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Investigations of C-H Activation and the Conversion of Methanol to Triptane
Get PDFBroadly speaking, this thesis represents research towards understanding the mechanisms and important species related to small molecule conversion, namely methane to methanol and methanol to higher hydrocarbons. The first section is on understanding the catalytic formation of methanol from methane, with specific interest in using gold (Au). While this transformation is known to occur catalytically, very little is understood about how it happens. To study this reaction, well-defined Au-complexes were synthesized and reactions relevant to the possible catalytic cycles were examined. In doing so, the first simple Au(III)-monoalkyl complex was generated and characterized: (Idipp)AuI2Me, where Idipp = 1,3-bis(2,6-diisopropylphenyl)imidazol-2-ylidene). Kinetics experiments demonstrated that the complex reductively eliminates methyl iodide, which is relevant to the functionalization step in CH activation. At low concentrations of iodide, the reductive elimination happens faster, from an unobserved 3-coordinate intermediate. However, at high iodide concentrations, the pathway is still consistent with reductive elimination, but from a 5-coordinate intermediate. This is in contrast to the related platinum-system, as well as to density functional theory calculations done on the Au-system.
The second section studies the C-H activation step alone by close examination of the microscopic reverse: protonation of a metal-alkyl. It had previously been noted that the observed kinetic isotope effects (KIEs) were unusually high for the protonolysis of a few Pd complexes and one Pt complex. It was hypothesized that these high KIEs and involvement of quantum mechanical tunneling may indicate a change in the mechanism of the protonolysis reaction, from protonation at the metal center and reductive coupling to direct protonation of the M-Me bond. The experiments described here were designed to explicitly test this theory and demonstrated that no correlation can be made between mechanism and tunneling.
The third section is focused on the study of the conversion of methanol to highly branched alkanes that make good fuel additives, namely 2,2,3-trimethylbutane (triptane), amidst other alkanes, olefins, and aromatics. Catalyzed by ZnI2 or InI3 at high temperatures, the reaction is hydrogen deficient: aromatics are formed as unsaturated by-products necessary for alkane generation. While the product distributions are somewhat different for the two different catalysts, the general mechanism is the same. While typical InI3 reactions generate more alkanes, more aromatics, and fewer olefins than ZnI2 reactions, longer reaction times and higher temperatures make the ZnI2 reaction look like the InI3 profile. Furthermore, InI3 can activate alkanes; it was found that InI3 can “upgrade” other alkanes with methanol. Notably, a 1:1 mixture of 2,3-dimethylbutane and methanol can be converted into triptane with good selectivity and little aromatic formation; ZnI2 can carry out similar chemistry at higher temperatures. Quantification of the iodine-containing products in each reaction mixture was attempted because of its relevance to the system’s industrial viability and found that these concentrations were significantly higher than would be acceptable in an industrial setting.</p
Mechanics of Thin Carbon Fiber Composites with a Silicone Matrix
Get PDFThis thesis presents an experimental, numerical and analytical study of the behavior of thin fiber composites with a silicone matrix. The main difference with respect to traditional composites with epoxy matrix is the fact that the soft matrix allows the fibers to microbuckle without breaking. This process acts as a stress relief mechanism during folding, and allows the material to reach very high curvatures, which makes them particularly interesting as components of space deployable structures. The goal of this study is to characterize the behavior and understand the mechanics of this type of composite.
Experimental testing of the bending behavior of unidirectional composites with a silicone matrix shows a highly non-linear moment vs. curvature relationship, as well as strain softening under cyclic loading. These effects are not usually observed in composites with an epoxy matrix. In the case of tension in the direction transverse to the fibers, the behavior shows again non-linearity and strain softening, as well as an initial stiffness much higher than what would be expected based on the traditional estimates for fiber composites.
