Studies of the equation of state and elasticity of mantle minerals

Because the Earth’s upper mantle is inaccessible to us, in order to understand the chemical and physical processes that occur in the Earth’s interior we must rely on both experimental work and computational modeling. This thesis addresses both of these geochemical methods. In the first chapter, I develop an internally consistent comprehensive molar volume model for spinels in the oxide system FeO-MgO-Fe₂O₃-Cr₂O₃-Al₂O₃-TiO₂. The model is compared to the current MELTS spinel model with a demonstration of the impact of the model difference on the estimated spinel-garnet lherzolite transition pressure. In the second chapter, I calibrate a molar volume model for cubic garnets in the system SiO₂-Al₂O₃-TiO₂-Fe₂O₃-Cr₂O₃-FeO-MnO-MgO-CaO-Na₂O. I use the method of singular value analysis to calibrate excess volume of mixing parameters for the garnet model. The implications the model has for the density of the lithospheric mantle are explored. In the third chapter, I discuss the nuclear inelastic X-ray scattering (NRIXS) method, and present analysis of three orthopyroxene samples with different Fe contents. Longitudinal and shear wave velocities, elastic parameters, and other thermodynamic information are extracted from the raw NRIXS data.

Searches for new symmetries in pp collisions with the razor kinematic variables at √s = 7 TeV

The construction and LHC phenomenology of the razor variables M_R, an event-by-event indicator of the heavy particle mass scale, and R, a dimensionless variable related to the transverse momentum imbalance of events and missing transverse energy, are presented.  The variables are used  in the analysis of the first proton-proton collisions dataset at CMS  (35 pb^-1) in a search for superpartners of the quarks and gluons, targeting indirect hints of dark matter candidates in the context of supersymmetric theoretical frameworks. The analysis produced the highest sensitivity results for SUSY to date and extended the LHC reach far beyond the previous Tevatron results.  A generalized inclusive search is subsequently presented for new heavy particle pairs produced in √s = 7 TeV proton-proton collisions at the LHC using 4.7±0.1 fb^-1 of integrated luminosity from the second LHC run of 2011.  The selected events are analyzed in the 2D razor-space of M_R and R and the analysis is performed in 12 tiers of all-hadronic, single and double leptons final states in the presence and absence of b-quarks, probing the third generation sector using the event heavy-flavor content.   The search is sensitive to generic supersymmetry models with minimal assumptions about the superpartner decay chains. No excess is observed in the number or shape of event yields relative to Standard Model predictions. Exclusion limits are derived in the CMSSM framework with  gluino masses up to 800 GeV and squark masses up to 1.35 TeV excluded at 95% confidence level, depending on the model parameters. The results are also interpreted for a collection of simplified models, in which gluinos are excluded with masses as large as 1.1 TeV, for small neutralino masses, and the first-two generation squarks, stops and sbottoms are excluded for masses up to about 800, 425 and 400 GeV, respectively.

With the discovery of a new boson by the CMS and ATLAS experiments in the γ-γ and 4 lepton final states, the identity of the putative Higgs candidate must be established through the measurements of its properties. The spin and quantum numbers are of particular importance, and we describe a method for measuring the J^PC of this particle using the observed signal events in the H to ZZ^* to 4 lepton channel developed before the discovery. Adaptations of the razor kinematic variables are introduced for the H to WW^* to 2 lepton/2 neutrino channel, improving the resonance mass resolution and increasing the discovery significance. The prospects for incorporating this channel in an examination of the new boson J^PC is discussed, with indications that this it could provide complementary information to the H to ZZ^* to 4 lepton final state, particularly for measuring CP-violation in these decays.

Essays in mechanism design

This dissertation contains three essays on mechanism design. The common goal of these essays is to assist in the solution of different resource allocation problems where asymmetric information creates obstacles to the efficient allocation of resources. In each essay, we present a mechanism that satisfactorily solves the resource allocation problem and study some of its properties. In our first essay, ”Combinatorial Assignment under Dichotomous Preferences”, we present a class of problems akin to time scheduling without a pre-existing time grid, and propose a mechanism that is efficient, strategy-proof and envy-free. Our second essay, ”Monitoring Costs and the Management of Common-Pool Resources”, studies what can happen to an existing mechanism — the individual tradable quotas (ITQ) mechanism, also known as the cap-and-trade mechanism — when quota enforcement is imperfect and costly. Our third essay, ”Vessel Buyback”, coauthored with John O. Ledyard, presents an auction design that can be used to buy back excess capital in overcapitalized industries.

