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Understanding Selectivity and Activity in Z-selective Metathesis with Cyclometallated Ru-based Catalysts
Get PDFWith the advent of well-defined highly active catalysts, olefin metathesis has become a powerful tool for the formation of carbon–carbon double bonds in a variety of settings. However, these traditional catalysts preferentially form the E-alkene product. Recent efforts have yielded several families of Z-selective metathesis catalysts, including a family of Ru complexes with cyclometallated NHC ligands developed in our group. The work in this thesis describes efforts to develop an improved understanding of the catalyst features that govern activity and selectivity in the cyclometallated Ru-based catalysts, as well as to expand the scope of reactivity in these systems.
Chapter 1 provides an outline of the key features that govern selectivity in cross metathesis applications.
Chapter 2 describes the application of cyclometallated Ru-based catalysts in Z-selective cross metathesis (CM) of allylic-substituted olefins. Efficient CM is demonstrated in the case of acrolein acetals providing a new route to access Z-α,β-unsaturated acetals and aldehydes. For a variety of other allylic-substituted olefins, reactivity was lower but could be correlated with the structure of the catalyst and substrate. The implications of the observed reactivity are discussed and contextualized with regard to reactivity of previous metathesis catalysts.
Chapter 3 describes the development of a series of cyclometallated Z-selective metathesis with varying N-aryl groups that allow elucidation of the key catalyst features that govern activity and selectivity in these systems. The synthesis of the catalyst series is described, including several strategies employed to circumvent unexpected side-reactions. The second part of the chapter focuses on the dynamic behavior of the catalysts in solution and studies of an unusual C–H····F–C intramolecular interaction observed in some of these catalysts. Finally, the reactivity of these catalysts in a variety of CM applications are discussed, which allows for development of a refined model of how the N-aryl group affects Z-selectivity and activity in these catalysts systems and how this varies across different classes of substrate.</p
Wafer-Scalable Fabrication of Metal Nanostructures for Plasmonics-Assisted Biomedical Sensing Applications
Get PDFPlasmonics provides many opportunities of sensing and detection since it combines the nanoscale spatial confinement and the optical temporal resolution. The wireless nature of photonic investigation, moreover, is very desirable for biomedical applications. Plasmonic metals, however, are difficult to pattern with great nanoscopic precision, and traditional approaches were time-consuming, non-scalable, stochastically-manufactured, or highly-limiting in the pattern designs. In this work, wafer-scalable nanofabrication methods are presented for various plasmonic structures for biomedical sensing applications. The fabrication steps have ready counterparts in commercial semiconductor foundries and therefore can be directly applied for mass production.
The fabrication and measurement of extraordinary transmission (EOT) are discussed in Chapter 2. Fabrication options are available for substrates like silicon-on-sapphire and silicon-on-glass, so that the devices can be mechanically robust for user-friendliness. The metal layer can also be varied for EOT applications in different ranges of wavelengths. The EOT nanostructures can be fabricated to be polarization-sensitive, and the concept of fluorescence-based EOT assays is demonstrated.
The fabrication and applications of surface-enhanced Raman spectroscopy (SERS) are then discussed. With a hybrid approach, the top-down designing defines uniform SERS nanostructures on a chip, while the bottom-up process of thermal reflow increases the fabrication precision beyond the lithography resolution limit. Based on the thiophenol study, an enhancement factor greater than 1010 can be achieved. The first Raman spectrum of tracheal cytotoxin is demonstrated without any special sample preparation, and thrombin binding could be easily resolved through chip functionalization. The binding dynamics of ethyl mercaptan, which is similar to the highly toxic gas of hydrogen sulfide, can be detected with a good resolution in time at a low concentration.
