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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A Cross‐Linked Flexible Metaferroelectrolyte Regulated by 2D/2D Perovskite Heterostructures for High‐Performance Compact Solid‐State Sodium Batteries

Abstract To address the issues of limited ionic conductivity and poor interface stability at room and low temperatures in solid‐state electrolytes, a robust intrinsic ferroelectrolyte or nanoferroelectrolyte strategy for engineering solid‐state flexible ferroelectric composite electrolytes utilizing strongly coupled intrinsic ion conducting 2D/2D sodium‐rich anti‐perovskite (NaRAP)/ferroelectric perovskite heterostructures is introduced. Herein, highly scalable PVDF‐based metaferroelectrolytes with Na 2.99 Ba 0.005 OCl/Ca 2 Na 2 Nb 5 O 16 − (CNNO − ) nanosheets into a ferroelectric poly(vinylidene fluoride‐co‐hexafluoropropylene) (PVDF‐HFP) matrix, through an in situ cross‐linking and spontaneous bridging method, for compact solid‐state sodium batteries (SSBs), are reported. Benefiting from unique well‐dispersed 3D ferroelectric coupled network and the Na 2.99 Ba 0.005 OCl/CNNO − ‐induced PVDF‐HFP ferroelectric β phase, the Na + flux is regulated, thereby inhibiting Na dendrite growth at the interface. Notably, the optimized PH‐5% NC metaferroelectrolyte exhibits rapid ion transport (1.11 × 10 −4 S cm −1 at 25 °C), a wide electrochemical window (> 4.8V), superior conformal mechanical compatibility, improved flexibility, good elasticity and flame retardancy. The solid‐state Na 3 V 2 (PO 4 ) 3 /PH‐5% NC/Na batteries present a stable cycling performance (remaining 56.4 mAh g −1 after 500 cycles at 1 C) even at 0 °C, potential for cost‐effective, safe, stable and compact SSB energy storage over 600 Wh L −1 , vastly surpassing 365 Wh L −1 of the current commercial sodium‐ion liquid‐electrolyte batteries.

Chemistry↗
DOE OSTI2026

A multiscale packed-bed reactor model for sustainable ethylene production via chemical looping oxidative coupling of methane

The rising global warming concerns and shale gas discovery have prompted research in the direction of greenhouse gas (GHG), such as methane, reduction and conversion. Oxidative coupling of methane (OCM) offers a pathway to low carbon-intense valorization of methane while producing ethylene, a chemical regarded as central to the petrochemical industry. Even after decades of OCM discovery, researchers keep understanding the process and underlying chemical reactions in a pursuit to achieve industrial viability for OCM. Here, in general, OCM suffers from low C 2 selectivity, yield and reactor temperature runaways due to highly exothermic nature of its reactions. Computational Fluid Dynamics (CFD) tools help analyze spatial gradients within the reactor to deeply understand the diffusion of species, mass and heat transfer phenomena. Furthermore, challenges associated with scaling up such as hot spot formation and parametric sensitivity can be addressed without having to expend on costly experiments. The current paper presents a multiscale packed-bed reactor CFD model coupled with a chemical kinetic model for the chemical looping OCM. The CFD model includes two scales i.e., macroscale for catalyst bed and microscale for individual pellets. Moreover, a chemical kinetic model based on 10 gas-phase reactions is integrated with the CFD model. An additional surface reaction for the formation of gas-phase oxygen from catalyst surface is added to account for the absence of feed oxygen. The model is calibrated against experimental results. The calibrated model captures trends in CH 4 conversion, C 2 selectivity and C 2 yield within a ± 4.35 % range across a temperature range of 700-900 °C. Moreover, model fidelity is evaluated by varying key computational parameters such as mesh resolution and time step size. The model is also verified by varying the inlet methane concentration and the gas hourly space velocity (GHSV) and comparing the results with literature. A sensitivity analysis and scale-up of the current model is undergoing.