Cu2O substrates and epitaxial Cu2O/ZnO thin film hetero-structures for solar energy conversion

Future fossil fuel scarcity and environmental degradation have demonstrated the need for renewable, low-carbon sources of energy to power an increasingly industrialized world. Solar energy with its infinite supply makes it an extraordinary resource that should not go unused. However with current materials, adoption is limited by cost and so a paradigm shift must occur to get everyone on the same page embracing solar technology. Cuprous Oxide (Cu2O) is a promising earth abundant material that can be a great alternative to traditional thin-film photovoltaic materials like CIGS, CdTe, etc. We have prepared Cu2O bulk substrates by the thermal oxidation of copper foils as well Cu2O thin films deposited via plasma-assisted Molecular Beam Epitaxy. From preliminary Hall measurements it was determined that Cu2O would need to be doped extrinsically. This was further confirmed by simulations of ZnO/Cu2O heterojunctions. A cyclic interdependence between, defect concentration, minority carrier lifetime, film thickness, and carrier concentration manifests itself a primary reason for why efficiencies greater than 4% has yet to be realized. Our growth methodology for our thin-film heterostructures allow precise control of the number of defects that incorporate into our film during both equilibrium and nonequilibrium growth. We also report process flow/device design/fabrication techniques in order to create a device. A typical device without any optimizations exhibited open-circuit voltages Voc, values in excess 500mV; nearly 18% greater than previous solid state devices.

Selective hydroxylation of small alkanes by the particulate methane monooxygenase

The particulate methane monooxygenase (pMMO) catalyzes the oxidation of methane to methanol under ambient temperatures and pressures. Other small alkanes and alkenes are also substrates of this enzyme. We measured and compared the initial rate constants of oxidation of small alkanes (C1 to C5) catalyzed by pMMO. Both primary and secondary alcohols were formed from oxidation of n-butane and n-pentane. The alcohols produced from alkane oxidation can be further oxidized, probably by pMMO, to aldehydes and ketones. The apparent regioselectivity for n-butane and n-pentane is 100% 2-alcohols because the formation of primary alcohols is slower than further oxidation of these alcohols. The hydroxylation at the secondary carbons is highly stereoselective: (R)-alcohols are preferentially formed. The enantiomeric excess increases slightly with decreasing reaction temperature. The steric course of hydroxylation on primary carbons was also studied by using isotopically substituted ethane: (S)- or (R)-CH_3-CHDT, and (S)- or (R)-CD_3- CHDT and the reactions were found to proceed with 100% retention of configuration. A primary isotopic effect of k_H/k_D=5.0 was observed in these experiments.

Synthetic and structural studies of permethylscandocene and permethyltantalocene derivatives

Cp*_2Sc-H reacts with H_2 and CO at -78°C to yield Cp*_2ScOCH_3. A stepwise reduction of CO to an alkoxide is observed when CO reacts with Cp*_2ScC_6H_4CH_3-p to give the η^2-acyl Cp*_2Sc(CO)C_6H_4CH_3-p, which then reacts with H_2 to produce Cp*_2ScOCH_2C_6H_4CH_3-p. Cp*_2ScCH_3 and Cp*_2ScH(THF) react with CO to give unchar- uncharacterizable products. Cp*_2ScH and Cp*_2ScCH_3 react with Cp_2MCO (M = Mo, W) to give scandoxycarbenes, Cp_2M=C(CH_3)OScCp*_2, while a wide variety of Cp*_2ScX (X = H, CH_3, N(CH_3)_2, CH_2CH_2C_6H_5) reacts with CpM(CO)_2 (M = Co, Rh) to yield similar carbene complexes. An x-ray crystal structure determination of Cp(CO)Co=C(CH_3)- OScCp*_2 revealed a µ^2: η^1, η^1 carbonyl interaction between the Co-CO and Sc.

CO_2 inserts cleanly into Sc-phenyl bonds at -78°C to produce a carboxylate complex, Cp*_2Sc(O_2C)C_6H_4CH_3-p. The structure of this compound was determined by x-ray crystallographic techniques.

