I. Nickel-Exchanged Zincosilicate Catalysts for the Oligomerization of Propylene and II. Organic SDA-Free Catalysts for the Methanol-to-Olefins Reaction

Nickel-containing catalysts are developed to oligomerize light olefins. Two nickel-containing zincosilicates (Ni-CIT-6 and Ni-Zn-MCM-41) and two nickel-containing aluminosilicates (Ni-HiAl-BEA and Ni-USY) are synthesized as catalysts to oligomerize propylene into C_3n (C₆ and C₉) products. All catalysts oligomerize propylene, with the zincosilicates demonstrating higher average selectivities to C_3n products, likely due to the reduced acidity of the Zn heteroatom.

To test whether light alkanes can be incorporated into this oligomerization reaction, a supported homogeneous catalyst is combined with Ni-containing zincosilicates. The homogeneous catalyst is included to provide dehydrogenation/hydrogenation functions. When this tandem catalyst system is evaluated using a propylene/n-butane feed, no significant integration of alkanes are observed.

Ni-containing zincosilicates are reacted with 1-butene and an equimolar propylene/1-butene mixture to study other olefinic feeds. Further, other divalent metal cations such as Mn²⁺, Co²⁺, Cu²⁺, and Zn²⁺ are exchanged onto CIT-6 samples to investigate stability and potential use for other reactions. Co-CIT-6 oligomerizes propylene, albeit less effectively than Ni-CIT-6. The other M-CIT-6 samples, while not able to oligomerize light olefins, may be useful for other reactions, such as deNO_x.

Molecular sieves are synthesized, characterized, and used to catalyze the methanol-to-olefins (MTO) reaction. The Al concentration in SSZ-13 samples is varied to investigate the effect of Al number on MTO reactivity when compared to a SAPO-34 sample with only isolated Si Brønsted acid sites. These SSZ-13 samples display reduced transient selectivity behavior and extended reaction lifetimes as Si/Al increases; attributable to fewer paired Al sites. MTO reactivity for the higher Si/Al SSZ-13s resembles the SAPO-34 sample, suggesting that both catalysts owe their stable reaction behavior to isolated Brønsted acid sites.

Zeolites CHA and RHO are prepared without the use of organic structure-directing agents (OSDAs), dealuminated by steam treatments (500°C-800°C), and evaluated as catalysts for the MTO reaction. The effects of temperature and steam partial pressure during steaming are investigated. X-ray diffraction (XRD) and Ar physisorption show that steaming causes partial structural collapse of the zeolite, with degradation increasing with steaming temperature. ²⁷Al MAS NMR spectra of steamed materials reveal the presence of tetrahedral, pentacoordinate, and hexacoordinate aluminum.

Proton forms of as-synthesized CHA (Si/Al=2.4) and RHO (Si/Al=2.8) rapidly deactivate under MTO testing conditions (400°C, atmospheric pressure). CHA samples steamed at 600°C performed best among samples tested, showing increased olefin selectivities and catalyst lifetime. Acid washing these steamed samples further improved activity. Reaction results for RHO were similar to CHA, with the RHO sample steamed at 800°C producing the highest light olefin selectivities. Catalyst lifetime and C₂-C₃ olefin selectivities increase with increasing reaction temperature for both CHA-type and RHO-type steamed samples.

Relating thermodynamics to information theory : the equality of free energy and mutual information

In this thesis we uncover a new relation which links thermodynamics and information theory. We consider time as a channel and the detailed state of a physical system as a message. As the system evolves with time, ever present noise insures that the "message" is corrupted. Thermodynamic free energy measures the approach of the system toward equilibrium. Information theoretical mutual information measures the loss of memory of initial state. We regard the free energy and the mutual information as operators which map probability distributions over state space to real numbers. In the limit of long times, we show how the free energy operator and the mutual information operator asymptotically attain a very simple relationship to one another. This relationship is founded on the common appearance of entropy in the two operators and on an identity between internal energy and conditional entropy. The use of conditional entropy is what distinguishes our approach from previous efforts to relate thermodynamics and information theory.

Nonexistence of looping trajectories in hydromagnetic waves of finite amplitude. Breaking of waves in a cold collision-free plasma in a magnetic field. On stabilities of periodic waves in a cold collision-free plasma in a magnetic field.

