We give a strongly polynomial time combinatorial algorithm to minimise the largest eigenvalue of the weighted Laplacian of a bipartite graph. This is accomplished by solving the dual graph embedding problem which arises from a semidefinite programming formulation. In particular, the problem for trees can be solved in time cubic in the number of vertices.

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Nowadays, new approaches to fabricate high-performance electrode materials are of vital importance in the renewable energy field. Here, we present a facile synthesis procedure of 3D Ni(OH)2/graphene hybrids for supercapacitors via synchronous electrochemical-assisted exfoliation and assembly of graphene on 3D Ni(OH)2 networks. With the assistance of an electric field, the electrochemically exfoliated high-quality graphene can be readily, uniformly assembled on the surfaces of 3D Ni(OH)2. When serving as electrode materials for supercapacitors, the resulting 3D Ni(OH)2/graphene composites exhibited excellent specific capacitance (263 mF cm−2 at 2 mA cm−2), remarkable rate capability and super-long cycle life (retention of 94.1% even after 10 000 continuous charge–discharge cycles), which may be attributed to their highly porous, stable 3D architecture as well as uniform, firm anchoring of ultrathin graphene on their surfaces. Therefore, our approach provides a facile strategy for the large-scale synthesis of high-quality graphene based composites towards various applications.

Graphene-based conductor materials (GCMs) consist of stacked and decoupled layers of graphene flakes and could potentially transfer graphene’s outstanding material properties like its exceptional electrical conductivity to the macro scale, where alternatives to the heavy and expensive metallic conductors are desperately needed. To reach super-metallic conductivity however, a systematic electrical conductivity optimization regarding the structural and physical input parameters is required. Here, a new trend in the field of process and material optimization are data-based models which utilize data science methods to quickly identify and abstract information and relationships from the available data. In this work such data-based models for the conductivity of a real GCM thin-film sample are build on data generated with an especially improved and extended version of the network simulation approach by Rizzi et al. [1, 2, 3]. Appropriate methods to create data-based models for GCMs are thereby introduced and typical challenges during the modelling process are addressed, so that data-based models for other properties of GCMs can be easily created as soon as sufficient data is accessible. Combined with experimental measurements by Slawig et al. [4] the created data-based models allow for a coherent and comprehensive description of the thin-films’ electrical parameters across several length scales.:List of Figures List of Tables Symbol Directory List of Abbreviations 1 Introduction 2 Simulation approaches for graphene-based conductor materials 2.1 Traditional simulation approaches for GCMs 2.1.1 Analytical model for GCMs 2.1.2 Finite element method simulations for GCMs 2.2 A network simulation approach for GCMs 2.2.1 Geometry generation 2.2.2 Electrical network creation 2.2.3 Contact and probe setting 2.2.4 Conductivity computation 2.2.5 Results obtained with the network simulation approach 2.3 An improved implementation for the network simulation 2.3.1 Rizzi’s implementation of the network simulation approach 2.3.2 An network simulation tool for parameter studies 2.3.3 Extending the network simulation approach for anisotropy investigations and multilayer flakes 3 Data-based material modelling 3.1 Introduction to data-based modelling 3.2 Data-based modelling in material science 3.3 Interpretability of data-based models 3.4 The data-based modelling process 3.4.1 Preliminary considerations 3.4.2 Data acquisition 3.4.3 Preprocessing the data 3.4.4 Partitioning the dataset 3.4.5 Training the model 3.4.6 Model evaluation 3.4.7 Real-world applications 3.5 Regression estimators 3.5.1 Mathematical introduction to regression 3.5.2 Regularization and ridge regression 3.5.3 Support Vector Regression 3.5.4 Introducing non-linearity through kernels 4 Data-based models for a real GCM thin-film 4.1 Experimental measurements 4.2 Simulation procedure 4.3 Data generation 4.4 Creating data-based models 4.4.1 Quadlinear interpolation as benchmark model 4.4.2 KR, KRR and SVR 4.4.3 Enlarging the dataset 4.4.4 KR, KRR and SVR on the enlarged training dataset 4.5 Application to the GCM sample 5 Conclusion and Outlook 5.1 Conclusion 5.2 Outlook Acknowledgements Statement of Authorship

This diploma thesis deals with the preparation of the very thin films and their investigation by scanning probe microscopy methods. The ultrathin films of Pt on Pt(111) were created by pulsed laser deposition and the ultrathin films of Co on Pt(111) were deposited by thermal evaporation. The coverage of the substrate was much smaller than one monolayer (in order of hundredths of monolayer). The nucleation theory was verified by these experiments using so-called Onset method. Further graphene sheets were prepared on layer of Si/SiO2 by the mechanical exfoliation from the graphite crystal. The fabricated graphene sheets were studied by micro-Raman spectroscopy, microreflectometry, atomic force microscopy and similar techniques. These methods proved the thinnest graphite layers were consisted of two graphene monolayers.

