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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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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Influence of Ligand Structure on Excited State Surface Chemistry of Lead Sulfide Quantum Dots

The ligand-nanocrystal boundaries of colloidal quantum dots (QDs) mediate the primary energy and electron transfer processes that underpin photochemical and photocatalytic transformations at their surfaces. We use mid-infrared transient absorption spectroscopy to reveal the influence that ligand structure and bonding to nanocrystal surfaces have on the changes of the excited state surface chemistry of this boundary in PbS QDs and the corresponding impact on charge transfer processes between nanocrystals. We demonstrate that oleate ligands undergo marked changes in their bonding to surfaces in the excitonic excited states of the nanocrystals, indicating that oleate passivated PbS surfaces undergo significant structural changes following photoexcitation. These changes can impact the surface mobility of the ligands and the ability of redox shuttles to approach the nanocrystal surfaces to undergo charge transfer in photocatalytic reactions. In contrast, markedly different transient vibrational features are observed in iodide/mercaptoproprionic acid passivated PbS QD films that result from charge transfer between neighboring nanocrystals and localization of holes at the nanocrystal surfaces near MPA ligands. This ability to distinguish the influence that excitonic excited states vs charge transfer processes have on the surface chemistry of the ligand-nanocrystal boundary lays the groundwork for exploration of how this boundary can be understood and controlled for the design of nanocrystalline materials tailored for specific applications in solar energy harvesting and photocatalytic reactions.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Induced Metal-free Star Formation around a Massive Black Hole Seed

The direct formation of a massive black hole is a potential seeding mechanism of the earliest observed supermassive black holes. We investigate how the existence of a massive black hole seed impacts the ionization and thermal state of its pre-galactic host halo and subsequent star formation. We show that its X-ray radiation ionizes and heats the medium, enhancing H 2 formation in shielded regions, within the nuclear region in the span of a million years. The enhanced molecular cooling triggers the formation of a ~10 4 M⊙ metal-free stellar cluster at a star formation efficiency of ~0.1% in a single event. Star formation occurs near the edges of the H ii region that is partially ionized by X-rays; thus, the initial size depends on the black hole properties and surrounding environment. Furthermore, the simulated metal-free galaxy has an initial half-light radius of ~10 pc but expands to ~50 pc after 10 million years because of the outward velocities of their birth clouds. Supernova feedback then quenches any further star formation for tens of millions of years, allowing the massive black hole to dominate the spectrum once the massive metal-free stars die.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Jipole: A Differentiable ipole-based Code for Radiative Transfer in Curved Spacetimes

Recent imaging of supermassive black holes by the Event Horizon Telescope has relied on exhaustive parameter-space searches, matching observations to large, precomputed libraries of theoretical models. As observational data become increasingly precise, the limitations of this computationally expensive approach grow more acute, creating a pressing need for more efficient methods. In this work, we present Jipole, an automatically differentiable (AD), ipole-based code for radiative transfer in curved spacetimes, designed to compute image gradients with respect to underlying model parameters. These gradients quantify how parameter changes—such as the black hole’s spin or the observer’s inclination—affect the image, enabling more efficient parameter estimation and reducing the number of required images. We validate Jipole against ipole in two analytical tests and then compare pixelwise intensity derivatives from AD with those from finite-difference methods. We then demonstrate the utility of these gradients by performing parameter recovery for an analytical model in three increasingly complex cases for the injected image: ideal, blurred, and blurred with added noise. In most cases, high-accuracy fits are obtained in only a few optimization steps, failing only in cases with extremely low signal-to-noise ratios. These results highlight the potential of AD-based methods to accelerate robust, high-fidelity model-data comparisons in current and future black hole imaging efforts.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Solar cell contacts: quantifying the impact of interfacial layers on selectivity, recombination, charge transfer, and V oc

