Experimental study on inertial effects in liquid-solid flows

This thesis presents experimental measurements of the rheological behavior of liquid-solid mixtures at moderate Reynolds (defined by the shear rate and particle diameter) and Stokes numbers, ranging from 3 ≤ Re ≤ 1.6 × 10³ and 0.4 ≤ St ≤ 195. The experiments use a specifically designed Couette cylindrical rheometer that allows for probing the transition from transporting a pure liquid to transporting a dense suspension of particles. Measurements of the shear stress are presented for a wide range of particle concentration (10 to 60% in volume) and for particle to fluid density ratio between 1 and 1.05. The effective relative viscosity exhibits a strong dependence on the solid fraction for all density ratios tested. For density ratio of 1 the effective viscosity increases with Stokes number (St) for volume fractions (φ) lower than 40% and becomes constant for higher φ. When the particles are denser than the liquid, the effective viscosity shows a stronger dependance on St. An analysis of the particle resuspension for the case with a density ratio of 1.05 is presented and used to predict the local volume fraction where the shear stress measurements take place. When the local volume fraction is considered, the effective viscosity for settling and no settling particles is consistent, indicating that the effective viscosity is independent of differences in density between the solid and liquid phase. Shear stress measurements of pure fluids (no particles) were performed using the same rheometer, and a deviation from laminar behavior is observed for gap Reynolds numbers above 4× 10³, indicating the presence of hydrodynamic instabilities associated with the rotation of the outer cylinder. The increase on the effective viscosity with Stokes numbers observed for mixtures with φ ≤ 30% appears to be affected by such hydrodynamic instabilities. The effective viscosity for the current experiments is considerably higher than the one reported in non-inertial suspensions.

Heteroepitaxy of Group IV and Group III-V semiconductor alloys for photovoltaic applications

Photovoltaic energy conversion represents a economically viable technology for realizing collection of the largest energy resource known to the Earth -- the sun. Energy conversion efficiency is the most leveraging factor in the price of energy derived from this process. This thesis focuses on two routes for high efficiency, low cost devices: first, to use Group IV semiconductor alloy wire array bottom cells and epitaxially grown Group III-V compound semiconductor alloy top cells in a tandem configuration, and second, GaP growth on planar Si for heterojunction and tandem cell applications.

Metal catalyzed vapor-liquid-solid grown microwire arrays are an intriguing alternative for wafer-free Si and SiGe materials which can be removed as flexible membranes. Selected area Cu-catalyzed vapor-liquid solid growth of SiGe microwires is achieved using chlorosilane and chlorogermane precursors. The composition can be tuned up to 12% Ge with a simultaneous decrease in the growth rate from 7 to 1 μm/min^-1. Significant changes to the morphology were observed, including tapering and faceting on the sidewalls and along the lengths of the wires. Characterization of axial and radial cross sections with transmission electron microscopy revealed no evidence of defects at facet corners and edges, and the tapering is shown to be due to in-situ removal of catalyst material during growth. X-ray diffraction and transmission electron microscopy reveal a Ge-rich crystal at the tip of the wires, strongly suggesting that the Ge incorporation is limited by the crystallization rate.

Tandem Ga_1-xIn_xP/Si microwire array solar cells are a route towards a high efficiency, low cost, flexible, wafer-free solar technology. Realizing tandem Group III-V compound semiconductor/Si wire array devices requires optimization of materials growth and device performance. GaP and Ga_1-xIn_xP layers were grown heteroepitaxially with metalorganic chemical vapor deposition on Si microwire array substrates. The layer morphology and crystalline quality have been studied with scanning electron microscopy and transmission electron microscopy, and they provide a baseline for the growth and characterization of a full device stack. Ultimately, the complexity of the substrates and the prevalence of defects resulted in material without detectable photoluminescence, unsuitable for optoelectronic applications.

Coupled full-field optical and device physics simulations of a Ga_0.51In_0.49P/Si wire array tandem are used to predict device performance. A 500 nm thick, highly doped "buffer" layer between the bottom cell and tunnel junction is assumed to harbor a high density of lattice mismatch and heteroepitaxial defects. Under simulated AM1.5G illumination, the device structure explored in this work has a simulated efficiency of 23.84% with realistic top cell SRH lifetimes and surface recombination velocities. The relative insensitivity to surface recombination is likely due to optical generation further away from the free surfaces and interfaces of the device structure.

