Sur les équations de la division des fonctions abéliennes

Sans résuméExtrait d'un traité des équations algébriques en cours de publication.     

Different Reactivity of Rutile and Anatase TiO2 Nanoparticles: Synthesis and Surface States of Nanoparticles of Mixed-Valence Magnéli Oxides

Magnéli phases Ti_nO_2n−1 (3<n≤10) are mixed Ti⁴⁺/Ti³⁺ oxides with high electrical conductivity. When used for water remediation or electrochemical energy storage and conversion, they are nanostructured and exposed to various environments. Therefore, understanding their surface reactivity is of prime importance. Such studies have been hindered by carbon contamination from syntheses. Herein, this synthetic and characterization challenge is addressed through a new approach to 50 nm carbon-free Ti₄O₇ and Ti₆O₁₁ nanoparticles. It takes advantage of the different reactivities of rutile and anatase TiO₂ nanoparticles towards H₂, to use the former as precursor of Ti_nO_2n−1 and the latter as a diluting agent. This approach is combined with silica templating to restrain particle growth. The surface reactivity of the Magnéli nanoparticles under different atmospheres was then evaluated quantitatively by synchrotron-radiation-based X-ray photoelectron spectroscopy, which revealed oxidized surfaces with lower conductivity than the core. This finding sheds a new light on the charge transfer occurring in these materials.     

MOF/graphite oxide hybrid materials: exploring the new concept of adsorbents and catalysts

Two types of metal-organic framework (MOF)/graphite oxide hybrid materials were prepared. One is based on a zinc-containing, MOF-5 and the other on a copper-containing HKUST-1. The materials are characterized by X-ray diffraction, sorption of nitrogen, thermal analyses, Fourier Transform infrared spectroscopy (FT-IR) and scanning electron microscopy (SEM). Their features are compared to the ones of the parent materials. The water stability and ammonia adsorption capacity of the hybrid materials were also evaluated. It was found that the latter compounds exhibit features similar to the ones of the parent MOF. In most cases, their porosity increased compared to the one calculated considering the physical mixture of MOF and GO. This new porosity likely located between the two components of the hybrid materials is responsible for the enhanced ammonia adsorption capacity of the compounds. However, for both the zinc-based and the copper-based materials (MOFs and hybrid materials), a collapse of the framework was observed as a result of ammonia adsorption. This collapse is caused by the interactions of ammonia with the metallic centers of MOFs either by hydrogen bonding (zinc-based materials) or coordination and subsequent complexation (copper-based materials). Whereas the MOF-5 based compounds collapse in presence of humidity, the copper-based materials are stable.     

Literatur

Ohne Zusammenfassung     

Three-component synthesis of functionalized five-membered ring lactones under Barbier-like conditions

Five-membered ring lactones have been synthesized using a straightforward three-component reaction among in situ-generated arylzinc reagents, dimethyl itaconate and aromatic aldehydes. This Barbier-like procedure, which is characterized by its simplicity, allows the concise synthesis of a range of highly functionalized 4,5-substituted γ-butyrolactones.     

Non-abelian differentiable gerbes

We study non-abelian differentiable gerbes over stacks using the theory of Lie groupoids. More precisely, we develop the theory of connections on Lie groupoid G-extensions, which we call “connections on gerbes”, and study the induced connections on various associated bundles. We also prove analogues of the Bianchi identities. In particular, we develop a cohomology theory which measures the existence of connections and curvings for G-gerbes over stacks. We also introduce G-central extensions of groupoids, generalizing the standard groupoid S¹-central extensions. As an example, we apply our theory to study the differential geometry of G-gerbes over a manifold.     

Exploring the coordination chemistry of MOF-graphite oxide composites and their applications as adsorbents

Metal-organic frameworks (MOFs), besides being porous materials exhibit a very rich chemistry, which can be used for the synthesis of composites and/or the reactive adsorption of toxic gases. In this study, composites of MOFs (MOF-5, HKUST-1 or MIL-100(Fe)) and a graphitic compound (graphite or graphite oxide, GO) were synthesized and tested for the removal of NH(3), H(2)S and NO(2) under ambient conditions. The materials were characterized before and after exposure to the target gases by X-ray diffraction, thermogravimetric analysis, N(2) sorption measurement and FT-IR spectroscopy. The results indicate that strong chemical bonds exist between the MOF and GO as a result of the coordination between the GO oxygen groups and the MOFs' metallic centers. Depending on the structure of the MOF, such interactions induce the formation of a new pore space in the interface between the carbon layers and the MOF units, which enhances the physical adsorption capacity of the toxic gases. When unsaturated metallic sites are present in the MOFs, the target gases are also adsorbed via coordination to these centers. Further reaction with the framework leads to the formation of complexes. This is accompanied by the collapse of the MOF structure.