Chemical looping↗
DOE OSTI2026

CO2 Handling & Electrolyzer Efficiency Scaling Evaluator

CHEESE is an interactive dashboard tool for estimating the performance and material requirements of carbon dioxide electrolysis systems. It helps users evaluate how electrode area, current density, product selectivity, gas flow, cell voltage, and the number of cells in a stack affect system operation. The dashboard provides simple and advanced modes so it can be used for both quick estimates and more detailed engineering analysis. Users can estimate product output, carbon dioxide use, electrical power, electrode area, gas and liquid flow rates, energy efficiency, material cost per test, and the effect of scaling from a single cell to a multi cell stack. It also includes tools for examining carbon balance, equipment durability, component replacement, and changes in performance over time. This is intended to help both academia and industry researchers who are either getting into CO2 electrolysis on lab-scale or are trying to establish a larger footprint. CHEESE presents results through tables, charts, and simplified cell and stack diagrams. It is intended to support research planning, experimental design, comparison of operating conditions, and early stage scale up studies.

Prajapati, Aditya [Lawrence Livermore National Lab↗
DOE OSTI2026

Frontier Job-Centric Telemetry Dataset

Comprehensive analysis of high-performance computing (HPC) systems requires linking workload execution to system behavior. This kind of analysis is vital for diagnosing performance issues, managing capacity, detecting anomalous workloads, and understanding how applications interact with system hardware. This job-centric telemetry dataset unifies scheduler job records with node-level measurements, enabling direct association between workloads and their corresponding power, thermal, and performance characteristics. It contains sanitized, scheduler related metadata for 152,400 individual jobs that ran on the Frontier supercomputer and ended on selected days throughout 2024 and 2025, a subpopulation of ~6.8% of the total number of allocated jobs with non-zero run time on the system over that same period. Each is linked with files that contain telemetry time series records of the power utilization and temperature behavior of its allocated nodes and their processors during the run time of the job. Where available, a portion of the job files also contain network performance time series. Jobs are sampled from select days that reflect normal levels of user activity and possess job size distributions with large numbers of leadership class jobs (>20% of Frontier nodes). Jobs in this dataset attempt to best represent successful user workflows.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

Power Lane County Electric Grid Handbook

In 2024, Lane Couty was selected to participate in the U.S. Department of Energy’s Energy to Community program. Through the program, National Laboratory researchers from Lawrence Berkeley National Laboratory, Pacific Northwest National Laboratory, and the National Laboratory of the Rockies provide three years of technical assistance to Lane County and their project partners: the Center for Rural Livelihoods, Springfield Utility Board, and Emerald People’s Utility District. The project, named Power Lane County, aims to improve local electric system affordability, reliability and resilience in the face of natural hazards and potentially rising loads. The Power Lane County Electric Grid Handbook establishes a foundational understanding of the energy landscape and electric grid in Lane County to inform community engagement, education, and analysis in future project phases. This document synthesizes public data and utility and stakeholder engagement, including utility interviews to give the reader a comprehensive view of the challenges facing Lane County's electric system and the opportunities to address them

Electricity↗
DOE OSTI2026

Future Projection of Tropical Upper-Tropospheric Troughs and Implications for Tropical Cyclone Activity

Summertime tropical upper-tropospheric troughs (TUTTs) provide a unified framework to better understand how extratropical and tropical forcings jointly modulate basin-scale tropical cyclone (TC) activity. In this study, we examine future changes in TUTTs and their implications for TC activity. Multimodel ensemble-mean projections from 45 Coupled Model Intercomparison Project phase 6 (CMIP6) models suggest a contraction of the Pacific TUTT and an expansion of the Atlantic TUTT as the climate warms. Consistently, future changes in environment-based TC indices indicate that the large-scale conditions will become more favorable for TC genesis and intensification over the central North Pacific but less favorable over the tropical North Atlantic and Gulf of Mexico. Utilizing a TC-permitting large-ensemble dataset [i.e., the Database for Policy Decision-Making for Future Climate Change (d4PDF)] that adequately captures the observed interannual TUTT–TC relationships, we further confirm the impacts of projected TUTT changes on the TC activity in a warmer climate. In contrast, the TUTT–TC relationship is poorly represented in most CMIP6 High-Resolution Model Intercomparison Project (HighResMIP) models; such deficiencies call for caution when assessing future TC risk based on explicitly tracked TCs in these models. Additionally, CMIP6 projections show large intermodel spread in TUTT changes, implying uncertainty in projected TC activity, especially over the central-to-eastern Pacific and the North Atlantic. This intermodel spread is associated with interhemispheric sea surface temperature warming asymmetry, which leads to a meridional shift of the intertropical convergence zone (ITCZ) and the simultaneous weakening or strengthening of TUTTs in the North Pacific and North Atlantic. The potential contributions of anthropogenic aerosol forcing and oceanic circulation to this interhemispheric warming asymmetry are briefly examined.

