics simulations, we study the effect of Y on water uptake, nanoscale morphology, and the proton/water transport properties of p5PhSH- Y . The proton conductivity of p 5PhSH- Y increases with relative humidity and with Y and achieves values in excess of 0.1 S/cm. These high conductivities are attributed to high IEC and welldeveloped nanoscale percolated hydrophilic domains made possible by the flexible backbone. We quantitatively describe the nature of the water channels using the characteristic distance, channel width distribution, the area per sulfonate group at the hydrophilic/ hydrophobic interface, and the fractal dimension. Notably, the channel widths and the areas per sulfonate group are nominally independent of the level of sulfonation, while depending significantly on the level of hydration. The fractal dimension of the water channels correlates strongly with the water diffusion coefficients calculated from the molecular dynamics (MD) simulations. These findings demonstrate that the p 5PhSH- Y hydrocarbon copolymers can be modified to tune properties, particularly proton conductivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Thermal Experiments for Fractured Rock Characterization: Theoretical Analysis and Inverse Modeling

Abstract Field‐scale properties of fractured rocks play a crucial role in many subsurface applications, yet methodologies for identification of the statistical parameters of a discrete fracture network (DFN) are scarce. We present an inversion technique to infer two such parameters, fracture density and fractal dimension, from cross‐borehole thermal experiments data. It is based on a particle‐based heat‐transfer model, whose evaluation is accelerated with a deep neural network (DNN) surrogate that is integrated into a grid search. The DNN is trained on a small number of the heat‐transfer model runs and predicts the cumulative density function of the thermal field. The latter is used to compute fine posterior distributions of the (to be estimated) parameters. Our synthetic experiments reveal that fracture density is well constrained by data, while fractal dimension is harder to determine. Adding nonuniform prior information related to the DFN connectivity improves the inference of this parameter.

Zhou, Zitong↗

DOE OSTI2022

Black carbon aerosol number and mass concentration measurements by picosecond short-range elastic backscatter lidar

Abstract Black carbon aerosol emissions are recognized as contributors to global warming and air pollution. There remains, however, a lack of techniques to remotely measure black carbon aerosol particles with high range and time resolution. This article presents a direct and contact-free remote technique to estimate the black carbon aerosol number and mass concentration at a few meters from the emission source. This is done using the Colibri instrument based on a novel technique, referred to here as Picosecond Short-Range Elastic Backscatter Lidar (PSR-EBL). To address the complexity of retrieving lidar products at short measurement ranges, we apply a forward inversion method featuring radiometric lidar calibration. Our method is based on an extension of a well-established light-scattering model, the Rayleigh–Debye–Gans for Fractal-Aggregates (RDG-FA) theory, which computes an analytical expression of lidar parameters. These parameters are the backscattering cross-sections and the lidar ratio for black carbon fractal aggregates. Using a small-scale Jet A-1 kerosene pool fire, we demonstrate the ability of the technique to quantify the aerosol number and mass concentration with centimetre range-resolution and millisecond time-resolution.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2020

Shockwave dissipation by interface-dominated porous structures

The advent of additive manufacturing (AM) has enabled topological control of structures at the micrometer scale, transforming the properties of polymers for a variety of applications. Examples include tailored mechanical responses, acoustic properties, and thermal properties. Porous polymer materials are a class of materials used for shock and blast mitigation, yet they frequently possess a lack of structural order and are largely developed and evaluated via trial-and-error. Here, we demonstrate control of shockwave dissipation through interface-dominated structures prepared by AM using 2-photon polymerization. A fractal structure with voids, or free surfaces, arranged less than 100 μm apart, allows for rarefaction interactions on the timescale of the shockwave loading. Simulations and dynamic x-ray phase contrast imaging experiments show that fractal structures with interfaces assembled within a “critical” volume reduce shockwave stress and wave velocity by over an order of magnitude within the first unit cell.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Gaps labeling theorem for the bubble-diamond self-similar graphs

Abstract Motivated by the appearance of fractals in several areas of physics, especially in solid state physics and the physics of aperiodic order, and in other sciences, including the quantum information theory, we present a detailed spectral analysis for a new class of fractal-type diamond graphs, referred to as bubble-diamond graphs, and provide a gap-labeling theorem in the sense of Bellissard for the corresponding probabilistic graph Laplacians using the technique of spectral decimation. Labeling the gaps in the Cantor set by the normalized eigenvalue counting function, also known as the integrated density of states, we describe the gap labels as orbits of a second dynamical system that reflects the branching parameter of the bubble construction and the decimation structure. The spectrum of the natural Laplacian on limit graphs is shown generically to be pure point supported on a Cantor set, though one particular graph has a mixture of pure point and singularly continuous components.