This dissertation consists of three parts. In Part I, it is shown that looping trajectories cannot exist in finite amplitude stationary hydromagnetic waves propagating across a magnetic field in a quasi-neutral cold collision-free plasma. In Part II, time-dependent solutions in series expansion are presented for the magnetic piston problem, which describes waves propagating into a quasi-neutral cold collision-free plasma, ensuing from magnetic disturbances on the boundary of the plasma. The expansion is equivalent to Picard's successive approximations. It is then shown that orbit crossings of plasma particles occur on the boundary for strong disturbances and inside the plasma for weak disturbances. In Part III, the existence of periodic waves propagating at an arbitrary angle to the magnetic field in a plasma is demonstrated by Stokes expansions in amplitude. Then stability analysis is made for such periodic waves with respect to side-band frequency disturbances. It is shown that waves of slow mode are unstable whereas waves of fast mode are stable if the frequency is below the cutoff frequency. The cutoff frequency depends on the propagation angle. For longitudinal propagation the cutoff frequency is equal to one-fourth of the electron's gyrofrequency. For transverse propagation the cutoff frequency is so high that waves of all frequencies are stable.

Nearly free molecular heat transfer from a sphere

Consider a sphere immersed in a rarefied monatomic gas with zero mean flow. The distribution function of the molecules at infinity is chosen to be a Maxwellian. The boundary condition at the body is diffuse reflection with perfect accommodation to the surface temperature. The microscopic flow of particles about the sphere is modeled kinetically by the Boltzmann equation with the Krook collision term. Appropriate normalizations in the near and far fields lead to a perturbation solution of the problem, expanded in terms of the ratio of body diameter to mean free path (inverse Knudsen number). The distribution function is found directly in each region, and intermediate matching is demonstrated. The heat transfer from the sphere is then calculated as an integral over this distribution function in the inner region. Final results indicate that the heat transfer may at first increase over its free flow value before falling to the continuum level.

On-chip integrated label-free optical biosensing

This thesis investigates the design and implementation of a label-free optical biosensing system utilizing a robust on-chip integrated platform. The goal has been to transition optical micro-resonator based label-free biosensing from a laborious and delicate laboratory demonstration to a tool for the analytical life scientist. This has been pursued along four avenues: (1) the design and fabrication of high-$Q$ integrated planar microdisk optical resonators in silicon nitride on silica, (2) the demonstration of a high speed optoelectronic swept frequency laser source, (3) the development and integration of a microfluidic analyte delivery system, and (4) the introduction of a novel differential measurement technique for the reduction of environmental noise.

The optical part of this system combines the results of two major recent developments in the field of optical and laser physics: the high-$Q$ optical resonator and the phase-locked electronically controlled swept-frequency semiconductor laser. The laser operates at a wavelength relevant for aqueous sensing, and replaces expensive and fragile mechanically-tuned laser sources whose frequency sweeps have limited speed, accuracy and reliability. The high-$Q$ optical resonator is part of a monolithic unit with an integrated optical waveguide, and is fabricated using standard semiconductor lithography methods. Monolithic integration makes the system significantly more robust and flexible compared to current, fragile embodiments that rely on the precarious coupling of fragile optical fibers to resonators. The silicon nitride on silica material system allows for future manifestations at shorter wavelengths. The sensor also includes an integrated microfluidic flow cell for precise and low volume delivery of analytes to the resonator surface. We demonstrate the refractive index sensing action of the system as well as the specific and nonspecific adsorption of proteins onto the resonator surface with high sensitivity. Measurement challenges due to environmental noise that hamper system performance are discussed and a differential sensing measurement is proposed, implemented, and demonstrated resulting in the restoration of a high performance sensing measurement.

The instrument developed in this work represents an adaptable and cost-effective platform capable of various sensitive, label-free measurements relevant to the study of biophysics, biomolecular interactions, cell signaling, and a wide range of other life science fields. Further development is necessary for it to be capable of binding assays, or thermodynamic and kinetics measurements; however, this work has laid the foundation for the demonstration of these applications.

