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At least 73 records · Page 4

PtRu Catalysts on Nitrogen-Doped Carbon Nanotubes with Conformal Hydrogenated TiO 2 Shells for Methanol Oxidation

The methanol oxidation reaction (MOR) is the limiting factor in direct methanol fuel cells (DMFC). There is an urgent need to improve the catalytic activity and stability of MOR catalysts. This study reports a highly active PtRu catalyst for MOR based on a hybrid multifunctional catalyst support consisting of a conformal amorphous hydrogenated TiO 2 shell wrapped around the oxygenated N-doped carbon nanotube core, denoted as PtRu/TiO 2 / ONCNT-400. Both the TiO 2 shell and the subsequent PtRu nanoparticles are deposited by a rapid microwave-assisted synthesis processes. The hydrogenated TiO 2 shell is found to exhibit a strong interaction with the deposited PtRu catalyst nanoparticles and effectively prevent them from agglomeration during the postdeposition thermal annealing to form more active crystalline PtRu alloy catalysts. In addition, the defective hydrogenated TiO 2 shell enhances the PtRu catalyst activity by the synergistic effects of partial charge transfer from TiO 2 to PtRu and high oxophilicity, which improves the kinetics of oxidation of poisonous CO intermediate to CO 2 . The mass activity for MOR and long-cycling stability of the PtRu/TiO 2 /ONCNT-400 catalyst surpass the two benchmark commercial PtRu/C catalysts from Johnson Matthey (JM) and Tanaka KiKinzoku (TKK), respectively. Furthermore, the results demonstrate that PtRu/TiO 2 /ONCNT-400 can serve as an efficient catalyst for MOR in DMFC.

36 MATERIALS SCIENCE↗

Temperature-Dependent Communication between Pt/Al 2 O 3 Catalysts and Anatase TiO 2 Dilutant: the Effects of Metal Migration and Carbon Transfer on the Reverse Water–Gas Shift Reaction

In heterogeneous catalysis, unexpected effects from the supposedly inert reactor dilutant are not rare, but related understanding is lacking and inconsistent. Here we report investigations of the impacts of the anatase TiO 2 dilutant on the reverse water-gas shift (rWGS) reaction over Pt/Al 2 O 3 catalysts. Combining detailed kinetic data with microscopic and spectroscopic results, we demonstrate that the catalyst-dilutant communication depends on temperature. At high temperature (400 °C), Pt migrate from Al 2 O 3 to TiO 2 , resulting in higher dispersion and activity, without changing reaction mechanisms. The Pt migration is general to catalysts of different Pt nuclearity and various oxide dilutants. In contrast, at low temperature (250 °C), carboxylic acids (in particular acetic acid) present in the ambient air and adsorbed on TiO 2 are transferred onto Al 2 O 3 in close contact, effectively blocking the formate rWGS pathway. As a result, the rWGS can only proceed through the carboxyl pathway, and hence is significantly slower. The acetate transfer affects catalysts of different Pt nuclearity and support, but is unique to anatase TiO 2 dilutant. As the acetate layer is slowly removed under H 2 or the rWGS stream, the activity recovers. This work elucidates the complicated communication between catalysts and dilutants, which has general implications in heterogeneous catalysis, and resolves inconsistency in related reports in the literature. Finally, the impacts that anatase TiO 2 dilution has on the rWGS also unveil mechanistic understanding that further confirms the two co-existing rWGS pathways.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

In Situ Studies of Ru-CeO 2 –TiO 2 Catalysts for Selective CO 2 Hydrogenation to Methane: Importance of Metal ↔ Oxide–Oxide Interactions

