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At least 325 records · Page 18

3 d-d Excited States of Ni(II) Complexes Relevant to Photoredox Catalysis: Spectroscopic Identification and Mechanistic Implications

Synthetic organic chemistry has seen major advances due to the merger of nickel and photoredox catalysis. A growing number of Ni-photoredox reactions are proposed to involve generation of excited nickel species, sometimes even in the absence of a photoredox catalyst. To gain insights about these excited states, two of our groups previously studied the photophysics of Ni( t-Bu bpy)(o-Tol)Cl, which is representative of proposed intermediates in many Ni-photoredox reactions. This complex was found to have a long-lived excited state (τ = 4 ns), which was computationally assigned as a metal-to-ligand charge transfer (MLCT) state with an energy of 1.6 eV (38 kcal/mol). This work evaluates the computational assignment experimentally using a series of related complexes. Ultrafast UV–Vis and mid-IR transient absorption data suggest that a MLCT state is generated initially upon excitation but decays to a long-lived state that is 3 d-d rather than 3 MLCT in character. Dynamic cis,trans-isomerization of the square planar complexes was observed in the dark using 1 H NMR techniques, supporting that this 3 d-d state is tetrahedral and accessible at ambient temperature. Through a combination of transient absorption and NMR studies, the 3 d-d state was determined to lie ~0.5 eV (12 kcal/mol) above the ground state. Because the 3 d-d state features a weak Ni–aryl bond, the excited Ni(II) complexes can undergo Ni homolysis to generate aryl radicals and Ni(I), both of which are supported experimentally. Thus, photoinduced Ni–aryl homolysis offers a novel mechanism of initiating catalysis by Ni(I).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Woven Supramolecular Metal‐Organic Framework Comprising a Ruthenium Bis(terpyridine) Complex and Cucurbit[8]uril: Enhanced Catalytic Activity toward Alcohol Oxidation

Abstract The self‐assembly of a diamondoid woven supramolecular metal–organic framework wSMOF‐1 has been achieved from intertwined [Ru(tpy) 2 ] 2+ (tpy=2,2′,6′,2′′‐terpyridine) complex M1 and cucurbit[8]uril (CB[8]) in water, where the intermolecular dimers formed by the appended aromatic arms of M1 are encapsulated in CB[8]. wSMOF‐1 exhibits ordered pore periodicity in both water and the solid state, as confirmed by a combination of 1 H NMR spectroscopy, UV‐vis absorption, isothermal titration calorimetry, dynamic light scattering, small angle X‐ray scattering and selected area electron diffraction experiments. The woven framework has a pore aperture of 2.1 nm, which allows for the free access of both secondary and primary alcohols and tert ‐butyl hydroperoxide (TBHP). Compared with the control molecule [Ru(tpy) 2 ]Cl 2 , the [Ru(tpy) 2 ] 2+ unit of wSMOF‐1 exhibits a remarkably higher heterogeneous catalysis activity for the oxidation of alcohols by TBHP in n ‐hexane. For the oxidation of 1‐phenylethan‐1‐ol, the yield of acetophenone was increased from 10 % to 95 %.

Zhang, Yun‐Chang↗

Layer-by-Layer Freezing of Nanoconfined Water

Abstract Nanoconfined water plays a pivotal role in a vast number of fields ranging from biological and materials sciences to catalysis, nanofluidics and geochemistry. Here, we report the freezing and melting behavior of water (D 2 O) nanoconfined in architected silica-based matrices including Vycor glass and mesoporous silica SBA-15 and SBA-16 with pore diameters ranging between 4–15 nm, which are investigated using differential scanning calorimetry and 2 H nuclear magnetic resonance spectroscopy. The results provide compelling evidence that the extreme dynamical heterogeneity of water molecules is preserved over distances as small as a few angstroms. Solidification progresses in a layer-by-layer fashion with a coexistence of liquid-like and solid-like dynamical fraction at all temperatures during the transition process. The previously reported fragile-to-strong dynamic transition in nanoconfined water is argued to be a direct consequence of the layer-by-layer solidification.