Physics↗

DOE OSTI2025

Magnetic devil's staircaselike behavior in quasiperiodic qubit lattices

The devil's staircase (DS) phenomenon is a fractal response of magnetization to external fields, traditionally observed in periodic ferromagnetic systems, where the commensurability between spin arrangements, lattice parameters, and external magnetic fields governs abrupt changes in magnetization. Its occurrence in aperiodic, fractal-type systems has remained largely unexplored, despite their natural compatibility with such phenomena. Using a quantum annealing device, we uncover a wealth of abrupt magnetic transitions between spin manifolds driven by increasing external magnetic fields within a simple yet effective Ising-model framework. In contrast to periodic systems, where DS arises from long-range competing interactions, our findings reveal that short-range, purely antiferromagnetic couplings in aperiodic geometries produce equally rich ground-state magnetization patterns. Here, we demonstrate that while magnetic textures are determined by the lattice size, their formation remains remarkably robust and independent of scale, with commensurability emerging locally. Our results challenge the prevailing view that DS behavior is limited to periodic systems and establish quasiperiodic geometries as a natural host for this phenomenon.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Fractionalization of subsystem symmetries in two dimensions

The fractionalization of global symmetry charges is a striking hallmark of topological quantum order. Here, we discuss the fractionalization of subsystem symmetries in two-dimensional topological phases. In line with previous no-go arguments, we show that subsystem symmetry fractionalization is not possible in many cases due to the additional rigid geometric structure of the symmetries. However, we identify a mechanism that allows fractionalization, involving global relations between macroscopically many symmetry generators. We find that anyons can fractionalize such relations, meaning that the total charge carried under all generators involved in the global relation is nontrivial, despite the fact that these generators multiply to the identity. We first discuss the general algebraic framework needed to characterize this type of fractionalization, and then explore this framework using a number of exactly solvable models with Z 2 topological order, including models having line and fractal symmetries. These models all showcase another necessary property of subsystem symmetry fractionalization: Fractionalized anyons must have restricted mobility when the symmetry is enforced, such that they are confined to a single line or point in the case of line and fractal symmetries, respectively. Looking forward, we expect that our identification of the importance of global relations in fractionalization will hold significance for the classification of phases with subsystem symmetries in all dimensions.

2-dimensional systems↗

DOE OSTI2024

Particle-Hole Asymmetric Ferromagnetism and Spin Textures in the Triangular Hubbard-Hofstadter Model

In a lattice model subject to a perpendicular magnetic field, when the lattice constant is comparable to the magnetic length, one enters the “Hofstadter regime,” where continuum Landau levels become fractal magnetic Bloch bands. Strong mixing between bands alters the nature of the resulting quantum phases compared to the continuum limit; lattice potential, magnetic field, and Coulomb interaction must be treated on equal footing. Using determinant quantum Monte Carlo and density matrix renormalization group techniques, we study this regime numerically in the context of the Hubbard-Hofstadter model on a triangular lattice. In the field-filling phase diagram, we find a broad wedge-shaped region of ferromagnetic ground states for filling factor ν ≤ 1 , bounded below by filling factor ν = 1 and bounded above by half filling the lowest Hofstadter subband. We observe signatures of SU(2) quantum Hall ferromagnetism at filling factors ν = 1 and ν = 3 . The phases near ν = 1 are particle-hole asymmetric, and we observe a rapid decrease in ground-state spin polarization consistent with the formation of skyrmions only on the electron doped side. At large fields, above the ferromagnetic wedge, we observe a low-spin metallic region with spin correlations peaked at small momenta. We argue that the phenomenology of this region likely results from exchange interaction mixing fractal Hofstadter subbands. The phase diagram derived beyond the continuum limit points to a rich landscape to explore interaction effects in magnetic Bloch bands. Published by the American Physical Society 2024

Ding, Jixun K.↗

DOE OSTI2020

Review—Development of Highly Active and Durable Hybrid Compressive Platinum Lattice Catalysts for Polymer Electrolyte Membrane Fuel Cells: Mathematical Modeling and Experimental Work