Climate Change↗
DOE OSTI2026

Thermal property characterization of phase change materials in building applications: A systematic review of fundamentals, recent progress, and future directions

Phase change materials (PCMs) can reduce building peak loads and enable demand-responsive thermal energy storage (TES), but their deployment depends on reliable measurement and interpretation of thermal properties across laboratory, intermediate, and application scales. Here, this review systematically examines characterization methods, testing protocols, and recent advances for neat PCMs and PCM composites, emphasizing thermal conductivity, enthalpy-related properties (phase change temperature, latent heat, specific heat), and cycling stability. For thermal conductivity, we compare steady-state and transient techniques and note limitations when phase transition and contact resistance affect measurements. For enthalpy–temperature characterization, we discuss differential scanning calorimetry together with intermediate- and bulk-scale methods, including T-history, heat flow meter testing, and three-layer calorimetry (3LC), to generate application-relevant enthalpy–temperature profiles. Cycling stability is organized into four experimental families: thermoelectric–air, fully thermoelectric, water-bath, and in situ chamber approaches, with attention to separating reversible supercooling from true degradation such as phase segregation. We highlight emerging noncontact diagnostics, including infrared thermography and embedded sensing, for spatially resolved validation and multiscale interpretation. Finally, we review the growing use of AI and machine learning for property prediction, inverse characterization from experimental signals, and real-time state estimation in building-integrated TES. Key needs include harmonized protocols, interlaboratory benchmarking, uncertainty reporting, and metadata-rich datasets to accelerate reproducible PCM qualification for grid-flexible buildings.

AI↗
DOE OSTI2024

Heterogeneous Solid Electrolyte Interphase Interactions Dictate Interface Instability in Sodium Metal Electrodes

Sodium (Na) metal batteries have attracted recent attention due to their low cost and high abundance of Na. However, the advancement of Na metal batteries is impeded due to key challenges such as dendrite growth, solid electrolyte interphase (SEI) fracture, and low Coulombic efficiency. This study examines the coupled electro‐chemo‐mechanical interactions governing the electrodeposition stability and morphological evolution at the Na/electrolyte interface. The SEI heterogeneities influence transport and reaction kinetics leading to the formation of current and stress hotspots during Na plating. Further, it is demonstrated that the heterogeneity‐induced Na metal evolution and its influence on the stress distribution critically affect the mechanical overpotential, contributing to a faster SEI failure. The analysis reveals three distinct failure mechanisms—mechanical, transport, and kinetic—that govern the onset of instabilities at the interface. Finally, a comprehensive comparative study of SEI failure in Na and lithium (Li) metal anodes illustrates that the electrochemical and mechanical characteristics of the SEI are crucial in tailoring the anode morphology and interface stability. This work delineates mechanistic stability regimes cognizant of the SEI attributes and underlying failure modes and offers important guidelines for the design of artificial SEI layers for stable Na metal electrodes.