The micro mechanics of the material have been studied with a finite element model. It uses solid elements and a random fiber arrangement produced with a reconstruction process based on micrographs of the material cross section. The simulations capture the macroscopic non-linear response, as well as the fiber microbuckling, and show how microbuckling reduces the strain in the fibers. The model shows good agreement for the bending stiffness of specimens with low fiber volume fraction, but it overestimates the effect of the matrix for more densely packed fibers. This is due to the high matrix strain that derives from the assumption of perfect bonding between fiber and matrix. In the case of tension transverse to the fibers, the model shows a much better agreement with experiments than traditional composite theory, and shows that the reason for the observed high stiffness is the incompressibility of the matrix. In order to capture the strain softening due to fiber debonding, cohesive elements have been introduced between the fibers and the matrix. This allows the model to capture quantitatively the non-linear behavior in the case of loading transverse to the fibers, and the damage due to cyclic loading. A single set of parameters for the cohesive elements produce good agreement with the experimental results for very different values of the fiber volume fraction, and could also be used in the analysis of more complicated loading cases, such as bending or biaxial tension.
In addition to the simulations, a homogenized analytical model has also been created. It extends previous analysis of composites with a soft matrix to the case of very thin composites. It provides a good qualitative description of the material behavior, and it helps understand the mechanics that take place within the material, such as the equilibrium of energy terms leading to a finite wave length, as opposed to microbuckling under compression.</p
The Mechanisms of the Fuel Cell Oxygen Reduction Reaction on Pt and Other 8-11 Column Metal Surfaces
Get PDFTo better understand and improve the cathode process for Proton exchange membrane fuel cell, we studied systematically the mechanism of oxygen reduction reaction (ORR) on group 8–11 metals and their alloys using density functional theory calculations. To address the contribution of solvent effect, we developed a practical implicit solvation model based on Poisson-Boltzmann equation. We discovered that solvation changed greatly the reaction barriers and hence the pathways preferences. The two well known mechanisms O2-diss and OOH-form mechanisms become impossible with water solvation. Instead, we found three new alternative mechanisms, namely, O2-diss-hydr, OOH-form-hydr, and high-H mechanisms. We showed that the oxygen hydrolysis Oad + H2Oad -> 2OHad plays an important role in the ORR which leads to the preferred O2-diss-hydr mechanism. We also developed a method to study the processes involving electron transfer between the solvent and the electrode. We found that direct OH formation from Oad and H3O+ has a high barrier of 0.70eV and is hence unlikely to be the dominant way of forming OHad at the operating potential of 0.8V. The potential dependent barrier leads to an overall optimal operating potential of 0.68V. We also studied the ORR on Pt3Ni alloys and found that the sublayer Ni atoms imposes an inhomogeneity in surface binding sites. The different binding energies make the barriers coverage dependent. Pt3Ni can only outperform Pt at higher coverage. We also showed the general approach of studying an unknown alloying system using Pd-Cu system as an example. We studied the structural, surface cleavage, and binding site preferences for various types of PdCu alloys. We predicted that 1:1 PdCu alloy with L11 structure and layered surface is a better catalyst than pure Pd and Cu, which agrees with later experiments
Damage Evolution in Composite Materials and Sandwich Structures Under Impulse Loading
Get PDFDamage evolution in composite materials is a rather complex phenomenon. There are numerous failure modes in composite materials stemming from the interaction of the various constituent materials and the particular loading conditions. This thesis is concerned with investigating damage evolution in sandwich structures under repeated transient loading conditions associated with impulse loading due to hull slamming of high-speed marine craft. To fully understand the complex stress interactions, a full field technique to reveal stress or strain is required. Several full field techniques exist but are limited to materials with particular optical properties. A full field technique applicable to most materials is known as thermoelastic stress analysis (TSA) and reveals the variation in sum of principal stresses of a cyclically loaded sample by correlating the stresses to a small temperature change occurring at the loading frequency. Digital image correlation (DIC) is another noncontact full field technique that reveals the deformation field by tracking the motion of subsets of a random speckle pattern during the loading cycles.
