Flux-Across-Surfaces Theorem for a Dirac Particle

We consider the asymptotic evolution of a relativistic spin-1/2-particle. i.e. a particle whose wavefunction satisfies the Dirac equation with external static potential. We prove that the probability for the particle crossing a (detector) surface converges to the probability, that the direction of the momentum of the particle lies within the solid angle defined by the (detector) surface, as the distance of the surface goes to infinity. This generalizes earlier non relativistic results, known as flux across surfaces theorems, to the relativistic regime

The SURPRISE demonstrator: a super-resolved compressive instrument in the visible and medium infrared for Earth Observation

While Earth Observation (EO) data has become ever more vital to understanding the planet and addressing societal challenges, applications are still limited by revisit time and spatial resolution. Though low Earth orbit missions can achieve resolutions better than 100 m, their revisit time typically stands at several days, limiting capacity to monitor dynamic events. Geostationary (GEO) missions instead typically provide data on an hour-basis but with spatial resolution limited to 1 km, which is insufficient to understand local phenomena. In this paper, we present the SURPRISE project - recently funded in the frame of the H2020 programme – that gathers the expertise from eight partners across Europe to implement a demonstrator of a super-spectral EO payload - working in the visible (VIS) - Near Infrared (NIR) and in the Medium InfraRed (MIR) and conceived to operate from GEO platform -with enhanced performance in terms of at-ground spatial resolution, and featuring innovative on-board data processing and encryption functionalities. This goal will be achieved by using Compressive Sensing (CS) technology implemented via Spatial Light Modulators (SLM). SLM-based CS technology will be used to devise a super-resolution configuration that will be exploited to increase the at-ground spatial resolution of the payload, without increasing the number of detector’s sensing elements at the image plane. The CS approach will offer further advantages for handling large amounts of data, as is the case of superspectral payloads with wide spectral and spatial coverage. It will enable fast on-board processing of acquired data for information extraction, as well as native data encryption on top of native compression. SURPRISE develops two disruptive technologies: Compressive Sensing (CS) and Spatial Light Modulator (SLM). CS optimises data acquisition (e.g. reduced storage and transmission bandwidth requirements) and enables novel onboard processing and encryption functionalities. SLM here implements the CS paradigm and achieves a super-resolution architecture. SLM technology, at the core of the CS architecture, is addressed by: reworking and testing off-the-shelf parts in relevant environment; developing roadmap for a European SLM, micromirror array-type, with electronics suitable for space qualification. By introducing for the first time the concept of a payload with medium spatial resolution (few hundreds of meters) and near continuous revisit (hourly), SURPRISE can lead to a EO major breakthrough and complement existing operational services. CS will address the challenge of large data collection, whilst onboard processing will improve timeliness, shortening time needed to extract information from images and possibly generate alarms. Impact is relevant to industrial competitiveness, with potential for market penetration of the demonstrator and its components

Électrocatalyseurs potentiels pour l'électrolyse de l'eau - Challenges et opportunités de différentes familles de catalyseurs

