Magnetic impurities in gapless Fermi systems: perturbation theory

We consider a symmetric Anderson impurity model, with a soft-gap hybridization vanishing at the Fermi level with a power law r > 0. Three facets of the problem are examined. First the non-interacting limit, which despite its simplicity contains much physics relevant to the U > 0 case: it exhibits both strong coupling (SC) states (for r 1), with characteristic signatures in both spectral properties and thermodynamic functions. Second, we establish general conditions upon the interaction self-energy for the occurence of a SC state for U > 0. This leads to a pinning theorem, whereby the modified spectral function is pinned at the Fermi level for any U where a SC state exists; it generalizes to arbitrary r the familiar pinning condition for the normal r = 0 Anderson model. Finally, we consider explicitly spectral functions at the simplest level: second order perturbation theory in U, which we conclude is applicable for r 1 but not for 1/2 < r < 1. Characteristic spectral features observed in numerical renormalization group calculations are thereby recovered, for both SC and LM phases; and for the SC state the modified spectral functions are found to contain a generalized Abrikosov-Suhl resonance exhibiting a characteristic low-energy Kondo scale with increasing interaction strength.Comment: 24 pages, 7 figures, submitted to European Physical Journal

Design, Synthesis, Stability, and Photocatalytic Studies of Sustainable Metal-Organic Frameworks

The presented dissertation focuses on the design, synthesis, and characterization of metal-organic frameworks (MOFs) composed of earth-abundant elements the exhibit photoredox activity and studied their application as heterogeneous photocatalysts in organic synthesis and in solar-to-chemical energy conversion. In particular, the structure-property relationships of titanium-based MOFs relating the structure of the organic building unit and the photophysical and photochemical activity of the solid material is studied. The first novel family of seven MOFs isoreticular to MIL-125-NH2, includes functionalized with N-alkyl groups with increasing chain length (methyl to heptyl) and with varying connectivity (primary or secondary). The functionalized materials displayed reduced optical bandgaps correlated with the increased inductive donor ability of the alkyl substituents, enhanced excited-state lifetimes, mechanistic information towards visible light CO2 reduction, and improved water stability. The second family of titanium MOFs was prepared with a new secondary building unit and organic links of varying lengths, for which Their crystal structure was solved utilizing powder X-ray diffraction crystallography. This work provides guidelines for the next generation of photocatalyst for the conversion of solar-to-chemical energy and other organic transformations

Local quantum critical point in the pseudogap Anderson model: finite-T dynamics and omega/T scaling

The pseudogap Anderson impurity model is a paradigm for locally critical quantum phase transitions. Within the framework of the local moment approach we study its finite-T dynamics, as embodied in the single-particle spectrum, in the vicinity of the symmetric quantum critical point (QCP) separating generalized Fermi-liquid (Kondo screened) and local moment phases. The scaling spectra in both phases, and at the QCP itself, are obtained analytically. A key result is that pure omega/T-scaling obtains at the QCP, where the Kondo resonance has just collapsed. The connection between the scaling spectra in either phase and that at the QCP is explored in detail.Comment: 12 pages, 7 figure

CHANGES OVER TIME IN THE PRACTICE OF SELF-DEFENSE AMONG YOUNG MEN IN CANADA: AN EXAMINATION OF INSECURITY AND UFC HYPOTHESES

Using multiple waves of data (1999,2004, 2009) from the General Social Survey (GSS) on victimization, the following study analyzes a number of factors thought to be influential in the practice of self-defense among young Canadian men (N=9,049) over time. Two perspectives are examined: 1) The practice of self-defense is related to feelings of insecurity among young men, and is a rational, adaptive response to perceived or actual dangerous environmental threats; 2) In addition to the effects of insecurity, the practice of self-defense should increase over time as a result of the mainstream popularity of the Ultimate Fighting Championship (UFC) and mixed martial arts, and may be the result of a potential “UFC effect”. Results indicate a strong, positive relationship between measures of insecurity (e.g., prior experience of violent victimization) and the likelihood of practicing self-defense, while evidence in support of the UFC hypothesis is, for the most part, absent. However, supplementary analyses lend partial support for the presence of such an effect, though it is less than definitive and only applies to young men of lower income. The implications of these findings are presented and discussed from both a theoretical and policy-oriented perspective