Interfacial layers (IFLs) are ubiquitous in solar cells, but their precise impact on carrier transfer rates and the relation of these rates to performance metrics and the concepts of selectivity and recombination is lacking. We report the use of a well-defined interdigitated back-contact (IBC) silicon solar cell to determine the precise role of such IFLs. We characterize the action of the common IFL spiro-OMeTAD by making it a third contact to the IBC cell. This architecture creates three solar cells within a single structure that, with numerical simulation, provide the exchange current densities (i.e., charge transfer rates) for electrons ( J 0n ) and holes ( J 0p ) and the quasi Fermi-level splitting in the absorber, which measures the balance of generation and recombination. Further, we describe the relation of V oc to contact recombination, the asymmetry in electron/hole collection rates at a single contact (contact selectivity), and the asymmetry in collection rates of the same carrier at separate contacts (carrier selectivity). Relative to bare gold, neat spiro-OMeTAD reduces J 0n and J 0p (their geometric mean ( J 0n J 0p ) 0.5 decreases by 10 4 ), decreasing contact recombination. Addition of the common dopant Li-TFSI and air increase J 0p / J 0n by 10 6 with little effect on ( J 0n J 0p ) 0.5 , increasing contact hole selectivity. The significant increase in V oc observed by introducing spiro-OMeTAD/Li-TFSI IFLs into the cells studied, however, is due to an increase in the carrier selectivity rather than the contact selectivity or recombination of the spiro-OMeTAD-modified contact. Operando measurements further show voltage-dependent changes in the J 0 s, demonstrating that spiro-OMeTAD contributes to hysteresis. Broader context : Solar cells operate by photogenerating excess charge carriers in an absorber material and, in competition with recombination, asymmetrically extracting them at so-called carrier-selective contacts, one that ideally collects only electrons and the other, only holes. Particularly in emerging photovoltaics such as perovskites, thin layers of organic semiconductors or related materials are introduced between the absorber and contact to improve power conversion efficiency. In terms of interfacial charge transfer, a prevailing view is that such interfacial layers improve performance by helping block the collection of the undesired carrier, considered a form of recombination. We use a novel platform to study the simultaneous impact of spiro-OMeTAD, a common interfacial layer, on the collection of electrons, the collection of holes, and on the recombination of electrons and holes. We quantitatively demonstrate that spiro-OMeTAD layers indeed passivate the contact toward recombination, but that larger improvements in the open-circuit voltage, a key cell metric, can come not only from this but also from increasing the asymmetry of the collection of electrons in the system. Further, operando measurements show transient changes in the properties of spiro-OMeTAD which suggest that it contributes to hysteresis phenomena commonly observed in perovskite and other solar cells.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Electrochemical Characterization of Photo-Driven Hole-Scavenging by Cadmium Sulfide Quantum Dot-Nitrogenase Biohybrid Complexes

Light-driven biohybrid systems that couple semiconductor nanocrystals with enzymes offer a promising strategy for solar-to-chemical energy-conserving reduction reactions, yet are often limited by inefficient hole scavenging. Hole scavenging is critical for maintaining charge separation in the light-absorbing electron donor molecule and, thus, for sustaining catalytic turnover, making quantification essential to improving system efficiency. Here, we introduce a photoelectrochemical approach for real-time monitoring of hole scavenging in cadmium sulfide (CdS) quantum dot (QD)-nitrogenase MoFe protein biohybrids that catalyze the reduction of H+ and N2. Using hydroquinone (HQ) as the sacrificial electron donor (SED), oxidation of HQ to benzoquinone (BQ) by photogenerated valence-band holes is coupled to the electrochemical reduction of BQ at an electrode, enabling quantification of the hole-scavenging reaction via chronoamperometry. This approach provides a continuous, real-time readout of charge-transfer dynamics under illumination. Systematic variation of light intensity and donor concentration reveals that hole scavenging scales with photon flux and exhibits a non-linear dependence on SED concentration, with an optimum at intermediate HQ concentrations. These results establish chronoamperometry as a powerful tool for probing photoinduced charge transfer, advancing the quantitative understanding of hole-scavenging in biohybrid systems, and offering a generalizable framework for optimizing solar-driven biocatalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Time-Resolved Observation of Hole Tunneling in van der Waals Multilayer Heterostructures

