Electron Density Functional Theory Research Articles

Unit‐Cell‐Thickness Electron Confinement by Geometrically Constrained Antipolar Ordering

AbstractAchieving precise electron or spin confinement is essential for the progress of oxide electronics and emerging quantum information processing. While 2D electron confinement is commonly achieved with bare surfaces, heteroepitaxial interfaces, and charged domain walls, its practical application poses challenges, notably by diverse confinement widths, limited material selection, and the lack of freedom of positioning to a desired location within a given material system. Here, with scrutinizing a novel defect structure, the study suggests a new strategy with compelling evidence to trigger electron confinement down to single unit‐cell‐thickness, through geometrically constrained antipolar ordering facilitated by superlattice‐like periodic planar faults in metallic SrFeO3. Employing atomic resolution electron microscopy and density functional theory, the results demonstrate that electrons are confined two‐dimensionally to screen the positive bound charges on head‐to‐head antipolar state boundary, meanwhile oxygen vacancies segregated in the planar faults compensate the negative bound charges on the tail‐to‐tail one, leading to the stabilization of the antipolar ordering. Additionally, distinguished from traditional methods, this approach offers a potential programing capability for achieving precise charge and spin control by regulating planar fault structure at atomic scale.

Revealing the origin of single‐atom W activity in H2O2 electrocatalytic production: Charge symmetry‐breaking

AbstractThe low‐energy electrochemical production of hydrogen peroxide (H2O2) has garnered significant attention as a viable alternative to traditional industrial routes, with the goal of achieving carbon neutrality. For their H2O2 selectivity in the two‐electron oxygen reduction reaction (ORR), the coordination environment of tungsten (W)‐based materials is critical. In this study, atomically dispersed W single atoms were immobilized on N‐doped carbon substrates by a facile pyrolysis method to obtain a W single‐atom catalyst (W‐SAC). The coordination environment of an isolated W single atom with a tetra‐coordinated porphyrin‐like structure in W‐SAC was determined by X‐ray photoelectron spectroscopy and X‐ray absorption spectroscopy analysis. Notably, the as‐prepared W‐SAC showed superior two‐electron ORR activity in 0.1 M KOH solution, including high onset potential (0.89 V), high H2O2 selectivity (82.5%), and excellent stability. By using differential phase contrast‐scanning transmission electron microscopy and density functional theory calculations, it is revealed that the charge symmetry‐breaking of W atoms changes the adsorption behavior of the intermediates, leading to enhanced reactivity and selectivity for two‐electron ORR. This work broadens the avenue for understanding the charge transfer of W‐based electrocatalytic materials and the in‐depth reaction mechanism of SACs in two‐electron ORR.

The atomic configuration and metallic state of extrinsic defects in Nb-doped BiFeO3 thin films

Defects in ferroelectric materials can cause microscopic strain and electron doping, which opens up new possibilities for unique physical properties in nanoelectronics. However, comprehending the relationship between these deep-buried defect configurations and the resulting physical properties is a long-term challenge. Here, utilizing the integrated differential phase imaging technique equipped in scanning transmission electron microscopy combined with energy dispersive X-ray spectroscopy, we show the full element-resolved atomic configuration of characteristic extrinsic defects in Nb-doped epitaxial BiFeO3 thin films. Atomic-resolution characterization reveals that the Nb doping substitutes Fe at the center of an oxygen octahedron and creates Fe vacancies near the defect core, leading to the formation of one perovskite cell-wide BiNbO3 chain that is expanded by 19 % in perovskite cell volume and rotated by 45° relative to the matrix lattice. Further quantitative analysis of the defect demonstrates that the ferroelectric polarization distribution around the dopant-induced defects displays a “head-to-head” configuration, indicating the accumulation of negative charges. Supported by electron energy loss spectroscopy and density functional theory calculations, the linear defect leads to one-dimensional metallic channels embedded within the ferroelectric BiFeO3 matrix. These atomic-scale findings establish the structure-functionality relationship of extrinsic defect in Nb-doped BiFeO3 thin films, providing new insight into their fundamental understanding and potential use in low-dimensional nanoelectronics devices.

Bi Nanospheres Embedded in N-Doped Carbon Nanowires Facilitate Ultrafast and Ultrastable Sodium Storage.