Diffraction-limited imaging on the 200-inch telescope

We have used the technique of non-redundant masking at the Palomar 200-inch telescope and radio VLBI imaging software to make optical aperture synthesis maps of two binary stars, β Corona Borealis and σ Herculis. The dynamic range of the map of β CrB, a binary star with a separation of 230 milliarcseconds is 50:1. For σ Her, we find a separation of 70 milliarcseconds and the dynamic range of our image is 30:1. These demonstrate the potential of the non-redundant masking technique for diffraction-limited imaging of astronomical objects with high dynamic range.

We find that the optimal integration time for measuring the closure phase is longer than that for measuring the fringe amplitude. There is not a close relationship between amplitude errors and phase errors, as is found in radio interferometry. Amplitude self calibration is less effective at optical wavelengths than at radio wavelengths. Primary beam sensitivity correction made in radio aperture synthesis is not necessary in optical aperture synthesis.

The effects of atmospheric disturbances on optical aperture synthesis have been studied by Monte Carlo simulations based on the Kolmogorov theory of refractive-index fluctuations. For the non-redundant masking with τ_c-sized apertures, the simulated fringe amplitude gives an upper bound of the observed fringe amplitude. A smooth transition is seen from the non-redundant masking regime to the speckle regime with increasing aperture size. The fractional reduction of the fringe amplitude according to the bandwidth is nearly independent of the aperture size. The limiting magnitude of optical aperture synthesis with τ_c-sized apertures and that with apertures larger than τ_c are derived.

Monte Carlo simulations are also made to study the sensitivity and resolution of the bispectral analysis of speckle interferometry. We present the bispectral modulation transfer function and its signal-to-noise ratio at high light levels. The results confirm the validity of the heuristic interferometric view of image-forming process in the mid-spatial-frequency range. The signal-to- noise ratio of the bispectrum at arbitrary light levels is derived in the mid-spatial-frequency range.

The non-redundant masking technique is suitable for imaging bright objects with high resolution and high dynamic range, while the faintest limit will be better pursued by speckle imaging.

Organotitanium and niobium chemistry. I. Structure and reactivity of a titanium ethylene complex. II. Reactivity of decamethyl niobocene derivatives

The synthesis and X-ray diffraction study of bis(pentamethylcyclopentadienyl) ethylene titanium (I) are reported. This complex represents the first example of an isolable ethylene adduct of a group IV metal, a key intermediate in Ziegler-Natta olefin polymerization schemes. While treatment of I with ethylene leads to only traces of polymer after months, I participates in a wide range of stoichiometric and catalytic reactions. These include the catalytic conversion of ethylene specifically to butadiene and ethane and the catalytic isomerization of alkenes. Detailed studies have been carried out on the stoichiometric reactions of I with nitriles and alkynes. At low temperatures, nitriles react to form metallacycloimine species which more slowly undergo a formal 1,3-hydrogen shift to generate metallacycloeneamines. The lowest energy pathway for this rearrangement is an intramolecular hydrogen shift which is sensitive to the steric bulk of the R substituent. The reactions of I with alkynes yield metallacyclopentene complexes with high regioisomer selectivity. Carbonylation of the metallacyclopentene (η-C₅Me₅5)₂TiC(CH₃)=C(CH₃)CH₂ under relatively mild conditions cleanly produces the corresponding cyclopentenone and [C₅(CH₃)₅]₂Ti(CO)₂. Compounds derived from CO₂ and acetaldehyde have also been isolated.

The synthesis and characterization of bis-(η-pentamethylcyclopentadienyl) niobium(III) tetrahydroborate (II) are described and a study of its temperature-dependent proton NMR spectroscopic behavior is reported. The complex is observed to undergo a rapid intramolecular averaging process at elevated temperatures. The free energy of activation, ΔG^≠ = 16.4 ± 0.4 kcal/mol, is calculated. The reinvestigation of a related compound, bis(η-cyclopentadienyl)niobium(III) tetrahydroborate, established ΔG^≠ = 14.6 ± 0.2 kcal/mol for the hydrogen exchange process. The tetrahydroborate complex, II reacts with pyridine and dihydrogen to yield (η-C₅Me₅5)₂NbH₃ (III). The reactivity of III with CO and ethylene is reported.