42 ENGINEERING↗

Nanocluster superstructures assembled via surface ligand switching at high temperature

Superstructures with nanoscale building blocks, when coupled with precise control of the constituent units, open opportunities in rationally designing and manufacturing desired functional materials. Yet, synthetic strategies for the large-scale production of superstructures are scarce. We report a scalable and generalized approach to synthesizing superstructures assembled from atomically precise Ce24O28(OH)8 and other rare-earth metal-oxide nanoclusters alongside a detailed description of the self-assembly mechanism. Combining operando small-angle X-ray scattering, ex situ molecular and structural characterizations, and molecular dynamics simulations indicates that a high-temperature ligand-switching mechanism, from oleate to benzoate, governs the formation of the nanocluster assembly. The chemical tuning of surface ligands controls superstructure disassembly and reassembly, and furthermore, enables the synthesis of multicomponent superstructures. Here, this synthetic approach, and the accurate mechanistic understanding, are promising for the preparation of superstructures for use in electronics, plasmonics, magnetics and catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

pH-Driven Restructuring of Hydration Layers and Cation Ad-sorption at the Alumina-Water Interface

Oxide-water interfaces underpin ion separation, catalysis, and electrochemical energy technologies, where the electrical double layer (EDL) controls adsorption, transport, and reactivity. Yet, the molecular-scale link between pH-dependent surface protonation, hydration-layer structure, and counter-ion adsorption remains poorly defined. Here, we combine in situ crystal truncation rod (CTR) and resonant anomalous X-ray reflectivity (RAXR) with streaming potential measurements and ab initio molecular dynamics (AIMD) simulations to resolve the chemical and structural evolution of the EDL at the single-crystal alumina (012)-water interface in 10 mM Rb+ over pH 3-12. CTR measurements reveal two distinct adsorbed water layers at ~2.2 and ~3.5 Å above the surface that each shift toward the substrate at transition pHs near 6.5 and 10.6, respectively, directly reflecting changes in primary hydration layer structure in response to the deprotonation of bridging and terminal aluminol groups. RAXR shows a 10-fold increase in Rb+ coverage and a decrease in mean adsorption height from ~3.5 to ~2.7 Å with increasing pH, indicating enhanced counter-ion binding accompanied by Stern layer contraction. Streaming potential measurements demonstrate that the zeta potential, i.e., potential at the hydrodynamic shear plane, is positive at pH 3 and becomes negative at pH ≥3.5. This negative charge magnitude increases with increasing pH, consistent with progressive surface deprotonation at higher pH. AIMD identifies inner- and outer-sphere Rb+ complexes whose adsorption heights and coordination geometries depend sensitively on the protonation state of surface oxygens, providing atomistic support for the experimentally inferred trends. These measurements establish two discrete, site-specific pH transitions in hydration-layer structure that track aluminol (de)protonation and quantitatively link them to a pH-driven contraction of the Stern layer (increasing Rb+ coverage and decreasing adsorption height). This provides a direct structural basis for connecting surface acid-base chemistry to ion binding distances at an oxide-water interface.

Electrical double layer (EDL), Surface protonation↗

Tracing the transient reaction kinetics of adsorbed species by in situ/operando infrared spectroscopy

The dynamic reaction behavior (i.e., transient responses) of IR-observable adsorbed species and gaseous products obtained from transient kinetic studies provide valuable kinetic and mechanistic information, namely: the abundance of active intermediates and their reactivity distribution, the chemical structure of IR-observable active and spectator species, the sequence of their formation, and the kinetically significant and rate-determining step under reaction conditions of practical catalysis. We discuss the use of transient response data to elucidate the reaction mechanisms of several gas-solid reactions: CO/H 2 , CO/H 2 /C 2 H 4 , photocatalytic oxidation of ethanol, and the CO 2 -amine reaction. The IR coupled with transient kinetic techniques is especially useful for investigating the mechanisms of photocatalytic reactions because both photogenerated electrons and many adsorbed species are IR-active (exhibiting measurable IR bands), and their evolution occurs on a time scale of seconds at ambient temperature. We highlight the key features and limitations of in situ IR with transient kinetics, as well as their significance in catalyst design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Direct Evidence for Excited Ligand Field State-based Oxidative Photoredox Chemistry of a Cobalt(III) Polypyridyl Photosensitizer