Excess C_2H_2 reacts with Cp*_2ScR (R = H, alkyl, aryl, alkenyl, alkynyl, amide) at temperatures below -78°C to form the alkynyl species Cp*_2Sc-C≡C-H, which then reacts with the remaining acetylene to form polyacetylene. Cp*_2Sc-C≡C-H further reacts to yield Cp*_2sc-C≡C-ScCp*_2. This unusual C_2 bridged dimer was characterized by x-ray crystallography.

Attempts were made to model the C-N bond breaking step of hydrodenitrogenation by synthesizing Cp*_2TaH(η^2-H_2C=N(C_6H_4X)) and studying its rearrangement to Cp*_2Ta(=N(C_6H_4X))(CH_3). The 1,2 addition/elimination reactions of Cp*_2Ta(η^2- H_2C=N(CH_3)H and Cp*_2Ta(=X)H (X=O, S, NH, N(C_6H_5)) were investigated. Cp*_2Ta(=NH)H was found to react with D_2 to give Cp*_2Ta(=ND)H, implying a nonsymmetric amide-dihydride intermediate for the addition/elimination process. Cp*_2Ta(=S)H and H_2O equilibrate with Cp*_2Ta(=O)H and H_2S, which allowed determination of the difference in bond strengths for Ta=O and Ta=S. Ta=O was found to be approximately 41 kcals/mole stronger than Ta=S.

Catalytic conversion of nitrogen to ammonia by an iron model complex

Threefold symmetric Fe phosphine complexes have been used to model the structural and functional aspects of biological N₂ fixation by nitrogenases. Low-valent bridging Fe-S-Fe complexes in the formal oxidation states Fe(II)Fe(II), Fe(II)/Fe(I), and Fe(I)/Fe(I) have been synthesized which display rich spectroscopic and magnetic behavior. A series of cationic tris-phosphine borane (TPB) ligated Fe complexes have been synthesized and been shown to bind a variety of nitrogenous ligands including N₂H₄, NH₃, and NH₂-. These complexes are all high spin S = 3/2 and display EPR and magnetic characteristics typical of this spin state. Furthermore, a sequential protonation and reduction sequence of a terminal amide results in loss of NH₃ and uptake of N₂. These stoichiometric transformations represent the final steps in potential N₂ fixation schemes.

Treatment of an anionic FeN₂ complex with excess acid also results in the formation of some NH₃, suggesting the possibility of a catalytic cycle for the conversion of N₂ to NH₃ mediated by Fe. Indeed, use of excess acid and reductant results in the formation of seven equivalents of NH₃ per Fe center, demonstrating Fe mediated catalytic N₂ fixation with acids and protons for the first time. Numerous control experiments indicate that this catalysis is likely being mediated by a molecular species.

A number of other phosphine ligated Fe complexes have also been tested for catalysis and suggest that a hemi-labile Fe-B interaction may be critical for catalysis. Additionally, various conditions for the catalysis have been investigated. These studies further support the assignment of a molecular species and delineate some of the conditions required for catalysis.

Finally, combined spectroscopic studies have been performed on a putative intermediate for catalysis. These studies converge on an assignment of this new species as a hydrazido(2-) complex. Such species have been known on group 6 metals for some time, but this represents the first characterization of this ligand on Fe. Further spectroscopic studies suggest that this species is present in catalytic mixtures, which suggests that the first steps of a distal mechanism for N₂ fixation are feasible in this system.

Bimetallic olefin polymerization catalysis : mechanisms and applications of proximal effects

This dissertation covers progress with bimetallic polymerization catalysts. The complexes we have designed were aimed at expanding the capabilities of homogeneous polymerization catalysts by taking advantage of multimetallic effects. Such effects were examined in group 4 and group 10 bimetallic complexes; proximity and steric repulsion were determined to be major factors in the effects observed.

Chapters 2 and 3 introduce the rigid p-terphenyl dinucleating framework utilized in most of this thesis. The permethylation of the central arene allows for the separation of syn and anti atropisomers of the terphenyl compounds. Kinetic studies were carried out to examine the isomerization of the dinucleating bis(salicylaldimine) ligand precursors. Metallation of the syn and anti bis(salicylaldimine)s using Ni(Me)2(tmeda) and excess pyridine afforded dinickel bisphenoxyiminato complexes with a methyl and a pyridyl ligand on each nickel. The syn and anti atropisomers of the dinickel complexes were structurally characterized and utilized in ethylene and ethylene/α-olefin polymerizations. Monometallic analogues were also synthesized and tested for polymerization activity. Ethylene polymerizations were performed in the presence of primary, secondary, and tertiary amines – additives that generally deactivate nickel polymerization catalysts. Inhibition of this deactivation was observed with the syn atropisomer of the bimetallic species, but not with the anti or monometallic analogues. A mechanism was proposed wherein steric repulsion of the substituents on proximal nickel centers disfavors simultaneous ligation of base to both of the metal centers. The bimetallic effect has been explored with respect to size and binding ability of the added base.

