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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 541 records · Page 30
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

TiO 2 Nanoparticles Enabling Photocatalytic Desulfurization for C–C Coupling Reaction Using Visible Light

We uncover a surface-mediated mechanism for visible-light-driven photocatalytic desulfurization of thiols on titanium dioxide (TiO 2 ) nanoparticles under LED illumination (>420 nm). Combined diffuse reflectance, infrared, and cryogenic electron paramagnetic resonance spectroscopy verify the formation of a surface thiol–Ti charge-transfer complex that introduces visible-light absorption into an otherwise UV-active reaction system. Selective photoexcitation of this surface complex drives interfacial charge transfer, directly activating the adsorbed thiol and inducing C–S bond scission without the band gap excitation of TiO 2 . The resulting carbon-centered radical intermediates are intercepted by styrene to form C–C coupling products. These results uncover a distinct surface-mediated photocatalytic mechanism in which charge-transfer complex formation governs both light absorption and chemical activation, providing a mechanistic framework for extending visible-light reactivity to wide-bandgap metal oxide photocatalysts.

addition of carbon radical to vinyl groups↗
DOE OSTI2025

Spinel-Structured High Entropy Oxides: Low Temperature Synthesis, Characterization, and Potential Applications

High entropy oxides (HEOs) have recently attracted increasing attention due to their remarkable properties and relatively low cost. Herein we report a simple, highly scalable, and low temperature method for synthesizing spinel (FeNiCoCuZn) 3 O 4 (HEO). We heated an aqueous solution containing divalent cations in high alkali environments to temperatures of 25 - 95 °C for 24 h under atmospheric pressure. The HEO, synthesized at 95 °C for 24 h in 1 M KOH, was paramagnetic at room temperature, with a magnetic mass susceptibility of χ = (7.5 ± 0.2) × 10 –7 m 3 ·kg –1 . It demonstrated stable electrochemical lithium storage performance, with a gravimetric capacity of ∼300 mAh·g –1 at 100 mA·g –1 . It was also active in the electrocatalytic oxygen evolution reaction with an overpotential of 460 mV in alkaline media. The band gap energies were in the range of 2.4 eV. Our advancement in the synthesis and processing of transition metal-based HEOs will undoubtedly render them a viable solution for next generation materials for energy production and storage.

diffraction↗
DOE OSTI2022

Structure–Transport Properties Governing the Interplay in Humidity-Dependent Mixed Ionic and Electronic Conduction of Conjugated Polyelectrolytes

Polymeric mixed ionic-electronic conductors (MIECs) are of broad interest in the field of energy storage and conversion, opto-electronics, and bioelectronics. A class of polymeric MIECs are conjugated polyelectrolytes (CPEs), which possess a p-conjugated backbone imparting electronic transport characteristics along with side chains comprised of a pendant ionic group to allow for ionic transport. Here, our study focuses on the humidity-dependent structure-transport properties of poly[3-(potassium-n-alkanoate) thiophene-2,5-diyl] (P3KnT) CPEs with varied side-chain lengths of n = 4, 5, 6, and 7. UV-Vis spectroscopy along with electronic paramagnetic resonance (EPR) spectroscopy reveal the infiltration of water leads to a hydrated, self-doped state that allows for electronic transport. The resulting humidity-dependent ionic conductivity (σ i ) of the thin films shows a monotonic increase with relative humidity (RH) while electronic conductivity (σ e ) follows a nonmonotonic profile. The values of σ e continue to rise with increasing RH reaching a local maximum after which σ e begins to decrease. P3KnTs with higher n values demonstrate greater resiliency to increasing RH before suffering decrease in σ e . This drop in σ e is attributed to two factors. First, disruption of the locally-ordered π-stacked domains observed through in situ humidity-dependent grazing incidence wide angle X-ray scattering (GIWAXS) experiments can account for some of the decrease in σ e . A second and more dominant factor is attributed to the swelling of the amorphous domains where electronic transport pathways connecting ordered domains are impeded. P3K7T is most resilient to swelling (based on ellipsometry and water uptake measurements) where sufficient hydration allows for high σ i (1.0 × 10 -1 S/cm at 95% RH) while not substantially disrupting σ e (1.7 × 10 -2 S/cm at 85% RH and 8.0 × 10 -3 S/cm at 95% RH). Overall, our study highlights the complexity of balancing electronic and ionic transport in hydrated CPEs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Strong Electronic and Magnetic Coupling in M 4 (M = Ni, Cu) Clusters via Direct Orbital Interactions between Low-Coordinate Metal Centers

