The enrichment of heavy hydrogen isotopes (deuterium, tritium) is required to fulfill their increasing application demands, e.g., in isotope related tracing, cancer therapy and nuclear reaction plants. However, their exceedingly low natural abundance and the close resemblance of physiochemical properties to protium render them extremely difficult to be separated. In this thesis, we investigate hydrogen isotope transport and separation via layered and two-dimensional materials. Three different theoretical challenges are undertaken in this work: (1) identification of the transported hydrogen species (proton H+ or protium H atom) inside interstitial space of layered materials (hexagonal boron nitride, molybdenum disulfide and graphite) and elucidation of their transport mechanism; (2) separation of hydron (proton H+, deuteron D+, and triton T+) isotopes through vacancy-free graphene and hexagonal boron nitride monolayers; (3) capture of the extremely rare light helium isotope (3He) with atomically thin two-dimensional materials. In the case of hydrogen transport, the essential challenges are investigation of its mechanism as well as the identification of transported particles. Regarding the case of hydron isotope separation, the essential questions are whether or not pristine graphene is permeable to the isotopes, and how quantum tunneling and topological Stone-Wales 55-77 defects affect their permeation and separation through graphene. In the last case, to capture the light helium isotope, quantum tunneling, which favors the lighter particles, is utilized to harvest 3He using graphdiyne monolayer. Our results provide novel theoretical insights into hydrogen particle transport inside the interstitial space of van der Waals materials; they uncover the mechanism of hydron isotope separation through 2D graphene and hexagonal boron nitride monolayers; and they predict the influence of pure quantum tunneling on the enrichment of 3He through graphdiyne membrane.

Cette thèse est consacrée à l'étude approfondie de formes exotiques de matériaux nano-structurés qui pourraient conduire à une avancée significative dans les nano-composants. Deux thèmes distincts ont été ainsi abordés. Le premier concerne les nano-clusters aromatiques de silicium synthétisés par plasma (SiNCs), tandis que le second est dédié aux structures silicium et germanium bi-dimensionnelles. Grâce à des simulations de type dynamique moléculaire et des calculs ab initio, ainsi que sur des recherches expérimentales, nous nous proposons d’explorer les propriétés intrigantes, mais à fort potentiel, de ces matériaux exotiques.Dans la première partie, nous commençons par des études théoriques et montrons qu'il est possible d'obtenir un comportement aromatique pour des SiNCs hydrogénés ayant une taille de ~1nm. Nous démontrons que les plasmas silane/hydrogène à basse température, proches de la formation de particules de poussière, présentent l'environnement idéal pour exploiter la tendance naturelle du silicium à la sur-coordination et donc pour la synthèse de structures à liaisons déficitaires en électrons. Ces nano-clusters qui se forment spontanément par auto-assemblage dans le plasma, ne possèdent pas de structure tétraédrique, sont plus stables que tous les autres SiNCs connus de cette taille et ont de fortes propriétés aromatiques dues à leur forte délocalisation électronique. Nous montrons également que les SiNCs non tétraédriques, présentent des modes de liaison à caractère métallique qui ressemblent fortement à celui d'un gaz d'électrons homogène dans des nano-clusters de métaux. Les SiNCs tétraédriques standards de cette taille ne peuvent absorber que dans l'ultraviolet, alors que nos calculs ont montré que des SiNCs purs, mais sur-coordonnés, absorbent dans la région spectrale ultraviolette, mais aussi dans le visible et l’infrarouge. Nous présentons ensuite une première preuve expérimentale pour nos prédictions théoriques. Nous avons mesuré in situ, dans un réacteur plasma l'absorption de la lumière visible des SiNCs. De plus, nos mesures réalisées en présence d'un champ électrique ont prouvées clairement que les SiNCs aromatiques possèdent un moment dipolaire permanent, que nous avons estimé entre 2 et 2,5 Debye, en excellent accord avec les calculs ab initio. Enfin, nos images de microscopie électronique à transmission des SiNCs, déposés dans des conditions de plasma optimisées, ont révélé la présence d'une autre forme exotique de silicium à structure hexagonale. Une telle structure se forme habituellement à des pressions extrêmement élevées appliquées sur des structures cubiques (diamant) de silicium. Nous souhaitons affirmer que c’est grâce à la «chimie au marteau» que ces conditions ont été atteintes.Dans la seconde partie, nous avons entrepris des études théoriques et expérimentales approfondies sur la croissance d'une nouvelle forme allotropique de silicium et de germanium: le