Chapter 4 presents the optimization of the bisphenoxyimine ligand synthesis and synthesis of syn and anti m-terphenyl analogues. Metallation with NiClMe(PMe₃)₂ yielded phosphine-ligated dinickel complexes, which have been structurally characterized. Ethylene/1-hexene copolymerizations in the presence of amines using Ni(COD)₂ as a phosphine scavenger showed significantly improved activity relative to the pyridine-ligated analogues. Incorporation of amino olefins in copolymerizations with ethylene was accomplished, and a mechanism was proposed based on proximal effects. Copolymerization trials with a variety of amino olefins and ethylene/1-hexene/amino olefin terpolymerizations were completed.

Early transition metal complexes based on the rigid p-terphenyl framework were designed with a variety of donor sets (Chapter 5 and Appendix B). Chapter 5 details the use of syn dizirconium di[amine bis(phenolate)] complexes for isoselective 1-hexene and propylene homopolymerizations. Ligand variation and monometallic complexes were studied to determine the origin of tacticity control. A mechanistic proposal was presented based on the symmetry at zirconium and the steric effects of the proximal metal center. Appendix B covers additional studies of bimetallic early transition metal complexes based on the p-terphenyl. Dititanium, dizirconium, and asymmetric complexes with bisphenoxyiminato ligands and derivatives thereof were targeted. Progress toward the synthesis of these complexes is described along with preliminary polymerization data. 1-hexene/diene copolymerizations and attempted polymerizations in the presence of ethers and esters with the syn dizirconium di[amine bis(phenolate)] complexes demonstrate the potential for further applications of this system in catalysis.

Appendix A includes work toward palladium catalysts for insertion polymerization of polar monomers. These complexes were based on dioxime and diimine frameworks with the intent of binding Lewis acidic metals at the oxime oxygens, at pendant phenolic donors, or at pendant aminediol moieties. The synthesis and structural characterization of a number of palladium and Lewis acid complexes is presented. Due to the instability of the desired species, efforts toward isolation of the desired complexes proved unsuccessful, though preliminary ethylene/methyl acrylate copolymerizations using in situ activation of the palladium species were attempted.

Reactions of oxygen containing ligands in the coordination sphere of permethylhafnocene and permethyltantalocene

A series of terl-butylperoxide complexes of hafnium, Cp*₂Hf(R)(OOCMe₃) (Cp* = ((η⁵-C₅Me₅); R = Cl, H, CH₃, CH₂CH₃, CH₂CH₂CH₃, CH₂CH₂CH₂CH₃, CH₂CHMe₂, CH=CHCMe₃, C₆H₅, meta-C₆H₃(CH₂)2) and Cp*(η⁵-C₅(CH₃)₄CH₂CH₂CH₂)Hf(OOCMe₃), has been synthesized. One example has been structurally characterized, Cp*₂Hf(OOCMe₃)CH₂CH₃ crystallizes in space group P2₁/c, with a = 19.890(7)Å, b = 8.746(4)Å, c = 17.532(6)Å, β = 124.987(24)°, V = 2498(2)ų, Z = 4 and R_F = 0.054 (2222 reflections, I > 0). Despite the coordinative unsaturation of the hafnium center, the terl-butylperoxide ligand is coordinated in a mono-dentate ligand. The mode of decomposition of these species is highly dependent on the substituent R. For R = H, CH₂CH₃, CH₂CH₂CH₃, CH₂CH₂CH₂CH₃, CH₂CHMe₂ a clean first order conversion to Cp*₂Hf(OCMe₃)(OR) is observed (for R CH₂CH₃, ΔHǂ = 19.6 kcal•mol^-1, ΔSǂ = -13 e.u.). These results are discussed in terms of a two step mechanism involving η²-coordination of the terl-butylperoxide ligand. Homolytic O-O bond cleavage is observed upon heating of Cp*₂Hf(OOCMe₃) R (R = C₆H₆, meta-C₆H₃(CH₃)₂). In the presence of excess 9,10-dihydroanthracene thermolysis of Cp*₂Hf(OOCMe₃)C₆H₆ cleanly affords Cp*₂Hf(C₆H₆)OH and HOCMe₃ (ΔHǂ = 22.6 kcal•mol^-1, ΔSǂ = -9 e.u.). The O-O bond strength in these complexes is thus estimated to be 22 kcal•mol^-1.