Finally, GaP has been grown free of antiphase domains on Si (112) oriented substrates using metalorganic chemical vapor deposition. Low temperature pulsed nucleation is followed by high temperature continuous growth, yielding smooth, specular thin films. Atomic force microscopy topography mapping showed very smooth surfaces (4-6 Å RMS roughness) with small depressions in the surface. Thin films (~ 50 nm) were pseudomorphic, as confirmed by high resolution x-ray diffraction reciprocal space mapping, and 200 nm thick films showed full relaxation. Transmission electron microscopy showed no evidence of antiphase domain formation, but there is a population of microtwin and stacking fault defects.

Probing the thermodynamic properties of mantle rocks in solid and liquid states

Our understanding of the structure and evolution of the deep Earth is strongly linked to knowledge of the thermodynamic properties of rocky materials at extreme temperatures and pressures. In this thesis, I present work that helps constrain the equation of state properties of iron-bearing Mg-silicate perovskite as well as oxide-silicate melts. I use a mixture of experimental, statistical, and theoretical techniques to obtain knowledge about these phases. These include laser-heated diamond anvil cell experiments, Bayesian statistical analysis of powder diffraction data, and the development of a new simplified model for understanding oxide and silicate melts at mantle conditions. By shedding light on the thermodynamic properties of such ubiquitous Earth-forming materials, I hope to aid our community’s progress toward understanding the large-scale processes operating in the Earth’s mantle, both in the modern day and early in Earth’s history.

Theory of ozone isotopic effects and various electron transfer reactions

Three separate topics, each stimulated by experiments, are treated theoretically in this dessertation: isotopic effects of ozone, electron transfer at interfaces, and intramolecular directional electron transfer in a supramolecular system.

The strange mass-independent isotope effect for the enrichment of ozone, which has been a puzzle in the literature for some 20 years, and the equally puzzling unconventional strong mass-dependent effect of individual reaction rate constants are studied as different aspects of a symmetry-driven behavior. A statistical (RRKM-based) theory with a hindered-rotor transition state is used. The individual rate constant ratios of recombination reactions at low pressures are calculated using the theory involving (1) small deviation from the statistical density of states for symmetric isotopomers, and (2) weak collisions for deactivation of the vibrationally excited ozone molecules. The weak collision and partitioning among exit channels play major roles in producing the large unconventional isotope effect in "unscrambled" systems. The enrichment studies reflect instead the non-statistical effect in "scrambled" systems. The theoretical results of low-pressure ozone enrichments and individual rate constant ratios obtained from these calculations are consistent with the corresponding experimental results. The isotopic exchange rate constant for the reaction ^(16)O + ^(18)O ^(18)O→+ ^(16)O ^(18)O + ^(18)O provides information on the nature of a variationally determined hindered-rotor transition state using experimental data at 130 K and 300 K. Pressure effects on the recombination rate constant, on the individual rate constant ratios and on the enrichments are also investigated. The theoretical results are consistent with the experimental data. The temperature dependence of the enrichment and rate constant ratios is also discussed, and experimental tests are suggested. The desirability of a more accurate potential energy surface for ozone in the transition state region is also noted.

Electron transfer reactions at semiconductor /liquid interfaces are studied using a tight-binding model for the semiconductors. The slab method and a z-transform method are employed in obtaining the tight-binding electronic structures of semiconductors having surfaces. The maximum electron transfer rate constants at Si/viologen^(2-/+) and InP /Me_(2)Fc^(+/O) interfaces are computed using the tight-binding type calculations for the solid and the extended-Huckel for the coupling to the redox agent at the interface. These electron transfer reactions are also studied using a free electron model for the semiconductor and the redox molecule, where Bardeen's method is adapted to calculate the coupling matrix element between the molecular and semiconductor electronic states. The calculated results for maximum rate constant of the electron transfer from the semiconductor bulk states are compared with the experimentally measured values of Lewis and coworkers, and are in reasonable agreement, without adjusting parameters. In the case of InP /liquid interface, the unusual current vs applied potential behavior is additionally interpreted, in part, by the presence of surface states.

Photoinduced electron transfer reactions in small supramolecular systems, such as 4-aminonaphthalimide compounds, are interesting in that there are, in principle, two alternative pathways (directions) for the electron transfer. The electron transfer, however, is unidirectional, as deduced from pH-dependent fluorescence quenching studies on different compounds. The role of electronic coupling matrix element and the charges in protonation are considered to explain the directionality of the electron transfer and other various results. A related mechanism is proposed to interpret the fluorescence behavior of similar molecules as fluorescent sensors of metal ions.