This review provides a comprehensive overview on the development of highly active and durable platinum catalysts with ultra-low Pt loadings for polymer electrolyte membrane fuel cells (PEMFCs) through a combined mathematical modeling and experimental work. First, simulation techniques were applied to evaluate the validity of the Tafel approximation for the calculation of the mass activity (MA) and specific activity (SA). A one-dimensional agglomeration model was developed and solved to understand the effects of exchange current density, porosity, agglomerate size, Nafion ® film thickness, and Pt loading on the MA and SA. High porosity (> 60%) and agglomerations at high Pt loadings cause the loss of the Tafel approximation and consequently the decrease in MA and SA. A new structure parameter was introduced to estimate the real porous structure using the fractal theory. The volumetric catalyst density was corrected by the fractal dimension (measured by Hg porosimetry), which gave a good agreement with the experimental values. The loading-dependent Tafel equation was then derived, which contains both the utilization and the non-linear scaling factor. Second, activated carbon composite support (ACCS) with optimized surface area, porosity, pore size, and pore size distribution was developed. The hydrophilic/hydrophobic ratio, structural properties (amorphous/crystalline ratio), and the number of active sites were optimized through metal-catalyzed pyrolysis. Stability of ACCS and Pt/ACCS were evaluated using an accelerated stress test (AST). The results indicated that Pt/ACCS showed no significant loss of MA and power density after 5,000 cycles at 1.0–1.5 V, while the commercial Pt/C catalysts showed drastic losses of MA and power density. Finally, monolayers of compressed Pt (core–shell-type Pt 3 Co 1 ) catalysts were structured by diffusing Co atoms (previously embedded in ACCS) into Pt. Compressive Pt lattice (Pt * ) catalysts were synthesized through an annealing procedure developed at the University of South Carolina (USC). The Pt * /ACCS catalyst showed high initial power density (rated) of 0.174 g Pt kW −1 and high stability (24 mV loss) at 0.8 A cm −2 after 30,000 cycles (0.6–1.0 V). The outstanding performance of Pt * /ACCS is due to the synergistic effect of ACCS and compressive Pt * lattice.

25 ENERGY STORAGE↗

DOE OSTI2024

Phase and Morphology of Water-ice Grains Formed in a Cryogenic Laboratory Plasma

Abstract Grains of ice are formed spontaneously when water vapor is injected into a weakly ionized laboratory plasma in which the background gas has been cooled to cryogenic temperatures comparable to those of deep space. These ice grains are levitated indefinitely within the plasma so that their time evolution can be observed under free-floating conditions. Using microscope imaging, ice grains are shown to have a spindle-like fractal structure and grow over time. Both crystalline and amorphous phases of ice are observed using Fourier transform infrared spectroscopy. A mix of crystalline and amorphous grains coexists under certain thermal conditions, and a linear mixing model is used on the ice absorption band surrounding 3.2 μ m to examine the ice phase composition and its temporal stability. The extinction spectrum is also affected by inelastic scattering as grains grow, and characteristic grain radii are obtained from Mie scattering theory and compared to size measurements from direct imaging. Observations are used to compare possible ice nucleation mechanisms, and it is concluded that nucleation is likely catalyzed by ions, as ice does not nucleate in the absence of plasma and impurities are not detected. Ice grain properties and infrared extinction spectra show similarity to observations of some astrophysical ices observed in protoplanetary disks, implying that the fractal morphology of the ice and observed processes of homogeneous ice nucleation could occur as well in such astrophysical environments with weakly ionized conditions.

Astronomy & Astrophysics↗

DOE OSTI2021

From Anderson localization on random regular graphs to many-body localization

Highlights: • Anderson transition from ergodicity to localization on random regular graphs (RRG). • Analytical, pool method, and exact-diagonalization study of correlations on RRG. • Many-body localization (MBL) to ergodicity transition: quantum dots and spin chains. • Dynamical eigenstate correlation functions in RRG and MBL problems. • Anderson localization on RRG as a toy model for MBL. The article reviews the physics of Anderson localization on random regular graphs (RRG) and its connections to many-body localization (MBL) in disordered interacting systems. Properties of eigenstate and energy level correlations in delocalized and localized phases, as well at criticality, are discussed. In the many-body part, models with short-range and power-law interactions are considered, as well as the quantum-dot model representing the limit of the “most long-range” interaction. Central themes – which are common to the RRG and MBL problems – include ergodicity of the delocalized phase, localized character of the critical point, strong finite-size effects, and fractal scaling of eigenstate correlations in the localized phase.