Cp*₂Ta(CH₂)H, Cp*₂Ta(CHC₆H₅)H, Cp*₂Ta(C₆H₄)H, Cp*₂Ta(CH₂=CH₂)H and Cp*₂Ta(CH₂=CHMe)H react, presumably through Cp*₂Ta-R intermediates, with H₂O to give Cp*₂Ta(O)H and alkane. Cp*₂Ta(O)H was structurally characterized: space group P2₁/n, a= 13.073(3)Å, b = 19.337(4)Å, c = 16.002(3)Å, β = 108.66(2)°, V = 3832(1)ų, Z = 8 and R_F = 0.0672 (6730 reflections). Reaction of terlbutylhydroperoxide with these same starting materials ultimately yields Cp*₂Ta(O)R and HOCMe₃. Cp*₂Ta(CH₂=CHR)OH species are proposed as intermediates in the olefin hydride reactions. Cp*₂Ta(O₂)R species can be generated from the reaction of the same starting materials and O₂. Lewis acids have been shown to promote oxygen insertion in these complexes.

Polymerization of functionalized olefins with neutral group ten catalysts

This thesis describes the preparation, characterization, and application of welldefined single-component group ten salicylaldimine complexes for the polymerization of ethylene to high molecular weight materials as well as the copolymerization of ethylene and functionalized olefins. After an initial introduction to the field, Chapter 2 describes the preparation of PPh₃ complexes that contain a series of modified salicylaldimine and naphthaldimine ligands. Such complexes were activated for polymerization by the addition of cocatalysts such as Ni(COD)₂ or B(C₆F₅)₃. As the steric demand of the ligand set increased-the molecular weight, polymerization activity, and lifetime of the catalyst was observed to increase. In fact, complexes containing "bulky" ligands, such as the [^Anthr,HSal] ligand (2.5), were found to be highly-active single component complexes for the polymerization of ethylene. Model hydrido compound were prepared-allowing for a better understanding of both the mechanism of polymerization and one mode of decomposition.

Chapter 3 describes the effect which additives play on neutral Ni^II polymerization catalysts such as 2.5. The addition of excess ethers, esters, ketones, anhydrides, alcohols, and water do not deactivate the catalysts for polymerization. However, the addition of excess acid, thiols, and phosphines was observed to shut-down catalysis. Since excess phosphine was found to inhibit catalysis, "phosphine-free" complexes, such as the acetonittile complex (3.26), were prepared. The acetonitrile complex was found to be the most active neutral polymerization catalyst prepared to date.

Chapter 4 outlines the use of catalyst 2.5 and 3.26 for the preparation of linear functionalized copolymers containing alcohols, esters, anhydrides, and ethers. Copolymers can be prepared with γ-functionalized-α-olefins, functionalized norbornenes, and functionalized tricyclononenes, with up to 30 mol% comonomer incorporation.

Chapter 5 outlines the preparation of a series of Pt^II alkyl/olefin salicylaldimine complexes which serve as models for the active species in the Ni^II-catalyzed polymerization process. Understanding the nature of the M-olefin interaction as a the electronic and steric properties of the salicylaldimine ligand is varied has allowed for a number of predictions about the design of future polymerization systems.

The Flocculation of E. coli with Polyethyleneimine

A comprehensive study was made of the flocculation of dispersed E. coli bacterial cells by the cationic polymer polyethyleneimine (PEI). The three objectives of this study were to determine the primary mechanism involved in the flocculation of a colloid with an oppositely charged polymer, to determine quantitative correlations between four commonly-used measurements of the extent of flocculation, and to record the effect of varying selected system parameters on the degree of flocculation. The quantitative relationships derived for the four measurements of the extent of flocculation should be of direct assistance to the sanitary engineer in evaluating the effectiveness of specific coagulation processes.

A review of prior statistical mechanical treatments of absorbed polymer configuration revealed that at low degrees of surface site coverage, an oppositely- charged polymer molecule is strongly adsorbed to the colloidal surface, with only short loops or end sequences extending into the solution phase. Even for high molecular weight PEI species, these extensions from the surface are theorized to be less than 50 Å in length. Although the radii of gyration of the five PEI species investigated were found to be large enough to form interparticle bridges, the low surface site coverage at optimum flocculation doses indicates that the predominant mechanism of flocculation is adsorption coagulation.