I. Spectroscopic observation of discrete sites in simple liquids. II. Infrared intensity perturbations of hydrogen halide fundamentals in liquid xenon. III. Rotation of HCl in solid rare gases.

Part I

The spectrum of dissolved mercury atoms in simple liquids has been shown to be capable of revealing information concerning local structures in these liquids.

Part II

Infrared intensity perturbations in simple solutions have been shown to involve more detailed interaction than just dielectric polarization. No correlation has been found between frequency shifts and intensity enhancements.

Part III

Evidence for perturbed rotation of HCl in rare gas matrices has been found. The magnitude of the barrier to rotation is concluded to be of order of 30 cm^(-1).

Study of Solid-Phase Reactions of metals on GaAs

To make stable and reproducible contacts to GaAs, metals which react with GaAs in the solid-phase should be favored. In this study, contacts formed employing Pd/TiN/Pd/Ag, Pd:Mg/TiN/Pd:Mg/Ag and Ru/TiN/Ru/Ag are studied. The TiN layer is included to investigate its application as diffusion barrier in these metallizations. Contacts to n-GaAs are rectifying and the value of barrier height is modified upon annealing. Contacts to p-GaAs are initially rectifying but exhibit ohmic behaviour after annealing. The modifications in the electrical properties are attributed to the solid-phase reaction of metal and GaAs. The integrity of the contacts relies critically on the success of TiN to prevent the intermixing of Ag overlayer and the underlying layers. At elevated annealing temperatures (450°C), TiN fails to function as a diffusion barrier. As a result, the properties of the contact deteriorates.

Liquid silicate equation of state : using shock waves to understand the properties of the deep Earth

The equations of state (EOS) of several geologically important silicate liquids have been constrained via preheated shock wave techniques. Results on molten Fe₂SiO₄ (fayalite), Mg₂SiO₄ (forsterite), CaFeSi₂O₆ (hedenbergite), an equimolar mixture of CaAl₂Si₂O₈-CaFeSi₂O₆ (anorthite-hedenbergite), and an equimolar mixture of CaAl₂Si₂O₈-CaFeSi₂O₆-CaMgSi₂O₆(anorthite-hedenbergite-diopside) are presented. This work represents the first ever direct EOS measurements of an iron-bearing liquid or of a forsterite liquid at pressures relevant to the deep Earth (> 135 GPa). Additionally, revised EOS for molten CaMgSi₂O₆ (diopside), CaAl₂Si₂O₈ (anorthite), and MgSiO₃ (enstatite), which were previously determined by shock wave methods, are also presented.

The liquid EOS are incorporated into a model, which employs linear mixing of volumes to determine the density of compositionally intermediate liquids in the CaO-MgO-Al₂O₃-SiO₂-FeO major element space. Liquid volumes are calculated for temperature and pressure conditions that are currently present at the core-mantle boundary or that may have occurred during differentiation of a fully molten mantle magma ocean.

The most significant implications of our results include: (1) a magma ocean of either chondrite or peridotite composition is less dense than its first crystallizing solid, which is not conducive to the formation of a basal mantle magma ocean, (2) the ambient mantle cannot produce a partial melt and an equilibrium residue sufficiently dense to form an ultralow velocity zone mush, and (3) due to the compositional dependence of Fe2+ coordination, there is a threshold of Fe concentration (molar X_Fe ≤ 0.06) permitted in a liquid for which its density can still be approximated by linear mixing of end-member volumes.

Phase behavior of complex superprotonic solid acids

Superprotonic phase transitions and thermal behaviors of three complex solid acid systems are presented, namely Rb3H(SO4)2-RbHSO4 system, Rb3H(SeO4)2-Cs3H(SeO4)2 solid solution system, and Cs6(H2SO4)3(H1.5PO4)4. These material systems present a rich set of phase transition characteristics that set them apart from other, simpler solid acids. A.C. impedance spectroscopy, high-temperature X-ray powder diffraction, and thermal analysis, as well as other characterization techniques, were employed to investigate the phase behavior of these systems.