Sodium ion batteries (SIBs) are considered as the ideal candidates for the next generation of electrochemical energy storage devices. The major challenges of anode lie in poor cycling stability and the sluggish kinetics attributed to the inherent large Na+ size. In this work, Bi nanosphere encapsulated in N-doped carbon nanowires (Bi@N-C) is assembled by facile electrospinning and carbonization. N-doped carbon mitigates the structure stress/strain during alloying/dealloying, optimizes the ionic/electronic diffusion, and provides fast electron transfer and structural stability. Due to the excellent structure, Bi@N-C shows excellent Na storage performance in SIBs in terms of good cycling stability and rate capacity in half cells and full cells. The fundamental mechanism of the outstanding electrochemical performance of Bi@N-C has been demonstrated through synchrotron in-situ XRD, atomic force microscopy, ex-situ scanning electron microscopy (SEM) and density functional theory (DFT) calculation. Importantly, a deeper understanding of the underlying reasons of the performance improvement is elucidated, which is vital for providing the theoretical basis for application of SIBs.

Nonradical-dominated peroxymonosulfate activation by perylenetetracarboxylic acid nanosheet photocatalyst for efficient degradation of bisphenol a under visible-light irradiation

As a green, highly efficient, and sustainable technology, photocatalytic peroxymonosulfate (PMS) activation is a promising strategy for wastewater treatment. Moreover, the development of photocatalysts with excellent PMS activation performance is highly desirable for removing refractory organic contaminants from wastewater. Herein, perylenetetracarboxylic acid (PTA) nanosheets obtained using a facile method were explored as a highly efficient photocatalyst with a high PMS activation ability for bisphenol A (BPA) removal. Experimental results indicated that BPA can be removed within 16 min using PTA under optimal conditions. As confirmed through radical quenching, electron paramagnetic resonance spectroscopy, galvanic-oxidation-process experiments, and density functional theory calculations, photoinduced electrons and holes from PTA trigger PMS activation and thereby convert the reaction routes of BPA degradation from radical- to nonradical-dominated. The BPA degradation pathway was also studied using intermediate analysis and Fukui functions. Overall, the findings of this study shed light on organic semiconductor photocatalysts for nonradical-dominated PMS activation with regard to recalcitrant-organic-pollutant removal.

Oxide/metal interface enhancement for improved dispersion strengthening mechanism in oxide-strengthened tungsten

The addition of secondary ceramic particles has shown to be effective in enhancing the mechanical properties of tungsten alloys. The diverse strengthening effects observed with various secondary particles necessitate further investigation. Herein, three ultrafine-grained, oxide-dispersed-strengthened tungsten alloys were prepared using solution combustion synthesis combined with low-temperature sintering. We thoroughly investigated the influence of Al2O3, La2O3, and Y2O3 on the microstructure and mechanical properties of tungsten, as well as their respective strengthening mechanisms. A detailed comparison revealed discrepancies between the yield strength experimentally measured and the theoretically predicted strength based on conventional grain refinement strengthening and dispersion strengthening theories, highlighting the significance of the intrinsic nature of dispersed oxides. Electron microscopy analysis and density functional theory calculations revealed that, compared to other oxides, the heterogeneous interface of Al2O3 with W exhibited minimal lattice distortion and the highest work of separation, resulting in a robust interface bonding. The prepared W–Al2O3 alloy showed exceptional performance with Vickers hardness HV0.2 of 698.9 and yield strength of 2488 MPa. Its yield strength surpassed that of W–Y2O3 and W–La2O3 alloys, as well as other commonly reported refractory metal materials.

Low-nuclearity CuZn ensembles on ZnZrOx catalyze methanol synthesis from CO2

Metal promotion could unlock high performance in zinc-zirconium catalysts, ZnZrOx, for CO2 hydrogenation to methanol. Still, with most efforts devoted to costly palladium, the optimal metal choice and necessary atomic-level architecture remain unclear. Herein, we investigate the promotion of ZnZrOx catalysts with small amounts (0.5 mol%) of diverse hydrogenation metals (Re, Co, Au, Ni, Rh, Ag, Ir, Ru, Pt, Pd, and Cu) prepared via a standardized flame spray pyrolysis approach. Cu emerges as the most effective promoter, doubling methanol productivity. Operando X-ray absorption, infrared, and electron paramagnetic resonance spectroscopic analyses and density functional theory simulations reveal that Cu0 species form Zn-rich low-nuclearity CuZn clusters on the ZrO2 surface during reaction, which correlates with the generation of oxygen vacancies in their vicinity. Mechanistic studies demonstrate that this catalytic ensemble promotes the rapid hydrogenation of intermediate formate into methanol while effectively suppressing CO production, showcasing the potential of low-nuclearity metal ensembles in CO2-based methanol synthesis.