Increasing interest in sustainable chemistry coupled with the quest to explore new reactivity has spurred research on first-row transition metal complexes for potential applications in a variety of settings. One of the more active areas of research is photoredox catalysis, where the synthetically tunable nature of their electronic structures provides a rich palette of options for tailoring their reactivity to a desired chemical transformation. Understanding the mechanism of excited-state reactivity is critical for the informed development of next-generation catalysts, which in turn requires information concerning the propensity of their electronic excited states to engage in the desired electron or energy transfer processes. Herein we provide direct evidence of the highly oxidizing nature of the lowest-energy ligand-field (LF) excited state of a first-row d 6 -low-spin Co(III) photosensitizer [Co(4,4'-Br 2 bpy) 3 ] 3+ (where 4,4'-Br 2 bpy is 4,4'-dibromo-2,2'-bipyridine). The redox potential associated with the LF excited state of the Co(III) complex was bracketed by performing bimolecular quenching studies by using a series of simple organic electron donors. Time-resolved absorption spectroscopy confirmed a dynamic quenching process attributed to reductive quenching of the lowest-energy ligand-field excited state of the Co(III) chromophore. Analysis of the Stern–Volmer plots for each chromophore-quencher pair revealed a limiting value of E red * ~ 1.25 V vs Fc/Fc + for the metal-centered excited state, which is significantly stronger than that of more commonly employed transition metal-based photoredox agents such as [Ru(bpy) 3 ] 2+ (E red * = 0.32 V vs Fc/Fc + ) and [Ir(ppy) 2 (bpy)] + (E red * = 0.27 V vs Fc/Fc + ). Finally, these results suggest that this class of chromophores could find utility in applications requiring the activation of oxidatively resistant organic substrates for photoredox catalysis.

14 SOLAR ENERGY↗

Era of entropy: Synthesis, structure, properties, and applications of high-entropy materials

The field of high-entropy materials (HEMs) has emerged as a dynamic area of scientific exploration, driven by the exceptional properties arising from their compositional complexity. Encompassing both high-entropy alloys (HEAs) and high-entropy ceramics (HECs), these materials have garnered significant attention across diverse research domains. From investigations into phase evolution and mechanical characteristics to studies of ionic, electronic, and magnetic behaviors, HEMs demonstrate remarkable potential for a wide array of applications. These range from catalysis and tribology to energy storage and superconductivity. Fundamental research has shed light on crucial phenomena such as configurational entropy, lattice distortion, and sluggish diffusion. These discoveries are paving the way for materials design strategies that enable new functional tunability and resistance to application-specific harsh environments. This burgeoning field promises to revolutionize material design and performance across numerous technological sectors. Here, this special collection between Applied Physics Letters and the Journal of Applied Physics provides a timely overview of the latest research in this area. It highlights the growing interest in understanding the impact of high compositional complexity on conventional structure–process–property–performance relationships in HEMs.

36 MATERIALS SCIENCE↗

Stagnation-point heat-transfer rate predictions at aeroassist flight conditions

The results are presented for the stagnation-point heat-transfer rates used in the design process of the Aeroassist Flight Experiment (AFE) vehicle over its entire aeropass trajectory. The prediction methods used in this investigation demonstrate the application of computational fluid dynamics (CFD) techniques to a wide range of flight conditions and their usefulness in a design process. The heating rates were computed by a viscous-shock-layer (VSL) code at the lower altitudes and by a Navier-Stokes (N-S) code for the higher altitude cases. For both methods, finite-rate chemically reacting gas was considered, and a temperature-dependent wall-catalysis model was used. The wall temperature for each case was assumed to be radiative equilibrium temperature, based on total heating. The radiative heating was estimated by using a correlation equation. Wall slip was included in the N-S calculation method, and this method implicitly accounts for shock slip. The N-S/VSL combination of projection methods was established by comparison with the published benchmark flow-field code LAURA results at lower altitudes, and the direct simulation Monte Carlo results at higher altitude cases. To obtain the design heating rate over the entire forward face of the vehicle, a boundary-layer method (BLIMP code) that employs reacting chemistry and surface catalysis was used. The ratio of the VSL or N-S method prediction to that obtained from the boundary-layer method code at the stagnation point is used to define an adjustment factor, which accounts for the errors involved in using the boundary-layer method.