The effectiveness of the high-molecular weight PEI species 1n producing rapid flocculation at small doses is attributed to the formation of a charge mosaic on the oppositely-charged E. coli surfaces. The large adsorbed PEI molecules not only neutralize the surface charge at the adsorption sites, but also cause charge reversal with excess cationic segments. The alignment of these positive surface patches with negative patches on approaching cells results in strong electrostatic attraction in addition to a reduction of the double-layer interaction energies. The comparative ineffectiveness of low-molecular weight PEI species in producing E. coli flocculation is caused by the size of the individual molecules, which is insufficient to both neutralize and reverse the negative E.coli surface charge. Consequently, coagulation produced by low molecular weight species is attributed solely to the reduction of double-layer interaction energies via adsorption.

Electrophoretic mobility experiments supported the above conclusions, since only the high-molecular weight species were able to reverse the mobility of the E. coli cells. In addition, electron microscope examination of the seam of agglutination between E. coli cells flocculation by PEI revealed tightly- bound cells, with intercellular separation distances of less than 100-200 Å in most instances. This intercellular separation is partially due to cell shrinkage in preparation of the electron micrographs.

The extent of flocculation was measured as a function of PEl molecular weight, PEl dose, and the intensity of reactor chamber mixing. Neither the intensity of mixing, within the common treatment practice limits, nor the time of mixing for up to four hours appeared to play any significant role in either the size or number of E.coli aggregates formed. The extent of flocculation was highly molecular weight dependent: the high-molecular-weight PEl species produce the larger aggregates, the greater turbidity reductions, and the higher filtration flow rates. The PEl dose required for optimum flocculation decreased as the species molecular weight increased. At large doses of high-molecular-weight species, redispersion of the macroflocs occurred, caused by excess adsorption of cationic molecules. The excess adsorption reversed the surface charge on the E.coli cells, as recorded by electrophoretic mobility measurements.

Successful quantitative comparisons were made between changes in suspension turbidity with flocculation and corresponding changes in aggregate size distribution. E. coli aggregates were treated as coalesced spheres, with Mie scattering coefficients determined for spheres in the anomalous diffraction regime. Good quantitative comparisons were also found to exist between the reduction in refiltration time and the reduction of the total colloid surface area caused by flocculation. As with turbidity measurements, a coalesced sphere model was used since the equivalent spherical volume is the only information available from the Coulter particle counter. However, the coalesced sphere model was not applicable to electrophoretic mobility measurements. The aggregates produced at each PEl dose moved at approximately the same vlocity, almost independently of particle size.

PEl was found to be an effective flocculant of E. coli cells at weight ratios of 1 mg PEl: 100 mg E. coli. While PEl itself is toxic to E.coli at these levels, similar cationic polymers could be effectively applied to water and wastewater treatment facilities to enhance sedimentation and filtration characteristics.

Digested sludge: delineation and modeling for ocean disposal

Experimental work was performed to delineate the system of digested sludge particles and associated trace metals and also to measure the interactions of sludge with seawater. Particle-size and particle number distributions were measured with a Coulter Counter. Number counts in excess of 10¹² particles per liter were found in both the City of Los Angeles Hyperion mesophilic digested sludge and the Los Angeles County Sanitation Districts (LACSD) digested primary sludge. More than 90 percent of the particles had diameters less than 10 microns.

Total and dissolved trace metals (Ag, Cd, Cr, Cu, Fe, Mn, Ni, Pb, and Zn) were measured in LACSD sludge. Manganese was the only metal whose dissolved fraction exceeded one percent of the total metal. Sedimentation experiments for several dilutions of LACSD sludge in seawater showed that the sedimentation velocities of the sludge particles decreased as the dilution factor increased. A tenfold increase in dilution shifted the sedimentation velocity distribution by an order of magnitude. Chromium, Cu, Fe, Ni, Pb, and Zn were also followed during sedimentation. To a first approximation these metals behaved like the particles.

Solids and selected trace metals (Cr, Cu, Fe, Ni, Pb, and Zn) were monitored in oxic mixtures of both Hyperion and LACSD sludges for periods of 10 to 28 days. Less than 10 percent of the filterable solids dissolved or were oxidized. Only Ni was mobilized away from the particles. The majority of the mobilization was complete in less than one day.

