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The molecular structure of solvent and adsorbates at naturally occurring solid–liquid interfaces is a feature that defines much of the chemistry of the natural environment. Because of its importance, this chemistry has been studied for many decades. More recently, nonlinear optical techniques have emerged as a valuable tool for non-invasive investigation of environmental interfaces, in part because of their inherent surface specificity. Solid–aqueous interfaces are complex regions in which chemical and electrostatic forces combine to drive adsorption processes. Second-harmonic generation and sum-frequency generation (SFG) spectroscopies have been employed by many groups to investigate water structure at these interfaces over a range of pH and ionic strength environments. In this thesis, I report results of further investigation of water structure adjacent silica, fluorite, polystyrene, and poly (methyl methacrylate) surfaces in the presence of varying concentrations of Na+ and Cl– . A model is developed to describe the SFG response from the fused silica–solution interface as ionic strength is increased. This model reveals both details of interfacial water structure and the interplay between second- and third-order optical responses present at charged interfaces. In context of this model, water structure at the three other interfaces is discussed. Knowledge of the phase of the SFG response provides additional surface structural information that can be related to the polar orientation of a molecule or functional group, for example, a flip in the orientation of water at an interface. Methods to capture the phase information at exposed interfaces are well established, but buried interface phase measurement remains a challenge. Therefore, I focused on development of a systematic method for buried interface phase measurement. In this thesis, I demonstrate improvements in the precision and accuracy of two phase-sensitive SFG techniques for measurement of exposed interfaces. Results from efforts to extend the theory to the buried interface are presented, along with an examination of the challenges encountered along the way. / Graduate

Optical images of astronomical objects viewed through ground-based telescopes are blurred by the atmosphere. The atmosphere is turbulent and as a consequence the density of air is not evenly distributed. This results in random, time-varying variations in refractive index. The wave-fronts passing through the atmosphere become aberrated, degrading the quality of the images. One solution is to include an adaptive optics system in the telescope. The system estimates the aberration of the wave-fronts and compensates the wave-front in real time using a corrector element, typically a deformable mirror. An important problem is how to estimate the aberrations optimally using only a small amount of light. This procedure is called wave-front sensing and is the subject of the research of this thesis. For turbulence with Kolmogorov statistics, the wave-front slope contains 87% of the energy of the aberrations. Hence, it is crucial to estimate the slope accurately. The displacement of an image is directly proportional to the wave-front slope and is used to estimate the slope. The conventional way of measuring the average slope of the wave-front in a Shack-Hartmann sensor is from the centroid of the image at the focal plane. It is demonstrated that using the centroid estimator produces an estimate with infinite variance. The Cramer-Rao lower bound (CRLB) is a theoretical lower bound for the variance of an unbiased estimator. The variance of the maximum-likelihood (ML) estimate for the displacement of a diffraction-limited image approaches the CRLB using a relatively small number of photons. The ML estimator is extended to the case where the image is randomly blurred by atmospheric turbulence. It is found that the variance of the error of the slope estimator can be improved significantly at low turbulence levels by using the ML estimator instead of the centroid. Curvature sensors use two defocused images to estimate the wave-front aberrations. It is shown using the CRLB that the focal plane is the optimal plane to measure the slope and the error using defocused images is quantified. The effect of using broadband light on the accuracy of the slope estimate is also investigated. When using laser guide stars, it is not possible to estimate the slope of the wave-front directly from the image because the beam is displaced on both the upward and downward journey. However, the displacement is a weak function of wavelength due to dispersion. In theory, the difference in wave-front slope as a function of wavelength is proportional to the absolute slope. Centering algorithms were implemented on experimental data taken at the Observatoire de Lyon to confirm this relationship. There is strong evidence pointing to a linear relationship between two pairs of differential tilt measurements, but not between the differential and the absolute tilt. However, the data appears to have been affected by a systematic experimental error and a new experiment is needed. Phase retrieval is a non-linear technique used to recover the phase in the Fourier domain using intensity measurements at the image plane and additional constraints. A method is described to solve the phase retrieval problem using linear iterations near the solution, which provides both analytical insight into phase retrieval and numerical results. The algorithm finds the maximum a posteriori estimate of the phase using prior information about the statistics of the noise and the phase and converges well in practice. When phase retrieval is performed on data from subdivided apertures, there is a loss of information regarding the relative piston terms of the subapertures and this error is quantified. It is found that there is a smaller wavefront error when estimating the phase from a full aperture than from a subdivided aperture. Using a combination of intensity measurements from a full and a subdivided aperture is shown to result in a small improvement at very high photon levels only. Curvature sensors measure the wave-front aberrations via a linear relationship between the curvature of the wave-front and the intensity difference between two defocused images. In practice, their performance is limited by their non-linear behaviour, which is characterised by solving simultaneously the irradiance transport equation and the accompanying wave-front transport equation. It is shown how the presence of non-linear geometric terms limits the accuracy of the sensor and how diffraction effects limit the spatial resolution. The effect of photon noise on the sensor is also quantified. A novel technique for deriving wave-front aberrations from two defocused intensity measurements is derived. The intensity defines a probability density function and the method is based on the evolution of the cumulative density function of the intensity. In one dimension, the problem is easily solved using histogram specification with a linear relationship between the wave-front slope and the difference in the abscissas of the histograms. This method is insensitive to scintillation. In two dimensions, the procedure requires the use of the Radon transform. Simulation results demonstrate that very good reconstructions can be attained down to 100 photons in each detector.