A novel experimental technique to aid in the study of damage progression that combines TSA and DIC simultaneously utilizing a single infrared camera is presented in this thesis. A technique to reliably perform DIC with an infrared (IR) camera is developed utilizing variable emissivity paint. The thermal data can then be corrected for rigid-body motion and deformation such that each pixel represents the same material point in all frames. TSA is then performed on this corrected data, reducing motion blur and increasing accuracy. This combined method with a single infrared camera has several advantages, including a straightforward experimental setup without the need to correct for geometric effects of two spatially separate cameras. Additionally, there is no need for external lighting in TSA as the measured electromagnetic radiation is emitted by the sample’s thermal fields.
The particular stress resolution of TSA will depend on properties of the material of interest but the noise floor for the temperature variation is universal to the camera utilized. For the camera system in this thesis, the noise floor was found to be fairly frequency independent with a magnitude of 0.01 oC, giving the minimum measurable stress for 2024 aluminum alloy of 3.6 MPa and for Nylon of 0.84 MPa. The average displacement range found during a static DIC test with IR images was 0.1 pixels. The maximum displacement variation at 1 Hz was 0.018 pixels. The average variation in strain at 1 Hz was 25 microstrain comparable to traditional DIC measurements in the visible optical regime.
The combined TSA-DIC method in IR was validated with several benchmark example problems including plate structures with holes, cracks, and bimaterials. The validated technique was applied to foam-core sandwich composite beams under repeated simulated wave slamming loading. There are numerous failure modes in sandwich composite materials and the full field stress and strain from TSA and DIC, respectively, allow for improved failure analysis and prediction. Understanding damage in sandwich structures under impulse loading is a complex open area of research and the combined TSA-DIC method provides further insight into the failure process.</p
I: Retrieval of Atmospheric Carbon Dioxide from High-Resolution Spectra. II: Interannual Variability of the Stratospheric Quasi-Biennual Oscillation
Get PDFThis thesis is devoted to an understanding of climate changes in the troposphere and the stratosphere from different aspects. In the troposphere, projecting future climate depends on our understanding of the exchange of CO₂ between the atmosphere, oceans, and terrestrial ecosystems. To understand the carbon cycle, it is important to estimate the sources and sinks of CO₂. The so-called inverse approach has been widely used to retrieve the abundances of atmospheric species, such as CO₂, from global surface networks and subsequently estimate their surface fluxes and variability. Understanding of the global distribution and temporal variability of atmospheric CO₂ thus helps constrain the surface carbon sources and sinks. In the stratosphere, the equatorial quansi-biennual oscillation (QBO) affects the polar stratosphere during winter, with the easterly phase of the QBO creating the condition for a more perturbed and warmer polar vortex. Therefore, the variation of the QBO period has additional significance, especially with respect to the timing of its phase relative to the Northern Hemisphere (NH) winter. The study of the interannual variability of the QBO improves our understanding of the climate system.
In this thesis, a retrieval algorithm is developed to estimate both CO₂ column abundance and its profile using radiances in the near-infrared region. In addition, the interannual variability of QBO is explored by studying both observation data and the modeled results. The thesis includes two parts. Part I (chapters 1 and 2) is a summary of the work about the CO₂ retrievals. Part II (chapters 3 and 4) is devoted to the stratospheric dynamics.</p
Superconformal Chern-Simons Theories and Their String Theory Duals
Get PDFIn this thesis, we consider two aspects of the conjectured gauge theory/string theory correspondence between three-dimensional maximal supersymmetric conformal field theories, which describe the world-volume theory of multiple M2-branes in flat space, and M-theory on AdS4 x S7.
First we study three classes of N = 6,8 superconformal Chern-Simons theories that are related to the gauge theory side of the correspondence: the Bagger-Lambert (BL) theories based on 3-algebras, the Lorentzian signature 3-algebra theories, and the Aharony-Bergman-Jafferis-Maldacena (ABJM) theories. We verify the superconformal symmetry of the BL theory, prove that it is parity conserving and conjecture the (by now proven) uniqueness of its SO(4) realization. We then consider the Lorentzian signature 3-algebra theories and show that although the ghosts can be removed to ensure unitarity by gauging certain global symmetries, the resulting theories spontaneously break the conformal symmetry and reduce to maximally supersymmetric three-dimensional Yang-Mills theories. After this, we recast the ABJM theory in a form for which the SU(4) R-symmetry of the action is manifest; then we use this form to verify in complete detail the OSp(6|4) superconformal symmetry of the theory and to express the scalar potential as a sum of squares.
