Graphene is essentially a monolayer of sp2 bonded carbon atoms, arranged in a honeycomb lattice. Graphene has in recent years attracted phenomenal interest from researchers in materials science, condensed matter physics, and electronics since its first demonstration in 2004. The importance of graphene research was epitomised by the Nobel prize for physics being awarded to pioneers of the field in 2010. The main topic of this research was the development of epitaxial graphene on silicon carbide (SiC) substrates. The substrate inferred processability of epitaxial graphene enables graphene devices to be fabricated on full wafers using standard semiconductor processing techniques. Biosensor research is a rapidly expanding field. The major driver comes from the healthcare industry but there are also applications for biosensors in the food quality appraisal and environmental monitoring industries. The key advantages of electrochemical biosensors over competing sensor technologies are the low cost of mass production, and ability to make sensors into small compact systems. Smaller, portable sensors allow for the development of point-ofcare medical devices, which can be crucial in fast diagnosis and long-term monitoring of diseases. Graphene channel resistor devices have been fabricated using electron beam lithography and a successfully developed contact metallisation scheme - using Titanium / Gold contacts. The metal-graphene contacts have been characterised using XPS and electrical current-voltage measurements. The graphene channel device has been used as the basis of an electrochemical sensor for human chorionic gonadotropin (hCG), an indicator of pregnancy - which has also been linked to increased risk of several cancers. The immunosensor developed is a promising tool for point-of-care detection of hCG, due to its excellent detection capability, simplicity of fabrication, low-cost, high sensitivity and selectivity.

Grafeno e nanofitas de grafeno vêm, cada vez mais, atraindo o interesse da comunidade científica devido as suas notáveis propriedades. Neste trabalho realizou-se um estudo sistemático da estabilidade de defeitos do tipo divacância, vacância e Stone-Wales em grafeno e nanofitas de grafeno com bordas zigzag. Para tal, fizeram-se cálculos de primeiros princípios, baseados em teoria do funcional da densidade (DFT) na aproximação GGA com o uso de pseudopotenciais ultrasoft e uma base de ondas planas. Também foram feitas simulações de imagens de STM para os defeitos nas nanofitas. Além disso, foram encontrados dois novos defeitos, não publicados em nenhum outro lugar (até onde vai o conhecimento do autor), com energia de formação muito baixa. / Graphene and graphene nanoribbons have been attracting a lot of interest from the scientific community because of their novel properties. In this work, a systematic research has been done on the stability and energetics of divacancy, vacancy and Stone-Wales defects in graphene and zigzag graphene nanoribbons. With this goal in mind, ab initio density functional calculations within the GGA approximation, using ultrasoft pseudopotentials and a plane wave basis were done. Also, STM images were simulated for some selected defects. Besides, two new defects, not published elsewhere (to the best knowledge of the author), with very low formation energy are reported.

This thesis focuses on the mathematical analysis of two partial differential equation systems. Consistent improvement of mathematical computation allows more and more questions to be addressed in the form of numerical simulations. At the same time, novel materials arising from advances in physics and material sciences are creating new problems which must be addressed. This thesis is divided into two parts based on analysis of two such materials: organic semiconductors and graphene. In part one we derive a generalized reaction-drift-diffusion model for organic photovoltaic devices -- solar cells based on organic semiconductors. After formulating an appropriate self-consistent model (based largely on generalizing partly contradictory previous models), we study the operation of the device in several specific asymptotic regimes. Furthermore, we simulate such devices using a customized 2D hybrid discontinuous Galerkin finite element scheme and compare the numerical results to our asymptotics. Next, we use specialized asymptotic regimes applicable to a broad range of device parameters to justify several assumptions used in the formulation of simplified models which have already been discussed in the literature. We then discuss the potential applicability of the simulations to real devices by discussing which parameters will be the most important for a functioning device. We then give further generic 2D numerical results and discuss the limitations of the model in this regime. Finally, we give several perspectives on proving existence and uniqueness of the model. In part two we derive a second-order finite difference numerical scheme for simulation of the 2D Dirac equation and prove that the method converges in the electromagnetically static case. Of particular interest is the application to electrons in graphene. We demonstrate this convergence numerically with several examples for which explicit solutions are known and discuss the manner in which errors appear and propagate. We furthermore extend the Dirac system with Poisson's equation to investigate interesting electronic effects. In particular, we show that our numerical scheme can successfully simulate a beam-splitter and Veselago lens, both of which have been predicted analytically to appear in graphene.