Magnetic alignment of high-aspect ratio microwires into vertical arrays

Fundamental studies of magnetic alignment of highly anisotropic mesostructures can enable the clean-room-free fabrication of flexible, array-based solar and electronic devices, in which preferential orientation of nano- or microwire-type objects is desired. In this study, ensembles of 100 micron long Si microwires with ferromagnetic Ni and Co coatings are oriented vertically in the presence of magnetic fields. The degree of vertical alignment and threshold field strength depend on geometric factors, such as microwire length and ferromagnetic coating thickness, as well as interfacial interactions, which are modulated by varying solvent and substrate surface chemistry. Microwire ensembles with vertical alignment over 97% within 10 degrees of normal, as measured by X-ray diffraction, are achieved over square cm scale areas and set into flexible polymer films. A force balance model has been developed as a predictive tool for magnetic alignment, incorporating magnetic torque and empirically derived surface adhesion parameters. As supported by these calculations, microwires are shown to detach from the surface and align vertically in the presence of magnetic fields on the order of 100 gauss. Microwires aligned in this manner are set into a polydimethylsiloxane film where they retain their vertical alignment after the field has been removed and can subsequently be used as a flexible solar absorber layer. Finally, these microwires arrays can be protected for use in electrochemical cells by the conformal deposition of a graphene layer.

Label-free detection of single biological molecules using microtoroid optical resonators

Being able to detect a single molecule without the use of labels has been a long standing goal of bioengineers and physicists. This would simplify applications ranging from single molecular binding studies to those involving public health and security, improved drug screening, medical diagnostics, and genome sequencing. One promising technique that has the potential to detect single molecules is the microtoroid optical resonator. The main obstacle to detecting single molecules, however, is decreasing the noise level of the measurements such that a single molecule can be distinguished from background. We have used laser frequency locking in combination with balanced detection and data processing techniques to reduce the noise level of these devices and report the detection of a wide range of nanoscale objects ranging from nanoparticles with radii from 100 to 2.5 nm, to exosomes, ribosomes, and single protein molecules (mouse immunoglobulin G and human interleukin-2). We further extend the exosome results towards creating a non-invasive tumor biopsy assay. Our results, covering several orders of magnitude of particle radius (100 nm to 2 nm), agree with the `reactive' model prediction for the frequency shift of the resonator upon particle binding. In addition, we demonstrate that molecular weight may be estimated from the frequency shift through a simple formula, thus providing a basis for an ``optical mass spectrometer'' in solution. We anticipate that our results will enable many applications, including more sensitive medical diagnostics and fundamental studies of single receptor-ligand and protein-protein interactions in real time. The thesis summarizes what we have achieved thus far and shows that the goal of detecting a single molecule without the use of labels can now be realized.

Hall coefficient and resistivity of an amorphous palladium-silicon alloy

The Hall coefficient and resistance in several specimens of an amorphous metallic alloy containing 80 at.% palladium and 20 at.% silicon have been investigated at temperatures between 4.2°K and room temperature. An ideal limiting behavior of these transport coefficients was analyzed on the basis of the nearly free electron model to yield a carrier density of 9 x 10²² cm.^-3, or about 1.7 electrons per palladium atom, and a mean free path of about 9Å which is almost constant with temperature. The deviations of the individual specimens from this ideal behavior, which were small but noticeable in the relative resistivity and much greater in the Hall coefficient, can be explained by invoking disk-shaped crystalline regions with low resistivity and a positive Hall coefficient. A detailed calculation shows how a volume fraction of such crystalline material too small to be noticed in X-ray diffraction could have a significant effect on the resistivity and a much greater effect on the Hall coefficient.

Silicide formation and the interaction of metals with polycrystalline Si

The main factors affecting solid-phase Si-metal interactions are reported in this work. The influence of the orientation of the Si substrates and the presence of impurities in metal films and at the Si-metal interface on the formation of nickel and chromium silicides have been demonstrated. We have observed that the formation and kinetic rate of growth of nickel silicides is strongly dependent on the orientation and crystallinity of the Si substrates; a fact which, up to date, has never been seriously investigated in silicide formation. Impurity contaminations in the Cr film and at the Si-Cr interface are the most dominant influencing factors in the formation and kinetic rate of growth of CrSi₂. The potentiality and use of silicides as a diffusion barrier in metallization on silicon devices were also investigated.