Next, we study the one-loop correction to the energy of a point-particle and circular string solutions to type IIA string theory on AdS4 x CP3. We compute the spectrum of fluctuations for each of these solutions using two techniques, known as the algebraic curve approach and the world-sheet approach. We propose a new prescription for computing the one-loop corrections that gives well-defined results and agrees with the predictions of the all-loop Bethe ansatz for our point-particle and circular string solutions as well as for previous folded-spinning string solutions.</p
Experiments on the Dynamics of Community Formation
Get PDFI study the dynamics by which populations with heterogeneous preferences for local public good provision, or for other local policies, sort themselves into communities. I conduct a series of laboratory experiments to consider whether the ability to “vote with one's feet," by moving between communities, is sufficient for a population to reach optimal public good allocations and community compositions, and to assess which institutions may best facilitate efficient self-organization when residents are able to move freely between locations.
I find that communities allowing residents to make voluntary contributions toward the provision of a public good are characterized by instability, cyclical fluctuations in local provision, and a dynamic in which low demanders continually chase high demanders through locations. Institutions requiring all residents of a community to pay equal taxes enable subjects to sort by type into stable communities. However, populations can find themselves stuck at one of two types of local, inefficient equilibria. First, though sorted, residents may fail to attain the level of public good provision best suited for them, and, in that case, the system dynamics are crucial for determining whether subjects reach the communities that offer optimally designed expenditure bundles. When residents are able to vote for local tax policies with their ballots as well as with their feet, the inefficient local equilibria are eliminated, and I find that each community converges to the most efficient outcome for its population. Second, populations may sort into an inefficient equilibrium partition of residents across communities. I find that subjects moving between locations with fixed local policies segregate by type, even when pooling their resources with similar types is more efficient. When subjects are able to vote on local policies, they typically succeed in forming communities of the optimal size and membership composition.
These experimental results suggest that the ability to vote with one's feet may not be sufficient for achieving optimal outcomes and that voting, or another mechanism by which residents may influence local policy internally, may also be necessary.</p
Variational Studies of Exotic Bose Liquid, Spin Liquid, and Magnetic Phases
Get PDFThe strong interest in strongly correlated systems in condensed matter physics has continued unabated for the past few decades. In recent years, the number of novel, exotic quantum phases found in theoretical studies has seen a phenomenal rise. Among those interesting quantum states are bose liquids and spin liquids, where strong quantum fluctuations have prevented the systems from developing a long range order. Our work in this thesis seeks to further the understanding of frustrated systems. In the study of a hard-core boson model with ring-only exchange interactions on a square lattice, we obtain concrete numerical realization of the unconventional Exciton Bose Liquid (EBL) phase, which possesses interesting properties such as a "Bose surface" which resembles the Fermi surface in a metal, as well as unusual thermodynamic properties such as a T Log T dependence for specific heat. An equally important result from this work is the demonstration that the widely used Gutzwiller projection on slave-particle wave functions may generally fail to capture the correct long wavelength physics in the respective systems. For the Heisenberg antiferromagnet on the kagome lattice, which is a promising candidate for realizing a spin-disordered ground state, our variational study shows that the projected Schwinger boson wave function is energetically better than the Dirac spin liquid wave function when a small antiferromagnetic second-neighbor spin coupling is added to the nearest-neighbor model. We also study the anisotropic triangular Heisenberg antiferromagnetic in magnetic field, and find simple, yet accurate wave functions for various regions of the surprisingly rich phase diagram, thus providing insights into the energetics of the competing phases in this interesting model. Finally, our work also highlights permanent-type wave functions as potentially useful constructions in variational studies of systems with short-ranged correlations, e.g., a Mott insulator and a gapped spin liquid
Coarse-Graining Kohn-Sham Density Functional Theory
Get PDFDefects, though present in relatively minute concentrations, play a significant role in determining macroscopic properties. Even vacancies, the simplest and most common type of defect, are fundamental to phenomena like creep, spall and radiation ageing. This necessitates an accurate characterization of defects at physically relevant concentrations, which is typically in parts per million. This represents a unique challenge since both the electronic structure of the defect core as well as the long range elastic field need to be resolved simultaneously. Unfortunately, accurate ab-initio electronic structure calculations are limited to a few hundred atoms, which is orders of magnitude smaller than that necessary for a complete description. Thus, defects represent a truly challenging multiscale problem.