Here, this work investigates Ru-CeO 2 -TiO 2 catalysts for the CO 2 methanation reaction and compares their performance with previously studied Ru-CeO 2 systems. Despite the lower Ru loading, the TiO 2 -containing catalysts exhibit significantly higher activity. To understand this behavior, in situ X-ray absorption spectroscopy (XAS) was carried out at the Ru K-edge and Ce L 3 -edge. Unlike Ru-CeO 2 , which displays reversible redox behavior of Ru, the Ru-CeO 2 -TiO 2 catalysts show irreversible Ru reduction and a substantially higher fraction of Ce 3+ species under all tested conditions (H 2 , CO 2 , H 2 /CO 2 ). The stabilization of metallic Ru during methanation, together with the enhanced formation of Ce 3+ promoted by TiO 2 through interfacial electronic transfer, accounts for their superior performance. Complementary in situ DRIFTS measurements reveal the formation and rapid consumption of bidentate carbonates and formates. These species act as a key intermediate in methane formation. Overall, these findings highlight the crucial role of the mixed CeO 2 -TiO 2 oxide in tuning the surface chemistry of the catalysts by stabilizing metallic Ru, enhancing ceria reducibility, and promoting efficient reaction pathways for CO 2 methanation. The manipulation of metal↔oxide-oxide interactions can be a very useful tool when dealing with the valorization of CO 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Surface-Controlled TiO 2 Nanocrystals with Catalytically Active Single-Site Co Incorporation for the Oxygen Evolution Reaction

The design of advanced electrocatalysts is often hindered by uncertainties in identifying and controlling the active surfaces and catalytic centers within heterogeneous materials. Here we present the synthesis of single-site Co catalysts, substitutionally doped into surface-controlled TiO 2 anatase nanocrystals, aimed at enhancing the oxygen evolution reaction (OER). Grand canonical quantum mechanics calculations reveal that the kinetics of the OER, following an adsorbate evolution mechanism, is markedly influenced by the coordination environment of Co. The simulations suggest significantly higher turnover frequencies when Co is doped into the (001) surface of TiO 2 compared to the (101) surface. Consistent with the computational findings, experimental results show that Co-doped TiO 2 (Co-TiO 2 ) nanoplates with selectively exposed {001} surfaces exhibit enhanced current densities and turnover frequencies compared to Co-TiO 2 nanobipyramids with {101} surfaces. This study highlights the synergy between theoretical calculations and precision synthesis in the development of more effective catalysts.

25 ENERGY STORAGE↗

Magnetic and dielectric property control in the multivalent nanoscale perovskite Eu 0.5 Ba 0.5 TiO 3

We report nanoscale Eu 0.5 Ba 0.5 TiO 3 , a multiferroic in the bulk and candidate in the search to quantify the electric dipole moment of the electron. Eu 0.5 Ba 0.5 TiO 3 , in the form of nanoparticles and other nanostructures is interesting for nanocomposite integration, biomedical imaging and fundamental research, based upon the prospect of polarizability, f-orbital magnetism and tunable optical/radio luminescence. We developed a [non-hydrolytic]sol–[H 2 O-activated]gel route, derived from in-house metallic Ba (s) /Eu (s) alkoxide precursors and Ti{(OCH(CH 3 ) 2 } 4 . Two distinct nanoscale compounds of Ba:Ti:Eu with the parent perovskite crystal structure were produced, with variable dielectric, magnetic and optical properties, based on altering the oxidizing/reducing conditions. Eu 0.5 Ba 0.5 TiO 3 prepared under air/O 2 atmospheres produced a spherical core–shell nanostructure (30–35 nm), with perovskite Eu 0.5 Ba 0.5 TiO 3 nanocrystal core-insulating oxide shell layer (~3 nm), presumed a pre-pyrochlore layer abundant with Eu 3+ . Fluorescence spectroscopy shows a high intensity 5 D 0 → 7 F 2 transition at 622 nm and strong red fluorescence. The core/shell structure demonstrated excellent capacitive properties: assembly into dielectric thin films gave low conductivity (2133 GΩ mm -1 ) and an extremely stable, low loss permittivity of ε eff ~25 over a wide frequency range (tan δ < 0.01, 100 kHz–2 MHz). Eu 0.5 Ba 0.5 TiO 3 prepared under H 2 /argon produced more irregular shaped nanocrystals (20–25) nm, with a thin film permittivity around 4 times greater ( ε eff 101, tan δ < 0.05, 10 kHz–2 MHz, σ ~59.54 kΩ mm -1 ). Field-cooled magnetization values of 0.025 emu g -1 for EBTO-Air and 0.84 emu g -1 for EBTO-Argon were observed. X-ray photoelectron spectroscopy analysis reveals a complex interplay of Eu II/III /Ti III/IV configurations which contribute to the observed ferroic and fluorescence behavior.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Observation of interacting polaronic gas behavior in Ta-doped TiO 2 thin films via terahertz time-domain spectroscopy