Gupta, Roop N.↗

Scale-free, programmable design of morphable chain loops of kilobots and colloidal motors

Micron-scale robots require systems that can morph into arbitrary target configurations controlled by external agents such as heat, light, electricity, and chemical environment. Achieving this behavior using conventional approaches is challenging because the available materials at these scales are not programmable like their macroscopic counterparts. To overcome this challenge, we propose a design strategy to make a robotic machine that is both programmable and compatible with colloidal-scale physics. Our strategy uses motors in the form of active colloidal particles that constantly propel forward. We sequence these motors end-to-end in a closed chain forming a two-dimensional loop that folds under its mechanical constraints. We encode the target loop shape and its motion by regulating six design parameters, each scale-invariant and achievable at the colloidal scale. We demonstrate the plausibility of our design strategy using centimeter-scale robots called kilobots . We use Brownian dynamics simulation to explore the large design space beyond that possible with kilobots, and present an analytical theory to aid the design process. Multiple loops can also be fused together to achieve several complex shapes and robotic behaviors, demonstrated by folding a letter shape “M,” a dynamic gripper , and a dynamic pacman . The material-agnostic, scale-free, and programmable nature of our design enables building a variety of reconfigurable and autonomous robots at both colloidal scales and macroscales.

36 MATERIALS SCIENCE↗

Direct study of changes in catalyst structure-kinetic properties during redox transitions using a new time-resolved technique

Direct study of changes in catalyst structure-kinetic properties during redox transitions using a new time-resolved technique The Temporal Analysis of Products (TAP) pulse response methodology1 is a transient technique offering the time scale needed to deconvolve many reaction steps from the complex network typical to industrial catalytic processes. The traditional TAP measurement observes the gas phase dynamic response but, hereto now, has been devoid of any direct measurement of change in the catalyst itself. The development of an operando technique that couples gas phase transient kinetics to dynamic metal centers and surface species is presented. Significance Unification of the TAP methodology with time-resolved spectroscopic measurement can offer unprecedented insight into the complex kinetic phenomena regulated by the solid catalyst.

03 - NATURAL GAS↗

Vapor-phase self-assembly for generating thermally stable single-atom catalysts

Preparation of thermally stable metal single-atom catalysts (SACs) is a challenge in heterogeneous catalysis, especially on conventional supports that provide a weak metal-support interaction. In this work, we report that a modified support MgAl 2 O 4 can stabilize Pt single atoms by a mechanism of vapor-phase self-assembly in a high-temperature treatment (800°C, air). The experimental results on the formation mechanism and the structure are validated by DFT and ab initio molecular dynamics simulations. We infer that stable triangular K 3 O 3 structures help stabilize Pt single atoms at high temperatures in oxidizing conditions, exhibiting excellent reactivity for methane oxidation. The obtained Pt/K/MgAl 2 O 4 SAC presents excellent stability in methane oxidation after steam treatment at elevated temperatures, whereas the Pt/MgAl 2 O 4 nanocatalyst suffers from rapid deactivation due to Pt nanoparticle growth. Now this work paves the way for preparing thermally stable and highly active SACs using conventional high-surface-area supports, despite the weak metal-support interaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Atomic resolution coherent x-ray imaging with physics-based phase retrieval

Coherent x-ray imaging and scattering from accelerator based sources such as synchrotrons continue to impact biology, medicine, technology, and materials science. Many synchrotrons around the world are currently undergoing major upgrades to increase their available coherent x-ray flux by approximately two orders of magnitude. The improvement of synchrotrons may enable imaging of materials in operando at the atomic scale which may revolutionize battery and catalysis technologies. Current algorithms used for phase retrieval in coherent x-ray imaging are based on the projection onto sets method. These traditional iterative phase retrieval methods will become more computationally expensive as they push towards atomic resolution and may struggle to converge. Additionally, these methods do not incorporate physical information that may additionally constrain the solution. In this work, we present an algorithm which incorporates molecular dynamics into Bragg coherent diffraction imaging (BCDI). This algorithm, which we call PRAMMol (Phase Retrieval with Atomic Modeling and Molecular Dynamics) combines statistical techniques with molecular dynamics to solve the phase retrieval problem. We present several examples where our algorithm is applied to simulated coherent diffraction from 3D crystals and show convergence to the correct solution at the atomic scale.

