Water in silicate glasses

The speciation of water in a variety of hydrous silicate glasses, including simple and rhyolitic compositions, synthesized over a range of experimental conditions with up to 11 weight percent water has been determined using infrared spectroscopy. This technique has been calibrated with a series of standard glasses and provides a precise and accurate method for determining the concentrations of molecular water and hydroxyl groups in these glasses.

For all the compositions studied, most of the water is dissolved as hydroxyl groups at total water contents less than 3-4 weight percent; at higher total water contents, molecular water becomes the dominant species. For total water contents above 3-4 weight percent, the amount of water dissolved as hydroxyl groups is approximately constant at about 2 weight percent and additional water is incorporated as molecular water. Although there are small but measurable differences in the ratio of molecular water to hydroxyl groups at a given total water content among these silicate glasses, the speciation of water is similar over this range of composition. The trends in the concentrations of the H-bearing species in the hydrous glasses included in this study are similar to those observed in other silicate glasses using either infrared or NMR spectroscopy.

The effects of pressure and temperature on the speciation of water in albitic glasses have been investigated. The ratio of molecular water to hydroxyl groups at a given total water content is independent of the pressure and temperature of equilibration for albitic glasses synthesized in rapidly quenching piston cylinder apparatus at temperatures greater than 1000°C and pressures greater than 8 kbar. For hydrous glasses quenched from melts cooled at slower rates (i.e., in internally heated or in air-quench cold seal pressure vessels), there is an increase in the ratio of molecular water to hydroxyl group content that probably reflects reequilibration of the melt to lower temperatures during slow cooling.

Molecular water and hydroxyl group concentrations in glasses provide information on the dissolution mechanisms of water in silicate liquids. Several mixing models involving homogeneous equilibria of the form H_2O + O = 20H among melt species have been explored for albitic melts. These models can account for the measured species concentrations if the effects of non-ideal behavior or mixing of polymerized units are included, or by allowing for the presence of several different types of anhydrous species.

A thermodynamic model for hydrous albitic melts has been developed based on the assumption that the activity of water in the melt is equal to the mole fraction of molecular water determined by infrared spectroscopy. This model can account for the position of the watersaturated solidus of crystalline albite, the pressure and temperature dependence of the solubility of water in albitic melt, and the volumes of hydrous albitic melts. To the extent that it is successful, this approach provides a direct link between measured species concentrations in hydrous albitic glasses and the macroscopic thermodynamic properties of the albite-water system.

The approach taken in modelling the thermodynamics of hydrous albitic melts has been generalized to other silicate compositions. Spectroscopic measurements of species concentrations in rhyolitic and simple silicate glasses quenched from melts equilibrated with water vapor provide important constraints on the thermodynamic properties of these melt-water systems. In particular, the assumption that the activity of water is equal to the mole fraction of molecular water has been tested in detail and shown to be a valid approximation for a range of hydrous silicate melts and the partial molar volume of water in these systems has been constrained. Thus, the results of this study provide a useful thermodynamic description of hydrous melts that can be readily applied to other melt-water systems for which spectroscopic measurements of the H-bearing species are available.

Control of wettability of carbon nanotube array by reversible dry oxidation for superhydrophobic coating and supercapacitor applications

In this thesis, dry chemical modification methods involving UV/ozone, oxygen plasma, and vacuum annealing treatments are explored to precisely control the wettability of CNT arrays. By varying the exposure time of these treatments the surface concentration of oxygenated groups adsorbed on the CNT arrays can be controlled. CNT arrays with very low amount of oxygenated groups exhibit a superhydrophobic behavior. In addition to their extremely high static contact angle, they cannot be dispersed in DI water and their impedance in aqueous electrolytes is extremely high. These arrays have an extreme water repellency capability such that a water droplet will bounce off of their surface upon impact and a thin film of air is formed on their surface as they are immersed in a deep pool of water. In contrast, CNT arrays with very high surface concentration of oxygenated functional groups exhibit an extreme hydrophilic behavior. In addition to their extremely low static contact angle, they can be dispersed easily in DI water and their impedance in aqueous electrolytes is tremendously low. Since the bulk structure of the CNT arrays are preserved during the UV/ozone, oxygen plasma, and vacuum annealing treatments, all CNT arrays can be repeatedly switched between superhydrophilic and superhydrophobic, as long as their O/C ratio is kept below 18%.