Rb3H(SO4)2 is an atypical member of the M3H(XO4)2 class of compounds (M = alkali metal or NH4+ and X = S or Se) in that a transition to a high-conductivity state involves disproportionation into two phases rather than a simple polymorphic transition [1]. In the present work, investigations of the Rb3H(SO4)2-RbHSO4 system have revealed the disproportionation products to be Rb2SO4 and the previously unknown compound Rb5H3(SO4)4. The new compound becomes stable at a temperature between 25 and 140 °C and is isostructural to a recently reported trigonal phase with space group P3̅m of Cs5H3(SO4)4 [2]. At 185 °C the compound undergoes an apparently polymorphic transformation with a heat of transition of 23.8 kJ/mol and a slight additional increase in conductivity.

The compounds Rb3H(SeO4)2 and Cs3H(SeO4)2, though not isomorphous at ambient temperatures, are quintessential examples of superprotonic materials. Both adopt monoclinic structures at ambient temperatures and ultimately transform to a trigonal (R3̅m) superprotonic structure at slightly elevated temperatures, 178 and 183 °C, respectively. The compounds are completely miscible above the superprotonic transition and show extensive solubility below it. Beyond a careful determination of the phase boundaries, we find a remarkable 40-fold increase in the superprotonic conductivity in intermediate compositions rich in Rb as compared to either end-member.

The compound Cs6(H2SO4)3(H1.5PO4)4 is unusual amongst solid acid compounds in that it has a complex cubic structure at ambient temperature and apparently transforms to a simpler cubic structure of the CsCl-type (isostructural with CsH2PO4) at its transition temperature of 100-120 °C [3]. Here it is found that, depending on the level of humidification, the superprotonic transition of this material is superimposed with a decomposition reaction, which involves both exsolution of (liquid) acid and loss of H2O. This reaction can be suppressed by application of sufficiently high humidity, in which case Cs6(H2SO4)3(H1.5PO4)4 undergoes a true superprotonic transition. It is proposed that, under conditions of low humidity, the decomposition/dehydration reaction transforms the compound to Cs6(H2-0.5xSO4)3(H1.5PO4)4-x, also of the CsCl structure type at the temperatures of interest, but with a smaller unit cell. With increasing temperature, the decomposition/dehydration proceeds to greater and greater extent and unit cell of the solid phase decreases. This is identified to be the source of the apparent negative thermal expansion behavior.

References

[1] L.A. Cowan, R.M. Morcos, N. Hatada, A. Navrotsky, S.M. Haile, Solid State Ionics 179 (2008) (9-10) 305.

[2] M. Sakashita, H. Fujihisa, K.I. Suzuki, S. Hayashi, K. Honda, Solid State Ionics 178 (2007) (21-22) 1262.

[3] C.R.I. Chisholm, Superprotonic Phase Transitions in Solid Acids: Parameters affecting the presence and stability of superprotonic transitions in the MHnXO4 family of compounds (X=S, Se, P, As; M=Li, Na, K, NH4, Rb, Cs), Materials Science, California Institute of Technology, Pasadena, California (2003).

Carbon-carbon bond forming reactions from bis(carbene)-platinum(II) complexes and olefin polymerization and oligomerization using group 4 post-metallocene complexes

A long-standing challenge in transition metal catalysis is selective C–C bond coupling of simple feedstocks, such as carbon monoxide, ethylene or propylene, to yield value-added products. This work describes efforts toward selective C–C bond formation using early- and late-transition metals, which may have important implications for the production of fuels and plastics, as well as many other commodity chemicals.

The industrial Fischer-Tropsch (F-T) process converts synthesis gas (syngas, a mixture of CO + H₂) into a complex mixture of hydrocarbons and oxygenates. Well-defined homogeneous catalysts for F-T may provide greater product selectivity for fuel-range liquid hydrocarbons compared to traditional heterogeneous catalysts. The first part of this work involved the preparation of late-transition metal complexes for use in syngas conversion. We investigated C–C bond forming reactions via carbene coupling using bis(carbene)platinum(II) compounds, which are models for putative metal–carbene intermediates in F-T chemistry. It was found that C–C bond formation could be induced by either (1) chemical reduction of or (2) exogenous phosphine coordination to the platinum(II) starting complexes. These two mild methods afforded different products, constitutional isomers, suggesting that at least two different mechanisms are possible for C–C bond formation from carbene intermediates. These results are encouraging for the development of a multicomponent homogeneous catalysis system for the generation of higher hydrocarbons.