In this report we present an extensive study of tetranuclear transition-metal cluster compounds M 4 (NP t Bu 3 ) 4 and [M 4 (NP t Bu 3 ) 4 ][B(C 6 F 5 ) 4 ] (M = Ni, Cu; t Bu = tert -butyl), which feature low-coordinate metal centers and direct metal-metal orbital overlap. X-ray diffraction, electrochemical, magnetic, spectroscopic, and computational analysis elucidate the nature of the bonding interactions in these clusters and the impact of these interactions on the electronic and magnetic properties. Direct orbital overlap results in strongly coupled, large-spin ground states in the [Ni 4 (NP t Bu 3 ) 4 ] +/0 clusters and fully delocalized, spin-correlated electrons. Correlated electronic structure calculations confirm the presence of ferromagnetic ground states that arise from direct exchange between magnetic orbitals, and, in the case of the neutral cluster, itinerant electron magnetism similar to that in metallic ferromagnets. The cationic nickel cluster also possesses large magnetic anisotropy exemplified by a large, positive axial zero-field splitting parameter of D = +7.95 or +9.2 cm -1 , as determined by magnetometry or electron paramagnetic resonance spectroscopy, respectively. The [Ni 4 (NP t Bu 3 ) 4 ] + cluster is also the first molecule with easy-plane magnetic anisotropy to exhibit zero-field slow magnetic relaxation, and under a small applied field, it exhibits relaxation exclusively through an Orbach mechanism with a spin relaxation barrier of 16 cm -1 . The S = 1 / 2 complex [Cu 4 (NP t Bu 3 ) 4 ] + exhibits slow magnetic relaxation via a Raman process on the millisecond time scale, supporting the presence of slow relaxation via an Orbach process in the nickel analogue. Overall, this work highlights the unique electronic and magnetic properties that can be realized in metal clusters featuring direct metal-metal orbital interactions between low-coordinate metal centers.

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

Topochemical Deintercalation of Li from Layered LiNiB: toward 2D MBene

The pursuit of two-dimensional (2D) borides, MBenes, has proven to be challenging, not the least because of the lack of a suitable precursor prone to the deintercalation. Here, we studied room-temperature topochemical deintercalation of lithium from the layered polymorphs of the LiNiB compound with a considerable amount of Li stored in between [NiB] layers (33 at. % Li). Deintercalation of Li leads to novel metastable borides (Li~ 0.5 NiB) with unique crystal structures. Partial removal of Li is accomplished by exposing the parent phases to air, water, or dilute HCl under ambient conditions. Scanning transmission electron microscopy and solid-state 7 Li and 11 B NMR spectroscopy, combined with X-ray pair distribution function (PDF) analysis and DFT calculations, were utilized to elucidate the novel structures of Li~ 0.5 NiB and the mechanism of Li-deintercalation. We have shown that the deintercalation of Li proceeds via a “zip-lock” mechanism, leading to the condensation of single [NiB] layers into double or triple layers bound via covalent bonds, resulting in structural fragments with Li[NiB] 2 and Li[NiB] 3 compositions. The crystal structure of Li~ 0.5 NiB is best described as an intergrowth of the ordered single [NiB], double [NiB] 2 , or triple [NiB] 3 layers alternating with single Li layers; this explains its structural complexity. Here, the formation of double or triple [NiB] layers induces a change in the magnetic behavior from temperatureindependent paramagnets in the parent LiNiB compounds to the spin-glassiness in the deintercalated Li~ 0.5 NiB counterparts. LiNiB compounds showcase the potential to access a plethora of unique materials, including 2D MBenes (NiB).