Predicting Quantum-Mechanical Partial Charges in Arbitrarily Long Boron Nitride Nanotubes to Accurately Simulate Nanoscale Water Transport.

Single-walled boron nitride nanotubes (BNNTs) have been explored for various applications, ranging from water desalination to osmotic power harvesting. However, no simulation work so far has modeled the changes in the partial charge distribution when a flat sheet is rolled into a tube, hindering the ability to perform accurate molecular dynamics (MD) simulations of water flow through BNNTs. To address this knowledge gap, we employ electronic density functional theory (DFT) calculations to precisely estimate quantum-mechanically derived partial charges on boron (B) and nitrogen (N) atoms in BNNTs of varying lengths and diameters. We observe a spatially varying charge distribution inside both armchair and zigzag nanotubes of finite lengths. Performing DFT calculations for longer BNNTs is computationally intractable, even with state-of-the-art computing resources. To solve this issue, we devise a charge assignment scheme to predict partial charges for longer BNNTs using DFT data for shorter nanotubes, thus overcoming the need to perform more expensive DFT calculations. We show that these charges reproduce the electrostatic potential predicted from first-principles simulations. Subsequently, we carried out MD simulations to predict the effect of the charge distribution inside BNNTs on water flow enhancement via them. We find that using uniform charges leads to an underprediction in flow enhancement, as compared to using quantum-mechanical charges for both armchair and zigzag BNNTs. We also incorporate atomic vibrations into our simulations and show that these vibrations lead to a reduction in the water flow through aperiodic BNNTs. Our work demonstrates the requirement of a quantum-mechanical charge assignment scheme for BNNTs and evolves a framework to assign charges to nanotubes of arbitrary length, thus allowing realistic MD simulations of long BNNTs using accurate partial charges.

Ab initio generalized Langevin equation

We introduce a machine learning-based approach called ab initio generalized Langevin equation (AIGLE) to model the dynamics of slow collective variables (CVs) in materials and molecules. In this scheme, the parameters are learned from atomistic simulations based on ab initio quantum mechanical models. Force field, memory kernel, and noise generator are constructed in the context of the Mori-Zwanzig formalism, under the constraint of the fluctuation-dissipation theorem. Combined with deep potential molecular dynamics and electronic density functional theory, this approach opens the way to multiscale modeling in a variety of situations. Here, we demonstrate this capability with a study of two mesoscale processes in crystalline lead titanate, namely the field-driven dynamics of a planar ferroelectric domain wall, and the dynamics of an extensive lattice of coarse-grained electric dipoles. In the first case, AIGLE extends the reach of ab initio simulations to a regime of noise-driven motions not accessible to molecular dynamics. In the second case, AIGLE deals with an extensive set of CVs by adopting a local approximation for the memory kernel and retaining only short-range noise correlations. The scheme is computationally more efficient than molecular dynamics by several orders of magnitude and mimics the microscopic dynamics at low frequencies where it reproduces accurately the dominant far-infrared absorption frequency.

Designing a 3D framework NaVOPO4 as a high-power, low-strain and long-life positive electrode material for Na-ion batteries