Graphene nanoplatelets (GNP) with thickness of 6 ~ 8 nm and lateral dimension of 5 μm (M5) and 25 μm (M25) have been used to prepare epoxy composites. Epoxy composites were fabricated initially by shear mixing to investigate the effects of filler type on the structure and properties of composites. The complex viscosity of GNP-epoxy mixture was found to increase by almost three orders of magnitude going from the neat epoxy to the 8 wt.% loading, leading to difficulties in their processing. Scanning electron microscopy of the composites showed that both fillers aggregated at high loadings with the M25 buckling more easily due to its larger diameter, which compromises its aspect ratio advantage over M5, resulting in only slightly better mechanical performance. Polarized Raman spectroscopy revealed that both M5 and M25 were randomly distributed in the epoxy matrix, After adding M5 and M25 fillers, the storage modulus increase with the filler loadings, however, the glass transition temperature (Tg) drops slightly after initial incorporation, then rises with further filler addition attributed to the pin effects of filler aggregations. In terms of electrical property, M25 has lower percolation (1 wt.%) than M5 composites due to its bigger aspect ratio, which enable M25 to form a conductive network more efficiently. Furthermore, M25 composites also have slightly better thermal and mechanical properties over that of M5 composites. However, the difference is not significant considering the aspect ratio of M25 is five times of that of M5. The reason is that the aggregation and buckling of M25 compromise its advantage over M5. Due to the better performance of M25 as filler, M25/epoxy composites were prepared by shear mixing, solvent compounding and three-roll mill. Samples made by solvent compounding display the lowest percolation threshold (0.5 wt.%), related to its relatively uniform dispersion of M25 in matrix, resulting in higher thermal conductivity and better mechanical properties. Water uptake in a water bath at 50 °C took 75 days to be saturated. Higher loaded samples have lower diffusion coefficient because of the barrier effects of GNP fillers, but have higher maximum water absorbed, which is owing to filler aggregation. Properties test of aged and unaged specimens show thermal conductivity of the aged was enhanced due to water’s higher thermal conductivity than epoxy resin matrix, while electrical performance was compromised due to the swelling effects caused by absorbed water. The mechanical properties of aged samples also dropped slightly due to plasticization effects.

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>Magister Scientiae - MSc / Supercapacitors are one of the important subjects concerning energy storage which has proven to be a challenge in this country. Currently, the electrodes of most commercial supercapacitor are made of carbon which is known to be inexpensive and has high resistance to corrosion. These carbon based supercapacitors operate under EDLC. They offer fast charging/discharging rates and have the ability to sustain millions of cycles without degrading. With their high power densities, they bridge the gap between batteries which offer high energy densities but are slow in charging/discharging and conventional dielectric capacitors which are very fast but having very low energy densities. The objective of this work was to develop a high performance supercapacitor using polyanilino-graphene oxide intercalated with platinum group metal nanocomposites. Specific capacitance of each material was investigated with the objective of ascertaining the material that has the best capacitance. In this work, GO was functionalized with aniline and intercalated with Pt, Pd and Pd-Pt nanocomposites. The nanomaterials were characterized with FTIR, Ultravioletvisible (UV-visible) spectroscopy, high resolution scanning electron microscopy (HRSEM), high resolution transmission electron microscopy (HRTEM), energy dispersive x-ray microanalysis (EDS) and X-ray diffraction (XRD) analysis. The composites were tested for possible application as supercapacitor materials using potentiostatic-galvanostatic constant current charge/discharge. The synthesized materials had good electronic, mechanical, optical, physical etc. properties as proven by the various characterization techniques but they proved not to be ideal for application as supercapacitor materials. The materials tested negative when tested for both anodic and cathodic materials therefore we can conclude that the materials are not good supercapacitor materials and therefore cannot be used in application as novel as supercapacitors.