With a few more steps of fabrication, the plasmonic structures can be integrated into systems that do not call for laboratory infrastructures. A built-in micro-channel on a chip can make the device useful without dedicated support of a microscope or additional microfluidic structures. The nanostructures can also be transferred onto flexible substrates for better conformity onto various surfaces. Finally, the SERS structures can be transferred onto a fiber tip for in-field or through-the-needle applications, especially when combined with a portable Raman-scope.</p
Effect of Microstructural Interfaces on the Mechanical Response of Crystalline Metallic Materials
Get PDFAdvances in nano-scale mechanical testing have brought about progress in the understanding of physical phenomena in materials and a measure of control in the fabrication of novel materials. In contrast to bulk materials that display size-invariant mechanical properties, sub-micron metallic samples show a critical dependence on sample size. The strength of nano-scale single crystalline metals is well-described by a power-law function, σαD-n, where D is a critical sample size and n is a experimentally-fit positive exponent. This relationship is attributed to source-driven plasticity and demonstrates a strengthening as the decreasing sample size begins to limit the size and number of dislocation sources. A full understanding of this size-dependence is complicated by the presence of microstructural features such as interfaces that can compete with the dominant dislocation-based deformation mechanisms. In this thesis, the effects of microstructural features such as grain boundaries and anisotropic crystallinity on nano-scale metals are investigated through uniaxial compression testing. We find that nano-sized Cu covered by a hard coating displays a Bauschinger effect and the emergence of this behavior can be explained through a simple dislocation-based analytic model. Al nano-pillars containing a single vertically-oriented coincident site lattice grain boundary are found to show similar deformation to single-crystalline nano-pillars with slip traces passing through the grain boundary. With increasing tilt angle of the grain boundary from the pillar axis, we observe a transition from dislocation-dominated deformation to grain boundary sliding. Crystallites are observed to shear along the grain boundary and molecular dynamics simulations reveal a mechanism of atomic migration that accommodates boundary sliding. We conclude with an analysis of the effects of inherent crystal anisotropy and alloying on the mechanical behavior of the Mg alloy, AZ31. Through comparison to pure Mg, we show that the size effect dominates the strength of samples below 10 μm, that differences in the size effect between hexagonal slip systems is due to the inherent crystal anisotropy, suggesting that the fundamental mechanism of the size effect in these slip systems is the same
General-Domain Compressible Navier-Stokes Solvers Exhibiting Quasi-Unconditional Stability and High Order Accuracy in Space and Time
Get PDFThis thesis presents a new class of solvers for the subsonic compressible Navier-Stokes equations in general two- and three-dimensional spatial domains. The proposed methodology incorporates: 1) A novel linear-cost implicit solver based on use of higher-order backward differentiation formulae (BDF) and the alternating direction implicit approach (ADI); 2) A fast explicit solver; 3) Dispersionless spectral spatial discretizations; and 4) A domain decomposition strategy that negotiates the interactions between the implicit and explicit domains. In particular, the implicit methodology is quasi-unconditionally stable (it does not suffer from CFL constraints for adequately resolved flows), and it can deliver orders of time accuracy between two and six in the presence of general boundary conditions. In fact this thesis presents, for the first time in the literature, high-order time-convergence curves for Navier-Stokes solvers based on the ADI strategy---previous ADI solvers for the Navier-Stokes equations have not demonstrated orders of temporal accuracy higher than one. An extended discussion is presented in this thesis which places on a solid theoretical basis the observed quasi-unconditional stability of the methods of orders two through six. The performance of the proposed solvers is favorable. For example, a two-dimensional rough-surface configuration including boundary layer effects at Reynolds number equal to one million and Mach number 0.85 (with a well-resolved boundary layer, run up to a sufficiently long time that single vortices travel the entire spatial extent of the domain, and with spatial mesh sizes near the wall of the order of one hundred-thousandth the length of the domain) was successfully tackled in a relatively short (approximately thirty-hour) single-core run; for such discretizations an explicit solver would require truly prohibitive computing times. As demonstrated via a variety of numerical experiments in two- and three-dimensions, further, the proposed multi-domain parallel implicit-explicit implementations exhibit high-order convergence in space and time, useful stability properties, limited dispersion, and high parallel efficiency
Constraining the Interpretation of 2-Methylhopanoids through Genetic and Phylogenetic Methods
Get PDFHopanoids are a class of sterol-like lipids produced by select bacteria. Their preservation in the rock record for billions of years as fossilized hopanes lends them geological significance. Much of the structural diversity present in this class of molecules, which likely underpins important biological functions, is lost during fossilization. Yet, one type of modification that persists during preservation is methylation at C-2. The resulting 2-methylhopanoids are prominent molecular fossils and have an intriguing pattern over time, exhibiting increases in abundance associated with Ocean Anoxic Events during the Phanerozoic. This thesis uses diverse methods to address what the presence of 2-methylhopanes tells us about the microbial life and environmental conditions of their ancient depositional settings. Through an environmental survey of hpnP, the gene encoding the C-2 hopanoid methylase, we found that many different taxa are capable of producing 2-methylhopanoids in more diverse modern environments than expected. This study also revealed that hpnP is significantly overrepresented in organisms that are plant symbionts, in environments associated with plants, and with metabolisms that support plant-microbe interactions; collectively, these correlations provide a clue about the biological importance of 2-methylhopanoids. Phylogenetic reconstruction of the evolutionary history of hpnP revealed that 2-methylhopanoid production arose in the Alphaproteobacteria, indicating that the origin of these molecules is younger than originally thought. Additionally, we took genetic approach to understand the role of 2-methylhopanoids in Cyanobacteria using the filamentous symbiotic Nostoc punctiforme. We found that hopanoids likely aid in rigidifying the cell membrane but do not appear to provide resistance to osmotic or outer membrane stressors, as has been shown in other organisms. The work presented in this thesis supports previous findings that 2-methylhopanoids are not biomarkers for oxygenic photosynthesis and provides new insights by defining their distribution in modern environments, identifying their evolutionary origin, and investigating their role in Cyanobacteria. These efforts in modern settings aid the formation of a robust interpretation of 2-methylhopanes in the rock record
Topological Strings, Double Affine Hecke Algebras, and Exceptional Knot Homology
Get PDFIn this thesis, we consider two main subjects: refined, composite invariants and exceptional knot homologies of torus knots. The main technical tools are double affine Hecke algebras ("DAHA") and various insights from topological string theory.
