## Pages

Cluster Approach Applied to the One-Dimensional Anderson-Hubbard Model
S. Johri and R. Bhatt developed a real-space renormalization group approach aimed at extracting the localized single-particle eigenstates of the Anderson model from a large system by identifying clusters of resonant site potentials. E. Campbell generalized this real-space renormalization group approach using standard perturbation theory. Both approaches were intended to approximate the single-particle density of states of the Anderson model. In this thesis, we aimed to test the potential of applying a similar real-space renormalization group approach to calculate the density of states of the interacting Anderson-Hubbard model. Our interest in the density of states of this model is due to a V-shaped zero-bias anomaly in two-dimensional systems. A real-space renormalization group approach is best applied to a one-dimensional system. We found that the zero-bias anomaly is not V-shaped in one-dimension. To test the potential of a real-space renormalization group approach, we used the cluster approach which is the same as the non-interacting renormalization group approach but without the perturbation theory and found that for strong disorder this technique could accurately calculate the density of states over a wide range of energies but deviated from exact results at the band edge, at $\omega=\pm U$ and near $\omega=0$. The first two inaccuracies will be reduced with a proper real-space renormalization group approach. We suspect that the last inaccuracy is associated with long range physics and may be difficult to recover. We also developed a technique that adjusts the identification of clusters in the cluster approach to improve the computation time of the density of states with minimal loss of accuracy in a tunable range around the Fermi level. We found that this technique significantly reduced the computation time and was able to preserve the density of states near the Fermi level, except at the smallest energies near $\omega=0$. Author Keywords: Anderson-Hubbard model, renormalization group, Strong electron correlations, Zero-bias anomaly
Real-space renormalization group approach to the Anderson model
Many of the most interesting electronic behaviours currently being studied are associated with strong correlations. In addition, many of these materials are disordered either intrinsically or due to doping. Solving interacting systems exactly is extremely computationally expensive, and approximate techniques developed for strongly correlated systems are not easily adapted to include disorder. As a non-interacting disordered model, it makes sense to consider the Anderson model as a first step in developing an approximate method of solution to the interacting and disordered Anderson-Hubbard model. Our renormalization group (RG) approach is modeled on that proposed by Johri and Bhatt [23]. We found an error in their work which we have corrected in our procedure. After testing the execution of the RG, we benchmarked the density of states and inverse participation ratio results against exact diagonalization. Our approach is significantly faster than exact diagonalization and is most accurate in the limit of strong disorder. Author Keywords: disorder, localization, real-space renormalization, strong correlations
Modelling the Lanthanum Aluminate-Strontium Titanate Interface with a Modified Transverse Ising Model
In 2004 it was discovered that a two-dimensional electron gas (2DEG) forms at the interface between lanthanum aluminate (LAO) and strontium titanate (STO). This 2DEG exhibits a variety of electronic and magnetic phenomena, motivating intense research into its applicability to electronic devices. Over the years several models have been developed in theoretical exploration of this system. Here, the transverse Ising model is applied to the LAO/STO interface for the first time. It is shown that the model as it is traditionally formulated cannot accurately predict the structure of the electron density at the interface. I show that this can be fixed with a simple modification of the model, and discuss how this modification affects both the polarization distribution in ferroelectric thin films and the electron density at the LAO/STO interface. The importance of including the depolarizing field when modelling spatially inhomogeneous ferroelectric systems is also explored. Author Keywords: ferroelectric thin film, lanthanum aluminate, strontium titanate, transverse Ising model, two-dimensional electron gas
Novel Functional Materials From Renewable Lipids
