Covariant Phase Observables in Quantum Mechanics

The aim of this thesis is to present a solution to the quantum phase problem of the single-mode optical field. The solution is based on the use of phase shift covariant normalized positive operator measures. These measures describe realistic direct coherent state phase measurements such as the phase measurement schemes based on eight-port homodyne detection or heterodyne detection. The structure of covariant operator measures and, more generally, covariant sesquilinear form measures is analyzed in this work. Four different characterizations for phase shift covariant normalized positive operator measures are presented. The canonical covariant operator measure is definded and its properties are studied. Finally, some other suggested phase theories are introduced to investigate their connections to the covariant sesquilinear form measures.

Ion-exchange resins as stationary phase in reactive chromatography

Dynamic behavior of bothisothermal and non-isothermal single-column chromatographic reactors with an ion-exchange resin as the stationary phase was investigated. The reactor performance was interpreted by using results obtained when studying the effect of the resin properties on the equilibrium and kinetic phenomena occurring simultaneously in the reactor. Mathematical models were derived for each phenomenon and combined to simulate the chromatographic reactor. The phenomena studied includes phase equilibria in multicomponent liquid mixture¿ion-exchange resin systems, chemicalequilibrium in the presence of a resin catalyst, diffusion of liquids in gel-type and macroporous resins, and chemical reaction kinetics. Above all, attention was paid to the swelling behavior of the resins and how it affects the kinetic phenomena. Several poly(styrene-co-divinylbenzene) resins with different cross-link densities and internal porosities were used. Esterification of acetic acid with ethanol to produce ethyl acetate and water was used as a model reaction system. Choosing an ion-exchange resin with a low cross-link density is beneficial inthe case of the present reaction system: the amount of ethyl acetate as well the ethyl acetate to water mole ratio in the effluent stream increase with decreasing cross-link density. The enhanced performance of the reactor is mainly attributed to increasing reaction rate, which in turn originates from the phase equilibrium behavior of the system. Also mass transfer considerations favor the use ofresins with low cross-link density. The diffusion coefficients of liquids in the gel-type ion-exchange resins were found to fall rapidly when the extent of swelling became low. Glass transition of the polymer was not found to significantlyretard the diffusion in sulfonated PS¿DVB ion-exchange resins. It was also shown that non-isothermal operation of a chromatographic reactor could be used to significantly enhance the reactor performance. In the case of the exothermic modelreaction system and a near-adiabatic column, a positive thermal wave (higher temperature than in the initial state) was found to travel together with the reactive front. This further increased the conversion of the reactants. Diffusion-induced volume changes of the ion-exchange resins were studied in a flow-through cell. It was shown that describing the swelling and shrinking kinetics of the particles calls for a mass transfer model that explicitly includes the limited expansibility of the polymer network. A good description of the process was obtained by combining the generalized Maxwell-Stefan approach and an activity model that was derived from the thermodynamics of polymer solutions and gels. The swelling pressure in the resin phase was evaluated by using a non-Gaussian expression forthe polymer chain length distribution. Dimensional changes of the resin particles necessitate the use of non-standard mathematical tools for dynamic simulations. A transformed coordinate system, where the mass of the polymer was used as a spatial variable, was applied when simulating the chromatographic reactor columns as well as the swelling and shrinking kinetics of the resin particles. Shrinking of the particles in a column leads to formation of dead volume on top of the resin bed. In ordinary Eulerian coordinates, this results in a moving discontinuity that in turn causes numerical difficulties in the solution of the PDE system. The motion of the discontinuity was eliminated by spanning two calculation grids in the column that overlapped at the top of the resin bed. The reactive and non-reactive phase equilibrium data were correlated with a model derived from thethermodynamics of polymer solution and gels. The thermodynamic approach used inthis work is best suited at high degrees of swelling because the polymer matrixmay be in the glassy state when the extent of swelling is low.

Applying Active Front End To Multilevel Inverter

The aim of this work was to make an active front end from IGBTs for a multilevel inverter. The work was done for Mosart II, a long term still ongoing Vacon Oyj project. The purpose of the AFE is to balance the DC-voltage and to put the returning power back to the grid instead of the breaking chopper and the capacitor. With a diode rectifier the bridge only allows power to pass in one direction and the switching times are not controllable. That means the rectifier always takes the highest phase and the phases are always conducting the same 120◦. With an AFE it is possible to actively change the rectifiers switching pattern. A diode bridge also generates much greater losses than an IGBT bridge. With these arguments it is rational to start researching the possibility of an AFE in a multilevel inverter.