Ce travail porte sur la synthèse et la caractérisation de différentes classes de catalyseurs et de leur intégration comme électrodes de travail pour une cellule d'électrolyse. Les électrodes à base de complexes moléculaires de ruthénium fabriquées par sérigraphie (Article 2) présentent des activités et des stabilités élevées, à pH neutre, vis-à-vis de l'oxydation de l'eau. Les catalyseurs sous forme d'oligomères montrent des performances supérieures. La conductivité électronique de l'électrode est le facteur limitant de l'activité catalytique d'une telle anode moléculaire. De plus, le faible chargement en catalyseur impose des limitations supplémentaires pour atteindre des densités de courant élevées. L'étude de matériaux catalytiques, composés d'un Métal de transition, d'Azote et de Carbone (Article 3) montre que celui contenant du cobalt a la plus grande activité pour la production d'hydrogène en milieu acide tout en montrant une certaine stabilité. Cette dernière s'explique par la présence de sites atomiques uniques, au détriment de la formation de nanoparticules, obtenus par une méthode de synthèse sans solvant. Ce procédé présente donc une stratégie intéressante pour la synthèse à grande échelle. Cependant, l'augmentation du nombre de site catalytiques dans le matériau reste une difficulté à surmonter. Une méthode (Brevet I) de fabrication des assemblages membrane-électrode a aussi été mise en place. Elle permet le remplacement des membranes coûteuses couramment utilisées. Deux structures de Molybdate de Nickel ont été synthétisées (Article 1) pour fabriquer, après électro-activation, des nanoparticules de γ-NiOOH actif envers la production d'oxygène en pH alcalin. L'élimination du molybdène conduit à une surface électrochimique élevée avec un grand nombre de sites de nickel exposé et explique l'origine de l'activité catalytique élevée. La présence de Molybdène sert donc ici d'agent structurant et porogène. L'étude par spectroscopie Raman montre que le dépôt en forme de bâtonnets (mis en évidence par microscopie électronique) fabriqué sur une mousse de Nickel comporte aussi le signal de la structure en feuille après l'éviction du molybdène. La présence de cette structure s'explique par une couche intermédiaire entre l'électrode en mousse et les bâtonnets visibles par microscopie électronique. Cependant, les résultats semblent indiquer une activité plus élevée pour la structure en bâtonnets. Un résultat essentiel de cette étude est que lors de la synthèse d'une structure en bâtonnets de Molybdate de Nickel sur une électrode, l'absence de la structure en feuille doit être vérifiée. Les différences fondamentales (Article 4) entre les nanostructures ont été caractérisées plus en détail à l'aide de diverses techniques : MEB, DRX et Spectroscopie Raman. Bien que les structures cristallines des deux nanostructures ne soient pas encore totalement résolues, les analyses montrent clairement qu'il s'agit de deux matériaux différents avec leurs propriétés. En effet la structure hydratée en feuille présente une activité supérieure à celle déshydratée pour la production d'hydrogène en milieu alcalin. Il est clair qu'une étape de réduction préliminaire est nécessaire pour accéder à l'activité catalytique exceptionnelle rapportée. Parmi les différentes classes de catalyseurs étudiés, les catalyseurs à nanoparticules semblent être les plus prometteurs pour une intégration réussie dans une cellule d'électrolyse à grande échelle. L'utilisation généralisée de ce type de matériau pourra être envisagée une fois que la stabilité des catalyseurs et de la membrane échangeuse d'anions sera résolue.In this thesis work, different classes of catalysts and their suitability for integration into an electrolyzer cell has been investigated. Ruthenium-based molecular catalysts in Paper II have shown high activities and stabilities towards water oxidation in neutral pH. Especially the oligomeric catalysts exhibited a superior performance. The electrical conductivity of the electrode was discovered as limiting factor on the catalytic activity of such a molecular anode. In addition, the low loading of catalyst might impose limitations on reaching high current densities at reasonable potentials. Among the tested transition metal single atom catalysts synthesized by pyrolyzing transition metal doped ZIF-8 structures in Paper III, cobalt has shown the highest activity towards hydrogen evolution and a stable behaviour in acidic pH. The enhanced stability of single atomic sites compared to the corresponding nanoparticles was proposed. Only a low number of nanoparticles was suggested to have been formed during the solvent free synthesis. Hence, this process might present an interesting strategy for the large-scale synthesis of single atom hydrogen evolution catalysts. However, also for this class of catalyst, the low number of active sites seems to present a difficulty, which has to be overcome. With the novel method presented in Patent I to fabricate a membrane electrode assembly, the usage of commonly used expensive membranes could possibly be avoided. Both as-prepared nickel molybdate hydrate nanoparticle shapes - sheets and rods - have been proposed in Paper I to transform in an electrochemical activation step into γ-NiOOH as active phase for the oxygen evolution reaction in alkaline pH. With the removal of molybdenum a large electrochemical surface area with an increased number of exposed nickel sites was indicated to be the origin behind the high catalytic activity of the nanoparticles. Molybdenum was suggested to only act as structure and pore forming agent. Even for the sample on nickel foam with only rods initially visible by electron microscopy, Raman bands of the sheet structure was observed after selective molybdenum leaching and could be traced back to the intermediate layer between the foam electrode and the nanorods. However, preliminary results indicate a higher activity for the rod structure. The nanosheet layer between the rods and the foam might be an interesting observation for further works concerning nanorods on the electrode and the attribution of the catalytic activity. An essential outcome and proposal of Paper I is that when synthesizing especially a nickel molybdate rod structure on an electrode, the absence of the sheet structure should be verified, which could be done by either selective molybdenum leaching combined with Raman spectroscopy or XRD, or by investigating the volume between rods and the electrode with SEM. With Paper IV the fundamental differences between the nanostructures were characterized with various techniques, indicating strongly that those are two different materials. For the hydrogen evolution reaction in alkaline media, the hydrate sheet structure exhibited a higher activity compared to the anhydrate, but clearly a reduction step is necessary to access the outstanding catalytic activity reported. Among all the investigated catalysts of different classes, the nanoparticle catalysts seem to be the most promising for a successful integration in a large scale electrolyzer cell for widespread use, especially, once the stability of the catalysts and the anion exchange membrane is resolved

Symmetrical P₄ Cleavage at Cobalt: Characterization of Intermediates on the Way from P₄ to Coordinated P₂ Units