Transparent conductive oxides (TCOs)—materials that have the twin desirable features of high optical transmission and electrical conductivity—play an increasingly significant role in the fields of photovoltaics and information technology. As an excellent TCO, Ta-doped anatase TiO 2 shows great promise for a wide range of applications. Here, terahertz time-domain spectroscopy is used to study the complex optical conductivity $\tilde{σ}$ (ω) of the TCO—heavily Ta-doped TiO 2 thin films with different Ta-doping concentrations, in the frequency range of 0.3–2.7 THz and the temperature range of 10–300 K. Fitting the complex optical conductivity to a Drude-like behavior allows us to extract the temperature dependence of the effective mass, which suggests the existence of many-body large polarons. Moreover, the carrier scattering rate of Ta-doped TiO 2 with different carrier concentrations agrees with the interacting polaron gas theory. Our results suggest that with increasing electron density in TiO 2 , the interaction between polarons is larger and electron–phonon coupling is smaller, which is beneficial for achieving high mobility and conductivity in TiO 2 .

36 MATERIALS SCIENCE↗

TiO 2 Nanocoatings with Controllable Crystal Type and Nanoscale Topography on Zirconia Implants to Accelerate Bone Formation

In dentistry, zirconia implants have emerged as a promising alternative for replacing missing teeth due to their superior aesthetic performance and chemical stability. To improve the osseointegration of zirconia implants, modifying their surface with hierarchical micro/nanotopography and bioactive chemical composition are two effective ways. In this work, a microscale topography was prepared on a zirconia surface using hydrofluoric acid etching, and then a 50 nm TiO 2 nanocoating was deposited via atomic layer deposition (ALD). Subsequently, an annealing treatment was used to transform the TiO 2 from amorphous to anatase and simultaneously generate nanoscale topography. Various investigations into the coating surface morphology, topography, wettability, and chemical composition were carried out using scanning electron microscopy, white light interferometry, contact‐angle measurement, X‐ray diffraction, and X‐ray photoelectron spectroscopy. In addition, in vitro cytocompatibility and osteogenic potential performance of the coatings were evaluated by human bone marrow mesenchymal stem cells (hBMSCs), and in vivo osseointegration performance was assessed in a rat femoral condyle model. Moreover, the possible mechanism was also investigated. The deposition of TiO 2 film with/without annealing treatment did not alter the microscale roughness of the zirconia surface, whereas the nanotopography changed significantly after annealing. The in vitro studies revealed that the anatase TiO 2 coating with regular wavelike nanostructure could promote the adhesion and proliferation of osteoblasts and further improve the osteogenic potential in vitro and osseointegration in vivo. These positive effects may be caused by nanoscale topography via the canonical Wnt/ β ‐catenin pathway. The results suggest that using ALD in combination with annealing treatment to fabricate a nanotopographic TiO 2 coating is a promising way to improve the osteogenic properties of zirconia implants.

Li, Nan (ORCID:0000000255156737)↗

Nanoscale TiO 2 coating improves water stability of Cs 2 SnCl 6

To improve the stability of Cs 2 SnCl 6 under aqueous/moisture environments, we applied a concept of artificial passivation by depositing a protective TiO 2 coating of 10 nm on the surface of Cs 2 SnCl 6 . Static leaching experiments results indicate that the initial release rates of Cs + and Cl - are decreased by 20–30 times with TiO 2 coating, suggesting its possibility to improve the short-term water/environmental stability of Cs 2 SnCl 6 . An amorphous-to-crystalline phase transition in TiO 2 film was observed, possibly resulting in degradation of Cs 2 SnCl 6 . However, the crystalline TiO 2 film still remains after 21 days water exposure and can still act as an effective passivation layer to reduce the release rates of Cs + and Cl - by as much as about 17 and 7 times, respectively, relative to static leaching without artificial coatings. Therefore, the water/environmental stability of metal halide perovskite Cs 2 SnCl 6 , which is a highly soluble molecular salt, can be enhanced by the nanoscale TiO 2 coating as an artificial passivation film.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Self-Cleaning Highly Porous TiO 2 Coating Designed by Swelling-Assisted Sequential Infiltration Synthesis (SIS) of a Block Copolymer Template