Recent advances in experimental and computational methods have opened up new directions in graphene fundamental studies. In addition to understanding the basic properties of this material and its quasi-one dimensional structures, significant efforts are devoted to describing their long ranged dispersive interactions. Other two-dimensional materials, such as silicene, germanene, and transition metal dichalcogenides, are also being investigated aiming at finding complementary to graphene systems with other "wonder" properties. The focus of this work is to utilize first principles simulations methods to build our basic knowledge of structure-interaction relations in two-dimensional materials and design their properties. In particular, mechanical folding and extended defects in zigzag and armchair graphene nanoribbons can be used to modulate their electronic and spin polarization characteristics and achieve different stacking patterns. Our simulations concerning zigzag silicene nanoribbons show width-dependent antiferromagnetic-ferromagnetic transitions unlike the case of zigzag graphene nanoribbons, which are always antiferromagnetic. Heterostructures, build by stacking graphene, silicene, and MoS$_2$, are also investigated. It is found that hybridization alters the electronic properties of the individual layers and new flexural and breathing phonon modes display unique behaviors in the heterostructure compositions. Anchored to SiC substrate graphene nanoribbons are also proposed as possible systems to be used in graphene electronics. Our findings are of importance not only for fundamental science, but they could also be used for future experimental developments.

Fast carrier cooling is important for high power graphene based devices. Strongly coupled optical phonons play a major role in the relaxation of photo-excited carriers in graphene. Heterostructures of graphene and hexagonal boron nitride (hBN) have shown exceptional mobility and high saturation current, which makes them ideal for applications, but the effect of the hBN substrate on carrier cooling mechanisms is not understood. We track the cooling of hot photo-excited carriers in graphene-hBN heterostructures using ultrafast pump-probe spectroscopy. We find that the carriers cool down four times faster in the case of graphene on hBN than on a silicon oxide substrate thus overcoming the hot phonon bottleneck that plagues cooling in graphene devices. (C) 2017 Author(s).

The reinforcement mechanisms in graphene-based nanocomposites have been studied in this project, which primarily consists of three parts: the size and orientation effects of the graphene-based nano-fillers and their interfacial adhesion with the matrix. Overall Raman spectroscopy has been demonstrated to be a powerful technique to study the graphene-based nanocomposites. The deformation of small size graphene has been followed and a new model has been established to consider both the non-uniformity of strain along the graphene and laser intensity within the laser spot, which interprets the observed unusual Raman band shift well. Additionally, the deformation of monolayer graphene oxide (GO) has been followed for the first time. It appears that continuum mechanics is still valid, and the approximately constant strain distribution along the GO flake suggests a better stress transfer efficiency of GO than that of graphene. The spatial orientation of graphene has been studied based on the Raman scattering obtained from transverse sections of graphene, where the Raman bands intensities show a strong polarization dependence. Based on this, a new model has been established to quantify the spatial orientation of graphene in terms of an orientation distribution function, and the spatial orientation of monolayer graphene has been further confirmed by its surface roughness. This model has been extended to a variety of graphene-based materials and nanocomposites. It is also shown how the spatial orientation of graphene-based fillers affects the mechanical properties of the nanocomposites, through the first determination of the Krenchel orientation factor for nanoplatelets. The findings on both the size and orientation effects have been employed to study the deformation mechanics of bulk GO reinforced nanocomposite films. It has been demonstrated for the first time that the effective modulus of GO can be estimated using the Raman D band shift rate, and this is in agreement with the value measured using conventional mechanical testing. The effective modulus of GO is found to be lower than its Young’s modulus, probably due to the mis-orientation, waviness, wrinkling and agglomeration of the GO fillers.

This thesis discusses the two dimensional allotrope of carbon known as graphene in presence of magnetic field, with special focus on edge states. The structure of graphene is described in detail and from the structure, two models are formed. The Dirac equation is a good description of graphene for large samples, far away from edges, where the boundaries can be ignored. However, it causes problems with most types of edge and hard wall approximation has to be implemented. The Dirac equation is described in detail and used to obtain an energy spectrum, wavefunction and density of states for graphene edge in a strong magnetic field. For comparison, a Bohr-Sommerfield approximation was used to find the dispersion relation and compare it to the results obtained numerically from the Dirac equation. The second model, better fitting for nano-scale systems, is the tight binding model. This model was utilized to find Energy spectrum for graphene flakes in magnetic field, which resembles Hofstadter's butterfly spectrum. The spectrum was analyzed and periodic oscillations of magnetisation dependent on magnetic field (known as the de Haas-van Alphen effect) were described. The oscillation of magnetisation depends on the shape of the dot, even though the main properties remain the same: at low magnetic field, periodic oscillations due to Aharonov-Bohm effect, turning into more chaotic oscillations depending on the boundary conditions of the given quantum dot.