Three-dimensional (3D) TiO₂–SnO₂–graphene aerogels (TTGs)were built up from the graphene oxide nanosheets supported with both TiO₂ and SnO₂ nanoparticles (NPs) via a facile hydrothermal assembly process. The resulting TTGs exhibit a 3D hierarchical porous architecture with uniform distribution of SnO₂ and TiO₂ NPs on the graphene surface, which not only effectively prevents the agglomeration of SnO₂ NPs, but also facilitates the fast ion/electron transport in 3D pathways. As the anode materials in lithium ion batteries (LIBs), TTGs manifest a high reversible capacity of 750 mA h g⁻¹ at 0.1 A g⁻¹ for 100 cycles. Even at a high current density of 1 A g⁻¹, a reversible capacity of 470mA h g⁻¹ can still be achieved from the TTG based LIB anode over 150 cycles.

The synthesis, characterization and biological evaluation of different graphene-based nanoparticles with potential biomedical applications are explored. The results presented within this work show that eukaryotic cells can respond differently not only to different types of nanoparticles, but also identify slight differences in the morphology of nanoparticles, such as size. This highlights the great importance of the synthesis and thorough characterization of nanoparticles in the design of effective nanoparticle platforms for biological applications. In order to test the influence of morphology of graphene-based nanoparticles on the cell response, nanoparticles with different sizes were synthesized and tested on different cells. The synthesis of spherical iron-oxide nanoparticles coated with graphene was accomplished using a colloidal chemistry route. This synthesis route was able to render nanoparticle samples with narrow size distributions, which can be taken as monodispersed. Four different samples varying in diameter from 10 to 20 nm were produced and the material was systematically characterized prior to the biological tests. The characterization of the material suggests that the iron oxide nanoparticles consist of a mix of both magnetite and maghemite phases and are coated with a thin graphitic layer. All samples presented functional groups and were similar in all aspects except in diameter. The results suggest that cells can respond differently even to small differences in the size of the nanoparticles. An in situ study of the coating of the iron-oxide nanoparticles using a transmission electron microscope revealed that it is possible to further graphitize the remaining oleic acid on the nanoparticles. The thickness of the graphitic coating was controlled by varying the amount of oleic acid on the nanoparticles. The in situ observations using an electron beam were reproduced by annealing the nanoparticles in a dynamic vacuum. This procedure showed that it is not only possible to coat large amounts of iron oxide nanoparticles with graphene using oleic acid, but also to improved their magnetic properties for other applications such as hyperthermia. This study therefore revealed a facile route to grow 2D graphene takes on substrates using oleic acid as a precursor. The synthesis of nanographene oxide nanoparticles of different sizes was in a second approach accomplished by using the Hummers method to oxidize and expand commercially available graphite. The size of the oxidized graphite was adjusted by sonicating the samples for different periods of time. The material was also thoroughly characterized and demonstrated to have two distinctive average size distributions and possess functional groups. The results suggest that different size flakes can trigger different cell response. The synthesis, characterization and biological evaluation of graphene nanoshells were performed. The graphene nanoshells were produced by using magnesia nanoparticles as a template to the graphene nanoshells. The coating of magnesia with graphene layers was accomplished using chemical vapor deposition. The nanoshells were obtained by removing the magnesia core. The size of the nanoshells was determined by the size of the magnesia nanoparticles and presented a broad size distribution since the diameter of the magnesia nanoparticles could not be controlled. The nanoshells were also characterized and the biological evaluation was performed in the Swiss Federal Laboratories for Materials Science