Vegetable oils represent an ideal and renewable feedstock for the synthesis of a variety of functional materials. However, without financial incentive or unique applications motivating a switch, commercial products continue to be manufactured from petrochemical resources. Two different families of high value, functional materials synthesized from vegetable oils were studied. These materials demonstrate superior and unique performance to comparable petrochemical analogues currently on the market. In the first approach, 3 amphiphilic thermoplastic polytriazoles with differing lipophilic segment lengths were synthesized in a polymerization process without solvents or catalysts. Investigation of monomer structure influence on the resultant functional behaviour of these polymers found distinctive odd/even behaviour reliant on the number of carbon atoms in the monomers. Higher concentrations of triazole groups, due to shorter CH2 chains in the monomeric dialkynes, resulted in more brittle polymers, displaying higher tensile strengths but reduced elongation to break characteristics. These polymers had similar properties to commercial petroleum derived thermoplastics. One polymer demonstrated self-assembled surface microstructuring, and displayed hydrophobic properties. Antimicrobial efficacy of the polymers were tested by applying concentrated bacterial solutions to the surfaces, and near complete inhibition was demonstrated after 4 hours. Scanning electron microscope images of killed bacteria showed extensive membrane damage, consistent with the observed impact of other amphiphilic compounds in literature. These polytriazoles are suited for applications in medical devices and implants, where major concerns over antibiotic resistance are prevalent. In the second approach, a series of symmetric, saturated diester phase change materials (PCMs) were also synthesized with superior latent heat values compared to commercial petrochemical analogues. These diesters exhibit melting temperatures between 39 °C and 77 °C, with latent heats greater than 220 J/g; much greater than paraffin waxes, which are currently the industry standard. Assessment of the trends between differing monomer lengths, in terms of number of CH2 groups of the 24 diesters synthesized exhibited structure/function dependencies in latent heat values and phase change temperatures, providing an understanding of the influence of each monomer on PCM thermal properties. A synthetic procedure was developed to produce these PCMs from a low value biodiesel feedstock. Application of these PCMs in the thermoregulation of hot beverages was demonstrated using a representative diester. This PCM cooled a freshly brewed hot beverage to a desired temperature within 1 minute, compared to 18 minutes required for the control. Furthermore, the PCM kept the beverage within the desired temperature range for 235 minutes, 40 % longer than the control. Author Keywords: Antimicrobial Surface, Click Chemistry, Green Chemistry, Phase Change Material, Polytriazole, Renewable
Molecular Dynamics Simulations of Aqueous and Confined Systems Relevant to the Supercritical Water Cooled Nuclear Reactor
Supercritical water (SCW) is the intended heat transfer fluid and potential neutron moderator in the proposed GEN-IV Supercritical Water Cooled Reactor (SCWR). The oxidative environment poses challenges in choosing appropriate design materials, and the behaviour of SCW within crevices of the passivation layer is needed for developing a corrosion control strategy to minimize corrosion. Molecular Dynamics simulations have been employed to obtain diffusion coefficients, coordination number and surface density characteristics, of water and chloride in nanometer-spaced iron hydroxide surfaces. Diffusion models for hydrazine are evaluated along with hydration data. Results demonstrate that water is more likely to accumulate on the surface at low density conditions. The effect of confinement on the water structure diminishes as the gap size increases. The diffusion coefficient of chloride decreases with larger surface spacing. Clustering of water at the surface implies that the SCWR will be most susceptible to pitting corrosion and stress corrosion cracking. Author Keywords: Confinement, Diffusion, Hydration, MD Simulations, Supercritcal Water
Supercritical Water Chemistry
Supercritical water (SCW) exhibits unique properties that differentiates it from its low temperature behaviour. Hydrogen bonding is dramatically reduced, there is no phase boundary between liquid and gaseous states, heat capacity increases, and there is a drastic reduction of the dielectric constant. Efforts are underway for researchers to harness these properties in the applications of power generation and hazardous waste destruction. However, the extreme environment created by the high temperatures, pressures and oxidizing capabilities pose unique challenges in terms of corrosion not present in subcritical water systems. Molecular Dynamics (MD) simulations have been used to obtain mass transport, hydration numbers and the influence