Mathematical modelling and optimisation of the formulation and manufacture of aggregate food products

In this PhD study, mathematical modelling and optimisation of granola production has been carried out. Granola is an aggregated food product used in breakfast cereals and cereal bars. It is a baked crispy food product typically incorporating oats, other cereals and nuts bound together with a binder, such as honey, water and oil, to form a structured unit aggregate. In this work, the design and operation of two parallel processes to produce aggregate granola products were incorporated: i) a high shear mixing granulation stage (in a designated granulator) followed by drying/toasting in an oven. ii) a continuous fluidised bed followed by drying/toasting in an oven. In addition, the particle breakage of granola during pneumatic conveying produced by both a high shear granulator (HSG) and fluidised bed granulator (FBG) process were examined. Products were pneumatically conveyed in a purpose built conveying rig designed to mimic product conveying and packaging. Three different conveying rig configurations were employed; a straight pipe, a rig consisting two 45° bends and one with 90° bend. It was observed that the least amount of breakage occurred in the straight pipe while the most breakage occurred at 90° bend pipe. Moreover, lower levels of breakage were observed in two 45° bend pipe than the 90° bend vi pipe configuration. In general, increasing the impact angle increases the degree of breakage. Additionally for the granules produced in the HSG, those produced at 300 rpm have the lowest breakage rates while the granules produced at 150 rpm have the highest breakage rates. This effect clearly the importance of shear history (during granule production) on breakage rates during subsequent processing. In terms of the FBG there was no single operating parameter that was deemed to have a significant effect on breakage during subsequent conveying. A population balance model was developed to analyse the particle breakage occurring during pneumatic conveying. The population balance equations that govern this breakage process are solved using discretization. The Markov chain method was used for the solution of PBEs for this process. This study found that increasing the air velocity (by increasing the air pressure to the rig), results in increased breakage among granola aggregates. Furthermore, the analysis carried out in this work provides that a greater degree of breakage of granola aggregates occur in line with an increase in bend angle.

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.