Electrochemical analysis of photoelectro-, electro-, and thermal catalysis towards more efficient hydrogen peroxide production

Hydrogen peroxide is a chemical with growing industrial relevance but is plagued with high production costs. There are several compelling alternatives to produce H2O2, and most revolve around the 2-electron oxygen reduction reaction. There is a large amount of foundational research on the mechanisms and theoretical aspects of electrochemically reducing oxygen to form H2O2, but this production method remains to be implemented on the industrial scale due to a lack of effective catalysts. Explored here are alternative H2O2 production methods involving the 2-electron reduction of O2. Specifically, photoelectrochemical, electrocatalytic, and thermal catalytic methods are investigated further to draw out necessary catalyst properties and design parameters for producing H2O2. Each catalytic system is analyzed under the lens of electrochemically detecting H2O2 that is catalytically produced. Electrochemical analysis of these catalytic systems provides the added advantage of being able to utilize high throughput screening techniques to quickly discover and test novel catalyst compositions. Optimal catalyst design parameters are identified for each H2O2 production method and these parameters can be assessed over several catalyst compositions through high throughput electrochemical screening. The research presented here acts as a basis for further improvements onto these already compelling H2O2 production methods

Petrology and Geochemistry of the Enriched Poikilitic Shergottite Northwest Africa 10169: Insight into the Martian Interior

The martian meteorite Northwest Africa (NWA) 10169 is classified as a new member of the geochemically enriched poikilitic shergottites, based on mineral composition, Lu-Hf isotope systematics, and rare earth element (REE) composition. Akin to other poikilitic shergottites, it shows a similar bimodal texture to other enriched and intermediate poikilitic shergottites. In addition, olivine and pyroxene in the poikilitic zone have higher Mg#’s (Mg/Mg+Fe) than those in the interstitial areas, suggesting that the poikilitic texture represents early-stage crystallization, opposed to late-stage non-poikilitic crystallization. Calculated fO2 values are reduced (FMQ -2.3 ± 0.23) within the poikilitic texture, and more oxidized (FMQ -1.07 ± 0.14) within the interstitial areas likely representing auto-oxidation and degassing during magma crystallization. Melt inclusions within olivine crystals provide snapshots of magma composition throughout parent melt evolution. The calculated parental melt compositions share evolution trends with the enriched olivine-phyric shergottite Larkman Nunatuk (LAR) 06319, and suggest that two melts (K-poor and K-rich) were involved in the formation of NWA 10169, likely representing interaction with a metasomatized melt during the entrapment of the K-rich melt inclusions. The Lu-Hf crystallization age for NWA 10169 is 167 ± 31 Ma, consistent with the other enriched shergottites. Based on the isochron initial 176Hf/177Hf value, the modeled the source 176Lu/177Hf composition for NWA 10169 is 0.02748 ± 0.00037, identical within error to the source compositions of the enriched shergottites Shergotty, Zagami, LAR 06319, NWA 4468, and Roberts Massif (RBT) 04262, suggesting a shared, long-lived geochemical source, distinct from the source tapped by Los Angeles, NWA 856, and NWA 7320. This study reveals that at least two sources are responsible for the enriched shergottites, and a more heterogeneous martian mantle than previously thought. Additionally, the shared source with NWA 10169, coupled with consistent crystallization ages and magmatic histories indicates that a common magmatic system on Mars is likely responsible for the formation of this group of shergottites

THE FABRICATION AND CHARACTERIZATION OF METAL OXIDE NANOPARTICLES EMPLOYED IN ENVIRONMENTAL TOXICITY AND POLYMERIC NANOCOMPOSITE APPLICATIONS