and Technology (EMPA), in Switzerland. The results suggest that despite inducing the production of reactive oxygen species on cells, the nanoshells did not impede cell proliferation. / Die Herstellung, Charakterisierung und biologische Auswertung von verschiedenen Graphen-basierten Nanopartikeln mit einer potenziellen biomedizinischen Anwendung wurden erforscht. Die vorgestellten Ergebnisse im Rahmen dieser Arbeit zeigen, dass eukaryotische Zellen unterschiedlich reagieren können, wenn sie mit Nanopartikeln unterschiedlicher Morphologie interagieren. Die Zellen können geringe Unterschiede in der Morphologie, insbesondere der Größe der Nanopartikeln, identifizieren. Dies unterstreicht den Einfluss der Herstellungsmethoden und die Notwendigkeit einer gründlichen Charakterisierung, um ein effektives Design von Nanopartikeln für biologische Anwendungen zu erreichen. Um den Einfluss der Größe von Graphen-basierten Nanopartikel auf das Zellverhalten zu erforschen, wurden verschiedene Graphen-beschichte Eisenoxid-Nanopartikelproben durch eine kolloidchemische Methode hergestellt. Dieses Herstellungsverfahren ermöglicht die Synthese von Nanopartikeln mit engen Größenverteilungen, die als monodispers gelten können. Vier Proben mit unterschiedlichen Durchmessern (von 10 bis 20 nm) wurden hergestellt und vor den biologischen Untersuchungen systematisch charakterisiert. Die Probencharakterisierung deutet auf eine Mischung aus Magnetit- und Maghemit-Kristallphasen hin, außerdem besitzen die Nanopartikel eine dünne Graphitschicht. Die spektroskopischen Ergebnisse auch zeigen außerdem, dass alle Proben funktionelle Gruppen auf ihrer Oberfläche besitzen, sodass sie in allen Aspekten, außer Morphologie (Durchmesser), ähnlich sind. Die biologischen Untersuchungen deuten darauf hin, dass Zellen unterschiedliche Größen von Eisenoxid-Nanopartikeln reagieren können. Ein in situ Untersuchung der Beschichtung der Eisenoxid-Nanopartikel wurde mit einem Transmissionelektronenmikroskop durchgeführt. Die Ergebnisse zeigen, dass eine dünne Schicht von Ölsäure aus dem Syntheseprozess auf den Nanopartikeln verbleibt. Diese Schicht kann mit einem Elektronstrahl in Graphen umgewandelt werden. Die Dicke der Graphitschicht auf den Nanopartikeln kann durch die Menge der eingesetzten Ölsäure kontrolliert werden. Die in situ Beobachtungen der Graphenumwandlung konnte durch erhitzen der Nanopartikeln in einem dynamischen Vakuum reproduziert werden. Das Brennen der Eisenoxid-Nanopartikel ermöglicht nicht nur die Graphitisierung der Ölsäure, sondern auch eine Verbesserung der magnetischen Eigenschaften der Nanopartikel für weitere Anwendungen, z. B. der Hyperthermie. Die Umwandlung der Ölsäure in Graphen konnte so als relativ einfaches Verfahren der Beschichtung von zweidimensionalen (2D) Substraten etabliert werden. Die Herstellung von Nanographenoxid mit unterschiedlichen Größen wurde mit der Hummers-Method durchgeführt. Die unterschiedlichen Größen der Nanographenoxidpartikel wurde durch eine Behandlung in Ultraschallbad erreicht. Zwei Proben mit deutlicher Verteilung wurden mit mehreren Verfahren charakterisiert. Beide Proben haben Nanographenoxid Nanoteilchen mit verschiedenen funktionellen Gruppen. Die biologische Charakterisierung deutet darauf hin, dass unterschiedliche Größen des Nanographens ein unterschiedliches Zellverhalten auslösen. Abschließend, wurde die Herstellung, Charakterisierung und biologische Auswertung von Graphen-Nanoschalen durchgeführt. Die Graphen-Nanoschalen wurden mit Magnesiumoxid-Nanopartikeln als Template hergestellt. Die Beschichtung des Magnesia mit Graphen erforgte durch die chemische Gasphasenabscheidung. Die Nanoschalen wurden durch Entfernen des Magnesia-Kerns erhalten. Die Größe der Nanohüllen ist durch die Größe der Magnesia-Kerns bestimmt und zeigt eine breite Verteilung, da der Durchmesser der Magnesiumoxid-Nanopartikel gegeben war. Die Nanoschalen wurden ebenfalls mit Infrarot- und Röntgen Photoemissionspektroskopie charakterisiert und die biologische Bewertung wurde im Eidgenössische Materialprüfungs- und Forschungsanstalt (EMPA) durchgeführt, in der Schweiz. Die Ergebnisse zeigen, dass zwar die Produktion von reaktiven Sauerstoffspezies in den Zellen ausgelöst wird, diese sich aber weiterhin vermehren können.