Two phases, Ni₂Si and NiSi, form simultaneously in two distinct sublayers in the reaction of Ni with amorphous Si, while only the former phase was observed on other substrates. On (111) oriented Si substrates the growth rate is about 2 to 3 times less than that on <100> or polycrystalline Si. Transmission electron micrographs establish-·that silicide layers grown on different substrates have different microcrystalline structures. The concept of grain-boundary diffusion is speculated to be an important factor in silicide formation.

The composition and kinetic rate of CrSi₂ formation are not influenced by the underlying Si substrate. While the orientation of the Si substrate does not affect the formation of CrSi₂ , the purity of the Cr film and the state of Si-Cr interface become the predominant factors in the reaction process. With an interposed layer of Pd₂Si between the Cr film and the Si substrate, CrSi₂ starts to form at a much lower temperature (400°C) relative to the Si-Cr system. However, the growth rate of CrSi₂ is observed to be independent of the thickness of the Pd2Si layer. For both Si-Cr and Si-Pd₂Si-Cr samples, the growth rate is linear with time with an activation energy of 1.7 ± 0.1 ev.

A tracer technique using radioactive ³¹Si (T_1/2 = 2.26 h) was used to study the formation of CrSi₂ on Pd₂Si. It is established from this experiment that the growth of CrSi₂ takes place partly by transport of Si directly from the Si substrate and partly by breaking Pd₂Si bonds, making free Si atoms available for the growth process.

The role of CrSi₂ in Pd-Al metallization on Si was studied. It is established that a thin CrSi₂ layer can be used as a diffusion barrier to prevent Al from interacting with Pd₂Si in the Pd-Al metallization on Si.

As a generalization of what has been observed for polycrystalline-Si-Al interaction, the reactions between polycrystalline Si (poly Si) and other metals were studied. The metals investigated include Ni, Cr, Pd, Ag and Au. For Ni, Cr and Pd, annealing results in silicide formation, at temperatures similar to those observed on single crystal Si substrates. For Al, Ag and Au, which form simple eutectics with Si annealing results in erosion of the poly Si layer and growth of Si crystallites in the metal films.

Backscattering spectrometry with 2.0 and 2.3 MeV ⁴He ions was the main analytical tool used in all our investigations. Other experimental techniques include the Read camera glancing angle x-ray diffraction, scanning electron, optical and transmission electron microscopy. Details of these analytical techniques are given in Chapter II.

The modulated grating hologram

A phase and amplitude, off-axis hologram has been synthesized from three computer-generated transmission masks, using a multiple-exposure holographic recording method. Each of the masks controls one fixed-phase component of the complex hologram transmittance. The basic grating is generated optically, relieving the computer of the burden of drawing details the size of each fringe. The maximum information capacity of the computer plotting device can then be applied to the generation of the grating modulation function. By this method large digital holograms (25 mm by 25 mm) have been synthesized in dichromated gelatin. The recording method is applicable to virtually any holographic medium.

The modulated grating hologram was designed primarily for the application of spatial filtering, in which the requirement is a hologram with large dynamic range and large free spectral range. Choice of a low-noise, high-efficiency medium such as dichromated gelatin will allow exceptionally large dynamic range. Independence of the optically-generated carrier grating from the computer-generated modulation functions allows arbitrarily large free spectral range.

The performance of a holographic spatial filter will be limited ultimately by noise originating from imperfections in the holographic medium. The characteristics of this noise are analyzed, and in the case of a high diffraction efficiency hologram are shown to differ significantly from previous analyses. The dominant noise source in holograms of high diffraction efficiency will be scattering of the first order or imaging wave by deformations in the hologram surface or other effects of low spatial frequency. Experimental measurements in various low-noise holographic media verify these predictions.

Strong atom-light interactions along nanostructures: Transition from free-space to nanophotonic interfaces