In particular, we define and study the composite DAHA-superpolynomials of torus knots, which depend on pairs of Young diagrams and generalize the composite HOMFLY-PT polynomials from the full HOMFLY-PT skein of the annulus. We also describe a rich structure of differentials that act on homological knot invariants for exceptional groups. These follow from the physics of BPS states and the adjacencies/spectra of singularities associated with Landau-Ginzburg potentials. At the end, we construct two DAHA-hyperpolynomials which are closely related to the Deligne-Gross exceptional series of root systems.
In addition to these main themes, we also provide new results connecting DAHA-Jones polynomials to quantum torus knot invariants for Cartan types A and D, as well as the first appearance of quantum E6 knot invariants in the literature.</p
Essays in Behavioral Decision Theory
Get PDFThis thesis studies decision making under uncertainty and how economic agents respond to information. The classic model of subjective expected utility and Bayesian updating is often at odds with empirical and experimental results; people exhibit systematic biases in information processing and often exhibit aversion to ambiguity. The aim of this work is to develop simple models that capture observed biases and study their economic implications.
In the first chapter I present an axiomatic model of cognitive dissonance, in which an agent's response to information explicitly depends upon past actions. I introduce novel behavioral axioms and derive a representation in which beliefs are directionally updated. The agent twists the information and overweights states in which his past actions provide a higher payoff. I then characterize two special cases of the representation. In the first case, the agent distorts the likelihood ratio of two states by a function of the utility values of the previous action in those states. In the second case, the agent's posterior beliefs are a convex combination of the Bayesian belief and the one which maximizes the conditional value of the previous action. Within the second case a unique parameter captures the agent's sensitivity to dissonance, and I characterize a way to compare sensitivity to dissonance between individuals. Lastly, I develop several simple applications and show that cognitive dissonance contributes to the equity premium and price volatility, asymmetric reaction to news, and belief polarization.
The second chapter characterizes a decision maker with sticky beliefs. That is, a decision maker who does not update enough in response to information, where enough means as a Bayesian decision maker would. This chapter provides axiomatic foundations for sticky beliefs by weakening the standard axioms of dynamic consistency and consequentialism. I derive a representation in which updated beliefs are a convex combination of the prior and the Bayesian posterior. A unique parameter captures the weight on the prior and is interpreted as the agent's measure of belief stickiness or conservatism bias. This parameter is endogenously identified from preferences and is easily elicited from experimental data.
The third chapter deals with updating in the face of ambiguity, using the framework of Gilboa and Schmeidler. There is no consensus on the correct way way to update a set of priors. Current methods either do not allow a decision maker to make an inference about her priors or require an extreme level of inference. In this chapter I propose and axiomatize a general model of updating a set of priors. A decision maker who updates her beliefs in accordance with the model can be thought of as one that chooses a threshold that is used to determine whether a prior is plausible, given some observation. She retains the plausible priors and applies Bayes' rule. This model includes generalized Bayesian updating and maximum likelihood updating as special cases.</p
Structure-Function Studies of Nicotinic Acetylcholine Receptors Using Selective Agonists and Positive Allosteric Modulators
Get PDFThis dissertation primarily describes chemical-scale studies of nicotinic acetylcholine receptors (nAChRs) in order to better understand ligand-receptor selectivity and allosteric modulation influences during receptor activation. Electrophysiology coupled with canonical and non-canonical amino acids mutagenesis is used to probe subtle changes in receptor function.