Graphene nanoplatelets have been introduced into the interphase between electrically insulating glass fibre and polymer matrix to functionalize the traditional composite. Owing to the distribution of network structure of GNPs, the interphase can transfer the signals about various internal change of material. Consequently, due to the novel bio-inspired overlapping structure, our GNPs-glass fibre shows a unique opportunity as a micro-scale multifunctional sensor. The following conclusions can be drawn from present research: • We prepared GNPs solution via a scalable and highly effective liquid-phase exfoliation method. This method produces high-quality, unoxidized graphene flakes from flake graphite. We control the thickness and size of GNPs by varying the centrifugation rate. • A simple fibre oriented capillary flow which can suppress ‘coffee ring’ effect to deposit GNPs onto the curved glass fibre surface. The GNPs form continuous fish scales like overlapping structure. • The electrical conductivity of our GNPs-glass fibre shows semiconductive property. The electrical resistance value scattering and the advancing contact angle value scattering indicate a uniform deposit structure. The uniform overlapping structure is a key factor for higher electrical conductivity compared with our previous work with CNTs. • The contact angles of our GNPs-glass fibre with water indicate that the GNPs are almost unoxidized, so the inert GNPs coating decreases the interfacial shears strength. • A micro scale GNPs-glass fibre sensor for gas sensing is achieved by deposit GNPs onto glass fibre surface. This sensor can be used to detect solvents vapours, such as water, ethanol and acetone. All these vapours work as electron acceptor when reacting with GNPs. The acetone shows the highest sensitivity (45000%) compared with water and ethanol. • The doping-dedoping of GNPs-glass fibres during adsorption-desorption cycles of acetone result in the efficient “break-junction” (GNPs lost electron carrier concentration) mechanism, which provides the possibility to fabricate the electrochemical “switch” in a simple and unique way. • The resistance of our GNPs-glass fibre shows exponential relationship with RH. This is attributed to two points. Firstly, the water vapours show similar exponential adsorption on carbon surface; secondly, the bandgap of GNPs increases with the increase of adsorbed water vapour concentration. • Due to the weak van der Waals interaction when water molecules are adsorbed on GNPs surface, our GNPs-glass fibre shows extreme fast response and recovery time with RH. It is potential for our GNPs-glass fibre being used to monitor the breath frequency. • Utilizing the negative temperature coefficient of GNPs, our GNPs-glass fibre can be used as temperature sensor with a sensing region of -150 to 30 °C. • Through the observed abnormal resistance change at a temperature of about – 18 °C, we discovered a phase change of the trance confined water in graphene layers. Based on the resistance change, we can study the interaction of water and carbon nanoparticles. • The bio-inspired novel overlapped multilayer structure of GNPs coating shows structural colours. Even more, our GNPs-glass fibre can be used to monitor the loading force in the interphase when it is embedded into epoxy resin. • Our GNPs-glass fibre shows an excellent piezoresistive property, the single GNPs-glass fibre shows a larger gauge factor than the commercial strains sensor. • The semiconductive interphase was formed when the GNPs-glass fibre was embedded in polymer matrix. This semiconductive interphase is very sensitive to the deformation of material, therefore, an in-situ strain sensor was manufactured to real-time monitor the microcracks in a composite instead of external sensors. The area of resistance ‘jump’ increase can be seen as the feature area for damage’s early warning. • Monitoring the resistance variation of the single fibre composite was conducted under cyclic loading with progressively increasing the strain peaks in order to further investigate the response of in-situ sensor to the interphase damage process. The deviation of resistance/strain when the stress is larger than 2 % highlights the accumulation of damage, which gives insight into the mechanism of resistance change.

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Over the past decade, the bottom-up synthesis of structurally defined graphene nanoribbons (GNRs) with various topologies has attracted significant attention due to the extraordinary optical, electronic, and magnetic properties of GNRs, rendering them suitable for a wide range of potential applications (e.g., nanoelectronics, spintronics, photodetectors, and hydrothermal conversion). Remarkable achievements have been made in GNR synthesis with tunable widths, edge structures, and tailor-made functional substitutions. In particular, GNRs with liquid-phase dispersibility have been achieved through the decoration of various functional substituents at the edges, providing opportunities for revealing unknown GNR physiochemical properties. Because of the promise of liquid-phase dispersible GNRs, this mini-review highlights recent advances in their synthetic strategies, physiochemical properties, and potential applications. In particular, deep insights into the dvantages and challenges of their syntheses and chemical methodologies are provided to encourage future endeavors and developments.