Degradation of white phosphorus (P₄) in the coordination sphere of transition metals is commonly divided into two major pathways depending on the P_<i>x</i> ligands obtained. Consecutive metal-assisted P–P bond cleavage of four bonds of the P₄ tetrahedron leads to complexes featuring two P₂ ligands (symmetric cleavage) or one P₃ and one P₁ ligand (asymmetric cleavage). A systematic investigation of the degradation of white phosphorus P₄ to coordinated μ,η^2:2-bridging diphosphorus ligands in the coordination sphere of cobalt is presented herein as well as isolation of each of the decisive intermediates on the reaction pathway. The olefin complex [Cp*Co­(^<i>i</i>Pr₂Im)­(η²-C₂H₄)], <b>1</b> (Cp* = η⁵-C₅Me₅, ^<i>i</i>Pr₂Im = 1,3-di-isopropylimidazolin-2-ylidene), reacts with P₄ to give [Cp*Co­(^<i>i</i>Pr₂Im)­(η²-P₄)], <b>2</b>, the insertion product of [Cp*Co­(^<i>i</i>Pr₂Im)] into one of the P–P bonds. Addition of a further equivalent of the Co^I complex [Cp*Co­(^<i>i</i>Pr₂Im)­(η²-C₂H₄)], <b>1</b>, induces cleavage of a second P–P bond to yield the dinuclear complex [{Cp*Co­(^<i>i</i>Pr₂Im)}₂(μ,η^2:2-P₄)], <b>3</b>, in which a kinked cyclo-P₄^4– ligand bridges two cobalt atoms. Consecutive dissociation of the N-heterocyclic carbene with concomitant rearrangement of the cyclo-P₄ ligand and P–P dissociation leads to complexes [Cp*Co­(μ,η^4:2-P₄)­Co­(^<i>i</i>Pr₂Im)­Cp*], <b>4</b>, featuring a P₄ chain, and [{Cp*Co­(μ,η^2:2-P₂)}₂], <b>5</b>, in which two isolated P₂^2– ligands bridge two [Cp*Co] fragments. Each of these reactions is quantitative if performed on an NMR scale, and each compound can be isolated in high yields and large quantities

Real-Time Investigation of the H/D Exchange Kinetics of Porphyrins and Oligopeptides by Means of Neutral Cluster-Induced Desorption/Ionization Mass Spectrometry

The kinetics of the H/D exchange reaction in angiotensin II, hexaglycine (Gly₆), Co­(II)­tetra­(3-carboxyphenyl)­porphyrin, and tetra­(4-carboxyphenyl)­porphyrin were followed in real time by mass spectrometry employing desorption/ionization induced by neutral SO₂ clusters. The change of the isotope patterns with increasing degree of deuteration was recorded as a function of D₂O exposure and the underlying H/D exchange kinetics, i.e., the dependence of the different degrees of deuteration on time, were deduced. The results were modeled by means of Monte Carlo simulations taking into account different reaction constants for the H/D exchange reaction at different functional groups. In the case of the investigated porphyrins, the rate constants were directly assigned to the functional groups involved; in the case of the peptides, reaction at the explicit functional groups and the backbone chain of the molecules could be discriminated

Symmetrical P₄ Cleavage at Cobalt: Characterization of Intermediates on the Way from P₄ to Coordinated P₂ Units

Degradation of white phosphorus (P₄) in the coordination sphere of transition metals is commonly divided into two major pathways depending on the P_<i>x</i> ligands obtained. Consecutive metal-assisted P–P bond cleavage of four bonds of the P₄ tetrahedron leads to complexes featuring two P₂ ligands (symmetric cleavage) or one P₃ and one P₁ ligand (asymmetric cleavage). A systematic investigation of the degradation of white phosphorus P₄ to coordinated μ,η^2:2-bridging diphosphorus ligands in the coordination sphere of cobalt is presented herein as well as isolation of each of the decisive intermediates on the reaction pathway. The olefin complex [Cp*Co­(^<i>i</i>Pr₂Im)­(η²-C₂H₄)], <b>1</b> (Cp* = η⁵-C₅Me₅, ^<i>i</i>Pr₂Im = 1,3-di-isopropylimidazolin-2-ylidene), reacts with P₄ to give [Cp*Co­(^<i>i</i>Pr₂Im)­(η²-P₄)], <b>2</b>, the insertion product of [Cp*Co­(^<i>i</i>Pr₂Im)] into one of the P–P bonds. Addition of a further equivalent of the Co^I complex [Cp*Co­(^<i>i</i>Pr₂Im)­(η²-C₂H₄)], <b>1</b>, induces cleavage of a second P–P bond to yield the dinuclear complex [{Cp*Co­(^<i>i</i>Pr₂Im)}₂(μ,η^2:2-P₄)], <b>3</b>, in which a kinked cyclo-P₄^4– ligand bridges two cobalt atoms. Consecutive dissociation of the N-heterocyclic carbene with concomitant rearrangement of the cyclo-P₄ ligand and P–P dissociation leads to complexes [Cp*Co­(μ,η^4:2-P₄)­Co­(^<i>i</i>Pr₂Im)­Cp*], <b>4</b>, featuring a P₄ chain, and [{Cp*Co­(μ,η^2:2-P₂)}₂], <b>5</b>, in which two isolated P₂^2– ligands bridge two [Cp*Co] fragments. Each of these reactions is quantitative if performed on an NMR scale, and each compound can be isolated in high yields and large quantities