on water structure of molecular oxygen, chloride, ammonia and iron (II) cations in corrosion crevices in an iron (II) hydroxide passivation layer. Solvation regimes marking the transitions of solvation based versus charge meditated processes were explored by locating the percolation thresholds of both physically and hydrogen bonded water clusters. A SCW flow through reactor was used to study hydrogen evolution rates over metal oxide surfaces, metal release rates and the kinetics for the oxidation of hydrogen gas by oxygen in SCW. Insights into corrosion phenomena are provided from the MD results as well as the experimental determination of flow reactor water and hydrogen chemistry. Author Keywords: Flow Studies, Molecular Dynamics, Supercritical Water
Model for the Differential Susceptibility of Strontium Titanate
The appearance of a two-dimensional electron gas (2DEG) in oxide interfaces between strontium titanate (STO) and other materials has become a major area of study. The behaviour of the 2DEG in STO is not well understood in part because the dielectric properties of STO are not well characterized. The differential susceptibility has a major impact on the electric fields within strontium titanate, and therefore to understand the 2DEG a better understanding of the susceptibility is needed. An expression for the soft mode phonon frequency of bulk strontium titanate is derived and used to model the susceptibility as a function of spatially homogeneous electric field, temperature and wavevector. This model is used to discuss the effect of spatially inhomogeneous electric fields and the local vs. nonlocal nature of the susceptibility. The critical exponents and the free energy are determined and discussed. Author Keywords: critical exponents, differential susceptibility, quantum paraelectric, strontium titanate
Mitigating Cold Flow Problems of Biodiesel
The present thesis explores the cold flow properties of biodiesel and the effect of vegetable oil derived compounds on the crystallization path as well as the mechanisms at play at different stages and length scales. Model systems including triacylglycerol (TAG) oils and their derivatives, and a polymer were tested with biodiesel. The goal was to acquire the fundamental knowledge that would help design cold flow improver (CFI) additives that would address effectively and simultaneously the flow problems of biodiesel, particularly the cloud point (CP) and pour point (PP). The compounds were revealed to be fundamentally vegetable oil crystallization modifiers (VOCM) and the polymer was confirmed to be a pour point depressant (PPD). The results obtained with the VOCMs indicate that two cis-unsaturated moieties combined with a trans-/saturated fatty acid is a critical structural architecture for depressing the crystallization onset by a mechanism wherein while the straight chain promotes a first packing with the linear saturated FAMEs, the kinked moieties prevent further crystallization. The study of model binary systems made of a VOCM and a saturated FAME with DSC, XRD and PLM provided a complete phase diagram including the thermal transformation lines, crystal structure and microstructure that impact the phase composition along the different crystallization stages, and elicited the competing effects of molecular mass, chain length mismatch and isomerism. The liquid-solid boundary is discussed in light of a simple thermodynamic model based on the Hildebrand equation and pair interactions. In order to test for synergies, the PP and CP of a biodiesel (Soy1500) supplemented with several VOCM and PLMA binary cocktails were measured using a specially designed method inspired by ASTM standards. The results were impressive, the combination of additives depressed CP and PP better than any single additive. The PLM and DSC results suggest that the cocktail additives are most effective when the right molecular structure and optimal concentration are provided. The cocktail mixture achieves then tiny crystals that are prevented from aggregating for an extended temperature range. The results of the study can be directly used for the design of functional and economical CFI from vegetable oils and their derivatives. Author Keywords: Biodiesel, Microstructure, Polymorphism, Pour point depressants, Triacylglycerol, Vegetable Oil Based Crystal Modifier
Correlating density of states features with localization strength in disordered interacting systems