silicène et le germanène, à savoir, une mono-couche d'atomes intégrée dans un réseau hexagonal qui ressemble fortement au graphène. Afin d'exclure tout mélange entre les atomes de silicium ou de germanium avec le substrat et de conserver leurs caractéristiques prometteuses comme de nouveaux matériaux de Dirac, nous avons effectué nos dépôts, sur un substrat de graphite chimiquement inerte. Une de nos découvertes cruciales est que les mono-couches de silicène ou de germanène interagissent avec le substrat de graphite uniquement via des forces de van der Waals. Cette interaction est suffisamment forte pour stabiliser les mono-couches, déposées même au-dessus de la température ambiante, mais suffisamment faible pour empêcher toute hybridation ou alliage entre le silicium ou le germanium et les atomes de carbone du substrat. Par conséquent, les propriétés électroniques exceptionnelles du silicène et du germanène, tels que les cônes de Dirac et les électrons sans masse, sont préservées même après leur dépôt sur les surfaces de graphite. / This thesis is devoted to the study of advanced, exotic forms of nanostructured materials that could lead to the next big advance for nanodevices. Two distinct topics have been considered. The first one is related to plasma-born aromatic silicon nanoclusters (SiNCs), while the second is dedicated to two-dimensional silicon and germanium materials. Based on molecular dynamics simulations and ab initio calculations, as well as, on experimental investigations, we explore a variety of intriguing properties of those exotic materials that are expected to be far superior to those of their conventional counterparts.In the first part of the thesis, we begin with theoretical studies and show that it is possible to obtain aromatic behavior in simple hydrogenated SiNCs with size of ~1nm. We demonstrate that low-temperature silane/hydrogen plasmas close to dust formation present the ideal environment to exploit the natural tendency of silicon to over-coordination for the construction of structures with electron-deficient bonds. Those nanoclusters form spontaneously by self-assembly in plasmas, do not possess tetrahedral structures, are more stable than any other known SiNCs of this size, and have strong aromatic-like properties due to their high electron delocalization. We demonstrate that non-tetrahedral SiNCs exhibit metallic-like bonding schemes that strongly resemble the one of a homogeneous electron gas in small metal clusters. Standard tetrahedral SiNCs of this size can absorb light only in the ultraviolet, while our calculations have shown that pure, but over-coordinated SiNCs absorb light in the ultraviolet, visible, and infrared spectral region. In this thesis, we present first experimental evidence that supports our theoretical predictions. Using incoherent broadband cavity enhanced absorption spectroscopy, we have measured the absorption of SiNCs, in situ, in a plasma reactor and found that they do absorb light in the visible region. In addition, our absorption measurements in the presence of an applied electric field have provided clear evidence that aromatic SiNCs possess a permanent dipole moment, and we have measured it to be between 2 and 2.5 Debye, in excellent agreement to prior ab initio calculations. Finally, our transmission electron microscopy images of such SiNCs, after their deposition under optimized plasma conditions, have revealed the presence of another exotic form of silicon with a primitive hexagonal structure. Such a structure usually forms after exposing diamond-cubic silicon to extremely high pressures. We tentatively claim that those conditions were, actually, achieved in our experiments due to the “chemistry with a hammer”.In the second part of the thesis, we have undertaken in-depth theoretical and experimental studies on the growth of a new allotropic form of silicon and germanium: a single layer of silicon or germanium atoms, only one atom thick and packed in a hexagonal lattice that closely resembles the lattice of graphene, namely silicene and germanene. In order to rule out any intermixing between silicon or germanium atoms and the underneath substrate atoms, as it was the case for metallic substrates, and to maintain their promising features to be new Dirac materials, we have performed our depositions on a chemically inert graphite substrate. One of our crucial findings is that the silicene or germanene monolayers interact with the graphite substrate via van der Waals forces only. The van der Waals interaction is strong enough to stabilize the deposited monolayers even above room temperature, but weak enough to prevent any hybridization or alloying between silicon or germanium and carbon atoms. Consequently, the outstanding electronic properties of free-standing silicene and germanene, such as Dirac cones and massless electrons, are preserved even after their deposition on graphite surfaces.