Ceria (cerium oxide) nanomaterials, or nanoceria, have commercial catalysis and energy storage applications. The cerium atoms on the surface of nanoceria can store or release oxygen, cycling between Ce3+ and Ce4+, and can therefore act as a therapeutic to relieve oxidative stress within living systems. Nanoceria dissolution is present in acidic environments in vivo. In order to accurately define the fate of nanoceria in vivo, nanoceria dissolution or stabilization is observed in vitro using acidic aqueous environments. Nanoceria stabilization is a known problem even during its synthesis; in fact, a carboxylic acid, citric acid, is used in many synthesis protocols. Citric acid adsorbs onto nanoceria surfaces, capping particle formation and creating stable dispersions with extended shelf lives. Nanoceria was shown to agglomerate in the presence of some carboxylic acids over a time scale of up to 30 weeks, and degraded in others, at pH 4.5 (representing that of phagolysosomes). Sixteen carboxylic acids were tested: citric, glutaric, tricarballylic, α-hydroxybutyric, β-hydroxybutyric, adipic, malic, acetic, pimelic, succinic, lactic, tartronic, isocitric, tartaric, dihydroxymalonic, and glyceric acid. Each acid was introduced as 0.11 M, into pH 4.5 iso-osmotic solutions. Controls such as ammonium nitrate, sodium nitrate, and water were also tested to assess their effects on nanoceria dissolution and stabilization. To further test stability, nanoceria suspensions were subject to light and dark milieu, simulating plant environments and biological systems, respectively. Light induced nanoceria agglomeration in some, but not all ligands, and is likely to be a result of UV irradiation. Light initiates free radicals generated from the ceria nanoparticles. Some of the ligands completely dissolved the nanoceria when exposed to light. Citric and malic acids form coordination complexes with cerium on the surface of the ceria nanoparticle that can inhibit agglomeration. This approach identifies key functional groups required to prevent nanoceria agglomeration. The impact of each ligand on nanoceria was analyzed and will ultimately describe the fate of nanoceria in vivo. In addition, simulated biological fluid (SBF) exposure can change nanoceria’s surface properties and biological activity. The citrate-coated nanoceria physicochemical properties such as size, morphology, crystallinity, surface elemental composition, and charge were determined before and after exposure to simulated lung, gastric, and intestinal fluids. SBF exposure resulted in either loss or overcoating of nanoceria’s surface citrate by some of the SBF components, greater nanoceria agglomeration, and small changes in the zeta potential. Nanocomposites are comprised of a polymer matrix embedded with nanoparticles. These nanoparticles can alter material and optical properties of the polymer. SR-399 (dipentaerythritol pentaacrylate) is a fast cure, low skin irritant monomer that contains five carbon-carbon double bonds (C=C). It is a hard, flexible polymer, and also resistant to abrasion. It can be used as a sealant, binder, coating, and as a paint additive. In this case, metal oxide nanoparticles were added to the monomer prior to polymerization. Titania nanoparticles are known to absorb UV light due to their photocatalytic nature. Titania nanoparticles were chosen due to their high stability, non-toxicity, and are relatively quick, easy, and inexpensive to manufacture. Channels in thin monomer films were created using a ferrofluid manipulated by magnetic fields. The mechanical properties of a microfluidic device by rapid photopolymerization is dependent on the crosslinking gradient observed throughout the depth of the film. Quantitative information regarding the degree of polymerization of thin film polymers polymerized by free radical polymerization through the application of UV light is crucial to estimate material properties. In general, less cure leads to more flexibility, and more cure leads to brittleness. The objective was to quantify the degree of polymerization to approximate the C=C concentration and directly relate it to the mechanical properties of the polymer. Polymerization of C=C groups was conducted using a photoinitiator and an UV light source from one surface of a thin film of a multifunctional monomer. The C=C fraction in the film was found to vary with film depth and UV light intensity. The extents of conversion and crosslinking estimates were compared to local mechanical moduli and optical properties. A mathematical model linking the mechanical properties to the degree of polymerization, C=C composition, as a function of film depth and light intensity was then developed. For a given amount of light energy, one can predict the hardness and modulus of elasticity. The correlation between the photopolymerization and the mechanical properties can be used to optimize the mechanical properties of thin films within the manufacturing and energy constraints, and should be scalable to other multifunctional monomer systems

Single-particle dynamics of the Anderson model: a local moment approach

A non-perturbative local moment approach to single-particle dynamics of the general asymmetric Anderson impurity model is developed. The approach encompasses all energy scales and interaction strengths. It captures thereby strong coupling Kondo behaviour, including the resultant universal scaling behaviour of the single-particle spectrum; as well as the mixed valent and essentially perturbative empty orbital regimes. The underlying approach is physically transparent and innately simple, and as such is capable of practical extension to lattice-based models within the framework of dynamical mean-field theory.Comment: 26 pages, 9 figure