A second avenue of research focused on the design and synthesis of post-metallocene catalysts for olefin polymerization. The polymerization chemistry of a new class of group 4 complexes supported by asymmetric anilide(pyridine)phenolate (NNO) pincer ligands was explored. Unlike typical early transition metal polymerization catalysts, NNO-ligated catalysts produce nearly regiorandom polypropylene, with as many as 30-40 mol % of insertions being 2,1-inserted (versus 1,2-inserted), compared to <1 mol % in most metallocene systems. A survey of model Ti polymerization catalysts suggests that catalyst modification pathways that could affect regioselectivity, such as C–H activation of the anilide ring, cleavage of the amine R-group, or monomer insertion into metal–ligand bonds are unlikely. A parallel investigation of a Ti–amido(pyridine)phenolate polymerization catalyst, which features a five- rather than a six-membered Ti–N chelate ring, but maintained a dianionic NNO motif, revealed that simply maintaining this motif was not enough to produce regioirregular polypropylene; in fact, these experiments seem to indicate that only an intact anilide(pyridine)phenolate ligated-complex will lead to regioirregular polypropylene. As yet, the underlying causes for the unique regioselectivity of anilide(pyridine)phenolate polymerization catalysts remains unknown. Further exploration of NNO-ligated polymerization catalysts could lead to the controlled synthesis of new types of polymer architectures.

Finally, we investigated the reactivity of a known Ti–phenoxy(imine) (Ti-FI) catalyst that has been shown to be very active for ethylene homotrimerization in an effort to upgrade simple feedstocks to liquid hydrocarbon fuels through co-oligomerization of heavy and light olefins. We demonstrated that the Ti-FI catalyst can homo-oligomerize 1-hexene to C₁₂ and C₁₈ alkenes through olefin dimerization and trimerization, respectively. Future work will include kinetic studies to determine monomer selectivity by investigating the relative rates of insertion of light olefins (e.g., ethylene) vs. higher α-olefins, as well as a more detailed mechanistic study of olefin trimerization. Our ultimate goal is to exploit this catalyst in a multi-catalyst system for conversion of simple alkenes into hydrocarbon fuels.

Investigations of charge-carrier dynamics at semiconductor/liquid interfaces

Theoretical and experimental investigations of charge-carrier dynamics at semiconductor/liquid interfaces, specifically with respect to interfacial electron transfer and surface recombination, are presented.

Fermi's golden rule has been used to formulate rate expressions for charge transfer of delocalized carriers in a nondegenerately doped semiconducting electrode to localized, outer-sphere redox acceptors in an electrolyte phase. The treatment allows comparison between charge-transfer kinetic data at metallic, semimetallic, and semiconducting electrodes in terms of parameters such as the electronic coupling to the electrode, the attenuation of coupling with distance into the electrolyte, and the reorganization energy of the charge-transfer event. Within this framework, rate constant values expected at representative semiconducting electrodes have been determined from experimental data for charge transfer at metallic electrodes. The maximum rate constant (i.e., at optimal exoergicity) for outer-sphere processes at semiconducting electrodes is computed to be in the range 10^-17-10^-16 cm⁴ s^-1, which is in excellent agreement with prior theoretical models and experimental results for charge-transfer kinetics at semiconductor/liquid interfaces.

Double-layer corrections have been evaluated for semiconductor electrodes in both depletion and accumulation conditions. In conjuction with the Gouy-Chapman-Stern model, a finite difference approach has been used to calculate potential drops at a representative solid/liquid interface. Under all conditions that were simulated, the correction to the driving force used to evaluate the interfacial rate constant was determined to be less than 2% of the uncorrected interfacial rate constant.

Photoconductivity decay lifetimes have been obtained for Si(111) in contact with solutions of CH₃OH or tetrahydrofuran containing one-electron oxidants. Silicon surfaces in contact with electrolyte solutions having Nernstian redox potentials > 0 V vs. SCE exhibited low effective surface recombination velocities regardless of the different surface chemistries. The formation of an inversion layer, and not a reduced density of electrical trap sites on the surface, is shown to be responsible for the long charge-carrier lifetimes observed for these systems. In addition, a method for preparing an air-stable, low surface recombination velocity Si surface through a two-step, chlorination/alkylation reaction is described.

Phase transitions from the solid state of monatomic elements

The principle aims of this thesis include the development of models of sublimation and melting from first principles and the application of these models to the rare gases.