The experimental data of this work were combined with oceanographic, biological, and geochemical information to propose and model the discharge of digested sludge to the San Pedro and Santa Monica Basins. A hydraulic computer simulation for a round buoyant jet in a density stratified medium showed that discharges of sludge effluent mixture at depths of 730 m would rise no more than 120 m. Initial jet mixing provided dilution estimates of 450 to 2600. Sedimentation analyses indicated that the solids would reach the sediments within 10 km of the point discharge.

Mass balances on the oxidizable chemical constituents in sludge indicated that the nearly anoxic waters of the basins would become wholly anoxic as a result of proposed discharges. From chemical-equilibrium computer modeling of the sludge digester and dilutions of sludge in anoxic seawater, it was predicted that the chemistry of all trace metals except Cr and Mn will be controlled by the precipitation of metal sulfide solids. This metal speciation held for dilutions up to 3000.

The net environmental impacts of this scheme should be salutary. The trace metals in the sludge should be immobilized in the anaerobic bottom sediments of the basins. Apparently no lifeforms higher than bacteria are there to be disrupted. The proposed deep-water discharges would remove the need for potentially expensive and energy-intensive land disposal alternatives and would end the discharge to the highly productive water near the ocean surface.

Fundamental Studies of Carbon Oxygen Bond Activation in Nickel Diphosphine Ether Complexes. And, Metallomacrocycles as Ligands: Synthesis and Characterization of Aluminum-Bridged Bisglyoximato Complexes of Iron and Cobalt

In order to develop better catalysts for the cleavage of aryl-X bonds fundamental studies of the mechanism and individual steps of the mechanism have been investigated in detail. As the described studies are difficult at best in catalytic systems, model systems are frequently used. To study aryl-oxygen bond activation, a terphenyl diphosphine scaffold containing an ether moiety in the central arene was designed. The first three chapters of this dissertation focus on the studies of the nickel complexes supported by this diphosphine backbone and the research efforts in regards to aryl-oxygen bond activation.

Chapter 2 outlines the synthesis of a variety of diphosphine terphenyl ether ligand scaffolds. The metallation of these scaffolds with nickel is described. The reactivity of these nickel(0) systems is also outlined. The systems were found to typically undergo a reductive cleavage of the aryl oxygen bond. The mechanism was found to be a subsequent oxidative addition, β-H elimination, reductive elimination and (or) decarbonylation.

Chapter 3 presents kinetic studies of the aryl oxygen bond in the systems outlined in Chapter 2. Using a series of nickel(0) diphosphine terphenyl ether complexes the kinetics of aryl oxygen bond activation was studied. The activation parameters of oxidative addition for the model systems were determined. Little variation was observed in the rate and activation parameters of oxidative addition with varying electronics in the model system. The cause of the lack of variation is due to the ground state and oxidative addition transition state being affected similarly. Attempts were made to extend this study to catalytic systems.

Chapter 4 investigates aryl oxygen bond activation in the presence of additives. It was found that the addition of certain metal alkyls to the nickel(0) model system lead to an increase in the rate of aryl oxygen bond activation. The addition of excess Grignard reagent led to an order of magnitude increase in the rate of aryl oxygen bond activation. Similarly the addition of AlMe3 led to a three order of magnitude rate increase. Addition of AlMe₃ at -80 °C led to the formation of an intermediate which was identified by NOESY correlations as a system in which the AlMe3 is coordinated to the ether moiety of the backbone. The rates and activation parameters of aryl oxygen bond activation in the presence of AlMe3 were investigated.

The last two chapters involve the study of metalla-macrocycles as ligands. Chapter 5 details the synthesis of a variety of glyoxime backbones and diphenol precursors and their metallation with aluminum. The coordination chemistry of iron on the aluminum scaffolds was investigated. Varying the electronics of the aluminum macrocycle was found to affect the observed electrochemistry of the iron center.

Chapter 6 extends the studies of chapter 5 to cobalt complexes. The synthesis of cobalt dialuminum glyoxime metal complexes is described. The electrochemistry of the cobalt complexes was investigated. The electrochemistry was compared to the observed electrochemistry of a zinc analog to identify the redox activity of the ligand. In the presence of acid the cobalt complexes were found to electrochemically reduce protons to dihydrogen. The electronics of the ancillary aluminum ligands were found to affect the potential of proton reduction in the cobalt complexes. These potentials were compared to other diglyoximate complexes.