36 MATERIALS SCIENCE↗

DOE OSTI2025

In situ probing of structure and deagglomeration of SnO 2 colloids via small-angle X-ray scattering

Transforming dry nanopowders into stable colloidal dispersions remains challenging due to the cohesive forces between the nanoparticles (NPs) which promote agglomeration. Effective dispersion and deagglomeration of these agglomerates is a critical process in the formulation and preparation of nanoparticle-based functional materials via the colloidal route. Understanding the deagglomeration dynamics provides information to improve microstructural quality in various applications by enabling engineering of agglomerate size, structure and morphology. However, the deagglomeration process dynamics with respect to the evolution of the fractal agglomerate structures, particularly for very small NPs, is still poorly understood and requires further investigation. This study employs in situ small-angle X-ray scattering (SAXS) to investigate the sonication-induced deagglomeration of SnO 2 NPs. Electrostatically stabilized SnO 2 colloids with varying primary particle size (6–21 nm) are investigated in a specifically designed in situ cell using synchrotron-based SAXS to study the influence of sonication time and intensity on the nanoscaled agglomerates. Complete structural analysis via SAXS reveals a direct correlation between changes in agglomerate size and structure, size-dependent deagglomeration behavior and a dependence on the overall energy introduced during sonication into the dispersion regardless of the actual power as well as ultrasonic process parameters in case of SnO 2 NPs. The results suggest that control of the dispersion process during ultrasonic deagglomeration results in tailoring agglomerates with respect to size and structure.

Deagglomeration↗

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

Colloidal Clusters and Networks Formed by Oppositely Charged Nanoparticles with Varying Stiffnesses

Colloidal clusters and gels are ubiquitous in science and technology. Particle softness has a strong effect on interparticle interactions; however, our understanding of the role of this factor in the formation of colloidal clusters and gels is only beginning to evolve. Here, we report the results of experimental and simulation studies of the impact of particle softness on the assembly of clusters and networks from mixtures of oppositely charged polymer nanoparticles (NPs). Experiments were performed below or above the polymer glass transition temperature, at which the interaction potential and adhesive forces between the NPs were significantly varied. Hard NPs assembled in fractal clusters that subsequently organized in a kinetically arrested colloidal gel, while soft NPs formed dense precipitating aggregates, due to the NP deformation and the decreased interparticle distance. Importantly, interactions of hard and soft NPs led to the formation of discrete precipitating NP aggregates at a relatively low volume fraction of soft NPs. A phenomenological model was developed for interactions of oppositely charged NPs with varying softnesses. Furthermore, the experimental results were in agreement with molecular dynamics simulations based on the model. This work provides insight on interparticle interactions before, during, and after the formation of hard–hard, hard–soft, and soft–soft contacts and has impact for numerous applications of reversible colloidal gels, including their use as inks for additive manufacturing.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2021

Hamiltonian systems, Toda lattices, solitons, Lax pairs on weighted Z -graded graphs

In this study, we consider discrete one-dimensional nonlinear equations and present the procedure of lifting them to Z -graded graphs. We identify conditions that allow one to lift one-dimensional solutions to solutions on graphs. In particular, we prove the existence of solitons for static potentials on graded fractal graphs. We also show that even for a simple example of a topologically interesting graph, the corresponding non-trivial Lax pairs and associated unitary transformations do not lift to a Lax pair on the Z -graded graph.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Complex field reversal dynamics in nanomagnetic systems

Nanomagnetic materials, built from thin, patterned films of ferromagnetic materials, began as analogues to frustrated magnetism. Their low energy of operation and emergent properties make them strong candidates for physics-based devices. A recent model of how nanomagnetic domains flip, the Glauber mean-field model, is used here to understand how systems of nanomagnets evolve when opposed by external field. This reversal can be expressed in an analytical form in the case of one-dimensional chains and trees at zero temperature, where the cascade of spin flips gives rise to harmonic power spectra. Finally, the same cascades in two and three dimensions form fractal field reversal clusters whose shape depends on the strength of the field and the tuning of interactions between nanomagnets.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Galvanic Transformation Dynamics in Heterostructured Nanoparticles

Corrosion is a significant problem for the stability of structural metals and potentially for functional nanomaterials in operating environments. When two metals with different electrochemical potentials form a junction, galvanic corrosion occurs, resulting in the sacrificial dissolution of the metal with a higher oxidation potential (lower electrode potential). In this report it is shown that bimetallic hetero-nanostructures composed of phase-segregated metals undergo galvanic corrosion in aqueous environments. Such selective etching of the sacrificial metal in heterojunction particles leads to the formation of unusual and kinetically stabilized half-spheroid particles. By using a fluid cell and in situ scanning transmission electron microscopy, a two-stage corrosion process can be observed where the Cu experiences a fractal breakdown before the Ag corrodes due to the lack of a protective oxide layer. However, when treated with a mild Ar plasma, the stability of these structures against corrosion is enhanced due to the conversion of the amorphous native oxide to a denser, thin layer of CuO on the Cu surface. Taken together, this work highlights the importance of considering the effects of galvanic corrosion on the stability of multicomponent nanoparticles, and it shows how mass transport in a nanoscale system is influenced by redox processes.

36 MATERIALS SCIENCE↗