A simple physical model is constructed to represent the sublimation of monatomic elements. According to this model, the solid and gas phases are two states of a single physical system. The nature of the phase transition is clearly revealed, and the relations between the vapor pressure, the latent heat, and the transition temperature are derived. The resulting theory is applied to argon, krypton, and xenon, and good agreement with experiment is found.

For the melting transition, the solid is represented by an anharmonic model and the liquid is described by the Percus-Yevick approximation. The behavior of the liquid at high densities is studied on the isotherms kT/∈ = 1.3, 1.8, and 2.0, where k is Boltzmann's constant, T is the temperature, and e is the well depth of the Lennard-Jones 12-6 pair potential. No solutions of the PercusYevick equation were found for ρσ³ above 1.3, where ρ is the particle density and σ is the radial parameter of the Lennard-Jones potential. The liquid structure is found to be very different from the solid structure near the melting line. The liquid pressures are about 50 percent low for experimental melting densities of argon. This discrepancy gives rise to melting pressures up to twice the experimental values.

Sputtering of the gallium-indium eutectic alloy in the liquid phase

We have measured sputtering yields and angular distributions of sputtered atoms from both the solid and liquid phases of gallium, indium, and the gallium-indium eutectic alloy. This was done by Rutherford backscattering analysis of graphite collector foils. The solid eutectic target shows a predominance of indium crystallites on its surface which have to be sputtered away before the composition of the sputtered atoms equals the bulk target composition. The size of the crystallites depends upon the conditions under which the alloy is frozen. The sputtering of the liquid eutectic alloy by 15 keV Ar⁺ results in a ratio of indium to gallium sputtering yields which is 28 times greater than would be expected from the target stoichiometry. Furthermore, the angular distribution of gallium is much more sharply peaked about the normal to the target surface than the indium distribution. When the incident Ar⁺ energy is increased to 25 keV, the gallium distribution broadens to the same shape as the indium distribution. With the exception of the sharp gallium distribution taken from the liquid eutectic at 15 keV, all angular distributions from liquid targets fit a cos² θ function. An ion-scattering-spectroscopy analysis of the liquid eutectic alloy reveals a surface layer of almost pure indium. A thermodynamic explanation for this highly segregated layer is discussed. The liquid eutectic alloy provides us with a unique target system which allows us to estimate the fraction of sputtered material which comes from the first monolayer of the surface.

Particle fluid mechanics in shear flows, acoustic waves, and shock waves

Three different categories of flow problems of a fluid containing small particles are being considered here. They are: (i) a fluid containing small, non-reacting particles (Parts I and II); (ii) a fluid containing reacting particles (Parts III and IV); and (iii) a fluid containing particles of two distinct sizes with collisions between two groups of particles (Part V).

Part I

A numerical solution is obtained for a fluid containing small particles flowing over an infinite disc rotating at a constant angular velocity. It is a boundary layer type flow, and the boundary layer thickness for the mixture is estimated. For large Reynolds number, the solution suggests the boundary layer approximation of a fluid-particle mixture by assuming W = W_p. The error introduced is consistent with the Prandtl’s boundary layer approximation. Outside the boundary layer, the flow field has to satisfy the “inviscid equation” in which the viscous stress terms are absent while the drag force between the particle cloud and the fluid is still important. Increase of particle concentration reduces the boundary layer thickness and the amount of mixture being transported outwardly is reduced. A new parameter, β = 1/Ω τ_v, is introduced which is also proportional to μ. The secondary flow of the particle cloud depends very much on β. For small values of β, the particle cloud velocity attains its maximum value on the surface of the disc, and for infinitely large values of β, both the radial and axial particle velocity components vanish on the surface of the disc.

Part II

The “inviscid” equation for a gas-particle mixture is linearized to describe the flow over a wavy wall. Corresponding to the Prandtl-Glauert equation for pure gas, a fourth order partial differential equation in terms of the velocity potential ϕ is obtained for the mixture. The solution is obtained for the flow over a periodic wavy wall. For equilibrium flows where λ_v and λ_T approach zero and frozen flows in which λ_v and λ_T become infinitely large, the flow problem is basically similar to that obtained by Ackeret for a pure gas. For finite values of λ_v and λ_T, all quantities except v are not in phase with the wavy wall. Thus the drag coefficient C_D is present even in the subsonic case, and similarly, all quantities decay exponentially for supersonic flows. The phase shift and the attenuation factor increase for increasing particle concentration.

