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DOE OSTI2026

On the Trotter Error in Many-body Quantum Dynamics with Coulomb Potentials

Efficient simulation of many-body quantum systems is central to advances in physics, chemistry, and quantum computing, with a key question being whether the simulation cost scales polynomially with the system size. Here, in this work, we analyze many-body quantum systems with Coulomb interactions, which are fundamental to electronic and molecular systems. We prove that Trotterization for such unbounded Hamiltonians achieves a 1/4-order convergence rate, with explicit polynomial dependence on the number of particles. The result holds for all initial wavefunctions in the domain of the Hamiltonian, and the 1/4-order convergence rate is optimal, as previous work has numerically demonstrated that it can be saturated by a specific initial ground state. The main challenges arise from the many-body structure and the singular nature of the Coulomb potential. Our proof strategy differs from prior state-of-the-art Trotter analyses, addressing both difficulties in a unified framework. Our analysis treats the Coulomb potential as an unbounded operator without modification or regularization, and does not rely on spatial discretization, making it compatible with both first- and second-quantized circuit constructions.

Fang, Di [Duke Univ., Durham, NC (United States)]↗

DOE OSTI2025

Microbial Enrichments Contribute to Characterization Of Desert Tortoise Gut Microbiota

Abstract Desert tortoises play ecologically significant roles, including plant seed dispersal and mineral cycling, and yet little is known about microbial members that are critical to their gut and overall health. Tortoises consume recalcitrant plant material, which their gut microbiota degrades and converts into usable metabolites and nutrients for the tortoise. Findings from tortoise gut microbiomes may translate well into biotechnological applications as these microbes have evolved to efficiently degrade recalcitrant substrates and generate useful products. In this study, we cultivated microbial communities from desert tortoise fecal samples following a targeted anaerobic enrichment for microbes involved in deconstruction and utilization of plant biomass. We employed 16S rRNA amplicon sequencing to compare cultivated communities to initial fecal source material and found high abundances of Firmicutes and Bacteroidota typically associated with biomass deconstruction in all cultivated samples. Significantly decreased microbial diversity was observed in the cultivated microbial communities, yet several key taxa thrived in lignocellulose enrichments, includingLachnospiraceaeandEnterococcus. Additionally, cultivated communities produced short-chain fatty acids under anaerobic conditions, and their growth and metabolic output provide evidence of their viability in the initial fecal communities. Overall, this study adds to the limited understanding of reptilian herbivore microbiota, and offers a path towards biotechnological translation based on the ability of the cultivated communities to convert lignocellulose directly to acetate, propionate, and butyrate.

Environmental Sciences & Ecology↗

DOE OSTI2026

Parallel-in-Time Solution of Allen-Cahn Equations by Integrating Operator Learning into the Parareal Method

While recent advances in deep learning have shown promising efficiency gains in solving time-dependent partial differential equations (PDEs), matching the accuracy of conventional numerical solvers still remains a challenge. One strategy to improve the accuracy of deep learning-based solutions for time-dependent PDEs is to use the learned model as the coarse propagator in the Parareal method and a traditional numerical method as the fine solver. However, successful integration of deep learning into the Parareal method requires consistency between the coarse and fine solvers, particularly for PDEs exhibiting rapid changes such as sharp transitions. Here, to ensure this consistency, we propose using convolutional neural networks (CNNs) to learn the fully discrete time-stepping operator defined by the same numerical scheme employed as the fine solver. We demonstrate the effectiveness of the proposed method in solving the classical and mass-conservative Allen–Cahn (AC) equations. Through iterative updates in the Parareal algorithm, our approach achieves a significant computational speedup compared to traditional fine solvers while converging to high-accuracy solutions. Our results highlight that the proposed hybrid Parareal algorithm effectively accelerates simulations, particularly when implemented on multiple GPUs, and converges to the desired accuracy in only a few iterations. Another advantage of our method is that the CNN model is trained on trajectory-based data generated from random initial conditions, such that the trained model can be used to solve the AC equations with various initial conditions without retraining. This work demonstrates the potential of integrating neural network methods into parallel-in-time frameworks for efficient and accurate simulations of time-dependent PDEs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Competition Between Growth and Removal in Zirconia Nanocrystal-Derived Tribofilms: The Role of Co-additives