Tehokerrointa korjaava skalaariohjaus puoliohjatussa ja kuusikytkintasasuuntaajassa

Verkon harmonisvirtoja rajoittavien standardien tiukentuessa joudutaan etenkin suuritehoisissa tehoelektronisissa laitteissa siirtymään aktiivisiin transistoriohjattuihin tasasuuntaajiin, jotka korjaavat tehokerrointa ja siten pienentävät verkkoon kytkeytyviä häiriövirtoja. Tässä diplomityössä esitellään yleisimpien kolmivaiheisten tasasuuntaajatopologioiden eroja ja vertaillaan puoliohjatun kolmikytkintopologian ja kuusikytkintopologian suorituskykyä tehokertoimen ja harmonissärön osalta, 16 kilowatin teholuokan taajuusmuuttajassa. Tasasuuntaajille tehtiin skalaariohjaukseen perustuva simulointimalli. Työn tavoitteena esitellään simulointitulokset harmonistason sekä tehokertoimen osalta. Työ liittyy Lappeenrannan teknillisen yliopiston sovelletun elektroniikan laboratorion ja Vacon Oyj:n yhteiseen hankkeeseen.

Membrane emulsification in preparation of single site catalyst

In the theory part the membrane emulsification was studied. Emulsions are used in many industrial areas. Traditionally emulsions are prepared by using high shear in rotor-stator systems or in high pressure homogenizer systems. In membrane emulsification two immiscible liquids are mixed by pressuring one liquid through the membrane into the other liquid. With this technique energy could be saved, more homogeneous droplets could be formed and the amount of surfactant could be decreased. Ziegler-Natta and single-site catalysts are used in olefin polymerization processes. Nowadays, these catalysts are prepared according to traditional mixing emulsification. More homogeneous catalyst particles that have narrower particle size distribution might be prepared with membrane emulsification. The aim of the experimental part was to examine the possibility to prepare single site polypropylene catalyst using membrane emulsification technique. Different membrane materials and solidification techniques of the emulsion were examined. Also the toluene-PFC phase diagram was successfully measured during this thesis work. This phase diagram was used for process optimization. The polytetrafluoroethylene membranes had the largest contact angles with toluene and also the biggest difference between the contact angles measured with PFC and toluene. Despite of the contact angle measurement results no significant difference was noticed between particles prepared using PTFE membrane or metal sinter. The particle size distributions of catalyst prepared in these tests were quite wide. This would probably be fixed by using a membrane with a more homogeneous pore size distribution. It is also possible that the solidification rate has an effect on the particle sizes and particle morphology. When polymeric membranes are compared PTFE is probably still the best material for the process as it had the best chemical durability.

Modeling of electrolyte sorption – from phase equilibria to dynamic separation systems

In this thesis, general approach is devised to model electrolyte sorption from aqueous solutions on solid materials. Electrolyte sorption is often considered as unwanted phenomenon in ion exchange and its potential as an independent separation method has not been fully explored. The solid sorbents studied here are porous and non-porous organic or inorganic materials with or without specific functional groups attached on the solid matrix. Accordingly, the sorption mechanisms include physical adsorption, chemisorption on the functional groups and partition restricted by electrostatic or steric factors. The model is tested in four Cases Studies dealing with chelating adsorption of transition metal mixtures, physical adsorption of metal and metalloid complexes from chloride solutions, size exclusion of electrolytes in nano-porous materials and electrolyte exclusion of electrolyte/non-electrolyte mixtures. The model parameters are estimated using experimental data from equilibrium and batch kinetic measurements, and they are used to simulate actual single-column fixed-bed separations. Phase equilibrium between the solution and solid phases is described using thermodynamic Gibbs-Donnan model and various adsorption models depending on the properties of the sorbent. The 3-dimensional thermodynamic approach is used for volume sorption in gel-type ion exchangers and in nano-porous adsorbents, and satisfactory correlation is obtained provided that both mixing and exclusion effects are adequately taken into account. 2-Dimensional surface adsorption models are successfully applied to physical adsorption of complex species and to chelating adsorption of transition metal salts. In the latter case, comparison is also made with complex formation models. Results of the mass transport studies show that uptake rates even in a competitive high-affinity system can be described by constant diffusion coefficients, when the adsorbent structure and the phase equilibrium conditions are adequately included in the model. Furthermore, a simplified solution based on the linear driving force approximation and the shrinking-core model is developed for very non-linear adsorption systems. In each Case Study, the actual separation is carried out batch-wise in fixed-beds and the experimental data are simulated/correlated using the parameters derived from equilibrium and kinetic data. Good agreement between the calculated and experimental break-through curves is usually obtained indicating that the proposed approach is useful in systems, which at first sight are very different. For example, the important improvement in copper separation from concentrated zinc sulfate solution at elevated temperatures can be correctly predicted by the model. In some cases, however, re-adjustment of model parameters is needed due to e.g. high solution viscosity.