47 OTHER INSTRUMENTATION↗

Experimental and theoretical insights into the effects of pH on catalysis of bond-cleavage by the lignin peroxidase isozyme H8 from Phanerochaete chrysosporium

Abstract Background Lignin peroxidases catalyze a variety of reactions, resulting in cleavage of both β-O-4′ ether bonds and C–C bonds in lignin, both of which are essential for depolymerizing lignin into fragments amendable to biological or chemical upgrading to valuable products. Studies of the specificity of lignin peroxidases to catalyze these various reactions and the role reaction conditions such as pH play have been limited by the lack of assays that allow quantification of specific bond-breaking events. The subsequent theoretical understanding of the underlying mechanisms by which pH modulates the activity of lignin peroxidases remains nascent. Here, we report on combined experimental and theoretical studies of the effect of pH on the enzyme-catalyzed cleavage of β-O-4′ ether bonds and of C–C bonds by a lignin peroxidase isozyme H8 from Phanerochaete chrysosporium and an acid stabilized variant of the same enzyme. Results Using a nanostructure initiator mass spectrometry assay that provides quantification of bond breaking in a phenolic model lignin dimer we found that catalysis of degradation of the dimer to products by an acid-stabilized variant of lignin peroxidase isozyme H8 increased from 38.4% at pH 5 to 92.5% at pH 2.6. At pH 2.6, the observed product distribution resulted from 65.5% β-O-4′ ether bond cleavage, 27.0% C α -C 1 carbon bond cleavage, and 3.6% C α -oxidation as by-product. Using ab initio molecular dynamic simulations and climbing-image Nudge Elastic Band based transition state searches, we suggest the effect of lower pH is via protonation of aliphatic hydroxyl groups under which extremely acidic conditions resulted in lower energetic barriers for bond-cleavages, particularly β-O-4′ bonds. Conclusion These coupled experimental results and theoretical explanations suggest pH is a key driving force for selective and efficient lignin peroxidase isozyme H8 catalyzed depolymerization of the phenolic lignin dimer and further suggest that engineering of lignin peroxidase isozyme H8 and other enzymes involved in lignin depolymerization should include targeting stability at low pH.

09 BIOMASS FUELS↗

Observing Chemical and Morphological Changes in a Cu@TiO x Core@Shell Catalyst: Impact of Reversible Metal-Oxide Interactions on CO 2 Activation and Hydrogenation

A combination of several in-situ techniques (XRD, XAS, AP-XPS, E-TEM) was used to explore links between the structural and chemical properties of a Cu@TiO x catalyst under CO 2 hydrogenation conditions. The active phase of the catalyst involved an inverse oxide/metal configuration, but the initial core@shell motif was disrupted during the pre-treatment in H 2 . As a consequence of strong metal-support interactions, the titania shell cracked and Cu particles migrated from the core to on top of the oxide with the simultaneous formation of a Cu-Ti-O x phase. The generated Cu particles had a diameter of 20-40 nm and were decorated by small clusters of TiO x (< 5 nm in size). Results of in-situ XAS and XRD and images of E-TEM showed a very dynamic system, where the inverse oxide/metal configuration promoted the reactivity of the system towards CO 2 and H 2 . At room temperature, CO 2 oxidized the Cu nanoparticles (CO 2,gas → CO gas + O oxide ) inducing a redistribution of the TiO x clusters and big modifications in catalyst surface morphology. The generated oxide overlayer disappeared at elevated temperatures (> 180 °C) upon exposure to H 2 , producing a transient surface that was very active for the reverse water-gas shift reaction (CO 2 + H 2 → CO + H 2 O) but was not stable at 250 °C. When oxidation and reduction occurred at the same time, under a mixture of CO 2 and H 2 , the surface structure evolved toward a dynamic equilibrium that strongly depended on the temperature. Neither CO 2 nor H 2 can be considered as passive reactants. In the Cu@TiO x system, morphological changes were linked to variations in the composition of metal-oxide interfaces which were reversible with temperature or chemical environment and affected the catalytic activity of the system. Finally, the present study illustrates the dynamic nature of phenomena associated with the trapping and conversion of CO 2 .