Antiwear additives permit energy-efficient lubrication of gearboxes, bearings, and other tribological interfaces. We study zirconia (ZrO 2 ) nanocrystal additives, which readily form protective tribofilms in tribological contacts. Our prior work demonstrated cooperative antiwear performance between ZrO 2 and the S- and P-based co-additives in fully formulated hydrocarbon gear oils. Here, we extend that work by examining the growth kinetics of the ZrO 2 tribofilms, including the influence of the co-additives. In the boundary lubrication regime for mixed rolling-sliding contacts, the initial phase of ZrO 2 tribofilm growth is soon overtaken by removal processes, phenomena whose importance has gone unnoticed in prior work. Tribofilm removal affects the steady-state thickness and morphology of the tribofilm as well as its growth kinetics. The S- and P-based co-additives are incorporated into the ZrO 2 tribofilm, and alter the competition between the growth and removal processes, increasing initial net growth rates per contact cycle and contributing to a more polished final interface. This work highlights the significance of removal processes in determining tribofilm antiwear performance, and suggests several routes for improving tribofilm growth kinetics using co-additives.

Coadditives↗

DOE OSTI2025

Methods to Observe Tribological Failures in Self-Mated Steel Contacts

Scuffing, a type of wear found in highly stressed or poorly lubricated contacts, is characterized by a rapid increase in friction and severe plastic deformation of the near-surface material. Scuffing has proven difficult to study because it initiates unpredictably, progresses rapidly, and typically develops within an inaccessible contact interface. Although there have been successful in-situ studies of scuffing in real-time, the transparent counter body needed for these studies changes the interactions between the surfaces and the lubricant, which affects the scuffing process in unknown ways. This paper describes the development of X-ray-compatible tribometry to study the scuffing of self-mated steels in-situ and in real-time. The method uses a crossed cylinders configuration with a thin (500 μm thick) stationary component and a small (≈200 μm) contact width to maximize X-ray interactions with atoms within the stress field generated by the contact. The resulting instrument and method are used to benchmark the scuffing response of self-mated 52,100 steel under tribologically challenging ‘oil-off’ lubrication conditions. The results demonstrate reliable scuffing in this configuration despite the relatively small contact areas and loads used. Following scuffing, gross plastic deformation was observed on both surfaces along with significant subsurface grain refinement and flow only on the stationary surface, which experienced constant contact. Interestingly, high friction initiated at specific locations of the migratory surface, which experienced intermittent contact, and then propagated across the track over time, suggesting that local conditions of the migratory surface dominated friction leading into the failure event.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Microstructural Evolution of Tantalum During Deformation and Subsequent Annealing

Microstructure-aware models are necessary to predict the behavior of material based on process knowledge or to extrapolate mechanical properties of materials to environmental conditions which are not easily reproduced in the laboratory, e.g., nuclear reactor environments. Elemental Ta provides a relatively simple BCC system in which to develop a microstructural understanding of deformation processes which can then be applied to more complicated BCC alloys. In situ neutron diffraction during compressive deformation and subsequent heat treatment have been used to monitor the evolution of microstructural features in Ta throughout simulated processing steps. Crystallographic texture and dislocation density are determined as a function of first plastic strain, then temperature. Lattice strains are determined and attributed to stresses at macroscopic, grain and dislocation length scales. The increase of the dislocation density through deformation and subsequent recovery during heat treatment is monitored through the changing diffraction line profile. Also, randomization of the texture is used as a signature of recrystallization. The recovery of dislocations through annihilation is not observed to depend on the initial dislocation density in the range studied here. In contrast, recrystallization is observed to depend strongly on the initially dislocation density.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Validation Data for Benchmarking Wire Arc Additive Manufacturing Process Simulations