Part III

Using the boundary layer approximation, the initial development of the combustion zone between the laminar mixing of two parallel streams of oxidizing agent and small, solid, combustible particles suspended in an inert gas is investigated. For the special case when the two streams are moving at the same speed, a Green’s function exists for the differential equations describing first order gas temperature and oxidizer concentration. Solutions in terms of error functions and exponential integrals are obtained. Reactions occur within a relatively thin region of the order of λ_D. Thus, it seems advantageous in the general study of two-dimensional laminar flame problems to introduce a chemical boundary layer of thickness λ_D within which reactions take place. Outside this chemical boundary layer, the flow field corresponds to the ordinary fluid dynamics without chemical reaction.

Part IV

The shock wave structure in a condensing medium of small liquid droplets suspended in a homogeneous gas-vapor mixture consists of the conventional compressive wave followed by a relaxation region in which the particle cloud and gas mixture attain momentum and thermal equilibrium. Immediately following the compressive wave, the partial pressure corresponding to the vapor concentration in the gas mixture is higher than the vapor pressure of the liquid droplets and condensation sets in. Farther downstream of the shock, evaporation appears when the particle temperature is raised by the hot surrounding gas mixture. The thickness of the condensation region depends very much on the latent heat. For relatively high latent heat, the condensation zone is small compared with Ʌ_D.

For solid particles suspended initially in an inert gas, the relaxation zone immediately following the compression wave consists of a region where the particle temperature is first being raised to its melting point. When the particles are totally melted as the particle temperature is further increased, evaporation of the particles also plays a role.

The equilibrium condition downstream of the shock can be calculated and is independent of the model of the particle-gas mixture interaction.

Part V

For a gas containing particles of two distinct sizes and satisfying certain conditions, momentum transfer due to collisions between the two groups of particles can be taken into consideration using the classical elastic spherical ball model. Both in the relatively simple problem of normal shock wave and the perturbation solutions for the nozzle flow, the transfer of momentum due to collisions which decreases the velocity difference between the two groups of particles is clearly demonstrated. The difference in temperature as compared with the collisionless case is quite negligible.

1. Ultrasonic studies of binary liquid structure in the critical region. Theory and experiment for the 2,6-lutidine/water system. 2. Hartree-Fock calculations of electric polarizabilities of some simple atoms and molecules, and their practicality. 3. Calculation of vibrational transition probabilities in collinear atom-diatom and diatom-diatom collisions with Lennard-Jones interaction

Part 1. Many interesting visual and mechanical phenomena occur in the critical region of fluids, both for the gas-liquid and liquid-liquid transitions. The precise thermodynamic and transport behavior here has some broad consequences for the molecular theory of liquids. Previous studies in this laboratory on a liquid-liquid critical mixture via ultrasonics supported a basically classical analysis of fluid behavior by M. Fixman (e. g., the free energy is assumed analytic in intensive variables in the thermodynamics)--at least when the fluid is not too close to critical. A breakdown in classical concepts is evidenced close to critical, in some well-defined ways. We have studied herein a liquid-liquid critical system of complementary nature (possessing a lower critical mixing or consolute temperature) to all previous mixtures, to look for new qualitative critical behavior. We did not find such new behavior in the ultrasonic absorption ascribable to the critical fluctuations, but we did find extra absorption due to chemical processes (yet these are related to the mixing behavior generating the lower consolute point). We rederived, corrected, and extended Fixman's analysis to interpret our experimental results in these more complex circumstances. The entire account of theory and experiment is prefaced by an extensive introduction recounting the general status of liquid state theory. The introduction provides a context for our present work, and also points out problems deserving attention. Interest in these problems was stimulated by this work but also by work in Part 3.

Part 2. Among variational theories of electronic structure, the Hartree-Fock theory has proved particularly valuable for a practical understanding of such properties as chemical binding, electric multipole moments, and X-ray scattering intensity. It also provides the most tractable method of calculating first-order properties under external or internal one-electron perturbations, either developed explicitly in orders of perturbation theory or in the fully self-consistent method. The accuracy and consistency of first-order properties are poorer than those of zero-order properties, but this is most often due to the use of explicit approximations in solving the perturbed equations, or to inadequacy of the variational basis in size or composition. We have calculated the electric polarizabilities of H₂, He, Li, Be, LiH, and N₂ by Hartree-Fock theory, using exact perturbation theory or the fully self-consistent method, as dictated by convenience. By careful studies on total basis set composition, we obtained good approximations to limiting Hartree-Fock values of polarizabilities with bases of reasonable size. The values for all species, and for each direction in the molecular cases, are within 8% of experiment, or of best theoretical values in the absence of the former. Our results support the use of unadorned Hartree-Pock theory for static polarizabilities needed in interpreting electron-molecule scattering data, collision-induced light scattering experiments, and other phenomena involving experimentally inaccessible polarizabilities.