Lasers are increasingly used for a wide range of different applications for both civil and military purposes. Due to the distinct properties of laser light, use of lasers often comes with a risk of damage to the human eye and other optical sensors. Therefore, an effective laser protection is needed. 2D-materials is a relatively new class of materials, which have shown to possess many unique properties compared to its bulk counterparts. Some 2D-materials exhibit nonlinear optical (NLO) properties, and specifically optical power limiting (OPL) effects, and have therefore been researched for laser protection applications. In this work, two different 2D-materials, MXene Ti3C2 and graphene oxide (GO), have been combined with a hybrid organic-inorganic polymer, a so called melting gel (MG), to synthesise nanocomposites possessing OPL effects for laser protection applications. Different methods of incorporating the 2D-materials in the polymer matrix as well as the effect on optical properties of different concentrations of 2D-materials were investigated. The prepared nanocomposites were characterised using optical microscopy, spectroscopy and OPL measurements in order to investigate and quantify their linear and nonlinear optical properties. The MG was optically clear, mechanically stable and easy to synthesise, which makes it a suitable candidate as a matrix for a laser protection nanocomposite. Additionally, it was possible to dope the MG with the two different 2D-materials to create nanocomposites showing desirable optical properties in the visible spectrum. However, many samples showed signs of clustered 2D-particles indicating that the dispersion could be improved. Finally, OPL measurements, performed at 532 nm, showed that the MG itself exhibited OPL effects, both 2D-materials showed a stronger OPL effect than the non-doped MG and that GO-doped samples gave a better protection than the MXene samples.

<p>  </p> <p>Low-dimensional materials (LDMs) are substances that have at least one dimension with thicknesses in the nanometer (nm) scale. They have attracted tremendous research interests in many fields due to their unique properties that are absent in bulk materials. For instance, in quantum optics/photonics, LDMs offer unique advantages for effective light extraction and coupling with photonic/plasmonic structures; in chemistry, the large surface-to-volume ratio of LDMs enables more efficient chemical processes that are useful for numerous applications. In this thesis, several types of LDMs are studied and engineered with the goal to improve their impact in plasmonic and quantum photonic applications. Two-dimensional hexagonal boron nitride (hBN) is receiving increasing attention in quantum optics/photonics as it hosts various types of quantum emitters that are promising for quantum computing, quantum sensing, etc. In the first study, we explore and demonstrate a radiation- and lithography-free route to deterministically create single-photon emitters (SPEs) in hBN by nanoindentation with an atomic force microscopy. The method applies to hBN on flat, chip-compatible silicon-based substrates, and an SPE yield of up to 36% is achieved. This marks an important step toward the deterministic creation and integration of hBN SPEs with photonic and plasmonic devices. In the second study, the recently discovered negatively charged boron vacancy (V_B^-) spin defect in hBN is investigated. V_B^- defects are optically active with spin properties suitable for sensing at extreme scales. To resolve the low brightness issue of V_B^- defects, we couple them with an optimized nano-patch antenna structure and observe emission intensity enhancement that is nearly an order of magnitude higher than previous reports. Our achievements pave the way for the practical integration of V_B^- defects for quantum sensing. Zero-dimensional nanodiamond is another important host material for solid-state SPEs. Specifically, the negatively charged silicon vacancy (SiV) center in nanodiamonds exhibits optical properties that are suitable for quantum information technologies. In the third study, we, for the first time, demonstrate the creation of single SiV centers in nanodiamonds with an average size of ~20 nm using ion implantation. Stable single-photon emission is confirmed at room temperature, with zero-phonon line (ZPL) wavelengths in the range of 730 – 803 nm. This confirms the feasibility of single-photon emitter creation in nanodiamonds with ion implantation, and offers new opportunities to integrate diamond color centers for hybrid quantum photonic systems. Finally, we have also explored using metal-semiconductor hybrid nanoparticles for plasmon-enhanced photocatalysis. A core-shell nanoparticle structure is synthesized, with titanium nitride (TiN) and titanium dioxide (TiO₂) being the core and shell material respectively. It is observed that such core-shell nanoparticles effectively catalyze the generation of single oxygen molecules under 700-nm laser excitation. The main mechanism behind is the hot electron injection from the TiN core to the TiO₂ shell. Considering the chemical inertness and low cost of TiN, TiN@TiO₂ NPs hold great potential as plasmonic photosensitizers for photodynamic therapy and other photocatalytic applications at red-to-near-infrared (NIR) wavelengths.</p>

No description available.