Johri and Bhatt found singular behavior near the band edge in the density of states as well as in the inverse participation ratio of the Anderson model. These singularities mark a transition to an energy range dominated by resonant states. We study the interacting case using an ensemble of two-site Anderson-Hubbard systems. We find the ensemble-averaged density of states and generalized inverse participation ratio have more structure than in the non-interacting case because there are more transitions and in particular the transitions depend on the ground state. Nonetheless, there are regions of sharp decline in the generalized inverse participation ratio associated with specific density of state features. Moreover these features move closer to the Fermi level with the addition of interactions making them more experimentally accessible. Unfortunately resonances unique to interacting systems cannot be specifically identified. Author Keywords: Correlated electrons, Disorder, Localization
I have developed and improved a coherent anti-Stokes Raman scattering (CARS) microscope based on the spectral focusing (SF) technique. The CARS microscope uses an 800 nm oscillator and a photonic crystal fibre module to generate the supercontinuum Stokes. The photonic crystal fibre was originally designed to generate light beyond 945 nm which is useful for CARS microscopy in the CH/OH frequencies but essentially prevents access to the important fingerprint region at lower frequencies. With expert and nontraditional approaches to generating supercontinuum with sufficient power at wavelengths below 945 nm, I substantially extend the usefulness of the module for SF-CARS microscopy deep into the fingerprint region. Moreover, with the invention of a dynamic supercontinuum generation scheme we call "spectral surfing," I improve both the brightness of the CARS signal and extend the accessible CARS frequency range to frequencies as low as 350 cm$^{-1}$ and as high as 3500 cm$^{-1}$---all in a single scan-window. I demonstrate the capabilities of our broadband SF-CARS system through CARS and four-wave mixing hyperspectroscopy on samples such as astaxanthin, lily pollen and glass; liquid chemicals such as benzonitrile, nitrobenzene and dimethyl sulfoxide; and on pharmaceutical samples such as acetaminophen, ibuprofen, and cetirizine. Furthermore, In search of more useful Stokes supercontinuum sources, I compare the performance of two commercial photonic crystal fibre modules for use in SF-CARS applications, ultimately finding that one module provides better spectral characteristics for static supercontinuum use, while the other provides improved characteristics when spectral surfing is implemented. Author Keywords: coherent anti-Stokes Raman scattering, nonlinear microscopy, scanning microscopy, spectroscopy, supercontinuum generation, vibrational spectroscopy
Novel Aliphatic Lipid-Based Diesters for use in Lubricant Formulations
Structure-property relationships are increasingly valued for the identification of specifically engineered materials with properties optimized for targeted application(s). In this work, linear and branched diesters for use in lubricant formulations are prepared from lipid-based oleochemicals and their structure-property relationships reported. It is shown that the branched diesters possess exceptional physical property profiles, including suppression of crystallization, and are superior alternatives for use in lubricant formulations. For the linear aliphatic diesters, both high and low temperature properties were predictable functions of total chain length, and both were differently influenced by the fatty acid versus diol chain length. Symmetry did not influence either, although thermal stability decreased and thermal transition temperatures increased with increasing saturation. All of the linear diesters demonstrated Newtonian flow behaviour. Viscosity was also predictable as a function of total chain length; any microstructural features due to structural effects were superseded by mass effects. Author Keywords: Crystallization, Phase behaviour, Rheology, Structure-Function, Thermogravimetric analysis, Vegetable Oils
TWO-DIMENSIONAL CONDUCTIVITY AT LaAlO3/SrTiO3 INTERFACES
Experiments have observed a two-dimensional electron gas at the interface of two insulating oxides: strontium titanate (SrTiO3) and lanthanum aluminate (LaAlO3). These interfaces exhibit metallic, superconducting, and magnetic behaviours, which are strongly affected by impurities. Motivated by experiments, we introduce a simple model in which impurities lie at the interface. We treat the LaAlO3 as an insulator and model the SrTiO3 film. By solving a set of self-consistent Hartree equations for the charge density, we obtain the band structure of the SrTiO3 film. We then study the relative contributions made by the occupied bands to the two-dimensional conductivity of the LaAlO3/SrTiO3 interface. We find that the fractional conductivity of each band depends on several parameters: the mass anisotropy, the filling, and the impurity potential. Author Keywords: conductivity, impurities, insulating oxides, Two-dimensional electron gases

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