Photocatalytic self-cleaning coatings with a high surface area are important for a wide range of applications, including optical coatings, solar panels, mirrors, etc. Here, we designed a highly porous TiO 2 coating with photoinduced self-cleaning characteristics and very high hydrophilicity. This was achieved using the swelling-assisted sequential infiltration synthesis (SIS) of a block copolymer (BCP) template, which was followed by polymer removal via oxidative thermal annealing. The quartz crystal microbalance (QCM) was employed to optimize the infiltration process by estimating the mass of material infiltrated into the polymer template as a function of the number of SIS cycles. This adopted swelling-assisted SIS approach resulted in a smooth uniform TiO 2 film with an interconnected network of pores. The synthesized film exhibited good crystallinity in the anatase phase. The resulting nanoporous TiO 2 coatings were tested for their functional characteristics. Exposure to UV irradiation for 1 h induced an improvement in the hydrophilicity of coatings with wetting angle reducing to unmeasurable values upon contact with water droplets. Furthermore, their self-cleaning characteristics were tested by measuring the photocatalytic degradation of methylene blue (MB). The synthesized porous TiO 2 nanostructures displayed promising photocatalytic activity, demonstrating the degradation of approximately 92% of MB after 180 min under ultraviolet (UV) light irradiation. Thus, the level of performance was comparable to the photoactivity of commercial anatase TiO 2 nanoparticles of the same quantity. Our results highlight a new robust approach for designing hydrophilic self-cleaning coatings with controlled porosity and composition.

36 MATERIALS SCIENCE↗

Search for TiO and Optical Nightside Emission from the Exoplanet WASP-33b

With a temperature akin to an M dwarf, WASP-33b is among the hottest Jupiters known, making it an ideal target for high-resolution optical spectroscopy. By analyzing both transmission and emission spectra, we aim to substantiate previous reports of atmospheric TiO and a thermal inversion within the planet’s atmosphere. We observed two transits and six arcs of the phase curve with the Echelle SpectroPolarimetric Device for the Observation of Stars (ESPaDOnS) on the Canada–France–Hawaii Telescope and High Resolution Echelle Spectrometer (HIRES) on the Keck telescope, which provide high spectral resolution and ample wavelength coverage. We employ the Doppler cross-correlation technique to search for the molecular signatures of TiO and H{sub 2}O in these spectra, using models based on the TiO line list of Plez. Though we cannot exclude line-list-dependent effects, our data do not corroborate previous indications of a thermal inversion. Instead we place a 3σ upper limit of 10{sup −9} on the volume mixing ratio of TiO for the T–P profile we consider. While we are unable to constrain the volume mixing ratio of water, our strongest constraint on TiO comes from dayside emission spectra. This apparent absence of a stratosphere sits in stark contrast to previous observations of WASP-33b as well as theoretical predictions for the atmospheres of highly irradiated planets. The discrepancy could be due to variances between line lists, and we stress that detection limits are only as good as the line list employed, and are only valid for the specific T–P profile considered due to the strong degeneracy between lapse rate (dT/dlogP) and molecular abundance.

79 ASTRONOMY AND ASTROPHYSICS↗

Application of ultrathin TiO 2 layers in solar energy conversion devices

Abstract A vital pursuit in solar energy research is to achieve high efficiency and long‐term stability in energy conversion devices. Coating or sandwiching an ultrathin layer of TiO 2 onto active solar components has been demonstrated to be a remarkably effective and facile strategy to improve their stability. The TiO 2 film acts as a protection layer and enhances solar energy conversion efficiency by passivating surface recombination sites or facilitating electron transport. To date, numerous efforts have been devoted to applying ultrathin TiO 2 layers in various kinds of solar energy conversion devices. In this study, we review deposition techniques, characterization methods of the resulting ultrathin TiO 2 layer, as well as its applications in dye‐sensitized solar cells, organic–inorganic hybrid solar cells, and photoelectrochemical cells.