We reported a time-resolved study of quantum-mechanical tunneling of holes between two MoSe 2 monolayers that are separated by a monolayer WS 2 energy barrier. Four-layer heterostructures of MoSe 2 /WS 2 /MoSe 2 /graphene, as well as control samples, were fabricated by mechanical exfoliation and dry transfer techniques. To time-resolve the hole tunneling process, an ultrashort laser pulse was used to excite electrons and holes in both MoSe 2 layers. Here, by utilization of the graphene layer to eliminate carriers in the third MoSe 2 layer, the first MoSe 2 layer is selectively populated with the holes, which then tunnel to the third MoSe 2 layer. By monitoring decay of the hole population with an ultrashort probe pulse, we measure a hole tunneling time of about 20 ps, which is found to slightly increase with the injected carrier density. Besides the fundamental interests of real-time observation of the quantum-mechanical tunneling effect across a nanometer barrier, these results provide quantitative understanding on tunneling mechanisms of charge transfer in van der Waals heterostructures, which is useful for designing sophisticated van der Waals multilayer heterostructures.

36 MATERIALS SCIENCE↗
NASA NTRS2000

Effect of Film-Hole Shape on Turbine Blade Film Cooling Performance

The detailed heat transfer coefficient and film cooling effectiveness distributions as well as tile detailed coolant jet temperature profiles on the suction side of a gas turbine blade A,ere measured using a transient liquid crystal image method and a traversing cold wire and a traversing thermocouple probe, respectively. The blade has only one row of film holes near the gill hole portion on the suction side of the blade. The hole geometries studied include standard cylindrical holes and holes with diffuser shaped exit portion (i.e. fanshaped holes and laidback fanshaped holes). Tests were performed on a five-blade linear cascade in a low-speed wind tunnel. The mainstream Reynolds number based on cascade exit velocity was 5.3 x 10(exp 5). Upstream unsteady wakes were simulated using a spoke-wheel type wake generator. The wake Strouhal number was kept at 0 or 0.1. Coolant blowing ratio was varied from 0.4 to 1.2. Results show that both expanded holes have significantly improved thermal protection over the surface downstream of the ejection location, particularly at high blowing ratios. However, the expanded hole injections induce earlier boundary layer transition to turbulence and enhance heat transfer coefficients at the latter part of the blade suction surface. In general, the unsteady wake tends to reduce film cooling effectiveness.

Han, J. C.↗
DOE OSTI2025

Mahakala: A Python-based Modular Ray-tracing and Radiative Transfer Algorithm for Curved Spacetimes

We introduce Mahakala, a Python-based, modular, radiative ray-tracing code for curved spacetimes. We employ Google's JAX framework for accelerated automatic differentiation, which can efficiently compute Christoffel symbols directly from the metric, allowing the user to easily and quickly simulate photon trajectories through non-Kerr spacetimes. JAX also enables Mahakala to run in parallel on both CPUs and GPUs. Mahakala natively uses the Cartesian Kerr–Schild coordinate system, which avoids numerical issues caused by the pole in spherical coordinate systems. We demonstrate Mahakala's capabilities by simulating 1.3 mm wavelength images (the wavelength of Event Horizon Telescope observations) of general relativistic magnetohydrodynamic simulations of low-accretion rate supermassive black holes. The modular nature of Mahakala allows us to quantitatively explore how different regions of the flow influence different image features. We show that most of the emission seen in 1.3 mm images originates close to the black hole and peaks near the photon orbit. We also quantify the relative contribution of the disk, forward jet, and counterjet to 1.3 mm images.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1995

Some constraints on acceleration mechanisms in the solar wind at polar latitudes

Observations of solar Lyman alpha have been interpreted as indicating that the polar mass flux density is lower than the equatorial average. This led Lallement et al (1986) to make a parametric study of solar wind acceleration, along the lines of earlier the Munro-Jackson study (1977), in which they concluded that uncertainties in the polar mass flux were large enough to be consistent with two extreme opposites: (1) a substantial energy supply beyond classical thermal conduction is required; or (2) classical thermal conduction is adequate to drive the flow. This ambiguity has been clarified by Ulysses observations of the polar outflow (Phillips et al, 1994). The polar mass flux density lies in the middle of the range studies by Lallement et al (1986), which suggests that extended heating is going on out to at least approximately 5 AU. Independent, purely energetic arguments can be made to estimate the required coronal source (electron) temperature that would be required to account for the observed energy flux density. An electron temperature of at least 2 x 10(exp 6) K would be required for the classical conduction flux density to be comparable to the total energy flux density; such a high temperature is thought to be unlikely in a coronal hole. These arguments strongly suggest that some extended heating or momentum transfer mechanism is required to drive the solar wind from the polar coronal hole. A number of mechanisms are discussed.