Following a 15-year-long investigation on graphene, two-dimensional (2D) carbon-rich conjugated frameworks (CCFs) have attracted growing research interest as a new generation of multifunctional materials. Typical 2D CCFs include 2D π-conjugated polymers (also classified as 2D π-conjugated covalent organic frameworks) and 2D π-conjugated metal–organic frameworks, which are characterized by layer-stacked periodic frameworks with high in-plane π-conjugation. These unique structures endow 2D CCFs with regular porosities, large specific surface areas, and superior chemical stability. In addition, 2D CCFs exhibit certain notable properties (e.g., excellent electronic conductivity, designable topologies, and defined catalytic/redox-active sites), which have motivated increasing efforts to explore 2D CCFs for electrochemical energy applications. In this Perspective, the structural features and synthetic principles of 2D CCFs are briefly introduced. Moreover, we discuss recent achievements in 2D CCFs designed for various electrochemical energy conversion (electrocatalysis) and storage (supercapacitors and batteries) applications. Particular emphasis is placed on analyzing the precise structural regulation of 2D CCFs. Finally, we provide an outlook about the future development of synthetic 2D CCFs for electrochemical applications, which concerns novel monomer design, chemical methodology/strategy establishment, and a roadmap toward practical applications.

The anion-intercalation chemistries of graphite have the potential to construct batteries with promising energy and power breakthroughs. Here, we report the use of an ultrathin, positively charged two-dimensional poly(pyridinium salt) membrane (C2DP) as the graphite electrode skin to overcome the critical durability problem. Large-area C2DP enables the conformal coating on the graphite electrode, remarkably alleviating the electrolyte. Meanwhile, the dense face-on oriented single crystals with ultrathin thickness and cationic backbones allow C2DP with high anion-transport capability and selectivity. Such desirable anion-transport properties of C2DP prevent the cation/solvent co-intercalation into the graphite electrode and suppress the consequent structure collapse. An impressive PF6−-intercalation durability is demonstrated for the C2DP-covered graphite electrode, with capacity retention of 92.8% after 1000 cycles at 1 C and Coulombic efficiencies of > 99%. The feasibility of constructing artificial ion-regulating electrode skins with precisely customized two-dimensional polymers offers viable means to promote problematic battery chemistries.

<p dir="ltr">Creating synthetic materials that mimic native tissue is an overarching goal in tissue engineering and regenerative medicine. It is essential to embed molecular-resolution chemical patterning into soft synthetic polymers to achieve this. Even though fundamental principles from surface science offer broad control over the position of even individual atoms on a pristine surface, this degree of control remains restricted to two-dimensional hard crystalline materials under particular environmental conditions that are incompatible with life. Therefore, developing strategies to translate these principles into soft, amorphous interfaces is challenging<i>. </i>This will lead to the development of <i>nanopatterned soft materials</i> that closely resemble native tissue. Popular approaches in materials science fail to produce such <i>high-resolution polymers</i>.</p><p dir="ltr">Hydrogels are soft, three-dimensional networks that can hold large amounts of an aqueous solvent while retaining their structure. These materials have applicability in contexts where polymer materials must interface with biology (e.g., drug delivery, biosensing, tissue engineering, and regenerative medicine) as one can easily tune their mechanical, chemical, and biological properties. However, the main limitation of these materials is that the hydrogel network is amorphous, with substantial variability in mesh size up to the micron-scale. This limits their application when highly structured interactions with biomolecules, typically at sub-10 nm scales, are required. This dissertation shows a strategy to generate 1 nm-wide ordered patterns of functional groups on polyacrylamide (PAAm) hydrogel surfaces. When 1 nm-wide linear patterns are transferred to PAAm, patterning specific biological polyelectrolyte interactions at the hydrogel surface is possible. This represents a first step towards developing robust methods for nanopattern hydrogels at the proposed resolution.