Space-time coded systems developed in the last ten years have been designed primarily using linear modulation. Non-linear continuous phase modulation has desirable constant envelope properties and considerable potential in space-time coded systems. The work in this thesis is focussed on developing and analysing an integrated space-time coded continuous phase modulated (STC-CPM) system. The coding of the space-time encoder and the modulation is incorporated into a single trellis encoder. This allows state combining, which leads to complexity reduction due to the reduced number of states. Design criteria for STC-CPM are summarized and the Euclidean distance is shown to be important for code design. The integrated STC-CPM system design enables systematic spacetime code searches that find optimal space-time codes, to be easily implemented. Optimal rate-1/2 and rate-2/3 space-time codes are found by maximizing the system's minimum squared Euclidean distance. These codes can provide high throughput and good coding gains over un-optimized full rank codes, such as delay diversity, in a quasi-static flat fading environment. Performance bounds are developed using a union bound argument and the pairwise error probability. Approximations of the bounds are evaluated. These truncated upper bounds predict the slopes of the simulated performance curves at low error rates.

This thesis describes the development of a new generation of three-phase rectifier, used to power telecommunications equipment. The traditional topology for such power converters is a single-phase two-stage design, with a boost converter providing power factor correction at the input to the first stage and an isolated dc-dc converter making up the second stage. A two-stage design results in the output power being processed twice and this cascade effect results in an overall reduction in efficiency. A rectifier solution is sought that meets with all the requirements of the telecommunications industry, while not displaying the inherent weaknesses associated with a boost-derived topology, and which can be realised in a single-stage design. A number of common three-phase topologies exist that could be realised as telecommunication power supplies, however, they do not completely satisfy all the industry requirements. A new three-phase rectifier, which is a single-stage buck-derived topology, is proposed. As a consequence of incorporating a buck-derived topology, the three-phase rectifier does not exhibit any issues resulting from startup inrush currents, or high currents due to an output short circuit condition, as would result in a boost-derived topology. The new proposed rectifier is modular in nature, which has the added benefit of redundancy. As a result of the new three-phase rectifier having a single-stage topology, it is expected that the overall efficiency would able to reach close to 95%. This is due to the traditional two-stage designs having efficiencies around the 90% mark, and therefore by removing a stage, out of the power conversion process the overall losses would also be halved, resulting in the 5% gain in efficiency. The rectifier system requires only one controller as a result of being a single-stage design, thus also reducing the overall system cost. Simulations show that if this topology is combined with a three-phase phase-locked loop controller it can meet the industry compliance standards. The thesis follows the development of the three-phase power converter from the simulation stage to the realisation of the control hardware and stability modelling. It also provides a detailed report of an investigation into the power converter system’s performance. The thesis concludes with discussions concerning the viability of the new topology as a commercial product and indicates areas of possible future research and development.

An experimental investigation to study the influence of base metal composition on the time required to achieve complete isothermal solidification (tf) during TLP bonding of three Ni-base superalloys was performed. Alloys IN 738, DS Rene80 and DS IC 6 show similar behaviour when bonded at 1100 oC, with comparable tf. However, at higher temperatures, IN 738 requires extended period of time (as compared to DS Rene80 and DS IC 6) to achieve complete isothermal solidification. The prolonged tf in IN 738 appears to be caused by a more pronounced reduction in concentration gradient of the diffusing solute within the material during bonding. In contrast, the shorter complete isothermal solidification time experienced by alloy DS IC6 is attributable to its capability to better accommodate the diffusing solute, through the formation of densely packed second-phase precipitates in the diffusion affected zone (DAZ).