Residual stresses cause geometric distortion and affect mechanical performance of additively manufactured structures, yet they are notoriously difficult to assess and predict. Distortion (warpage) can drive parts outside dimensional tolerance limits, leading to part rejection or rework. For parts that meet tolerance, locked-in residual stress fields can affect structural integrity during operation, particularly subcritical cracking by fatigue, creep, or corrosion. This work develops benchmark data for a common additive manufacturing process (Wire Arc Additive Manufacturing) that can be applied for calibration and validation of physical process models that predict residual stress fields. The work includes design of two different samples of differing geometry, detailed manufacturing records for a set of physical samples, and an extensive set of residual stress measurement data developed using two diverse techniques (the contour method and neutron diffraction). An initial application of the work is also reported, where a modeling challenge was issued to secure residual stress model predictions from two independent laboratories that were blind to residual stress measurement data. These initial blind residual stress predictions show significant discrepancies relative to the measurement data, illustrating the potential value of the underlying validation data. An open repository for this work, including the sample designs, manufacturing process records, and the residual stress data, is also provided for future application in non-blind validation efforts.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Design of a Three-Layer Impactor for Material Strength Measurements at Multi-Megabar Pressures

Off-Hugoniot loading methods for dynamic compression have been a topic of interest for many years as a means of accessing high pressures without melting a material. Simulations and an initial test experiment of a three-layer gas-gun impactor suitable for use in measuring dynamic material strength at multi-megabar pressures are described. As shown through ARES hydrocode simulations, an impactor consisting of a low-, medium-, and high-impedance material, such as TPX, Al, and Ta or Pt, can produce a quasi-isentropic loading path up to 4.6 Mbar pressure with a low homologous temperature (T/T melt = 0.1–0.25). These impactors can also be tailored to create a pressure drive suitable for a Lagrangian sound speed experiment. Simulated in-situ velocities were analyzed to determine the change in calculated strength due to non-uniformity in the impactor, which provides a measure of error sensitivity. An initial test of a three-layer projectile onto a flat target at 4.4 km/s impact velocity is reported. Finally, while the impactor incurred some delamination during firing, the measured sample/window interface velocity generally agrees with the simulated peak velocity and subsequent release, indicating the feasibility of this approach for measuring material strength.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Causality-respecting adaptive refinement for PINNs: enabling precise interface evolution in phase field modeling

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving physical systems described by partial differential equations (PDEs). However, their accuracy in dynamical systems, particularly those involving sharp moving boundaries with complex initial morphologies, remains a challenge. Here, this study introduces an approach combining residual-based adaptive refinement (RBAR) with causality-informed training to enhance the performance of PINNs in solving spatio-temporal PDEs. Our method employs a three-step iterative process: initial causality-based training, RBAR-guided domain refinement, and subsequent causality training on the refined mesh. Applied to the Allen-Cahn equation, a widely-used model in phase field simulations, our approach demonstrates significant improvements in solution accuracy and computational efficiency over traditional PINNs. Notably, we observe an ‘overshoot and relocate’ phenomenon in dynamic cases with complex morphologies, showcasing the method’s adaptive error correction capabilities. This synergistic interaction between RBAR and causality training enables accurate capture of interface evolution, even in challenging scenarios where traditional PINNs fail. Our framework not only resolves the limitations of uniform refinement strategies but also provides a generalizable methodology for solving a broad range of spatio-temporal PDEs. The enhanced performance of the RBAR–causality combined framework demonstrates its strong potential for advancing PINN-based modeling of physical systems characterized by complex, evolving interfaces.

Allen-Cahn equations↗

DOE OSTI2024

Microstructure effects on high velocity microparticle impacts of copper

Constitutive models can fail to predict high-rate deformation behavior due to their inability to account for microstructural effects. In part, this is because of a dearth of experimental benchmarking data in the high strain-rate, low pressure regime, since many high-rate experiments also probe a region of strong shockwaves, at which point microstructure effects no longer play a primary role. This work uses laser-induced particle impact testing to quantitatively study high velocity impacts of small, rigid alumina microspheres on flat copper substrates with varying amounts of initial cold work in the weak shock regime, but at very high strain rates up to ~10 7 s –1 . Through paired experiments and numerical simulations, this work shows that the initial microstructure condition can have significant influence on dynamical mechanical properties in this range. Specifically, prior work hardening of the copper substrate leads to increased rebounding of the microparticles (i.e., less plastic dissipation in the impact) as well as smaller craters. Each of these experimental measurables can be converted into a strength measure, i.e., the dynamic yield strength or dynamic hardness, respectively, neither of which is well predicted consistently by existing constitutive laws. The general trend of hardening can be captured by such models by incorporating an existing “pre-strain,” suggesting that future calibration of the materials parameters may yield a good fit over a broader range of conditions. Our results emphasize the importance of reporting the microstructural condition in dynamic studies, as well as the necessity of accounting for these factors when formulating and optimizing constitutive models.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Microstructure-sensitive mechanical behavior of an additively manufactured psuedoelastic shape memory alloy