</p><p dir="ltr">One last subject this thesis dissertation seeks to explore is the extension of chemical patterning to a dynamic range of scales to adapt this technological advancement to industrial setups. Enabling the practical applicability of nanopatterned soft materials in macroscopic contexts (e.g., synthetic tissue development, wearable electronics, etc). However, extending this degree of control to a high throughput process applicable to heterogeneous interfaces remains a challenge. We demonstrated a scalable inkjet printing method to produce functional hierarchical patterns on two-dimensional crystalline substrates, which can be transferred to hydrogels. Finally, we studied the specific biosensing capabilities of these micro-patterned surfaces.</p>

Cette thèse est consacrée à la production de matériaux 2D en phase liquide, en utilisant des approches pouvant permettre la production en masse de graphène et de matériaux apparentés. Notre objectif est de surmonter certains problèmes critiques pour le traitement et l'utilisation pratique des encres à base de matériaux 2D et de fournir une compréhension approfondie de la relation structure-propriétés dans ces matériaux, constituant des étapes obligatoires pour leurs applications futures. Cette thèse porte principalement sur l'UILPE et l'exfoliation électrochimique du graphène et du disulfure de molybdène (MoS2), qui ont été choisis comme matériaux prototypes à 2 dimensions. Les approches synthétiques sont combinées à une caractérisation physico-chimique des matériaux produits, à l'aide de techniques telles que l'AFM, la microscopie électronique, la spectroscopie XPS et Raman, ainsi qu'à une caractérisation électrique. Des applications dans le domaine de la détection et de l'électronique ont été explorées et ont permis de démontrer que des approches d'exfoliation en phase liquide pouvaient être utilisées pour obtenir un contrôle précis des propriétés des matériaux 2D ouvrant la voie à leur intégration en tant que matériaux actifs dans de nouveaux dispositifs multifonctionnels. / This thesis is devoted to the production in liquid-phase of two-dimensional materials, by using approaches that may enable mass production of graphene and related materials. We aim to overcome some issues that are critical for the processing and practical use of 2D materials-inks and to provide a deep understanding of the structure-properties relationship in such materials being mandatory steps toward their future applications. This thesis mainly focuses on ultrasound-induced liquid-phase exfoliation and electrochemical exfoliation of graphene and molybdenum disulfide, which have been chosen as prototypical 2D materials. The synthetic approaches have been combined with a multiscale physico-chemical and electrical characterization of the produced materials, by employing techniques such as AFM, XPS and Raman spectroscopy. Applications in the field of sensing and electronics have been explored and allowed to demonstrate that liquid-phase exfoliation approaches can be conveniently employed to achieve a fine control on the properties of 2D materials paving the way to their integration as active materials in novel multifunctional devices.

This dissertation works out the vibrational properties of epitaxial silicene, which was discovered by Vogt et al. in 2012 by the epitaxial synthesis on the silver substrate. Its two-dimensional (2D) character is modified in comparison to the free-standing silicene due to its epitaxial nature, since the underlying substrate alters the physical properties of silicene as a result of the strong hybridization of the electronic levels of the substrate and adlayer. The growth of silicene layers is complicated by the sensitivity of the Si structures to the experimental conditions, mainly temperature, resulting in the formation of several seemingly different surface reconstructions. Another Si structure appears on the Ag surface at a supramonolayer coverage. The Raman spectroscopy was utilized to understand the relation between different Si structures and reveal their origin as well as to investigate the phonon-related physical properties of two-dimensional Si sheets. The central core of this work is the growth and characterization of these 2D silicene monolayers on the Ag (111) surface as well as the formation of silicene multilayer structures. The characterization of these materials was performed using in situ surface-sensitive measurement methods such as Raman spectroscopy and low-energy electron diffraction under ultra-high vacuum conditions due to high chemical reactivity of epitaxial silicene. Additional characterization was done ex situ by means of scanning