The first half of this dissertation focuses on differential agonist selectivity of α4β2-containing nAChRs. The α4β2 nAChR can assemble in alternative stoichiometries as well as assemble with other accessory subunits. Chapter 2 identifies key structural residues that dictate binding and activation of three stoichiometry-dependent α4β2 receptor ligands: sazetidine-A, cytisine, and NS9283. These do not follow previously suggested hydrogen-bonding patterns of selectivity. Instead, three residues on the complementary subunit strongly influence binding ability of a ligand and receptor activation. Chapter 3 involves isolation of a α5α4β2 receptor-enriched population to test for a potential alternative agonist binding location at the α5 α4 interface. Results strongly suggest that agonist occupation of this site is not necessary for receptor activation and that the α5 subunit only incorporates at the accessory subunit location.
The second half of this dissertation seeks to identify residue interactions with positive allosteric modulators (PAMs) of the α7 nAChR. Chapter 4 focuses on methods development to study loss of potentiation of Type I PAMs, which indicate residues vital to propagation of PAM effects and/or binding. Chapter 5 investigates α7 receptor modulation by a Type II PAM (PNU 120596). These results show that PNU 120596 does not alter the agonist binding site, thus is relegated to influencing only the gating component of activation. From this, we were able to map a potential network of residues from the agonist binding site to the proposed PNU 120596 binding site that are essential for receptor potentiation.</p
Exploring the Kinetics of Domain Switching in Ferroelectrics for Structural Applications
Get PDFThe complex domain structure in ferroelectrics gives rise to electromechanical coupling, and its evolution (via domain switching) results in a time-dependent (i.e. viscoelastic) response. Although ferroelectrics are used in many technological applications, most do not attempt to exploit the viscoelastic response of ferroelectrics, mainly due to a lack of understanding and accurate models for their description and prediction. Thus, the aim of this thesis research is to gain better understanding of the influence of domain evolution in ferroelectrics on their dynamic mechanical response.
There have been few studies on the viscoelastic properties of ferroelectrics, mainly due to a lack of experimental methods. Therefore, an apparatus and method called Broadband Electromechanical Spectroscopy (BES) was designed and built. BES allows for the simultaneous application of dynamic mechanical and electrical loading in a vacuum environment. Using BES, the dynamic stiffness and loss tangent in bending and torsion of a particular ferroelectric, viz. lead zirconate titanate (PZT), was characterized for different combinations of electrical and mechanical loading frequencies throughout the entire electric displacement hysteresis. Experimental results showed significant increases in loss tangent (by nearly an order of magnitude) and compliance during domain switching, which shows promise as a new approach to structural damping.
A continuum model of the viscoelasticity of ferroelectrics was developed, which incorporates microstructural evolution via internal variables and associated kinetic relations. For the first time, through a new linearization process, the incremental dynamic stiffness and loss tangent of materials were computed throughout the entire electric displacement hysteresis for different combinations of mechanical and electrical loading frequencies. The model accurately captured experimental results.
Using the understanding gained from the characterization and modeling of PZT, two applications of domain switching kinetics were explored by using Micro Fiber Composites (MFCs). Proofs of concept of set-and-hold actuation and structural damping using MFCs were demonstrated
Chains of Non-Regular de Branges Spaces
Get PDFWe consider canonical systems with singular left endpoints, and discuss the concept of a scalar
spectral measure and the corresponding generalized Fourier transform associated with a canonical
system with a singular left endpoint. We use the framework of de Branges’ theory of Hilbert spaces
of entire functions to study the correspondence between chains of non-regular de Branges
spaces, canonical systems with singular left endpoints, and spectral measures.
We find sufficient integrability conditions on a Hamiltonian H which ensure the existence of a
chain of de Branges functions in the first generalized Pólya class with Hamiltonian H. This result
generalizes de Branges’ Theorem 41, which showed the sufficiency of stronger integrability
conditions on H for the existence of a chain in the Pólya class. We show the conditions that de
Branges came up with are also necessary. In the case of Krein’s strings, namely when the Hamiltonian
is diagonal, we show our proposed conditions are also necessary.
We also investigate the asymptotic conditions on chains of de Branges functions as t approaches
its left endpoint. We show there is a one-to-one correspondence between chains of de Branges
functions satisfying certain asymptotic conditions and chains in the Pólya class. In the case of
Krein’s strings, we also establish the one-to-one correspondence between chains satisfying certain
asymptotic conditions and chains in the generalized Pólya class.</p