Determination of chlorophenols from water by solid phase microextraction - ion mobility spectrometry (SPME-IMS)

Chlorophenols have been classified as possible carcinogens for humans. Chlorophenols have been used as pesticides and wood preservatives. In Finland, during 1930 – 1980s, saw mills used KY-5 wood preservative that contained 2,4,6-TCP, 2,3,4,6-TeCP and PCP. Especially in Finland chlorophenols have entered the environment by leaking from contaminated grounds of old saw mills. Although chlorophenol concentrations found in environment do not cause acute concern, long term exposure can increase the risk of cancer. SPME is relatively cheap and simple sampling method, in which the sample extraction and concentration are performed in a single step. Solvents are not required in SPME. IMS is based on the detection of sample ion drift times. Based on the drift times, reduced mobilities are calculated, which are comparable despite the measurement conditions. SPME-IMS coupling has not been used earlier in the determination of chlorophenols from water samples. The scope of this work was to study, if SPME-IMS system is suitable for detecting chloro-phenols from water samples. The aim was to determine the most optimal extraction condi-tions, which were then applied to real water samples. Following detection limits were deter-mined: 2,4,6-TCP: 0.33 mg/l; 2,3,4,6-TeCP: 0.63 mg/l and PCP: 1.63 mg/l. Detection limits were high compared to the highest possible chlorophenol concentration that is allowed in Finnish drinking water, 10 μg/l. Detected concentrations from water sample differed from verified concentrations in the case of 2,3,4,6-TeCP by 4.6 % and in the case of 2,4,6-TCP by 48.4 %. Based on the results it can be said that SPME-IMS setup is suitable for preliminary analysis of mg/l chlorophenol concentrations from water samples.

Surface transformation hardening of carbon steel with high power fiber laser

This study investigated the surface hardening of steels via experimental tests using a multi-kilowatt fiber laser as the laser source. The influence of laser power and laser power density on the hardening effect was investigated. The microhardness analysis of various laser hardened steels was done. A thermodynamic model was developed to evaluate the thermal process of the surface treatment of a wide thin steel plate with a Gaussian laser beam. The effect of laser linear oscillation hardening (LLOS) of steel was examined. An as-rolled ferritic-pearlitic steel and a tempered martensitic steel with 0.37 wt% C content were hardened under various laser power levels and laser power densities. The optimum power density that produced the maximum hardness was found to be dependent on the laser power. The effect of laser power density on the produced hardness was revealed. The surface hardness, hardened depth and required laser power density were compared between the samples. Fiber laser was briefly compared with high power diode laser in hardening medium-carbon steel. Microhardness (HV0.01) test was done on seven different laser hardened steels, including rolled steel, quenched and tempered steel, soft annealed alloyed steel and conventionally through-hardened steel consisting of different carbon and alloy contents. The surface hardness and hardened depth were compared among the samples. The effect of grain size on surface hardness of ferritic-pearlitic steel and pearlitic-cementite steel was evaluated. In-grain indentation was done to measure the hardness of pearlitic and cementite structures. The macrohardness of the base material was found to be related to the microhardness of the softer phase structure. The measured microhardness values were compared with the conventional macrohardness (HV5) results. A thermodynamic model was developed to calculate the temperature cycle, Ac1 and Ac3 boundaries, homogenization time and cooling rate. The equations were numerically solved with an error of less than 10-8. The temperature distributions for various thicknesses were compared under different laser traverse speed. The lag of the was verified by experiments done on six different steels. The calculated thermal cycle and hardened depth were compared with measured data. Correction coefficients were applied to the model for AISI 4340 steel. AISI 4340 steel was hardened by laser linear oscillation hardening (LLOS). Equations were derived to calculate the overlapped width of adjacent tracks and the number of overlapped scans in the center of the scanned track. The effect of oscillation frequency on the hardened depth was investigated by microscopic evaluation and hardness measurement. The homogeneity of hardness and hardened depth with different processing parameters were investigated. The hardness profiles were compared with the results obtained with conventional single-track hardening. LLOS was proved to be well suitable for surface hardening in a relatively large rectangular area with considerable depth of hardening. Compared with conventional single-track scanning, LLOS produced notably smaller hardened depths while at 40 and 100 Hz LLOS resulted in higher hardness within a depth of about 0.6 mm.

Mass transfer and reaction kinetics in single droplet systems

As reactive extraction grown more and more popular in a variety of technological applications, optimizing its performance becomes more and more important. The process of complex formation is affected by a great number of both physical and chemical properties of all the components involved, and sometimes their interference with one another makes improving the effectiveness of such processes very difficult. In this Master’s Theses, the processes of complex formation between the aqueous phase - represented by copper sulfate water solution, and organic phase – represented by Acorga M5640 solvent extractor, were studied in order to establish the effect these components have on reactive extraction performance and to determine which step is bottlenecking the process the most.