The additive manufacturing of shape memory alloys into complex geometries enables fabrication of advanced functional systems across a variety of fields and domains. This work presents results focused on the mechanical behavior of additively manufactured shape memory pseudoelastic NiTi. The deformation induced solid state phase transformation from austenite to martensite allows this system to accommodate large recoverable strains. This deformation behavior is fundamentally driven by crystal-scale transformation physics. Laser powder bed fusion processing reveals that the resulting microstructure, both grain morphology and crystallographic texture, is strongly dependent on the manufacturing processing history. Exhaustive mechanical testing demonstrates that these microstructural factors strongly impact both tensile and cyclic stress–strain behavior. Cyclic dissipative behavior, however, is similar across all tested microstructures following an initial transient period. Remarkably, analysis of spatial strain fields during tensile loading reveals two distinctly different localization “modes”. The first is initiation of localized deformation bands which continuously propagate through the tensile bar during loading. In the second mode localization is observed but lacks propagation; instead additional localization cites nucleate during subsequent loading. The latter phenomena is suspected to be driven by grain-scale deformation physics as the localized band morphologies coincide with grain morphologies. These phenomena strongly impact the resulting aggregate stress–strain behavior. Hence, manufacturers and designers of psuedoelastic functional components must at the very least consider the potential variability in properties when considering additive manufacturing processing. More ideally the process–structure–property relations can be used to further tailor and optimize final functional performance.

Additive manufacturing↗

DOE OSTI2026

Reduction of baseplate distortion during directed energy deposition using compliant features

Distortion in additive manufacturing (AM) remains a barrier to its adoption in precision industries. Baseplate warpage is one such issue which compromises the feasibility of post-process precision machining. The restriction to thermal contraction of the deposited part, imposed by the baseplate, generates bending moments, that in turn causes warpage. A novel distortion mitigation strategy using baseplates with integrated compliant features, which enables thermal contraction of the build is presented. Six unique design concepts are evaluated, including a solid reference, using two deposition geometries. A laser, hot-wire, directed energy deposition (DED) process is used to deposit a symmetric cylindrical part (C-part) and a T-shaped asymmetric part (T-part). Flatness deviation of baseplates is measured using structured light 3D scanning. Measurements reveal a reduction in net flatness deviation of 58.8% for the C-part and 40.9% for the T-part, compared to the solid reference. While most designs yielded reductions exceeding 30% and 20% for the C- and T-parts, respectively, one configuration resulted in increased deviation. Finite element (FE) simulations are performed to elucidate the underlying mechanisms affecting distortion of compliant baseplates during DED. Despite variations between predictions and measurements, agreement in the general trend is observed. It also revealed that initial flatness errors in baseplates significantly affect its deviation during deposition. Predictions indicate that compliant features significantly affect the thermal distribution as well as the evolution of flatness deviation in the baseplate during deposition. Notably, one design exhibited a reduction in distortion during cooling, following its initial increase during deposition. FE predictions show a maximum reduction of 60.9% and 38.8% in net flatness deviation for the C- and T-parts, respectively. The performance of compliant baseplates is found to be governed by both its the thermal and mechanical characteristics, which are crucial factors to be considered during design.