25 ENERGY STORAGE↗
DOE OSTI2026

Used Nuclear Fuel Management Using the Next Generation System Analysis Model

The U.S. Department of Energy (DOE) is leading the National effort to manage the back end of the nuclear fuel cycle, encompassing the safe transportation, storage/staging, and/or eventual disposal of used nuclear fuel (UNF) and high-level radioactive waste. The Next Generation System Analysis Model (NGSAM) is DOE’s discrete-event, agent-based simulation tool designed to model the full life cycle of UNF from reactor discharge to final disposal. NGSAM supports the DOE Office of Spent Fuel and High-Level Waste Disposition by enabling a detailed, scenario-based analysis of logistics, infrastructure, and shipping strategies. NGSAM replaces legacy models with a modern, flexible platform built on Repast Simphony and enhanced by the Process Analysis Tool. NGSAM simulates the movement and interaction of individual fuel assemblies with system components such as canisters, casks, railcars, and facilities. The model integrates with the Java Transportation Operations Model to plan and execute transportation scenarios, supporting both constrained and unconstrained resource allocation. Key features include customizable allocation and acceptance algorithms, detailed facility-level operations, and a Quick Edit tool for rapid scenario adjustments. NGSAM supports multimodal transportation modeling (e.g. rail, road, barge) and provides comprehensive cost, schedule, and infrastructure data. NGSAM utilizes data from sources such as DOE’s STANDARDS UNF database and DOE’s Stakeholder Tool for Assessing Radioactive Transportation, while also allowing user-defined inputs for scenario customization. NGSAM enables stakeholders to evaluate complex UNF management strategies, assess system performance under varying assumptions, and inform decision making for future infrastructure investments. Its modular architecture and integration with other Integrated Waste Management System tools make it a critical asset for planning the safe and efficient disposition of the Nation’s growing UNF inventory.

Craig, Brian [Argonne National Laboratory (ANL)]↗
DOE OSTI2024

Mitigating Sodium Ordering for Enhanced Solid Solution Behavior in Layered NaNiO 2 Cathodes

The O-type layered nickel oxides suffer from undesired cooperative Jahn–Teller distortion stemming from Ni 3+ ions and undergo multiple biphasic structural transformations during the insertion/extraction of large Na + ions, posing a significant challenge to stabilize the structural integrity. We present here a systematic investigation of the impact of substituting 5 % divalent (Mg 2+ ) or trivalent (Al 3+ or Co 3+ ) ions for Ni 3+ to alleviate Na + ion ordering and perturb the Jahn–Teller effect to enhance structural stability. Here, we gauge a fundamental understanding of the Mg−O and Na−O or Mg−O−Na bonding interactions, noting that the ionicity of the Mg−O bond deshields the electronic cloud of oxygen from Na + ions. Furthermore, calculations of the Van Vleck distortion modes reveal a relaxation of NiO 6 octahedra from Jahn–Teller distortion and a reduced electron density at the interlayer with Mg 2+ substitution. Long-range (operando X-ray diffraction) and short-range (magic angle spinning nuclear magnetic resonance) structural analyses provide insights into reduced ordering, allowing a stable continuous solid solution. Overall, Mg-substitution results in a high-capacity retention of ~96 % even after 100 cycles, showcasing the potential of this strategy for overcoming the structural instabilities and enhancing the performance of sodium-ion batteries.

25 ENERGY STORAGE↗
DOE OSTI2026

Scaling Demand Flexibility: Building on 30 Years of Energy Efficiency Success

With electricity consumption across the United States (US) and Canada anticipated to grow, energy efficiency program administrators have a key role to play in helping to ensure energy affordability and reliability in support of the broader economic systems utilities and grid support. Connected, demand side load balancing solutions, such as load shifting heating, ventilation and air conditioning (HVAC) systems and managed charging for electric vehicles (EVs), can dynamically manage energy, allowing for more volumetric electricity consumption without incurring the expense of upgraded transmission and distribution capabilities. When combined, or aggregated, many small loads can be managed to have meaningful impact on energy demand on the grid. Utilities and their partners have an opportunity to leverage decades of experience and the infrastructure needed to assess, design, implement, and measure programs to scale up the adoption of equipment with built-in load flexibility capabilities. Current efforts among a wide variety of electricity system service providers, utilities, standards agencies, regulators, national labs and private industry stakeholders aim to identify common standards, metrics, and methodologies for valuing grid services offered by demand side equipment. By combining those efforts with decades of proven energy efficiency resources, utilities are poised to effectuate a scaling up of equipment with energy management capabilities installed in homes and businesses across the US and Canada. This paper will provide an overview of how utilities are approaching this era of load growth and new peak demands across the United States and Canada. It will highlight the specific strategies that program administrators are employing to advance market transformation for grid-enabled products and devices that have the greatest potential to reduce energy use and increase load flexibility.