The Project in Canada to Search for Supersymmetric Objects (PICASSO) searches for cold dark matter through the direct detection of Weakly Interacting Massive Particles (WIMPs) via spin-dependent and spin independent interactions with 19F nuclei. The detection principle is based on the superheated droplet technique; the detectors consist of a gel matrix with millions of liquid droplets of superheated fluorocarbon (C4F10) dispersed in it. In order to reduce the background, it is essential to distinguish the signature of different background particles interacting in the detector. A dedicated setup was developed in order to study the response of the C4F10 droplets in the presence of different backgrounds. The main objectives of this research are to identify the actual size (diameter) of the droplet increases due to phase transition and to check and establish the correlation between the droplet size and the maximum amplitude of the signal. In addition, the alpha-neutron discrimination was studied by observing each event’s image frames and the associated acoustic signal to get the amplitude distribution. The mean ratio of bubble size to droplet size was found to be 5.48, independent of temperature and type of interacting particle. Furthermore, no correlation was found between the droplet size and the maximum amplitude of the signal. As for the discrimination studies, the analysis of the signal events has confirmed that alphas generated outside the active liquid in the gel are much more difficult to discriminate from neutron than when alphas are generated inside the active liquid.

Since the discovery of Wilkinson’s catalyst and its usefulness in the homogeneous hydrogenation of olefins many investigations have been carried out on trivalent, tertiary phosphine–rhodium complexes.¹ Studies have shown that N-Heterocyclic carbenes as ligands offer increased stability to the complex and possess similar electronic properties as phosphine ligands.² The applications of the traditional catalyst are limited due to the limited stability of its solutions and its susceptibility to attack from the environment i.e. oxygen and moisture. The hydrogenation of olefins and other unsaturated compound is of great importance for the fine chemical and petroleum industries. The aim is to produce more stable and active versions of the traditional catalyst and also to demonstrate their improved stability and activity in catalytic applications. This study involves the investigation of the effects of ligand modification on Wilkinson type hydrogenation catalysts. Five Rhodium-phosphine complexes 1a: Rh(PPh₃)₃Cl, 1b: Rh(PPh₂Me)₃Cl, 1c: Rh(PPh₂Et)₃Cl, 1d: Rh(PPhMe₂)₃Cl, 1e: Rh(PPhMe₂)₃Cl have been synthesised and characterised by means of melting point,¹H NMR, ¹³C NMR, ³¹P NMR, IR and Mass Spectroscopy. Complexes 1d and 1e have also been characterised by means of elemental analysis and single crystal XRD. Five rhodium-N-heterocyclic carbene complexes 2a: Rh(COD)ImesCl [Imes =1,3-bis(2,4,6-trimethylphenyl)imidazol-2-ylidene] , 2b: Rh(COD)(diisopropylphenyl)₂Cl 2c: Rh(COD)(adamantyl)²Cl, 2d: Rh(COD)(diisopropyl)²Cl 2e: Rh(COD)(ditertbutyl)²Cl have been synthesised and characterised by means of melting point, ¹H NMR, ¹³C NMR, IR and Mass Spectroscopy. Five rhodium-NHC-CO complexes 3a: Rh(CO)₂ImesCl, 3b: Rh(CO)₂(diisopropylphenyl)₂Cl, 3c: Rh(CO)₂(adamantyl)₂Cl , 3d: Rh(CO)₂(diisopropyl)₂Cl, 3e: Rh(CO)₂(ditertbutyl)₂Cl, have been synthesised and characterised by means of ¹H NMR, ¹³C NMR, IR and Mass Spectroscopy. Complexes 1a, 1d, 1e, 2a, 2b, 2c, 2d, 2e were tested in the hydrogenation of simple alkenes under mild conditions. For the rhodium-phosphine complexes the catalyst efficiency based on TOF increases in the following order: 1a > 1d > 1e or RhCl₃(PPhMe₂)₃ > RhCl₃(PPhEt₂)₃ > RhCl(PPh₃)₃. For the rhodium-(COD)-NHC complexes catalyst efficiency based on TOF increases in the following order: 2d > 2b > 2e > 2a > 2c. While rhodium-phosphine complexes are far more active than rhodium-(COD)-NHC complexes, the latter seem to be active for a longer time and hence more stable under mild hydrogenation conditions. / Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2010.