The effect of oxidation using UV/ozone and oxygen plasma treatments is highly reversible as long as the O/C ratio of the CNT arrays is kept below 18%. At O/C ratios higher than 18%, the effect of oxidation is no longer reversible. This irreversible oxidation is caused by irreversible changes to the CNT atomic structure during the oxidation process. During the oxidation process, CNT arrays undergo three different processes. For CNT arrays with O/C ratios lower than 40%, the oxidation process results in the functionalization of CNT outer walls by oxygenated groups. Although this functionalization process introduces defects, vacancies and micropores opening, the graphitic structure of the CNT is still largely intact. For CNT arrays with O/C ratios between 40% and 45%, the oxidation process results in the etching of CNT outer walls. This etching process introduces large scale defects and holes that can be obviously seen under TEM at high magnification. Most of these holes are found to be several layers deep and, in some cases, a large portion of the CNT side walls are cut open. For CNT arrays with O/C ratios higher than 45%, the oxidation process results in the exfoliation of the CNT walls and amorphization of the remaining CNT structure. This amorphization process can be implied from the disappearance of C-C sp2 peak in the XPS spectra associated with the pi-bond network.

The impact behavior of water droplet impinging on superhydrophobic CNT arrays in a low viscosity regime is investigated for the first time. Here, the experimental data are presented in the form of several important impact behavior characteristics including critical Weber number, volume ratio, restitution coefficient, and maximum spreading diameter. As observed experimentally, three different impact regimes are identified while another impact regime is proposed. These regimes are partitioned by three critical Weber numbers, two of which are experimentally observed. The volume ratio between the primary and the secondary droplets is found to decrease with the increase of Weber number in all impact regimes other than the first one. In the first impact regime, this is found to be independent of Weber number since the droplet remains intact during and subsequent to the impingement. Experimental data show that the coefficient of restitution decreases with the increase of Weber number in all impact regimes. The rate of decrease of the coefficient of restitution in the high Weber number regime is found to be higher than that in the low and moderate Weber number. Experimental data also show that the maximum spreading factor increases with the increase of Weber number in all impact regimes. The rate of increase of the maximum spreading factor in the high Weber number regime is found to be higher than that in the low and moderate Weber number. Phenomenological approximations and interpretations of the experimental data, as well as brief comparisons to the previously proposed scaling laws, are shown here.

Dry oxidation methods are used for the first time to characterize the influence of oxidation on the capacitive behavior of CNT array EDLCs. The capacitive behavior of CNT array EDLCs can be tailored by varying their oxygen content, represented by their O/C ratio. The specific capacitance of these CNT arrays increases with the increase of their oxygen content in both KOH and Et4NBF4/PC electrolytes. As a result, their gravimetric energy density increases with the increase of their oxygen content. However, their gravimetric power density decreases with the increase of their oxygen content. The optimally oxidized CNT arrays are able to withstand more than 35,000 charge/discharge cycles in Et4NBF4/PC at a current density of 5 A/g while only losing 10% of their original capacitance.

Tools for the study of dynamical spacetimes

This thesis covers a range of topics in numerical and analytical relativity, centered around introducing tools and methodologies for the study of dynamical spacetimes. The scope of the studies is limited to classical (as opposed to quantum) vacuum spacetimes described by Einstein's general theory of relativity. The numerical works presented here are carried out within the Spectral Einstein Code (SpEC) infrastructure, while analytical calculations extensively utilize Wolfram's Mathematica program.