Barnes, A.↗
NASA NTRS2014

Long Hole Film Cooling Dataset for CFD Development - Flow and Film Effectiveness

An experiment investigating flow and heat transfer of long (length to diameter ratio of 18) cylindrical film cooling holes has been completed. In this paper, the thermal field in the flow and on the surface of the film cooled flat plate is presented for nominal freestream turbulence intensities of 1.5 and 8 percent. The holes are inclined at 30 deg above the downstream direction, injecting chilled air of density ratio 1.0 onto the surface of a flat plate. The diameter of the hole is 0.75 in. (approx. 0.02 m) with center to center spacing (pitch) of 3 hole diameters. Coolant was injected into the mainstream flow at nominal blowing ratios of 0.5, 1.0, 1.5, and 2.0. The Reynolds number of the freestream was approximately 11,000 based on hole diameter. Thermocouple surveys were used to characterize the thermal field. Infrared thermography was used to determine the adiabatic film effectiveness on the plate. Hotwire anemometry was used to provide flowfield physics and turbulence measurements. The results are compared to existing data in the literature. The aim of this work is to produce a benchmark dataset for Computational Fluid Dynamics (CFD) development to eliminate the effects of hole length to diameter ratio and to improve resolution in the near-hole region. In this report, a Time Filtered Navier Stokes (TFNS), also known as Partially Resolved Navier Stokes (PRNS), method that was implemented in the Glenn-HT code is used to model coolant-mainstream interaction. This method is a high fidelity unsteady method that aims to represent large scale flow features and mixing more accurately.

Shyam, Vikram↗
DOE OSTI2025

Charge Separation at Organic Interfaces with Near-Zero Energy Offset: A Step toward Designing Inorganic-like Organic Semiconductors

For organic semiconductors, it is often presumed that an energy level offset at the donor–acceptor (D-A) interface is required to provide the driving force for charge separation (CS). This energy level offset unavoidably leads to a voltage loss in organic photovoltaics. In this work, by using zinc phthalocyanine (ZnPc) and fluorinated zinc phthalocyanine (F 4 ZnPc) as a model D/A interface, we found that spontaneous CS, with an enthalpy increase of ∼0.3–0.4 eV, can occur even with an interfacial energy offset as small as ∼0.1 eV. This enthalpy-increase CS process is driven by entropy. The entropic driving force can be enhanced by two factors: (1) a point-like spatial contact between the delocalized electron and hole wave function in the charge transfer exciton; (2) a small band bending near the interface originating from long-range electrostatic interaction. Our work demonstrates that effective CS can occur at interfaces with a near-zero energy level offset, which means that the energy loss at the D/A interface can be avoided.

36 MATERIALS SCIENCE↗
NASA NTRS1999

A Numerical Analysis of Heat Transfer and Effectiveness on Film Cooled Turbine Blade Tip Models

A computational study has been performed to predict the distribution of convective heat transfer coefficient on a simulated blade tip with cooling holes. The purpose of the examination was to assess the ability of a three-dimensional Reynolds-averaged Navier-Stokes solver to predict the rate of tip heat transfer and the distribution of cooling effectiveness. To this end, the simulation of tip clearance flow with blowing of Kim and Metzger was used. The agreement of the computed effectiveness with the data was quite good. The agreement with the heat transfer coefficient was not as good but improved away from the cooling holes. Numerical flow visualization showed that the uniformity of wetting of the surface by the film cooling jet is helped by the reverse flow due to edge separation of the main flow.