36 MATERIALS SCIENCE↗

Creating self-assembled arrays of mono-oxo (MoO 3 ) 1 species on TiO 2 (101) via deposition and decomposition of (MoO 3 ) n oligomers

Significance The design and synthesis of hierarchically ordered oxides remains a critical challenge in material science and catalysis. Here, we demonstrate that well-ordered homotopic arrays of mono-oxo (MoO 3 ) 1 can be easily prepared on anatase TiO 2 (101) via the deposition of (MoO 3 ) n oligomers. As revealed by our combined experiential and theoretical studies, the oligomers spontaneously decompose and self-assemble into chemically identical and thermally stable monomers. The oligomer decomposition is permitted at room temperature due to the dynamic coupling of decomposition steps to the lattice phonons of TiO 2 . We identify transient mobility of the oligomers as key to the self-assembly of the complete overlayer. The ease of preparation and thermal stability of this atomically precise system makes it highly suitable for a broad range of applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Direct Synthesis of Layer-Tunable and Transfer-Free Graphene on Device-Compatible Substrates Using Ion Implantation Toward Versatile Applications

Direct synthesis of layer-tunable and transfer-free graphene on technologically important substrates is highly valued for various electronics and device applications. State of the art in the field is currently a two-step process: a high-quality graphene layer synthesis on metal substrate through chemical vapor deposition (CVD) followed by delicate layer transfer onto device-relevant substrates. Here, we report a novel synthesis approach combining ion implantation for a precise graphene layer control and dual-metal smart Janus substrate for a diffusion-limiting graphene formation to directly synthesize large area, high quality, and layer-tunable graphene films on arbitrary substrates without the post-synthesis layer transfer process. Carbon (C) ion implantation was performed on Cu–Ni film deposited on a variety of device-relevant substrates. A well-controlled number of layers of graphene, primarily monolayer and bilayer, is precisely controlled by the equivalent fluence of the implanted C-atoms (1 monolayer ~4 × 10 15 C-atoms/cm 2 ). Upon thermal annealing to promote Cu-Ni alloying, the pre-implanted C-atoms in the Ni layer are pushed toward the Ni/substrate interface by the top Cu layer due to the poor C-solubility in Cu. As a result, the expelled C-atoms precipitate into a graphene structure at the interface facilitated by the Cu-like alloy catalysis. After removing the alloyed Cu-like surface layer, the layer-tunable graphene on the desired substrate is directly realized. The layer-selectivity, high quality, and uniformity of the graphene films are not only confirmed with detailed characterizations using a suite of surface analysis techniques but more importantly are successfully demonstrated by the excellent properties and performance of several devices directly fabricated from these graphene films. Molecular dynamics (MD) simulations using the reactive force field (ReaxFF) were performed to elucidate the graphene formation mechanisms in this novel synthesis approach. With the wide use of ion implantation technology in the microelectronics industry, this novel graphene synthesis approach with precise layer-tunability and transfer-free processing has the promise to advance efficient graphene-device manufacturing and expedite their versatile applications in many fields.

36 MATERIALS SCIENCE↗

Plasmonic Energetic Electrons Drive CO 2 Reduction on Defective Cu 2 O

Plasmonic photoreduction of CO 2 is valuable for decarbonization and producing value-added chemicals. However, insights into the mechanisms of this reaction remain elusive, particularly regarding the roles of structural defects and their interplay with the nonequilibrium charge carriers. Here, we report density functional theory calculations on Cu 2 O, a prototype photocatalyst, through which we investigate CO 2 reduction over three defected facets to reveal the interfacial charge transfer and bond dynamics under plasmonic excitation. We find that the activation barrier of C–O bond cleavage decreases from 3.2 to about 1 eV, assisted by oxygen vacancies, and that the remaining barrier can be further reduced or eliminated at the plasmon-excited states when Cu 2 O is integrated with plasmonic metals. The regeneration of oxygen vacancies (by H 2 to form water) on Cu 2 O to complete the catalysis cycle is feasible and not affected by the energetic electrons. Furthermore, our calculations thus show the important synergistic effect of energetic electrons and point defects to promote CO 2 reduction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