Advances in sodium-ion batteries hugely rely on perfecting the performance of active electrode materials. In this paper, we offer a new NaVOPO4 polymorph adopting a KTiOPO4-type framework as a promising high-rate, low-strain and long-life positive electrode material for sodium-ion batteries. NaVOPO4 is prepared via a facile hydrothermally-assisted solid-state ion exchange. The crystal structure is refined based on synchrotron X-ray powder diffraction (XRD) and validated by X-ray absorption spectroscopy (XAS), transmission electron microscopy analysis and density functional theory (DFT) calculations. The electrochemical performance of NaVOPO4 is evaluated through galvanostatic charge/discharge tests, cyclic voltammetry, potentiostatic intermittent titration and electrochemical impedance spectroscopy. A carbon-coated NaVOPO4 demonstrates a specific capacity of ∼110 mAh g–1 at a C/10 rate at an average potential of ∼3.93 V vs. Na+/Na. The material exhibits decent capacity retention and rate capability, maintaining over 74 % of the initial capacity after 1000 cycles at a C/2 rate and around 87% at a 2C charge/discharge rate. Diffusion coefficients of 10–11 cm2 s–1 and DFT-calculated energy barriers of ∼0.15–0.35 eV indicate fast Na+ ion diffusion within the NaVOPO4 framework. The vanadium oxidation state and charge compensation mechanism in NaVOPO4 are studied by XAS and DFT. Moreover, the operando XRD analysis coupled with DFT elucidates several phase transitions occurring in NaVOPO4 with an exceptionally low volume variation of 2.4% in total, highlighting the reversibility and structural stability during Na+ de/insertion. Overall, NaVOPO4 exhibits attractive electrochemical performance and stability, making it a potential candidate for sodium-ion battery cathode materials.

Quantum symmetrization transition in superconducting sulfur hydride from quantum Monte Carlo and path integral molecular dynamics

AbstractWe study the structural phase transition, originally associated with the highest superconducting critical temperature Tc measured in high-pressure sulfur hydride. A quantitative description of its pressure dependence has been elusive for any ab initio theory attempted so far, raising questions on the actual mechanism leading to the maximum of Tc. Here, we estimate the critical pressure of the hydrogen bond symmetrization in the Im$$\bar{3}$$ 3 ¯ m structure, by combining density functional theory and quantum Monte Carlo simulations for electrons with path integral molecular dynamics for quantum nuclei. We find that the Tc maximum corresponds to pressures where local dipole moments dynamically form on the hydrogen sites, as precursors of the ferroelectric Im$$\bar{3}$$ 3 ¯ m-R3m transition, happening at lower pressures. For comparison, we also apply the self-consistent harmonic approximation, whose ferroelectric critical pressure lies in between the ferroelectric transition estimated by path integral molecular dynamics and the local dipole formation. Nuclear quantum effects play a major role in a significant reduction (≈50 GPa) of the classical ferroelectric transition pressure at 200 K and in a large isotope shift (≈25 GPa) upon hydrogen-to-deuterium substitution of the local dipole formation pressure, in agreement with the corresponding change in the Tc maximum location.

Nanoscale Localized Phonons at Al2O3 Grain Boundaries.

Nanoscale defects like grain boundaries (GBs) would introduce local phonon modes and affect the bulk materials' thermal, electrical, optical, and mechanical properties. It is highly desirable to correlate the phonon modes and atomic arrangements for individual defects to precisely understand the structure-property relation. Here we investigated the localized phonon modes of Al2O3 GBs by combination of the vibrational electron energy loss spectroscopy (EELS) in scanning transmission electron microscope and density functional perturbation theory (DFPT). The differences between GB and bulk obtained from the vibrational EELS show that the GB exhibited more active vibration at the energy range of <50 meV and >80 meV, and further DFPT results proved the wide distribution of bond lengths at GB are the main factor for the emergence of local phonon modes. This research provides insights into the phonon-defect relation and would be of importance in the design and application of polycrystalline materials.

Atomic structure of clusters and GP-zones in an Al-Mg-Si alloy

The structures of atomic clusters and GP-zones preceding precipitation in an Al-0.70Mg-0.85Si-0.15Fe-0.25Mn (wt. %) alloy have been investigated by annular dark field scanning transmission electron microscopy imaging and density functional theory calculations. One analysed condition consisted of one-month natural aging, and another was in a pre-baked state after 24 h aging at 90 °C. To quantify the effect of clusters and GP-zones on microstructure development during a subsequent isothermal artificial aging at 185 °C, hardness evolution was measured, and precipitate statistics was performed at the peak hardness corresponding to 5 h aging. Several types of clusters and GP-zones have been observed and based on structure and visual appearance named 'Disordered Frank-Kasper', 'Square', 'Binocular', and 1β", 2β", 3β", 4β". The first four are most common in the natural aged condition and are associated with a well-known influence on the initial hardness evolution. The last three are fractions of the hardening β" phase and refer to the number of structural units they contain. These GP-zones have an increased density in the pre-baked condition, leading to a rapid increase in hardness during artificial aging and to a finer microstructure of high-density small needle precipitates at peak hardness.