36 MATERIALS SCIENCE↗

Materials Data on TiO by Materials Project

TiO crystallizes in the tetragonal I4/mmm space group. The structure is two-dimensional and consists of six TiO sheets oriented in the (0, 0, 1) direction. In two of the TiO sheets, there are two inequivalent Ti2+ sites. In the first Ti2+ site, Ti2+ is bonded in a 5-coordinate geometry to five O2- atoms. There are four shorter (2.09 Å) and one longer (2.32 Å) Ti–O bond lengths. In the second Ti2+ site, Ti2+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Ti–O bond distances ranging from 2.07–2.77 Å. There are two inequivalent O2- sites. In the first O2- site, O2- is bonded in a 5-coordinate geometry to six Ti2+ atoms. In the second O2- site, O2- is bonded in a 5-coordinate geometry to five Ti2+ atoms. In four of the TiO sheets, Ti2+ is bonded in a distorted square co-planar geometry to four equivalent O2- atoms. All Ti–O bond lengths are 2.07 Å. O2- is bonded in a 4-coordinate geometry to four equivalent Ti2+ atoms.

36 MATERIALS SCIENCE↗

TiO2 Nanocrystal-Framed Li 2 TiSiO 5 Platelets for Low-Voltage Lithium Battery Anode

Titanium-based anode materials are attracting considerable attention for use in high-performance lithium-ion batteries, but the compromised energy density caused by high voltage plateaus and unsatisfactory capacities severely retards their practical applications. Herein, a molten-salt synthesis of Li 2 TiSiO 5 crystalline platelets and a subsequent selective facet modification by in situ growth of TiO 2 nanocrystal frames are facilely achieved. The discharge voltage plateau at around 0.5 V renders the Li 2 TiSiO 5 anode safe compared with graphite and confers a high energy density compared with zero-strain Li 4 Ti 5 O 12 anode. With the optimized size, structure, and content of modified TiO2 nanocrystals associated with the exposed (001) plane of Li 2 TiSiO 5 , the Li 2 TiSiO 5 -based anodes can deliver a capacity of above 300 mAh g -1 , enhanced rate performance, and a capacity retention of 66% after 10 000 cycles. In situ X-ray diffraction and ex situ transmission electron microscopy have demonstrated the structural stability of the anodes upon charge/discharge. Further theoretical calculation reveals 3D migration paths of Li + ions in Li 2 TiSiO 5 . The selective modification of in situ grown TiO2 nanocrystals on certain facets of crystallites opens a new door for the development of electrode materials possessing superior electrochemical properties.

anodes↗

Polarity‐Driven Atomic Displacements at the 2D Mg 2 TiO 4 ‐MgO (001) Oxide Interface for Hosting Potential Interlayer Excitons

Abstract Interlayer excitons in solid‐state systems have emerged as candidates for realizing novel platforms ranging from excitonic transistors and optical qubits to exciton condensates. Interlayer excitons have been discovered in 2D transition metal dichalcogenides, with large exciton binding energies and the ability to form various van der Waals heterostructures. Here, an oxide system consisting of a single unit cell of Mg 2 TiO 4 on MgO (001) is proposed as a platform for hosting interlayer excitons. Using a combination of density functional theory (DFT) calculations, molecular beam epitaxy growth, and in situ crystal truncation rod measurements, it is shown that the Mg 2 TiO 4 ‐MgO interface can be precisely controlled to yield an internal electric field suitable for hosting interlayer excitons. The atoms in the polar Mg 2 TiO 4 layers are observed to be displaced to reduce polarity at the interface with the non‐polar MgO (001) surface. Such polarity‐driven atomic displacements strongly affect electrostatics of the film and the interface, resulting in localization of filled and empty band‐edge states in different layers of the Mg 2 TiO 4 film. The DFT calculations suggest that the electronic structure is favorable for localization of photoexcited electrons in the bottom layer and holes in the top layer, which may bind to form interlayer exciton states.

