Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

Simultaneous chemical reaction and distillation of formaldehyde

The thesis is concerned with the development and testing of a mathematical model of a distillation process in which the components react chemically. The formaldehyde-methanol-water system was selected and only the reversible reactions between formaldehyde and water giving methylene glycol and between formaldehyde and methanol producing hemiformal were assumed to occur under the distillation conditions. Accordingly the system has been treated as a five component system. The vapour-liquid equilibrium calculations were performed by solving iteratively the thermodynamic relationships expressing the phase equilibria with the stoichiometric equations expressing the chemical equilibria. Using optimisation techniques, the Wilson single parameters and Henry's constants were calculated for binary systems containing formaldehyde which was assumed to be a supercritical component whilst Wilson binary parameters were calculated for the remaining binary systems. Thus the phase equilibria for the formaldehyde system could be calculated using these parameters and good accuracy was obtained when calculated values were compared with experimental values. The distillation process was modelled using the mass and energy balance equations together with the phase equilibria calculations. The plate efficiencies were obtained from a modified A.I.Ch.E. Bubble Tray method. The resulting equations were solved by an iterative plate to plate calculation based on the Newton Raphson method. Experiments were carried out in a 76mm I.D., eight sieve plate distillation column and the results were compared with the mathematical model calculations. Overall, good agreement was obtained but some discrepancies were observed in the concentration profiles and these may have been caused by the effect of limited physical property data and a limited understanding of the reactions mechanism. The model equations were solved in the form of modular computer programs. Although they were written to describe the steady state distillation with simultaneous chemical reaction of the formaldehyde system, the approach used may be of wider application.

Improvement of bio-oil stability in wood pyrolysis process

Pyrolysis is one of several thermochemical technologies that convert solid biomass into more useful and valuable bio-fuels. Pyrolysis is thermal degradation in the complete or partial absence of oxygen. Under carefully controlled conditions, solid biomass can be converted to a liquid known as bie-oil in 75% yield on dry feed. Bio-oil can be used as a fuel but has the drawback of having a high level of oxygen due to the presence of a complex mixture of molecular fragments of cellulose, hemicellulose and lignin polymers. Also, bio-oil has a number of problems in use including high initial viscosity, instability resulting in increased viscosity or phase separation and high solids content. Much effort has been spent on upgrading bio-oil into a more usable liquid fuel, either by modifying the liquid or by major chemical and catalytic conversion to hydrocarbons. The overall primary objective was to improve oil stability by exploring different ways. The first was to detennine the effect of feed moisture content on bio-oil stability. The second method was to try to improve bio-oil stability by partially oxygenated pyrolysis. The third one was to improve stability by co-pyrolysis with methanol. The project was carried out on an existing laboratory pyrolysis reactor system, which works well with this project without redesign or modification too much. During the finishing stages of this project, it was found that the temperature of the condenser in the product collection system had a marked impact on pyrolysis liquid stability. This was discussed in this work and further recommendation given. The quantity of water coming from the feedstock and the pyrolysis reaction is important to liquid stability. In the present work the feedstock moisture content was varied and pyrolysis experiments were carried out over a range of temperatures. The quality of the bio-oil produced was measured as water content, initial viscosity and stability. The result showed that moderate (7.3-12.8 % moisture) feedstock moisture led to more stable bio-oil. One of drawbacks of bio-oil was its instability due to containing unstable oxygenated chemicals. Catalytic hydrotreatment of the oil and zeolite cracking of pyrolysis vapour were discllssed by many researchers, the processes were intended to eliminate oxygen in the bio-oil. In this work an alternative way oxygenated pyrolysis was introduced in order to reduce oil instability, which was intended to oxidise unstable oxygenated chemicals in the bio-oil. The results showed that liquid stability was improved by oxygen addition during the pyrolysis of beech wood at an optimum air factor of about 0.09-0.15. Methanol as a postproduction additive to bio-oil has been studied by many researchers and the most effective result came from adding methanol to oil just after production. Co-pyrolysis of spruce wood with methanol was undertaken in the present work and it was found that methanol improved liquid stability as a co-pyrolysis solvent but was no more effective than when used as a postproduction additive.