Structural study of nickelate based heterostructures

Heterostructures consisting of SmNiO3 and NdNiO3 alternating layers with additional LaAlO3 spacer layers were grown and fully characterized by means of x-ray diffraction, atomic force microscopy, and scanning transmission electron microscopy. A change in the orientation of the orthorhombic long-axis of the nickelate layers is observed when a single unit cell of LaAlO3 is inserted between SmNiO3 and NdNiO3, in agreement with density functional theory calculations. At the same time, the structure of the ultra-thin rhombohedral LaAlO3 layers is affected by their proximity to orthorhombic nickelate layers, with both scanning transmission electron microscopy studies and density functional theory calculations revealing a weak antipolar motion of the La-cation in the LaAlO3 layers that is not present in the bulk rhombohedral structure of this compound.

New Azo Derivative of β-Diketones and Its Cu(II), Co(II) Complexes: Synthesis, Theoretical Study and Biological Activity.

The paper is focused on biological activity and theoretical study of the structure and properties of a new azo derivative of β-diketones and its complexes with some metals. The aim of our work was to study the structure and properties of the newly synthesized compound as well as to theoretically determine the possibility of complex formation with the Cu(II) or Co(II) ions. A compound with the same substituents R1=R2=CH3 was chosen for the study. A synthesized azo compound based on 4-amino antipyrine and its complexes with Cu(II), Co(II) in solution and solid phase is reported. The structures of these compounds have been testified by X-ray, IR and NMR spectroscopy. The combined experimental and theoretical approach was used. To study the structure and properties of the synthesized compound, as well as its possible complex formation with the Cu(II), quantum-chemical calculations were carried out the 6-31G basis set and the electron density functional theory (DFT) method. These 3-(1-phenyl-2,3-dimethyl-pyrazolone-5) azopentadione-2,4 (PDPA) with Cu(II) and Co(II) complexes had effective inhibition against butyrylcholinesterase and acetylcholinesterase. IC50 values were found as 19.03, 3.64 μM for AChE and 28.47, 8.01 μM for BChE, respectively. Cholinesterase inhibitors work to slow down the acetylcholine's deterioration.

In Situ Modulation of Oxygen Vacancies on 2D Metal Hydroxide Organic Frameworks for High-Efficiency Oxygen Evolution Reaction.

The discovery of non-precious catalysts for replacing the precious metal of ruthenium in the oxygen evolution reaction (OER) represents a key step in reducing the cost of green hydrogen production. The 2D d-MHOFs, a new 2D materials with controllable oxygen vacancies formed by controlling the degree of coordination bridging between metal hydroxyl oxide and BDC ligands are synthesized at room temperature, exhibit excellent OER properties with low overpotentials of 207 mV at 10mA cm-2 . High-resolution transmission electron microscopy images and density functional theory calculations demonstrate that the introduction of oxygen vacancy sites leads to a lattice distortion and charge redistribution in the catalysts, enhancing the OER activity of 2D d-MHOFs comprehensively. Synchrotron radiation and in situ Raman/Fourier transform infrared spectroscopy indicate that part of oxygen defect sites on the surface of 2D d-MHOFs are prone to transition to highly active metal hydroxyl oxides during the OER process. This work provides a mild strategy for scalable preparation of 2D d-MHOFs nanosheets with controllable oxygen defects, reveals the relationship between oxygen vacancies and OER performance, and offers a profound insight into the basic process of structural transformation in the OER process.

Identification and quantification of electron-generated atomic hydrogen through in-situ electron spin resonance and density functional theory

Electro-generated atomic hydrogen (H*) plays a crucial role in the electrochemical reduction process, serving as the key species that mediates the electrocatalytic hydrogenation reduction of stubborn contaminants in wastewater treatment. However, precisely identifying and quantifying transient atomic H* presents a significant challenge due to its limited lifespan and its existence solely within the boundary layer at the electrode/solution interface. Herein, we developed the electrodeposition of palladium nanoparticles onto carbon cloth and assessed its effectiveness as a cathode for generating and stabilizing atomic H*. The environmental application of atomic H* was validated through the dechlorination of 2, 4-dichlorophenol wastewater and the reduction of antimonite wastewater. Additionally, the identification of atomic H* was verified by electrochemical measurements, high-resolution mass spectra, and density functional theory. Moreover, introducing an excess of a spin trapping agent (5,5-dimethyl-1-pyrroline-N-oxide) and fast in-situ spin trapping facilitated creating favorable conditions for efficient trapping of atomic H* and subsequent electron spin resonance (ESR) spectroscopy quantification analysis. Subsequently, the quantification of atomic H* was achieved by double integration of the ESR signal of spin adduct and comparison with the external standard agent (4-hydroxy-2,2,6,6-tetramethyl-1-piperidine 1-oxyl). This study introduces a novel method for in-situ spin trapping and quantification of atomic H*, facilitating the advancement of electrochemical reduction technology and its application in wastewater treatment.