We begin by examining highly dynamical spacetimes such as binary black hole mergers, which can be investigated using numerical simulations. However, there are difficulties in interpreting the output of such simulations. One difficulty stems from the lack of a canonical coordinate system (henceforth referred to as gauge freedom) and tetrad, against which quantities such as Newman-Penrose Psi_4 (usually interpreted as the gravitational wave part of curvature) should be measured. We tackle this problem in Chapter 2 by introducing a set of geometrically motivated coordinates that are independent of the simulation gauge choice, as well as a quasi-Kinnersley tetrad, also invariant under gauge changes in addition to being optimally suited to the task of gravitational wave extraction.

Another difficulty arises from the need to condense the overwhelming amount of data generated by the numerical simulations. In order to extract physical information in a succinct and transparent manner, one may define a version of gravitational field lines and field strength using spatial projections of the Weyl curvature tensor. Introduction, investigation and utilization of these quantities will constitute the main content in Chapters 3 through 6.

For the last two chapters, we turn to the analytical study of a simpler dynamical spacetime, namely a perturbed Kerr black hole. We will introduce in Chapter 7 a new analytical approximation to the quasi-normal mode (QNM) frequencies, and relate various properties of these modes to wave packets traveling on unstable photon orbits around the black hole. In Chapter 8, we study a bifurcation in the QNM spectrum as the spin of the black hole a approaches extremality.

Density functional theory embedding for correlated wavefunctions

Methods that exploit the intrinsic locality of molecular interactions show significant promise in making tractable the electronic structure calculation of large-scale systems. In particular, embedded density functional theory (e-DFT) offers a formally exact approach to electronic structure calculations in which the interactions between subsystems are evaluated in terms of their electronic density. In the following dissertation, methodological advances of embedded density functional theory are described, numerically tested, and applied to real chemical systems.

First, we describe an e-DFT protocol in which the non-additive kinetic energy component of the embedding potential is treated exactly. Then, we present a general implementation of the exact calculation of the non-additive kinetic potential (NAKP) and apply it to molecular systems. We demonstrate that the implementation using the exact NAKP is in excellent agreement with reference Kohn-Sham calculations, whereas the approximate functionals lead to qualitative failures in the calculated energies and equilibrium structures.

Next, we introduce density-embedding techniques to enable the accurate and stable calculation of correlated wavefunction (CW) in complex environments. Embedding potentials calculated using e-DFT introduce the effect of the environment on a subsystem for CW calculations (WFT-in-DFT). We demonstrate that WFT-in-DFT calculations are in good agreement with CW calculations performed on the full complex.

We significantly improve the numerics of the algorithm by enforcing orthogonality between subsystems by introduction of a projection operator. Utilizing the projection-based embedding scheme, we rigorously analyze the sources of error in quantum embedding calculations in which an active subsystem is treated using CWs, and the remainder using density functional theory. We show that the embedding potential felt by the electrons in the active subsystem makes only a small contribution to the error of the method, whereas the error in the nonadditive exchange-correlation energy dominates. We develop an algorithm which corrects this term and demonstrate the accuracy of this corrected embedding scheme.

The Equation of State and Petrogenesis of Komatiite

(1) Equation of State of Komatiite

The equation of state (EOS) of a molten komatiite (27 wt% MgO) was detennined in the 5 to 36 GPa pressure range via shock wave compression from 1550°C and 0 bar. Shock wave velocity, U_S, and particle velocity, U_P, in km/s follow the linear relationship U_S = 3.13(±0.03) + 1.47(±0.03) U_P. Based on a calculated density at 1550°C, 0 bar of 2.745±0.005 glee, this U_S-U_P relationship gives the isentropic bulk modulus K_S = 27.0 ± 0.6 GPa, and its first and second isentropic pressure derivatives, K'_S = 4.9 ± 0.1 and K"_S = -0.109 ± 0.003 GPa^-1.