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

High Ammonia Adsorption in MFM-300 Materials: Dynamics and Charge Transfer in Host–Guest Binding

Ammonia (NH 3 ) is a promising energy resource owing to its high hydrogen density. However, its widespread application is restricted by the lack of efficient and corrosion-resistant storage materials. In this work, we report high NH 3 adsorption in a series of robust metal-organic framework (MOF) materials, MFM-300(M) (M = Fe, V, Cr, In). MFM-300(M) (M = Fe, V III , Cr) show fully reversible capacity for >20 cycles, reaching capacities of 16.1, 15.6, and 14.0 mmol g -1 , respectively, at 273 K and 1 bar. Under the same conditions, MFM-300(V IV ) exhibits the highest uptake among this series of MOFs of 17.3 mmol g -1 . In situ neutron powder diffraction, single-crystal X-ray diffraction, and electron paramagnetic resonance spectroscopy confirm that the redox-active V center enables host-guest charge transfer, with V IV being reduced to V III and NH 3 being oxidized to hydrazine (N 2 H 4 ). A combination of in situ inelastic neutron scattering and DFT modeling has revealed the binding dynamics of adsorbed NH 3 within these MOFs to afford a comprehensive insight into the application of MOF materials to the adsorption and conversion of NH 3 .

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

Tunable Cr 4+ Molecular Color Centers

The inherent atomistic precision of synthetic chemistry enables bottom-up structural control over quantum bits, or qubits, for quantum technologies. Tuning paramagnetic molecular qubits that feature optical-spin initialization and readout is a crucial step toward designing bespoke qubits for applications in quantum sensing, networking, and computing. In this work, we demonstrate that the electronic structure that enables optical-spin initialization and readout for S = 1, Cr(aryl) 4 , where aryl = 2,4-dimethylphenyl (1), o-tolyl (2), and 2,3-dimethylphenyl (3), is readily translated into Cr(alkyl) 4 compounds, where alkyl = 2,2,2-triphenylethyl (4), (trimethylsilyl)methyl (5), and cyclohexyl (6). The small ground state zero field splitting values (<5 GHz) for 1–6 allowed for coherent spin manipulation at X-band microwave frequency, enabling temperature-, concentration-, and orientation-dependent investigations of the spin dynamics. Electronic absorption and emission spectroscopy confirmed the desired electronic structures for 4–6, which exhibit photoluminescence from 897 to 923 nm, while theoretical calculations elucidated the varied bonding interactions of the aryl and alkyl Cr 4+ compounds. The combined experimental and theoretical comparison of Cr(aryl) 4 and Cr(alkyl) 4 systems illustrates the impact of the ligand field on both the ground state spin structure and excited state manifold, laying the groundwork for the design of structurally precise optically addressable molecular qubits.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Effective Storage of Electrons in Water by the Formation of Highly Reduced Polyoxometalate Clusters

Aqueous solutions of polyoxometalates (POMs) have been shown to have potential as high-capacity energy storage materials due to their potential for multi-electron redox processes, yet the mechanism of reduction and practical limits are currently unknown. Herein, we explore the mechanism of multi-electron redox processes that allow the highly reduced POM clusters of the form {MO 3 } y to absorb y electrons in aqueous solution, focusing mechanistically on the Wells-Dawson structure X 6 [P 2 W 18 O 62 ], which comprises 18 metal centers and can uptake up to 18 electrons reversibly (y = 18) per cluster in aqueous solution when the countercations are lithium. This unconventional redox activity is rationalized by density functional theory, molecular dynamics simulations, UV-vis, electron paramagnetic resonance spectroscopy, and small-angle X-ray scattering spectra. These data point to a new phenomenon showing that cluster protonation and aggregation allow the formation of highly electron-rich meta-stable systems in aqueous solution, which produce H 2 when the solution is diluted. Finally, we show that this understanding is transferrable to other salts of [P 5 W 30 O 110 ] 15- and [P 8 W 48 O 184 ] 40- anions, which can be charged to 23 and 27 electrons per cluster, respectively.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Tale of Three Molecular Nitrides: Mononuclear Vanadium (V) and (IV) Nitrides As Well As a Mixed-Valence Trivanadium Nitride Having a V 3 N 4 Double-Diamond Core