Mathews, Ritin [ORNL] (ORCID:0000000301440828)↗

DOE OSTI2025

Parameter Study of the Running-In Process for the Generic Pebble Bed Reactor (GPBR200)

The run-in period of a pebble bed reactor is complex and difficult to model given significant heterogeneity in core composition, power, and temperature. While it is understood that the initial composition of the core should eventually result in the same equilibrium core composition, the approach to equilibrium can vary significantly depending on factors such as start-up fuel enrichment and power ramp rate. To explore this, a high-fidelity model of the General Pebble Bed Reactor was used to vary power ramp schemes and start-up core compositions. It was found that both the initial core composition and power ramp rate had a significant impact on the flow rate of pebbles during early time steps, with higher ramp rates and low enrichment resulting in non-physical flow rates. Power ramp rate alone was found to dictated maximum pebble power peaking observed during the run-in process, with higher ramp rates resulting in greater peak pebble powers. Start-up fuel enrichment and power ramp were found to both impact total fuel consumption, although the impact of start-up fuel enrichment was generally secondary to ramp rate.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Evaluating advanced nuclear fission technologies for future decarbonized power grids

Advanced nuclear fission, which encompasses various innovative nuclear reactor designs, could contribute to the decarbonization of the United States electricity sector. However, little is known about how cost-competitive these reactors would be compared to other technologies, or about which aspects of their designs offer the most value to a decarbonized power grid. We employ an electricity system optimization model and a case study of a decarbonized U.S. Eastern Interconnection circa 2050 to generate initial indicators of future economic value for advanced reactors and the sensitivity of future value to various design parameters, the availability of competing technologies, and the underlying policy environment. These results can inform long-term cost targets and guide near-term innovation priorities, investments, and reactor design decisions. We find that advanced reactors should cost $\$5.7$–$\$7.3$/W to gain an initial market share (assuming 30 year asset life and 3.5 %–6.5 % real weighted average cost of capital), while those that include thermal storage in their designs can cost up to $\$6.0$/W–$\$7.7$/W (not including cost of storage). Since the marginal value of advanced fission reactors declines as market penetration increases, break-even costs fall ~32 % at 100 GW of cumulative capacity and ~51 % at 300 GW. Additionally, policies that provide investment tax credits for nuclear energy create the most favorable environment for advanced nuclear fission. In conclusion, these findings can inform near-term resource allocation decisions by stakeholders, innovators and investors working in the energy technology sector.

Capacity expansion↗

DOE OSTI2024

Orientation-dependent structural properties during growth and growth mechanism of CoO films

The orientation-dependent local structural properties of CoO films on sapphire substrates during growth were investigated through linearly-polarized extended X-ray absorption fine structure (EXAFS) measurements. Specifically, CoO(1 1 1) and (100) crystals with a rock-salt structure (Fm3m) were epitaxially grown on alpha-Al2O3(0001) and (1012) substrates, respectively, at 700 degrees C using a radio-frequency sputtering system. The local structural properties of CoO films in the in-plane and out-of-plane orientations were quantitatively determined using linearly-polarized EXAFS at the Co K-edge during growth. The EXAFS analysis revealed that during the initial stages of growth, the local structural properties exhibit significant differences compared to thick films, with short atomic distances and large (small) Debye-Waller factors observed in the out-of-plane (in-plane) orientations. The local structural strain mostly diminished when approximately 20 CoO layers accumulated on the substrate. Density functional theory (DFT) calculations further supported these findings by confirming that cobalt atoms initially form stable bonds with the sapphire surface, leading to the simultaneous growth of oxygen and cobalt layers in a coordinated manner through layer-by-layer growth.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Highly crystalline, low-ash, graphite from coal using an Fe 2 O 3 -based catalytic process with recovery and reuse of catalyst and process acid

This study presents a sustainable process for producing highly crystalline, low-ash graphite from sub-bituminous coal using an Fe 2 O 3 -based catalytic method. The process integrates coal mineral removal, catalyst regeneration, and reagent recycling into a closed-loop system. Acid-soluble Fe-residue and mineral impurities are eliminated from the solid graphite through HCl treatment, followed by hydrolytic distillation to regenerate Fe 2 O 3 and recover HCl for reuse. Coal-derived silica is removed with a KOH rinse, yielding low-ash graphite suitable for high-performance applications. The closed-loop catalytic graphitization, where the recovered Fe 2 O 3 and HCl are used in subsequent graphitization runs, produces graphite with a degree of graphitization exceeding 95%. The L a and L c crystallite sizes reach 65–78 nm and 44–48 nm, respectively, with BET surface areas of 4–10 m 2 /g and an ash content below 0.1 wt.%. Lithium-ion battery testing reveals that anodes fabricated with this graphite deliver an initial discharge capacity between 384.5 and 421.2 mAh/g, averaging 395.0 ± 19.1 mAh/g, along with initial coulombic efficiencies of 85.0–89.1%. After 100 discharge–charge cycles at 0.25C, reversible capacities remain between 358.8 and 369.7 mAh/g, while coulombic efficiency stays above 99.9%. The findings highlight that coal can serve as a viable precursor for high-quality graphite production under relatively mild conditions, avoiding the need for extreme temperatures or aggressive reagents such as hydrofluoric acid, commonly employed in conventional processes. This work demonstrates both technical feasibility and environmental benefits, emphasizing its potential to support large-scale, sustainable graphite production for applications such as lithium-ion batteries.