force microscopy. The experimentally determined spectral signature of the prototypical epitaxial (3x3)/(4x4) silicene structure was confirmed by ab initio calculations, in collaboration with theory groups. The Raman signatures of the other 2D and 3D Si phases on Ag (111) were determined which allowed us to provide a clear picture of their formation depending on the preparation conditions. The monitoring of the silicene multi-layer growth yielded the vibrational signature of the top layer, reconstructed in a (√3x√3) fashion. It was compared to the inverse, (√3x√3)-Ag/Si(111), system showing the vast amount of similarities, which suggest that the (√3x√3) reconstruction belong to the silver layer. The chemical and physical properties of this surface structure additionally strengthen this equivalence. The possibility of functionalization of epitaxial silicene was demonstrated via exposure to the atomic hydrogen under UHV conditions. The adsorbed hydrogen covalently bonds to the silicene lattice modifying it and reducing its symmetry. As shown by Raman spectroscopy, such modification can be reversed by thermal desorption of hydrogen. The excitation-dependent Raman measurements also suggest the change of the electronic properties of epitaxial silicene upon hydrogenation suggesting that its originally semi-metallic character is modified into a semiconducting one. / Die experimentellen Forschungsarbeiten zum Thema Silicen basieren auf den 2012 von Vogt et al. durchgeführten Untersuchungen zu dessen Synthese auf Silbersubstraten. Diese Untersuchungen lieferten die Grundlage, auf der zweidimensionales (2D) epitaktisches Silicen sowie weitere 2D Materialien untersucht werden konnten. In den anfänglichen Arbeiten konnte dabei gezeigt werden, dass sich die Eigenschaften von epitaktischem Silicen gegenüber den theoretischen Vorhersagen von frei-stehendem Silicen unterscheiden. Darüber hinaus verkomplizieren sich die experimentellen Untersuchungen dieses 2D Materials, da auf dem Ag(111) Wachstumssubstrat sechs verschiedene 2D Si Polytypen existieren. Eine detaillierte Darstellung dieser Untersuchungen findet sich in dem einführenden Kapitel der vorliegen Promotionsschrift. Der zentrale Kern dieser Arbeit beschäftigt sich mit dem Wachstum und der Charakterisierung dieser 2D Silicen Monolagen auf Ag(111) Oberflächen sowie der Bildung von Silicen- Multilagen Strukturen. Die Charakterisierung dieser Materialien wurde in situ mit oberflächenempfindlichen Messmethoden wie der Raman Spektroskopie und der niederenergetischen Elektronenbeugung unter Ultrahochvakuum-Bedingungen durchgeführt. Eine zusätzliche Charakterisierung erfolgte ex situ mittels Raster-KraftMikroskopie. Die experimentell bestimmte spektrale Raman-Signatur der prototypischen epitaktischen (3x3)/(4x4) Silicene Struktur wurde durch ab initio Rechnungen, in Zusammenarbeit mit Theoriegruppen, bestätigt. Durch diesen Vergleich wir die zweidimensionale Natur der epitaktischen Silicen-Schichten vollständig bestätigt, wodurch andere mögliche Interpretationen ausgeschlossen werden können. Darüber hinaus wurden die Ramans-Signaturen der weiteren 2D und 3D Siliziumphasen auf Ag(111) bestimmt, wodurch sich ein klares Bild der Bildung dieser Strukturen in Abhängigkeit von den Präparationsbedingungen ergibt. Um die Möglichkeit der Funktionalisierung von Silicen und der weiteren 2D Si Strukturen zu testen, wurden diese unter UHV Bedingungen atomarem Wasserstoff ausgesetzt. Durch die Bindung zu den Wasserstoffamen wird die kristalline Struktur der Silicen-Schichten modifiziert und die Symmetrie reduziert, was sich deutlich in der spektralen Raman-Signatur zeigt. Wie mittels Raman Spektroskopie gezeigt werden konnte, kann diese Modifikation durch thermische Desorption des Wasserstoffs rückgängig gemacht werden, ist also reversibel. Raman Messungen mit verschiedenen Anregungswellenlängen deuten darüber hinaus auf die Änderung der elektronischen Eigenschaften der Silicen-Schichten durch die Hydrierung hin. Der ursprüngliche halbmetallische Charakter der epitaktischen Silicen-Schicht geht möglicherweise in einen halbleitenden Zustand über. Das Wachstum von Silicen Multilagen wurde ebenfalls mit in situ Ramanspektroskopie verfolgt. Die sich dabei ergebene Raman-Signatur wurde mit der Raman-Signatur von Ag terminiertem Si(111) verglichen. Hier zeigen sich große Ähnlichkeiten, die auf eine ähnliche atomare Struktur hindeuten und zeigen, dass Ag Atome für die Ausbildung der Oberflächenstruktur während des Wachstums der Si-Lagen verantwortlich sind. Die chemischen und physikalischen Eigenschaften dieser Struktur bestärken zusätzlich diese Äquivalenz.