Here, transmetallation of [VCl 3 (THF) 3 ] and [TlTp tBu,Me ] afforded [(Tp tBu,Me )VCl 2 ] (1, Tp tBu,Me = hydro-tris(3-tert-butyl-5-methylpyrazol-1-yl)borate), which was reduced with KC 8 to form a $C_{3v}$ symmetric V II complex, [(Tp tBu,Me )VCl] (2). Complex 1 has a high-spin ($\textit{S}$ = 1) ground state and displays rhombic high-frequency and -field electron paramagnetic resonance (HFEPR) spectra, while complex 2 has an $\textit{S}$ = 3/2 4 A 2 ground state observable by conventional EPR spectroscopy. Complex 1 reacts with NaN 3 to form the V V nitride-azide complex [(Tp tBu,Me )V≡N(N 3 )] (3). A likely V III azide intermediate en route to 3, [(Tp tBu,Me )VCl(N 3 )] (4), was isolated by reacting 1 with N 3 SiMe 3 . Complex 4 is thermally stable but reacts with NaN3 to form 3, implying a bis-azide intermediate, [(Tp tBu,Me )V(N 3 ) 2 ] (A), leading to 3. Reduction of 3 with KC 8 furnishes a trinuclear and mixed-valent nitride, [{(Tp tBu,Me )V} 2 ($μ_{4-}$VN 4 )] (5), conforming to a Robin–Day class I description. Complex 5 features a central vanadium ion supported only by bridging nitride ligands. Contrary to 1, complex 2 reacts with NaN 3 to produce an azide-bridged dimer, [{(Tp tBu,Me )V} 2 (1,3-$μ_2$-N 3 ) 2 ] (6), with two antiferromagnetically coupled high-spin V II ions. Complex 5 could be independently produced along with [($κ_2$-Tp tBu,Me ) 2 V] upon photolysis of 6 in arene solvents. The putative {V IV ≡N} intermediate, [(Tp tBu,Me )V≡N] (B), was intercepted by photolyzing 6 in a coordinating solvent, such as tetrahydrofuran (THF), yielding [(Tp tBu,Me )V≡N(THF)] (B-THF). In arene solvents, B-THF expels THF to afford 5 and [($κ_2$-Tp tBu,Me ) 2 V]. A more stable adduct (B-OPPh 3 ) was prepared by reacting B-THF with OPPh 3 . These adducts of B are the first neutral and mononuclear V IV nitride complexes to be isolated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Direct Observation of Ammonia Storage in UiO-66 Incorporating Cu(II) Binding Sites

The presence of active sites in metal–organic framework (MOF) materials can control and affect their performance significantly in adsorption and catalysis. However, revealing the interactions between the substrate and active sites in MOFs at atomic precision remains a challenging task. Here, we report the direct observation of binding of NH 3 in a series of UiO-66 materials containing atomically dispersed defects and open Cu(I) and Cu(II) sites. While all MOFs in this series exhibit similar surface areas (1111–1135 m 2 g –1 ), decoration of the -OH site in UiO-66-defect with Cu(II) results in a 43% enhancement of the isothermal uptake of NH 3 at 273 K and 1.0 bar from 11.8 in UiO-66-defect to 16.9 mmol g –1 in UiO-66-Cu II . A 100% enhancement of dynamic adsorption of NH 3 at a concentration level of 630 ppm from 2.07 mmol g –1 in UiO-66-defect to 4.15 mmol g –1 in UiO-66-Cu II at 298 K is observed. In situ neutron powder diffraction, inelastic neutron scattering, and electron paramagnetic resonance, solid-state nuclear magnetic resonance, and infrared spectroscopies, coupled with modeling reveal that the enhanced NH 3 uptake in UiO-66-Cu II originates from a {Cu(II)···NH 3 } interaction, with a reversible change in geometry at Cu(II) from near-linear to trigonal coordination. This work represents the first example of structural elucidation of NH 3 binding in MOFs containing open metal sites and will inform the design of new efficient MOF sorbents by targeted control of active sites for NH 3 capture and storage.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Spin–Lattice Relaxation Decoherence Suppression in Vanishing Orbital Angular Momentum Qubits

