Catalyst, additive and substrate effects in intramolecular aromatic additions of alpha-diazoketones

This thesis is focused on transition metal catalysed reaction of α-diazoketones leading to aromatic addition to form azulenones, with particular emphasis on enantiocontrol through use of chiral copper catalysts. The first chapter provides an overview of the influence of variation of the substituent at the diazo carbon on the outcome of subsequent reaction pathways, focusing in particular on C-H insertion, cyclopropanation, aromatic addition and ylide formation drawing together for the first time input from a range of primary reports. Chapter two describes the synthesis of a range of novel α-diazoketones. Rhodium and copper catalysed cyclisation of these to form a range of azulenones is described. Variation of the transition metal catalyst was undertaken using both copper and rhodium based systems and ligand variation, including the design and synthesis of a novel bisoxazoline ligand. The influence of additives, especially NaBARF, on the enantiocontrol was explored in detail and displayed an interesting impact which was sensitive to substituent effects. Further exploration demonstrated that it is the sodium cation which is critical in the additive effects. For the first time, enantiocontrol in the aromatic addition of terminal diazoketones was demonstrated indicating enantiofacial control in the aromatic addition is feasible in the absence of a bridgehead substituent. Determination of the enantiopurity in these compounds was particularly challenging due to the lability of the products. A substantial portion of the work was focused on determining the stereochemical outcome of the aromatic addition processes, both the absolute stereochemistry and extent of enantiopurity. Formation of PTAD adducts was beneficial in this regard. The third chapter contains the full experimental details and spectral characterisation of all novel compounds synthesised in this project, while details of chiral stationary phase HPLC and 1H NMR analysis are included in the appendix.

Interaction of additive and quantization noises in digital PLLs

Phase-locked loops (PLLs) are a crucial component in modern communications systems. Comprising of a phase-detector, linear filter, and controllable oscillator, they are widely used in radio receivers to retrieve the information content from remote signals. As such, they are capable of signal demodulation, phase and carrier recovery, frequency synthesis, and clock synchronization. Continuous-time PLLs are a mature area of study, and have been covered in the literature since the early classical work by Viterbi [1] in the 1950s. With the rise of computing in recent decades, discrete-time digital PLLs (DPLLs) are a more recent discipline; most of the literature published dates from the 1990s onwards. Gardner [2] is a pioneer in this area. It is our aim in this work to address the difficulties encountered by Gardner [3] in his investigation of the DPLL output phase-jitter where additive noise to the input signal is combined with frequency quantization in the local oscillator. The model we use in our novel analysis of the system is also applicable to another of the cases looked at by Gardner, that is the DPLL with a delay element integrated in the loop. This gives us the opportunity to look at this system in more detail, our analysis providing some unique insights into the variance `dip' seen by Gardner in [3]. We initially provide background on the probability theory and stochastic processes. These branches of mathematics are the basis for the study of noisy analogue and digital PLLs. We give an overview of the classical analogue PLL theory as well as the background on both the digital PLL and circle map, referencing the model proposed by Teplinsky et al. [4, 5]. For our novel work, the case of the combined frequency quantization and noisy input from [3] is investigated first numerically, and then analytically as a Markov chain via its Chapman-Kolmogorov equation. The resulting delay equation for the steady-state jitter distribution is treated using two separate asymptotic analyses to obtain approximate solutions. It is shown how the variance obtained in each case matches well to the numerical results. Other properties of the output jitter, such as the mean, are also investigated. In this way, we arrive at a more complete understanding of the interaction between quantization and input noise in the first order DPLL than is possible using simulation alone. We also do an asymptotic analysis of a particular case of the noisy first-order DPLL with delay, previously investigated by Gardner [3]. We show a unique feature of the simulation results, namely the variance `dip' seen for certain levels of input noise, is explained by this analysis. Finally, we look at the second-order DPLL with additive noise, using numerical simulations to see the effects of low levels of noise on the limit cycles. We show how these effects are similar to those seen in the noise-free loop with non-zero initial conditions.

Investigation of additive effects in enantioselective copper-catalysed C-H insertion and aromatic addition reactions of α-diazocarbonyl compounds

Significant enhancements in enantioselectivities and reaction efficiencies in asymmetric copper-catalysed C-H insertion and aromatic addition reactions of α-diazocarbonyl compounds in the presence of various group I salts are reported. For the first time in carbenoid chemistry, evidence for the critical role of the metal cation is described.