Ameri, A. A.↗
NASA NTRS1997

Comparison of Two-Equation Turbulence Models for Prediction of Heat Transfer on Film-Cooled Turbine Blades

A three-dimensional Navier-Stokes code has been used to compute the heat transfer coefficient on two film-cooled turbine blades, namely, the VKI rotor with six rows of cooling holes, including three rows on the shower head and the C3X vane with nine rows of holes, including five rows on the shower head. Predictions of heat transfer coefficient at the blade surface using three two-equation turbulence model specifically, Coakley's q-omega model, Chien's k-epsilon model and Wilcox's k-omega model with Menter's modifications, have been compared with the experimental data of Camci and Arts for the VKI rotor, and of Hylton et al. for the C3X vane along with predictions using the Baldwin-Lomar (B-L) model taken from Garg and Gaugler. It is found that for the cases considered here the two equation models predict the blade heat transfer somewhat better than the B-L model except immediately downstream of the film-cooled holes on the suction surface of the VKI rotor, and over most of the suction surface of the C3X vane. However, all two-equation models require 40% more computer core than the B-L model for solution, and while the q-omega and k-epsilon models need 40% more computer time than the B-L model the k-omega model requires at least 65% more time because of the slower rate of convergence. It is found that the heat transfer coefficient exhibit a strong spanwise as well as streamwise variation for both blades and all turbulence models.

Garg, Vijay K.↗
DOE OSTI2023

Harvesting electrons and holes from photodriven symmetry-breaking charge separation within a perylenediimide photosynthetic model dimer

Understanding how to utilize symmetry-breaking charge separation (SB-CS) offers a path toward increasingly efficient light-harvesting technologies. This process plays a central role in the first step of photosynthesis, in which the dimeric “special pair” of the photosynthetic reaction center enters a coherent SB-CS state after photoexcitation. Previous research on SB-CS in both biological and synthetic chromophore dimers has focused on increasing the efficiency of light-driven processes. In a chromophore dimer undergoing SB-CS, the energy of the radical ion pair product is nearly isoenergetic with that of the lowest excited singlet (S 1 ) state of the dimer. This means that very little energy is lost from the absorbed photon. In principle, the relatively high energy electron and hole generated by SB-CS within the chromophore dimer can each be transferred to adjacent charge acceptors to extend the lifetime of the electron–hole pair, which can increase the efficiency of solar energy conversion. To investigate this possibility, we have designed a bis-perylenediimide cyclophane (mPDI 2 ) covalently linked to a secondary electron donor, peri-xanthenoxanthene (PXX) and a secondary electron acceptor, partially fluorinated naphthalenediimide (FNDI). Upon selective photoexcitation of mPDI 2 , transient absorption spectroscopy shows that mPDI 2 undergoes SB-CS, followed by two secondary charge transfer reactions to generate a PXX •+ -mPDI 2 -FNDI •– radical ion pair having a nearly 3 µs lifetime. In conclusion, this strategy has the potential to increase the efficiency of molecular systems for artificial photosynthesis and photovoltaics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Efficient interlayer electron transfer in a MoTe 2 /WS 2 /MoS 2 trilayer heterostructure

Electron transfer and carrier dynamics in MoTe 2 /WS 2 /MoS 2 trilayer heterostructures are investigated by transient absorption and photoluminescence measurements. Monolayer flakes of MoTe 2 , WS 2 , and MoS 2 are obtained by mechanical exfoliation from their bulk crystals and are used to fabricate the heterostructures by a dry-transfer technique. Here, photoluminescence spectroscopic measurements indicate that the recombination of the MoS 2 and WS 2 intralayer excitons is significantly suppressed in the heterostructure, illustrating the efficient interlayer charge transfer processes. Layer-selective time-resolved differential reflectance measurements show that the electrons excited in MoTe 2 can transfer to MoS 2 within 0.3 ps. The transferred electrons show a long lifetime of several hundred picoseconds due to their slow recombination with the spatially separated holes that reside in MoTe 2 . Furthermore, the charge transfer and recombination processes are weakly dependent on the injected carrier density. These results demonstrate the feasibility of constructing van der Waals multilayer heterostructures involving the infrared-sensitive MoTe 2 with emergent properties and provide important information to quantify the performance of MoTe 2 - based devices.