Multifrequency electron paramagnetic resonance spectroscopy on oriented single crystals of magnetically dilute Gd(III) ions in Gd 0.004 Y 0.996 (trensal) is used to determine the Hamiltonian parameters of the ground 8 S 7/2 term and its phase memory time, Tm, characterizing its coherent spin dynamics. Here, the vanishing orbital angular momentum of the 8 S 7/2 term makes it relatively insensitive to spin–lattice relaxation mediated by magnetoelastic coupling and leads to a T m of 12 μs at 3 K, which is not limited by spin–lattice relaxation.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Room-Temperature Quantitative Quantum Sensing of Lithium Ions with a Radical-Embedded Metal–Organic Framework

Recent advancements in quantum sensing have sparked transformative detection technologies with high sensitivity, precision, and spatial resolution. Owing to their atomic-level tunability, molecular qubits and ensembles thereof are promising candidates for sensing chemical analytes. Here, in this study, we show quantum sensing of lithium ions in solution at room temperature with an ensemble of organic radicals integrated in a microporous metal–organic framework (MOF). The organic radicals exhibit electron spin coherence and microwave addressability at room temperature, thus behaving as qubits. The high surface area of the MOF promotes accessibility of the guest analytes to the organic qubits, enabling unambiguous identification of lithium ions and quantitative measurement of their concentration through relaxometric and hyperfine spectroscopic methods based on electron paramagnetic resonance (EPR) spectroscopy. The sensing principle presented in this work is applicable to other metal ions with nonzero nuclear spin.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Investigation of the Structure of Atomically Dispersed NiN x Sites in Ni and N-Doped Carbon Electrocatalysts by 61 Ni Mössbauer Spectroscopy and Simulations

Ni and nitrogen-doped carbons are selective catalysts for CO 2 reduction to CO (CO 2 R), but the hypothesized NiNx active sites are challenging to probe with traditional characterization methods. Here, we synthesize 61 Ni-enriched model catalysts, termed 61 NiPACN, in order to apply 61 Ni Mössbauer spectroscopy using synchrotron radiation ( 61 Ni-SR-MS) to characterize the structure of these atomically dispersed NiNx sites. First, we demonstrate that the CO 2 R results and standard characterization techniques (SEM, PXRD, XPS, XANES, EXAFS) point to the existence of dispersed Ni active sites. Then, 61 Ni-SR-MS reveal significant internal magnetic fields of ~5.4 T, which is characteristic of paramagnetic, high-spin Ni 2+ , in the 61NiPACN samples. Finally, theoretical calculations for a variety of Ni-N x moieties confirm that high-spin Ni 2+ is stable in non-planar, tetrahedrally distorted geometries, which results in calculated isotropic hyperfine coupling that is consistent with 61 Ni-SR-MS measurements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

A Telomerase-Activated Magnetic Resonance Imaging Probe for Consecutively Monitoring Tumor Growth Kinetics and In Situ Screening Inhibitors