Catalytic graphitization↗

DOE OSTI2026

From atomistic models to machine learning: Predictive design of nanocarbons under extreme conditions

The formation of technologically valuable nanocarbon structures under extreme conditions, such as those produced during high-explosive detonations, remains poorly understood but holds significant potential for the development of controlled synthesis pathways. While detonation shockwaves provide the high-pressure, high-temperature environment required for nanodiamond formation, subsequent cooling and decompression dictate whether the diamond phase is preserved or transformed into other nanocarbon structures. Here, in this study, we employ GPU-accelerated reactive molecular dynamics (ReaxFF) simulations to investigate the graphitization and structural remodeling of detonation nanodiamond under nonlinear quench and pressure-release trajectories. We further investigate how the initial nanodiamond morphology; cuboctahedral, octahedral, or hexagonal prism influences the resulting transformation products. Evolution of nanostructure, allotrope (via simulated x-ray diffraction), carbon hybridization, and ring statistics are tracked during a two-stage quench from 5000 K to 60 GPa. Rapid cooling combined with slow decompression optimizes cubic diamond retention, whereas slow cooling with rapid pressure release promotes surface-to-core graphitization, producing concentric sp 2 -hybridized layers and hollowed inner shells. Octahedral nanodiamonds evolve into carbon nano-onions, initially forming bucky diamonds that progressively transform into fully sp 2 -hybridized structures, while hexagonal prisms preferentially form parallel-stacked graphite layers resembling carbon dots. Transient hexagonal diamond (lonsdaleite) emerges as an interfacial phase, suggesting potential reversibility in the shock-induced graphite-to-diamond transformation pathway transformation route. To extend predictive capabilities, we trained machine learning (ML) regressors on over 10 5 node-hours of molecular dynamics (MD) trajectories. A multilayer perceptron (MLP) model reliably predicts the number of graphitized layers from temperature–pressure trajectories with a coefficient of determination (R 2 ) exceeding 0.90. This high predictive fidelity enables efficient, high-throughput mapping of the synthesis parameter space for optimized graphitization outcomes. Collectively, morphological control combined with optimized quench–decompression conditions promote the selective synthesis of nanocarbon allotropes. This work establishes a data-driven framework for the rational, a priori design of carbon nanomaterials for applications in energy storage, sensing, and biomedicine.

Detonation nanodiamond remodeling↗

DOE OSTI2025

Synergistically combining peracetic acid and reduced graphene oxide membranes to degrade trace organic contaminants

The removal of trace organic contaminants is a critical step for the reuse of municipal and industrial wastewater. Herein, we demonstrate a catalytic membrane platform synergistically integrating reduced graphene oxide (rGO) membranes and peracetic acid (PAA) oxidation, using a dye of methylene blue (MB) and a pesticide of 2,4-dichlorophenoxyacetic acid (2,4-D) as model contaminants. In a crossflow system with rGO membrane and 25 ppm PAA, the degradation rates of MB and 2,4-D were 22 and 0.12 g h −1 per g rGO, with an initial concentration of 10 and 1.1 ppm, respectively. The degradation time profile of MB and 2,4-D follows a pseudo-first-order model, and the degradation rate constant increases with increasing initial PAA doses. Here, the rGO membranes also exhibited good stability over a 1-month test for 2,4-D degradation. In addition to the nanofiltration performance of the rGO membrane, the integrated PAA-rGO membrane process shows great potential to degrade various organic contaminants without the need to separate and recover the metal-free catalyst in downstream treatment.

2,4-D↗