2D materials↗
NASA NTRS2000

Residual Strength Analyses of Riveted Lap-Splice Joints

The objective of this paper was to analyze the crack-linkup behavior in riveted-stiffened lap-splice joint panels with small multiple-site damage (MSD) cracks at several adjacent rivet holes. Analyses are based on the STAGS (STructural Analysis of General Shells) code with the critical crack-tip-opening angle (CTOA) fracture criterion. To account for high constraint around a crack front, the "plane strain core" option in STAGS was used. The importance of modeling rivet flexibility with fastener elements that accurately model load transfer across the joint is discussed. Fastener holes are not modeled but rivet connectivity is accounted for by attaching rivets to the sheet on one side of the cracks that simulated both the rivet diameter and MSD cracks. Residual strength analyses made on 2024-T3 alloy (1.6-mm thick) riveted-lap-splice joints with a lead crack and various size MSD cracks were compared with test data from Boeing Airplane Company. Analyses were conducted for both restrained and unrestrained buckling conditions. Comparison of results from these analyses and results from lap-splice-joint test panels, which were partially restrained against buckling indicate that the test results were bounded by the failure loads predicted by the analyses with restrained and unrestrained conditions.

Seshadri, B. R.↗
DOE OSTI2021

Solution-phase p-type doping of highly enriched semiconducting single-walled carbon nanotubes for thermoelectric thin films

Single-walled carbon nanotubes (SWCNTs) are attractive materials for next-generation energy-harvesting technologies, including thermoelectric generators, due to their tunable opto-electronic properties and high charge carrier mobilities. Controlling the Fermi level within these unique 1D nanomaterials is often afforded by charge transfer interactions between SWCNTs and electron or hole accepting species. Conventional methods to dope SWCNT networks typically involve the diffusion of molecular redox dopant species into solid-state thin films, but solution-phase doping could potentially provide routes and/or benefits for charge carrier transport, scalability, and stability. Here, we develop a methodology for solution-phase doping of polymer-wrapped, highly enriched semiconducting SWCNTs using a p-type charge transfer dopant, F4TCNQ. This allows doped SWCNT inks to be cast into thin films without the need for additional post-deposition doping treatments. We demonstrate that the introduction of the dopant at varying stages of the SWCNT dispersion process impacts the ultimate thermoelectric performance and observe that the dopant alters the polymer selectivity for semiconducting vs metallic SWCNTs. In contrast to dense semiconducting polymer films, where solution-phase doping typically leads to disrupted morphologies and poorer TE performance than solid-state doping, thin films of solution-doped s-SWCNTs perform similarly to their solid-state doped counterparts. Interestingly, our results also suggest that solution-phase F4TCNQ doping leads to fully ionized and dimerized F4TCNQ anions in solid-state films that are not observed in films doped with F4TCNQ after deposition. Our results provide a framework for the application of solution-phase doping to a broad array of high-performance SWCNT-based thermoelectric materials and devices that may require high-throughput deposition techniques.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Highly Efficient Surface Charge Transfer in Fe 2 TiO 5 Epitaxial Thin Film Photoanodes

Pseudobrookite (Fe 2 TiO 5 ) has attracted significant attention as an emerging photoanode for water oxidation due to reports of enhanced performance in polycrystalline heterostructures with α-Fe 2 O 3 or TiO 2 . However, the specific properties and contribution of Fe 2 TiO 5 remain unknown. Here, we present the first photoelectrochemical characterization of epitaxial thin film Fe 2 TiO 5 , an ideal platform for probing the inherent response of this earth-abundant photoanode for solar water splitting. Moreover, by using an electrolyte containing a hole scavenger, we find highly efficient charge transfer at the Fe 2 TiO 5 –electrolyte interface. This notable surface property is exploited in the form of an Fe 2 TiO 5 /α-Fe 2 O 3 heterostructure photoanode, for which we observe a photocurrent density increase by 1 order of magnitude and an onset potential improvement by ~300 mV. Establishing these fundamental properties elucidates the nature of reaction mechanisms on Fe 2 TiO 5 and informs the design of highly efficient water photo-oxidation devices by incorporating this material with other photoanodes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