An exciting frontier in quantum information science is the integration of otherwise "simple'' quantum elements into complex quantum networks. The laboratory realization of even small quantum networks enables the exploration of physical systems that have not heretofore existed in the natural world. Within this context, there is active research to achieve nanoscale quantum optical circuits, for which atoms are trapped near nano-scopic dielectric structures and "wired'' together by photons propagating through the circuit elements. Single atoms and atomic ensembles endow quantum functionality for otherwise linear optical circuits and thereby enable the capability of building quantum networks component by component. Toward these goals, we have experimentally investigated three different systems, from conventional to rather exotic systems : free-space atomic ensembles, optical nano fibers, and photonics crystal waveguides. First, we demonstrate measurement-induced quadripartite entanglement among four quantum memories. Next, following the landmark realization of a nanofiber trap, we demonstrate the implementation of a state-insensitive, compensated nanofiber trap. Finally, we reach more exotic systems based on photonics crystal devices. Beyond conventional topologies of resonators and waveguides, new opportunities emerge from the powerful capabilities of dispersion and modal engineering in photonic crystal waveguides. We have implemented an integrated optical circuit with a photonics crystal waveguide capable of both trapping and interfacing atoms with guided photons, and have observed the collective effect, superradiance, mediated by the guided photons. These advances provide an important capability for engineered light-matter interactions, enabling explorations of novel quantum transport and quantum many-body phenomena.

Free algebras in Von Neumann-Bernays-Gӧdel set theory and positive elementary inductions in reasonable structures

This thesis consists of two independent chapters. The first chapter deals with universal algebra. It is shown, in von Neumann-Bernays-Gӧdel set theory, that free images of partial algebras exist in arbitrary varieties. It follows from this, as set-complete Boolean algebras form a variety, that there exist free set-complete Boolean algebras on any class of generators. This appears to contradict a well-known result of A. Hales and H. Gaifman, stating that there is no complete Boolean algebra on any infinite set of generators. However, it does not, as the algebras constructed in this chapter are allowed to be proper classes. The second chapter deals with positive elementary inductions. It is shown that, in any reasonable structure ᶆ, the inductive closure ordinal of ᶆ is admissible, by showing it is equal to an ordinal measuring the saturation of ᶆ. This is also used to show that non-recursively saturated models of the theories ACF, RCF, and DCF have inductive closure ordinals greater than _ω.

Norbornenyl- and nortricyclyl free radicals

The number, symmetry, and product-forming capabilities of the intermediates in the photoinitiated reductions of endo- and exo-5- bromonorbornene and 2-bromonortricyclene with tri-n-butyltin hydride at temperatures between -10° and 22° were investigated.

Three mechanisms were evaluated:

1. The 5-norbornenyl- and 2-nortricyclyl radicals isomerize reversibly with the former producing nortricyclene by abstraction of hydrogen from tri-n-butyltin hydride.

2. The 5-norbornenyl- and 2-nortricyclyl radicals isomerize reversibly, but some norbornene can be formed from the 2-nortricyclyl radical or some nortricyclene can be formed from the 5-norbornenyl radical by abstraction of hydrogen.

3. There is intervention of a "bridged" radical which may be for med reversibly or irreversibly from the 5-norbornenyl- and 2-nortricyclyl radicals.

Within small error limits, the ratios of norbornene to nortricyclene as a function of the concentration of tri-n-butyltin hydride are consistent with the first mechanism.

In the reductions with tri-n-butyltin deuteride, primary deuterium isotope effects of 2. 3 and 2. 1 for the abstraction of deuterium by the 2-nortricyclyl- and 5-norbornenyl radicals, respectively, were found. The primary deuterium isotope effects were invariant with the concentration of tri-n-butyltin deuteride, although the ratios of norbornene to nortricyclene changed appreciably over this range. This is consistent with the first mechanism, and can accommodate the formation of either product from more than one intermediate only if the primary kinetic deuterium isotope effects are nearly equal for all reactions leading to the single product.

The reduction of endo-5-bromonorbornene-5, 6, 6-d₃ with tri-n-butyltin hydride or tri-n-butyltin deuteride leads to both unrearranged and rearranged norbornenes. The ratios of unrearranged to rearranged norbornene require that the 5-norbornenyl-5, 6, 6-d₃ radical isomerize to an intermediate with the symmetry expected of a nortricyclyl free radical. The results are consistent with mechanism 1, but imply a surprising normal secondary kinetic deuterium isotope effect of about 1.25 for the abstraction of hydrogen by the 5-norbornenyl- 5, 6, 6-d₃ radical.

Approximate calculations show that there does not appear to be any substantial difference in the stabilities of the 5-norbornenyl and 2-nortricyclyl radicals.

Although the results can not exclude a small contribution by a mechanism other than mechanism 1, no such contribution is required to adequately explain the results.