Grant, Peter↗
DOE OSTI2022

Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum Computers

The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wave functions that are relevant in the behavior of the system under study. Hamiltonian symmetries are important instruments used to classify relevant many-particle wave functions and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions based on the addition theorem of angular momentum, and heuristic approximation of total spin eigenfunctions based on the variational optimization of a suitable cost function. The construction of these quantum circuits is illustrated in detail, and the preparation of total spin eigenfunctions is demonstrated on IBM quantum devices, focusing on three- and five-spin systems on graphs with triangle connectivity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Enhancing NO Reduction by CO Over NiO/CeO 2 Catalyst by Optimizing the Metal Oxide–Support Interaction

Noble metal catalysts are widely used in three-way catalysts (TWCs) due to their high efficiency, but their scarcity and high cost drive the need for effective, low-cost alternatives. Here, in this work, a series of NiO/CeO 2 catalysts were engineered by modulating the OH content and crystallite size of the CeO 2 support. This approach yielded Ni species ranging from isolated single atoms to small clusters and larger aggregates, with varied NiO/CeO 2 interaction strengths. Evaluation of their performance in NO reduction by CO, CO oxidation, and the water–gas shift reaction revealed that the NiO/CeO 2 -300 catalyst, featuring small CeO 2 crystallites and highly dispersed NiO clusters, delivered superior activity for NO reduction and CO oxidation. It was demonstrated that small NiO clusters, due to their efficient CO adsorption and activation, were more active than Ni single atoms. Furthermore, the presence of water was found to influence the catalyst stability, with NiO clusters less stable than single atoms likely due to the hydroxylation effect leading to the formation of Ni(OH) 2 . Oxygen storage capacity measurements revealed that performance was governed by a combination of CeO 2 crystallite size and the abundance of NiO/CeO 2 interfaces. These findings demonstrated that the catalytic performance of Ni/CeO 2 systems could be maximized by optimizing the Ni nanostructure and its interaction with CeO 2 support, positioning them as a promising, multifunctional nonprecious alternative for three-way catalysis application.

36 MATERIALS SCIENCE↗
DOE OSTI2023

2,5‐Dimercapto‐1,3,4‐Thiadiazole (DMCT)‐Based Polymers for Rechargeable Metal–Sulfur Batteries

Organosulfur materials are a sustainable alternative to the present-day layered oxide cathodes in lithium-based batteries. One such organosulfur material that was intensely explored from the 1990s to early 2010s is 2,5-dimercapto-1,3,4-thiadiazole (DMCT). However, research interest declined as the electrode reactions with DMCT were assumed to be too sluggish to be practical. Armed with the advances in metal–sulfur batteries, we revisit DMCT-based materials in the form of poly[tetrathio-2,5-(1,3,4-thiadiazole)], referred to as pDMCT-S. With an appropriate choice of electrode design and electrolyte, pDMCT-S cathode paired with a Li-metal anode shows a capacity of 715 mA h g −1 and a Coulombic efficiency of 97.7% at a C/10 rate, thus quelling the concerns of sluggish reactions. Surprisingly, pDMCT-S shows significantly improved long-term cyclability compared to a sulfur cathode. Investigations into the origin of the stability reveals that the discharge product Li-DMCT in its mesomeric form can strongly bind to polysulfides, preventing their dissolution into the electrolyte and shuttling. This unique mechanism solves a critical problem faced by sulfur cathodes. Encouragingly, this mechanism results in a stable performance of pDMCT-S with Na-metal cells as well. In conclusion, this study opens the potential for exploring other organic materials that have inherent polysulfide sequestering capabilities, enabling long-life metal–sulfur batteries.