The calculated liquidus compression curve agrees within error with the static compression results of Agee and Walker [1988a] to 6 GPa. We detennine that olivine (FO₉₄) will be neutrally buoyant in komatiitic melt of the composition we studied near 8.2 GPa. Clinopyroxene would also be neutrally buoyant near this pressure. Liquidus garnet-majorite may be less dense than this komatiitic liquid in the 20-24 GPa interval, however pyropic-garnet and perovskite phases are denser than this komatiitic liquid in their respective liquidus pressure intervals to 36 GPa. Liquidus perovskite may be neutrally buoyant near 70 GPa.

At 40 GPa, the density of shock-compressed molten komatiite would be approximately equal to the calculated density of an equivalent mixture of dense solid oxide components. This observation supports the model of Rigden et al. [1989] for compressibilities of liquid oxide components. Using their theoretical EOS for liquid forsterite and fayalite, we calculate the densities of a spectrum of melts from basaltic through peridotitic that are related to the experimentally studied komatiitic liquid by addition or subtraction of olivine. At low pressure, olivine fractionation lowers the density of basic magmas, but above 14 GPa this trend is reversed. All of these basic to ultrabasic liquids are predicted to have similar densities at 14 GPa, and this density is approximately equal to the bulk (PREM) mantle. This suggests that melts derived from a peridotitic mantle may be inhibited from ascending from depths greater than 400 km.

The EOS of ultrabasic magmas was used to model adiabatic melting in a peridotitic mantle. If komatiites are formed by >15% partial melting of a peridotitic mantle, then komatiites generated by adiabatic melting come from source regions in the lower transition zone (≈500-670 km) or the lower mantle (>670 km). The great depth of incipient melting implied by this model, and the melt density constraint mentioned above, suggest that komatiitic volcanism may be gravitationally hindered. Although komatiitic magmas are thought to separate from their coexisting crystals at a temperature =200°C greater than that for modern MORBs, their ultimate sources are predicted to be diapirs that, if adiabatically decompressed from initially solid mantle, were more than 700°C hotter than the sources of MORBs and derived from great depth.

We considered the evolution of an initially molten mantle, i.e., a magma ocean. Our model considers the thermal structure of the magma ocean, density constraints on crystal segregation, and approximate phase relationships for a nominally chondritic mantle. Crystallization will begin at the core-mantle boundary. Perovskite buoyancy at > 70 GPa may lead to a compositionally stratified lower mantle with iron-enriched mangesiowiistite content increasing with depth. The upper mantle may be depleted in perovskite components. Olivine neutral buoyancy may lead to the formation of a dunite septum in the upper mantle, partitioning the ocean into upper and lower reservoirs, but this septum must be permeable.

(2) Viscosity Measurement with Shock Waves

We have examined in detail the analytical method for measuring shear viscosity from the decay of perturbations on a corrugated shock front The relevance of initial conditions, finite shock amplitude, bulk viscosity, and the sensitivity of the measurements to the shock boundary conditions are discussed. The validity of the viscous perturbation approach is examined by numerically solving the second-order Navier-Stokes equations. These numerical experiments indicate that shock instabilities may occur even when the Kontorovich-D'yakov stability criteria are satisfied. The experimental results for water at 15 GPa are discussed, and it is suggested that the large effective viscosity determined by this method may reflect the existence of ice VII on the Rayleigh path of the Hugoniot This interpretation reconciles the experimental results with estimates and measurements obtained by other means, and is consistent with the relationship of the Hugoniot with the phase diagram for water. Sound waves are generated at 4.8 MHz at in the water experiments at 15 GPa. The existence of anelastic absorption modes near this frequency would also lead to large effective viscosity estimates.

(3) Equation of State of Molybdenum at 1400°C

Shock compression data to 96 GPa for pure molybdenum, initially heated to 1400°C, are presented. Finite strain analysis of the data gives a bulk modulus at 1400°C, K'_S. of 244±2 GPa and its pressure derivative, K'_OS of 4. A fit of shock velocity to particle velocity gives the coefficients of U_S = C_O+S U_P to be C_O = 4.77±0.06 km/s and S = 1.43±0.05. From the zero pressure sound speed, C_O, a bulk modulus of 232±6 GPa is calculated that is consistent with extrapolation of ultrasonic elasticity measurements. The temperature derivative of the bulk modulus at zero pressure, θK_OSθT|_P, is approximately -0.012 GPa/K. A thermodynamic model is used to show that the thermodynamic Grüneisen parameter is proportional to the density and independent of temperature. The Mie-Grüneisen equation of state adequately describes the high temperature behavior of molybdenum under the present range of shock loading conditions.