Semiconductor nanowire fabrication via bottom-up & top-down paradigms

Semiconductor nanowires are pseudo 1-D structures where the magnitude of the semiconducting material is confined to a length of less than 100 nm in two dimensions. Semiconductor nanowires have a vast range of potential applications, including electronic (logic devices, diodes), photonic (laser, photodetector), biological (sensors, drug delivery), energy (batteries, solar cells, thermoelectric generators), and magnetic (spintronic, memory) devices. Semiconductor nanowires can be fabricated by a range of methods which can be categorised into one of two paradigms, bottom-up or top-down. Bottom-up processes can be defined as those where structures are assembled from their sub-components in an additive fashion. Top-down fabrication strategies use sculpting or etching to carve structures from a larger piece of material in a subtractive fashion. This seminar will detail a number of novel routes to fabricate semiconductor nanowires by both bottom-up and top-down paradigms. Firstly, a novel bottom-up route to fabricate Ge nanowires with controlled diameter distributions in the sub-20 nm regime will be described. This route details nanowire synthesis and diameter control in the absence of a foreign seed metal catalyst. Additionally a top-down route to nanowire array fabrication will be detailed outlining the importance of surface chemistry in high-resolution electron beam lithography (EBL) using hydrogen silsesquioxane (HSQ) on Ge and Bi2Se3 surfaces. Finally, a process will be described for the directed self-assembly of a diblock copolymer (PS-b-PDMS) using an EBL defined template. This section will also detail a route toward selective template sidewall wetting of either block in the PS-b-PDMS system, through tailored functionalisation of the template and substrate surfaces.

Investigation of catalyst effects in enantioselective copper- and rhodium-mediated transformations of α-diazocarbonyl compounds

This thesis describes the synthesis and reactivity of a series of α-diazocarbonyl compounds with particular emphasis on the use of copper-bis(oxazoline)-mediated enantioselective C–H insertion reactions leading to enantioenriched cyclopentanone derivatives. Through the use of additives, the enantioselectivity achieved with the copper catalysts for the first time reaches synthetically useful levels (up to 91% ee). Chapter one provides a comprehensive overview of enantioselective C–H insertions with α-diazocarbonyl compounds from the literature. The majority of reports in this section involve rhodium-catalysed systems with limited reports to date of asymmetric C–H insertion reactions in the presence of copper catalysts. Chapter two focuses on the synthesis and C–H insertion reactions of α-diazo-β-keto sulfones leading to α-sulfonyl cyclopentanones as the major product. Detailed investigation of the impact of substrate structure (both the sulfonyl substitutent and the substituent at the site of insertion), the copper source, ligand, counterion, additive and solvent was undertaken to provide an insight into the mechanistic basis for enantiocontrol in the synthetically powerful C–H insertion process and to enable optimisation of enantiocontrol and ligand design. Perhaps the most significant outcome of this work is the enhanced enantioselection achieved through use of additives, substantially improving the synthetic utility of the asymmetric C–H insertion process. In addition to the C–H insertion reaction, mechanistically interesting competing reaction pathways involving hydride transfer are observed. Chapter three reports the extension of the catalyst-additive systems, developed for C–H insertions with α-diazo-β-keto sulfones in chapter two, to C–H insertion in analogous α-diazo-β-keto phosphonate and α-diazo-β-keto ester systems. While similar patterns were seen in terms of ligand effects, the enantiopurities achieved for these reactions were lower than those in the cyclisations with analogous α-diazo-β-keto sulfones. Extension of this methodology to cyclopropanation and oxium ylide formation/[2,3]-sigmatropic rearrangement was also explored. Chapter four contains the full experimental details and spectral characterisation of all novel compounds synthesised in this project, while details of chiral stationary phase HPLC analysis and X-ray crystallography are included in the appendix.

Analysing energy detector diversity receivers for spectrum sensing

The analysis of energy detector systems is a well studied topic in the literature: numerous models have been derived describing the behaviour of single and multiple antenna architectures operating in a variety of radio environments. However, in many cases of interest, these models are not in a closed form and so their evaluation requires the use of numerical methods. In general, these are computationally expensive, which can cause difficulties in certain scenarios, such as in the optimisation of device parameters on low cost hardware. The problem becomes acute in situations where the signal to noise ratio is small and reliable detection is to be ensured or where the number of samples of the received signal is large. Furthermore, due to the analytic complexity of the models, further insight into the behaviour of various system parameters of interest is not readily apparent. In this thesis, an approximation based approach is taken towards the analysis of such systems. By focusing on the situations where exact analyses become complicated, and making a small number of astute simplifications to the underlying mathematical models, it is possible to derive novel, accurate and compact descriptions of system behaviour. Approximations are derived for the analysis of energy detectors with single and multiple antennae operating on additive white Gaussian noise (AWGN) and independent and identically distributed Rayleigh, Nakagami-m and Rice channels; in the multiple antenna case, approximations are derived for systems with maximal ratio combiner (MRC), equal gain combiner (EGC) and square law combiner (SLC) diversity. In each case, error bounds are derived describing the maximum error resulting from the use of the approximations. In addition, it is demonstrated that the derived approximations require fewer computations of simple functions than any of the exact models available in the literature. Consequently, the regions of applicability of the approximations directly complement the regions of applicability of the available exact models. Further novel approximations for other system parameters of interest, such as sample complexity, minimum detectable signal to noise ratio and diversity gain, are also derived. In the course of the analysis, a novel theorem describing the convergence of the chi square, noncentral chi square and gamma distributions towards the normal distribution is derived. The theorem describes a tight upper bound on the error resulting from the application of the central limit theorem to random variables of the aforementioned distributions and gives a much better description of the resulting error than existing Berry-Esseen type bounds. A second novel theorem, providing an upper bound on the maximum error resulting from the use of the central limit theorem to approximate the noncentral chi square distribution where the noncentrality parameter is a multiple of the number of degrees of freedom, is also derived.