2,5-dimercapto-1,3,4-thiadiazole↗
DOE OSTI2026

Time-Resolved Neutron Imaging for Hydrogen Uptake in Subsurface Lithologies

Geologic hydrogen production and underground storage are increasingly important for meeting rising energy demands while providing clean-combustion advantages. However, hydrogen’s high diffusivity and propensity for leakage through porous media necessitate direct evaluation of its transport behavior in subsurface materials. Whereas X-ray microcomputed tomography (μCT) studies often employ contrast agents or surrogate gases, this study leverages neutron transmission radiography/CT to observe hydrogen migration in situ. This work represents the first demonstration of real-time neutron radiography of hydrogen migration in reservoir and caprock lithologies. Cylindrical cores of Indiana limestone, Amherst Gray sandstone, and Tumey shale were subjected to constant-pressure hydrogen charging and scanned in real time using high-resolution neutron radiography. Results indicate immediate hydrogen infiltration in sandstone and limestone, with homogeneous distribution detected throughout their pore structure. In contrast, hydrogen remained largely absent from fine-grained shale under the same pressure, except in an apparently localized fracture zone, where neutron signatures confirmed the presence of hydrogen. Subsequent neutron CT of the sandstone sample, using image subtraction against an uncharged reference, corroborated hydrogen distribution patterns. Even under lowpressure, single-phase conditions, distinct neutron imaging signatures of hydrogen were achieved. These preliminary findings underscore the potential of neutron imaging for advancing subsurface hydrogen migration research.

08 HYDROGEN↗
DOE OSTI2026

Design Trade-Offs in Composite Fuel Cell Membranes: Effects of Reinforcement and Chemical Additives

Perfluorosulfonic acid (PFSA) membranes are critical components in proton exchange membrane fuel cells, where performance depends on balancing ionic conductivity, mechanical durability, and chemical stability. This study characterizes a composite membrane (NC700) featuring PFSA-impregnated expanded polytetrafluoroethylene (ePTFE) reinforcement and cerium-based radical scavengers, benchmarked against unreinforced NR211. Complementary techniques, including electron microscopy, X-ray scattering, infrared spectroscopy, thermogravimetric analysis, and dynamic mechanical analysis, identify the structural and compositional strategies employed in NC700. Water sorption isotherms reveal lower water uptake for NC700 across all conditions, attributed to reinforcement and cerium incorporation. Reinforcement reduces in-plane swelling from 11% to 2.1% at 90% RH, confirming strong swelling anisotropy, while maintaining mechanical properties at elevated temperatures. While the ionic conductivity of NC700 is approximately 10% lower than that of NR211, the reduced thickness yields a 40% decrease in calculated area-specific resistance, suggesting the composite architecture can favorably shift the conductivity-stability trade-off. The composite structure also reduces gas permeability, indicating potential for improved separator function alongside favorable transport properties. Systematic deconvolution of reinforcement and additive contributions shows that conductivity losses from cerium incorporation are largely offset by gains from the lower equivalent-weight polymer, providing quantitative relationships that may guide composite membrane design for fuel cells and other electrochemical applications.

25 ENERGY STORAGE↗
DOE OSTI2026

Thermally Stable Co@C3N4 Single-Atom Catalysts for CO Oxidation: Atomic-Level Insights into Structure and Activity

Single Co atoms supported on C3N4 (Co@C3N4) have demonstrated high activity and selectivity in photocatalysis. However, the investigation of structure–function relationships and reaction mechanisms under photocatalytic conditions is very challenging due to the complex conditions of light absorption, charge transfer, and catalysis. In this study, we employed thermal CO oxidation as a prototypical probe reaction to benchmark the intrinsic catalytic performance and track the active-site evolution of Co@C3N4. Single Co atoms were identified and shown to be the catalytically active sites for CO oxidation based on control experiments and isotope-labeling experiments. The Co sites remained atomically dispersed before, during, and after the reaction with temperatures up to 400 °C, as established by in situ X-ray absorption fine structure (XAFS) combined with density functional theory (DFT), FDMNES simulations, and dynamic-time-warping (DTW)-assisted X-ray absorption near edge structure (XANES) matching. Together with theoretical calculations, the integrated analysis reveals a stable coordination environment under reaction conditions, which correlates with sustained activity, establishing Co@C3N4 single-atom catalysts as thermally stable CO oxidation catalysts. Beyond these findings, the current study provides a workflow for unambiguously assigning active sites in Co@C3N4 for thermal CO oxidation. This workflow will aid the understanding of their behavior in photocatalysis in the future, where light-driven dynamics obscure direct structure–function links. Notably, this study provides fundamental insights for the rational design of robust single-atom catalysts and a foundation for the broader application of Co@C3N4 catalysts in oxidation reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