Part 3. Numerical integration of the close-coupled scattering equations has been carried out to obtain vibrational transition probabilities for some models of the electronically adiabatic H₂-H₂ collision. All the models use a Lennard-Jones interaction potential between nearest atoms in the collision partners. We have analyzed the results for some insight into the vibrational excitation process in its dependence on the energy of collision, the nature of the vibrational binding potential, and other factors. We conclude also that replacement of earlier, simpler models of the interaction potential by the Lennard-Jones form adds very little realism for all the complication it introduces. A brief introduction precedes the presentation of our work and places it in the context of attempts to understand the collisional activation process in chemical reactions as well as some other chemical dynamics.

New Catalysts for the Renewable Production of Monomers for Bioplastics

Terephthalic acid (PTA) is one of the monomers used for the synthesis of the polyester, polyethylene terephthalate (PET), that is used for the large-scale manufacture of synthetic fibers and plastic bottles. PTA is largely produced from the liquid-phase oxidation of petroleum-derived p-xylene (PX). However, there are now ongoing worldwide efforts exploring alternative routes for producing PTA from renewable, biomass resources.

In this thesis, I present a new route to PTA starting from the biomass-derived platform chemical, 5-hydroxymethylfurfural (HMF). This route utilizes new, selective Diels-Alder-dehydration reactions involving ethylene and is advantageous over the previously proposed Diels-Alder-dehydration route to PTA from HMF via 2,5-dimethylfuran (DMF) since the H₂ reduction of HMF to DMF is avoided. Specifically, oxidized derivatives of HMF are reacted as is, or after etherification-esterification with methanol, with ethylene over solid Lewis acid catalysts that do not contain strong Brønsted acids in order to synthesize intermediates of PTA and its equally important diester, dimethyl terephthalate (DMT). The partially oxidized HMF, 5-(hydroxymethyl)furoic acid (HMFA) is reacted with high pressure ethylene over a pure-silica molecular sieve catalyst containing framework tin (Sn-Beta) to produce the Diels-Alder-dehydration product, 4-(hydroxymethyl)benzoic acid (HMBA), with ~30% selectivity at ~20% yield. If HMFA is protected with methanol to form methyl 5-(methoxymethyl)furan-2-carboxylate (MMFC), MMFC can react with ethylene in the presence of a pure-silica molecular sieve containing framework zirconium (Zr-Beta) to produce methyl 4-(methoxymethyl)benzenecarboxylate (MMBC) with >70% selectivity at >20% yield. HMBA and MMBC can then be oxidized to produce PTA and DMT, respectively. When Lewis acid containing mesoporous silica (MCM-41) and amorphous silica, or Brønsted acid containing zeolites (Al-Beta), are used as catalysts, a significant decrease in selectivity/yield of the Diels-Alder-dehydration product is observed.

An investigation to elucidate the reaction network and side products in the conversion of MMFC to MMBC was performed, and the main side products are found to be methyl 4-formylcyclohexa-1,3-diene-1-carboxylate and the ethylene Diels-Alder adduct of this cyclohexadiene. These products presumably form by a different dehydration pathway of the MMFC/ethylene Diels-Alder adduct and should be included when determining the overall selectivity to PTA or DMT since, like MMBC, these compounds are precursors to PTA or DMT.

Fundamental physical and chemical information on the ethylene Diels-Alder-dehydration reactions catalyzed by the Lewis acid-containing molecular sieves was obtained. Madon-Boudart experiments using Zr-Beta as catalyst show that the reaction rates are limited by chemical kinetics only (physical transport limitations are not present), all the Zr⁴⁺ centers are incorporated into the framework of the molecular sieve, and the whole molecular sieve crystal is accessible for catalysis. Apparent activation energies using Zr-Beta are low, suggesting that the overall activation energy of the system may be determined by a collection of terms and is not the true activation energy of a single chemical step.