Density functional theory developed by Hohenberg, Kohn and Sham (DFT) is a widely accepted, reliable ab-initio method for computing a wide range of material properties. We present a real-space, non-periodic, finite-element and max-ent formulation for DFT. We transform the original variational problem into a local saddle-point problem, and show its well-posedness by proving the existence of minimizers. Further, we prove the convergence of finite-element approximations including numerical quadratures. Based on domain decomposition, we develop parallel finite-element and max-ent implementations of this formulation capable of performing both all-electron and pseudopotential calculations. We assess the accuracy of the formulation through selected test cases and demonstrate good agreement with the literature.
Traditional implementations of DFT solve for the wavefunctions, a procedure which has cubic-scaling with respect to the number of atoms. This places serious limitations on the size of the system which can be studied. Further, they are not amenable to coarse-graining since the wavefunctions need to be orthonormal, a global constraint. To overcome this, we develop a linear-scaling method for DFT where the key idea is to directly evaluate the electron density without solving for the individual wavefunctions. Based on this linear-scaling method, we develop a numerical scheme to coarse-grain DFT derived solely based on approximation theory, without the introduction of any new equations and resultant spurious physics. This allows us to study defects at a fraction of the original computational cost, without any significant loss of accuracy. We demonstrate the efficiency and efficacy of the proposed methods through examples. This work enables the study of defects like vacancies, dislocations, interfaces and crack tips using DFT to be computationally viable.</p
Practical Compressed Sensing: Modern Data Acquisition and Signal Processing
Get PDFSince 2004, the field of compressed sensing has grown quickly and seen tremendous interest because it provides a theoretically sound and computationally tractable method to stably recover signals by sampling at the information rate. This thesis presents in detail the design of one of the world's first compressed sensing hardware devices, the random modulation pre-integrator (RMPI). The RMPI is an analog-to-digital converter (ADC) that bypasses a current limitation in ADC technology and achieves an unprecedented 8 effective number of bits over a bandwidth of 2.5 GHz. Subtle but important design considerations are discussed, and state-of-the-art reconstruction techniques are presented.
Inspired by the need for a fast method to solve reconstruction problems for the RMPI, we develop two efficient large-scale optimization methods, NESTA and TFOCS, that are applicable to a wide range of other problems, such as image denoising and deblurring, MRI reconstruction, and matrix completion (including the famous Netflix problem). While many algorithms solve unconstrained l1 problems, NESTA and TFOCS can solve the constrained form of l1 minimization, and allow weighted norms. In addition to l1 minimization problems such as the LASSO, both NESTA and TFOCS solve total-variation minimization problem. TFOCS also solves the Dantzig selector and most variants of the nuclear norm minimization problem. A common theme in both NESTA and TFOCS is the use of smoothing techniques, which make the problem tractable, and the use of optimal first-order methods that have an accelerated convergence rate yet have the same cost per iteration as gradient descent. The conic dual methodology is introduced in TFOCS and proves to be extremely flexible, covering such generic problems as linear programming, quadratic programming, and semi-definite programming. A novel continuation scheme is presented, and it is shown that the Dantzig selector benefits from an exact-penalty property. Both NESTA and TFOCS are released as software packages available freely for academic use.</p