36 MATERIALS SCIENCE↗

In Situ Dispersion of Palladium on TiO 2 During Reverse Water–Gas Shift Reaction: Formation of Atomically Dispersed Palladium

The application of single-atom catalysts (SACs) to high-temperature hydrogenation requires materials that thermodynamically favor metal atom isolation over cluster formation. Here, we show that Pd can be predominantly dispersed as isolated atoms onto TiO 2 during the reverse water-gas shift (rWGS) reaction at 400 °C. Achieving atomic dispersion requires an artificial increase of the absolute TiO 2 surface area by an order of magnitude and can be accomplished by physically mixing a precatalyst (Pd/TiO 2 ) with neat TiO 2 prior to the rWGS reaction. Furthermore, the in situ dispersion of Pd was reflected through a continuous increase of rWGS activity over 92 h and supported by kinetic analysis, infrared and X-ray absorption spectroscopies and scanning transmission electron microscopy. The thermodynamic stability of Pd under high-temperature rWGS conditions is associated with Pd-Ti coordination, which manifests upon O-vacancy formation and the artificial increase in TiO 2 surface area.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Machine‐Learning‐Driven Exploration of Surface Reconstructions of Reduced Rutile TiO 2

Abstract Titanium dioxide (TiO 2 ) is widely used as a catalyst support due to its stability, tunable electronic properties, and surface oxygen vacancies, which are crucial for catalytic processes such as the reverse water‐gas shift (RWGS) reaction. Reduced TiO 2 surfaces undergo complex surface reconstructions that endow unique properties but are computationally challenging to describe. In this study, we utilize machine‐learning interatomic potentials (MLIPs) integrated with an active‐learning workflow to efficiently explore reduced rutile TiO 2 surfaces. This approach enabled the prediction of a phase diagram as a function of oxygen chemical potential, revealing a variety of reconstructed phases, including a previously unreported subsurface shear plane structure. We further investigate the electronic properties of these surfaces and validate our results by comparing experimental and theoretical high‐resolution transmission electron microscopy (HRTEM). Our findings provide new insights into how extreme surface reductions influence the structural and electronic properties of TiO 2 , with potential implications for catalyst design.

Lee, Yonghyuk [Chemistry and Biochemistry Universi↗

Machine‐Learning‐Driven Exploration of Surface Reconstructions of Reduced Rutile TiO 2

Titanium dioxide (TiO 2 ) is widely used as a catalyst support due to its stability, tunable electronic properties, and surface oxygen vacancies, which are crucial for catalytic processes such as the reverse water-gas shift (RWGS) reaction. Reduced TiO 2 surfaces undergo complex surface reconstructions that endow unique properties but are computationally challenging to describe. In this study, we utilize machine-learning interatomic potentials (MLIPs) integrated with an active-learning workflow to efficiently explore reduced rutile TiO 2 surfaces. This approach enabled the prediction of a phase diagram as a function of oxygen chemical potential, revealing a variety of reconstructed phases, including a previously unreported subsurface shear plane structure. We further investigate the electronic properties of these surfaces and validate our results by comparing experimental and theoretical high-resolution transmission electron microscopy (HRTEM). Our findings provide new insights into how extreme surface reductions influence the structural and electronic properties of TiO 2 , with potential implications for catalyst design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effect of Ambient Organic Acids on the Water Structure at ${\rm TiO}_{2}$ Interfaces

A molecular-level understanding of the effects of ambient organic compounds on the wettability of titanium dioxide ( ${\rm TiO}_{2}$ ) surfaces is relevant to many of its energy-related and environmental applications. Herein, we focus on two common atmospheric carboxylic acids, formic and acetic acid, and characterize their adsorption/ desorption at the aqueous interfaces of anatase and rutile ${\rm TiO}_{2}$ using molecular dynamics with an ab initio deep neural network potential. Our simulations show that these acids prefer to be localized in the interfacial water layers close to the ${\rm TiO}_{2}$ surface where they are stabilized by the interaction/exchange of their acid proton with a surface oxygen, rather than chemisorb at the surface Ti sites by displacing the adsorbed water. Notably, these acids make the surface of anatase hydrophobic, whereas the larger fraction of adsorbed water dissociation can offset their effect on rutile. Furthermore, these results provide a picture where carboxylic acids control the wettability of ${\rm TiO}_{2}$ largely through acid-base chemistry at the interface rather than chemisorption on the oxide surface, a finding that can help improve the design of self-cleaning surfaces and photocatalytic devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