Investigations of noise and of quantum interference in proximity effect bridges

This work reports investigations upon weakly superconducting proximity effect bridges. These bridges, which exhibit the Josephson effects, are produced by bisecting a superconductor with a short (<1µ) region of material whose superconducting transition temperature is below that of the adjacent superconductors. These bridges are fabricated from layered refractory metal thin films whose transition temperature will depend upon the thickness ratio of the materials involved. The thickness ratio is changed in the area of the bridge to lower its transition temperature. This is done through novel photolithographic techniques described in the text, Chapter 2.

If two such proximity effect bridges are connected in parallel, they form a quantum interferometer. The maximum zero voltage current through this circuit is periodically modulated by the magnetic flux through the circuit. At a constant bias current, the modulation of the critical current produces a modulation in the dc voltage across the bridge. This change in dc voltage has been found to be the result of a change in the internal dissipation in the device. A simple model using lumped circuit theory and treating the bridges as quantum oscillators of frequency ω = 2eV/h, where V is the time average voltage across the device, has been found to adequately describe the observed voltage modulation.

The quantum interferometers have been converted to a galvanometer through the inclusion of an integral thin film current path which couples magnetic flux through the interferometer. Thus a change in signal current produces a change in the voltage across the interferometer at a constant bias current. This work is described in Chapter 3 of the text.

The sensitivity of any device incorporating proximity effect bridges will ultimately be determined by the fluctuations in their electrical parameters. He have measured the spectral power density of the voltage fluctuations in proximity effect bridges using a room temperature electronics and a liquid helium temperature transformer to match the very low (~ 0.1 Ω) impedances characteristic of these devices.

We find the voltage noise to agree quite well with that predicted by phonon noise in the normal conduction through the bridge plus a contribution from the superconducting pair current through the bridge which is proportional to the ratios of this current to the time average voltage across the bridge. The total voltage fluctuations are given by <V^2(f ) > = 4kTR^2_d I/V where R_d is the dynamic resistance, I the total current, and V the voltage across the bridge . An additional noise source appears with a strong 1/f^(n) dependence , 1.5 < n < 2, if the bridges are fabricated upon a glass substrate. This excess noise, attributed to thermodynamic temperature fluctuations in the volume of the bridge, increases dramatically on a glass substrate due to the greatly diminished thermal diffusivity of the glass as compared to sapphire.

Theory of s-d exchange scattering in dilute magnetic alloys

The problem of s-d exchange scattering of conduction electrons off localized magnetic moments in dilute magnetic alloys is considered employing formal methods of quantum field theoretical scattering. It is shown that such a treatment not only allows for the first time, the inclusion of multiparticle intermediate states in single particle scattering equations but also results in extremely simple and straight forward mathematical analysis. These equations are proved to be exact in the thermodynamic limit. A self-consistent integral equation for electron self energy is derived and approximately solved. The ground state and physical parameters of dilute magnetic alloys are discussed in terms of the theoretical results. Within the approximation of single particle intermediate states our results reduce to earlier versions. The following additional features are found as a consequence of the inclusion of multiparticle intermediate states;

(i) A non analytic binding energy is pre sent for both, antiferromagnetic (J < o) and ferromagnetic (J > o) couplings of the electron plus impurity system.

(ii) The correct behavior of the energy difference of the conduction electron plus impurity system and the free electron system is found which is free of unphysical singularities present in earlier versions of the theories.

(iii) The ground state of the conduction electron plus impurity system is shown to be a many-body condensate state for J < o and J > o, both. However, a distinction is made between the usual terminology of "Singlet" and "Triplet" ground states and nature of our ground state.

(iv) It is shown that a long range ordering, leading to an ordering of the magnetic moments can result from a contact interaction such as the s-d exchange interaction.

(v) The explicit dependence of the excess specific heat of the Kondo systems is obtained and found to be linear in temperatures as T→ o and T ℓnT for 0.3 T_K ≤ T ≤ 0.6 T_K. A rise in (ΔC/T) for temperatures in the region 0 < T ≤ 0.1 T_K is predicted. These results are found to be in excellent agreement with experiments.

(vi) The existence of a critical temperature for Ferromagnetic coupling (J > o) is shown. On the basis of this the apparent contradiction of the simultaneous existence of giant moments and Kondo effect is resolved.