Chemical and physical characterization of clay bodies

Suitable methods for the assessment of the effect of freeze-thaw action upon ceramic tiles have been determined. The results obtained have been shown to be reproducible with some work in this area still warranted. The analysis of Whichford Potteries clays via a variety of analytical techniques has shown them to be a complex mix of both clay and non-clay minerals. 57Fe Mössbauer spectroscopy has highlighted the presence of both small and large particleα-Fe203, removable via acid washing. 19F MAS NMR has demonstrated that the raw Whichford Pottery clays examined have negligible fluorine content. This is unlikely to be detrimental to ceramic wares during the heating process. A unique technique was used for the identification of fluorine in solid-state systems. The exchange of various cations into Wyoming Bentonite clay by microwave methodology did not show the appearance of five co-ordinate aluminium when examined by 27Al MAS NMR. The appearance of Qo silicate was linked to an increase in the amount of tetrahedrally bound aluminium in the silicate framework. This is formed as a result of the heating process. The analysis of two Chinese clays and two Chinese clay raw materials has highlighted a possible link between the two. These have also been shown to be a mix of both clay and non-clay minerals. Layered double hydroxides formed by conventional and microwave methods exhibited interesting characteristics. The main differences between the samples examined were not found to be solely attributable to the differences between microwave and conventional methods but more attributable to different experimental conditions used.

The chemical modification of polymer blends by reactive processing

The primary objective of this research was to examine the concepts of the chemical modification of polymer blends by reactive processing using interlinking agents (multi-functional, activated vinyl compounds; trimethylolpropane triacrylates {TRIS} and divinylbenzene {DVD}) to target in-situ interpolymer formation between immiscible polymers in PS/EPDM blends via peroxide-initiated free radical reactions during melt mixing. From a comprehensive survey of previous studies of compatibility enhancement in polystyrene blends, it was recognised that reactive processing offers opportunities for technological success that have not yet been fully realised; learning from this study is expected to assist in the development and application of this potential. In an experimental-scale operation for the simultaneous melt blending and reactive processing of both polymers, involving manual injection of precise reactive agent/free radical initiator mixtures directly into molten polymer within an internal mixer, torque changes were distinct, quantifiable and rationalised by ongoing physical and chemical effects. EPDM content of PS/EPDM blends was the prime determinant of torque increases on addition of TRIS, itself liable to self-polymerisation at high additions, with little indication of PS reaction in initial reactively processed blends with TRIS, though blend compatibility, from visual assessment of morphology by SEM, was nevertheless improved. Suitable operating windows were defined for the optimisation of reactive blending, for use once routes to encourage PS reaction could be identified. The effectiveness of PS modification by reactive processing with interlinking agents was increased by the selection of process conditions to target specific reaction routes, assessed by spectroscopy (FT-IR and NMR) and thermal analysis (DSC) coupled dichloromethane extraction and fractionation of PS. Initiator concentration was crucial in balancing desired PS modification and interlinking agent self-polymerisation, most particularly with TRIS. Pre-addition of initiator to PS was beneficial in the enhancement of TRIS binding to PS and minimisation of modifier polymerisation; believed to arise from direct formation of polystyryl radicals for addition to active unsaturation in TRIS. DVB was found to be a "compatible" modifier for PS, but its efficacy was not quantified. Application of routes for PS reaction in PS/EPDM blends was successful for in-situ formation of interpolymer (shown by sequential solvent extraction combined with FT-IR and DSC analysis); the predominant outcome depending on the degree of reaction of each component, with optimum "between-phase" interpolymer formed under conditions selected for equalisation of differing component reactivities and avoidance of competitive processes. This was achieved for combined addition of TRIS+DVB at optimum initiator concentrations with initiator pre-addition to PS. Improvements in blend compatibility (by tensiles, SEM and thermal analysis) were shown in all cases with significant interpolymer formation, though physical benefits were not; morphology and other reactive effects were also important factors. Interpolymer from specific "between-phase" reaction of blend components and interlinking agent was vital for the realisation of positive performance on compatibilisation by the chemical modification of polymer blends by reactive processing.

Chemical modification of polymers

Based on the knowledge of PVC degradation and stabilisation, chemical modifications were imposed on degraded PVC and raw PVC with the aim of obtaining non-migrating additives. The modifications were carried out mainly in the presence of dibutyl maleate (DBM), and the resulting polymer contained dibutyl maleic residues. Such modifications result in a polymer which contain substantive additives which resist migration under aggressive environments. Previous studies have shown that stable nitroxyl radicals function as stabilisers in polymer during processing (e.g. PP, PVC) by deactivating a large number of kinetic chains via a redox process whereby the concentrations of the nitroxyl and its reduced form, the hydroxylamine, fluctuate reciprocally and rhythmically. In order to understand the major reactions involved in such systems, a simulation method was used which resulted in a mathematical model and some rate constants, explaining the kinetic behaviour exhibited by such system. In the process of forming a suitable model, two nonlinear oscillators were proposed, which could be of interest in the study of nonlinear phenomenon because of their chaotic behaviour.