Novel complex compounds of nickel with 3-(1-phenyl-2,3-dimethyl-pyrazolone-5)azopentadione-2,4: synthesis, NBO analysis, reactivity descriptors and in silico and in vitro anti-cancer and bioactivity studies

A synthesized azo compound based on 4-amino antipyrine and its complexes with Ni(II) in solution and solid phase is reported. The structures of these compounds have been testified by IR and NMR spectroscopy. The combined experimental and theoretical approach was used. To study the structure and properties of the synthesized compound, as well as its possible complex formation with the Ni(II), ab initio quantum-chemical calculations were carried out using the Hartree-Fock (HF) method with the 6-31 G basis set and the electron density functional theory (DFT) method with hybrid three-parameter potential B3LYP and extended basis set 6-311++G(d,p) taking into account polarization and diffuse functions for all atoms. The geometric, energy, and electronic parameters were calculated and analyzed. The HOMO-LUMO energy gap has been calculated to determine chemical activity. Both complexes had effective inhibition against butyrylcholinesterase and acetylcholinesterase. IC50 values were found as 19.43 and 27.08 µM for AChE, 2.37 and 7.40 µM for BChE, respectively. For the anticancer outcome, high doses of compound E1 inhibited viability by about 40–45%, while this rate was around 65–70% for compound E2 at the same doses. Anticholinesterase and anticancer potential of compounds E1 and E2 also evaluated by in silico techniques. Both compounds show strong binding to VEGFR1, with E2 exhibiting superior inhibitory activity in hAChE and hBChE through shorter and stronger interactions. MD simulations suggest that E2 forms more stable complexes with hAChE and hBChE compared to E1, making it a promising candidate for further exploration in anticancer and anticholinesterase therapies. Communicated by Ramaswamy H. Sarma

Segregation-induced strength anomalies in complex single-crystalline superalloys

Pushing the maximum service temperature of aircraft engines and industrial gas turbines is the major pathway to improve their energy efficiency and reduce CO2 emissions. This maximum is mostly limited by the temperature capability of key-component materials, including superalloys. In this alloy class, segregation of elements facilitates plastic deformation and is generally considered to cause softening during high-temperature deformation. Here, we show that segregation-assisted processes can also lead to strengthening and induce an anomalous increase of the yield strength. Atomic-resolution transmission electron microscopy and density functional theory calculations reveal a segregation-assisted dissociation process of dislocations at precipitate-matrix interfaces in combination with atomic-scale reordering processes. These processes lead to an inhibition of athermal deformation mechanisms and a transition to stacking fault shearing, which causes the strengthening effect. Unraveling these elementary mechanisms might guide a mechanism-based alloy design of future superalloys with enhanced high-temperature capabilities.

Continuous ammonia synthesis from water and nitrogen via contact electrification

We synthesized ammonia (NH3) by bubbling nitrogen (N2) gas into bulk liquid water (200 mL) containing 50 mg polytetrafluoroethylene (PTFE) particles (~5 µm in diameter) suspended with the help of a surfactant (Tween 20, ~0.05 vol.%) at room temperature (25 °C). Electron spin resonance spectroscopy and density functional theory calculations reveal that water acts as the proton donor for the reduction of N2. Moreover, isotopic labeling of the N2 gas shows that it is the source of nitrogen in the ammonia. We propose a mechanism for ammonia generation based on the activation of N2 caused by electron transfer and reduction processes driven by contact electrification. We optimized the pH of the PTFE suspension at 6.5 to 7.0 and employed ultrasonic mixing. We found an ammonia production rate of ~420 μmol L-1 h-1 per gram of PTFE particles for the conditions described above. This rate did not change more than 10% over an 8-h period of sustained reaction.