Telomerase has long been considered as a biomarker for cancer diagnosis and a therapeutic target for drug discovery. Detecting telomerase activity in vivo could provide more direct information of tumor progression and response to drug treatment, which, however, is hampered by the lack of an effective probe that can generate an output signal without a tissue penetration depth limit. Here in this study, using the principle of distance-dependent magnetic resonance tuning, we constructed a telomerase-activated magnetic resonance imaging probe (TAMP) by connecting superparamagnetic ferroferric oxide nanoparticles (SPFONs) and paramagnetic Gd-DOTA (Gd(III) 1,4,7,10- tetraazacyclododecane-1,4,7,10-tetraazacyclododecane-1,4,7,10-tet-raacetic acid) complexes via telomerase-responsive DNA motifs. Upon telomerase-catalyzed extension of the primer in TAMP, Gd-DOTA-conjugated oligonucleotides can be liberated from the surface of SPFONs through a DNA strand displacement reaction, restoring the T 1 signal of the Gd-DOTA for a direct readout of the telomerase activity. Here we show that, by tracking telomerase activity, this probe provides consistent monitoring of tumor growth kinetics during progression and in response to drug treatment and enables in situ screening of telomerase inhibitors in whole-animal models. This study provides an alternative toolkit for cancer diagnosis, treatment response assessment, and anticancer drug screening.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Direct Conversion of Methane to Ethylene and Acetylene over an Iron-Based Metal–Organic Framework

Conversion of methane (CH 4 ) to ethylene (C 2 H 4 ) and/or acetylene (C 2 H 2 ) enables routes to a wide range of products directly from natural gas. However, high reaction temperatures and pressures are often required to activate and convert CH 4 controllably, and separating C 2+ products from unreacted CH 4 can be challenging. Here, we report the direct conversion of CH 4 to C 2 H 4 and C 2 H 2 driven by non-thermal plasma under ambient (25 °C and 1 atm) and flow conditions over a metal–organic framework material, MFM-300(Fe). The selectivity for the formation of C 2 H 4 and C 2 H 2 reaches 96% with a high time yield of 334 μmol g cat –1 h –1 . At a conversion of 10%, the selectivity to C 2+ hydrocarbons and time yield exceed 98% and 2056 μmol g cat –1 h –1 , respectively, representing a new benchmark for conversion of CH 4 . In situ neutron powder diffraction, inelastic neutron scattering and solid-state nuclear magnetic resonance, electron paramagnetic resonance (EPR), and diffuse reflectance infrared Fourier transform spectroscopies, coupled with modeling studies, reveal the crucial role of Fe–O(H)–Fe sites in activating CH 4 and stabilizing reaction intermediates via the formation of an Fe–O(CH 3 )–Fe adduct. In addition, a cascade fixed-bed system has been developed to achieve online separation of C 2 H 4 and C 2 H 2 from unreacted CH 4 for direct use. Integrating the processes of CH 4 activation, conversion, and product separation within one system opens a new avenue for natural gas utility, bridging the gap between fundamental studies and practical applications in this area.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Unraveling Triplet Formation Mechanisms in Acenothiophene Chromophores

The evolution of molecular platforms for singlet fission (SF) chromophores has fueled the quest for new compounds capable of generating triplets quantitatively at fast time scales. As the exploration of molecular motifs for SF has diversified, a key challenge has emerged in identifying when the criteria for SF have been satisfied. Here, we show how covalently bound molecular dimers uniquely provide a set of characteristic optical markers that can be used to distinguish triplet pair formation from processes that generate an individual triplet. These markers are contained within (i) triplet charge-transfer excited state absorption features, (ii) kinetic signatures of triplet-triplet annihilation processes, and (iii) the modulation of triplet formation rates using bridging moieties between chromophores. Our assignments are verified by time-resolved electron paramagnetic resonance (EPR) measurements, which directly identify triplet pairs by their electron spin and polarization patterns. Here we apply these diagnostic criteria to dimers of acenothiophene derivatives in solution that were recently reported to undergo efficient intermolecular SF in condensed media. While the electronic structure of these heteroatom-containing chromophores can be broadly tuned, the effect of their enhanced spin-orbit coupling and low-energy nonbonding orbitals on their SF dynamics has not been fully determined. We find that SF is fast and efficient in tetracenothiophene but that anthradithiophene exhibits fast intersystem crossing due to modifications of the singlet and triplet excited state energies upon functionalization of the heterocycle. We conclude that it is not sufficient to assign SF based on comparisons of the triplet formation kinetics between monomer and multichromophore systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