Development and Application of Embedding Methods for the Simulation of Large Chemical Systems

The high computational cost of correlated wavefunction theory (WFT) calculations has motivated the development of numerous methods to partition the description of large chemical systems into smaller subsystem calculations. For example, WFT-in-DFT embedding methods facilitate the partitioning of a system into two subsystems: a subsystem A that is treated using an accurate WFT method, and a subsystem B that is treated using a more efficient Kohn-Sham density functional theory (KS-DFT) method. Representation of the interactions between subsystems is non-trivial, and often requires the use of approximate kinetic energy functionals or computationally challenging optimized effective potential calculations; however, it has recently been shown that these challenges can be eliminated through the use of a projection operator. This dissertation describes the development and application of embedding methods that enable accurate and efficient calculation of the properties of large chemical systems.

Chapter 1 introduces a method for efficiently performing projection-based WFT-in-DFT embedding calculations on large systems. This is accomplished by using a truncated basis set representation of the subsystem A wavefunction. We show that naive truncation of the basis set associated with subsystem A can lead to large numerical artifacts, and present an approach for systematically controlling these artifacts.

Chapter 2 describes the application of the projection-based embedding method to investigate the oxidative stability of lithium-ion batteries. We study the oxidation potentials of mixtures of ethylene carbonate (EC) and dimethyl carbonate (DMC) by using the projection-based embedding method to calculate the vertical ionization energy (IE) of individual molecules at the CCSD(T) level of theory, while explicitly accounting for the solvent using DFT. Interestingly, we reveal that large contributions to the solvation properties of DMC originate from quadrupolar interactions, resulting in a much larger solvent reorganization energy than that predicted using simple dielectric continuum models. Demonstration that the solvation properties of EC and DMC are governed by fundamentally different intermolecular interactions provides insight into key aspects of lithium-ion batteries, with relevance to electrolyte decomposition processes, solid-electrolyte interphase formation, and the local solvation environment of lithium cations.

On an embedding property of generalized Carter subgroups

If E and F are saturated formations, we say that E is strongly contained in F if for any solvable group G with E-subgroup, E, and F-subgroup, F, some conjugate of E is contained in F. In this paper, we investigate the problem of finding the formations which strongly contain a fixed saturated formation E.

Our main results are restricted to formations, E, such that E = {G|G/F(G) ϵT}, where T is a non-empty formation of solvable groups, and F(G) is the Fitting subgroup of G. If T consists only of the identity, then E=N, the class of nilpotent groups, and for any solvable group, G, the N-subgroups of G are the Carter subgroups of G.

We give a characterization of strong containment which depends only on the formations E, and F. From this characterization, we prove:

If T is a non-empty formation of solvable groups, E = {G|G/F(G) ϵT}, and E is strongly contained in F, then

(1) there is a formation V such that F = {G|G/F(G) ϵV}.

(2) If for each prime p, we assume that T does not contain the class, S_p’, of all solvable p’-groups, then either E = F, or F contains all solvable groups.

This solves the problem for the Carter subgroups.

We prove the following result to show that the hypothesis of (2) is not redundant:

If R = {G|G/F(G) ϵS_r’}, then there are infinitely many formations which strongly contain R.

The oculomotor system: (1) Vertical-horizontal interaction and signal recognition, (2) Time delays and power spectra

In the first section of this thesis, two-dimensional properties of the human eye movement control system were studied. The vertical - horizontal interaction was investigated by using a two-dimensional target motion consisting of a sinusoid in one of the directions vertical or horizontal, and low-pass filtered Gaussian random motion of variable bandwidth (and hence information content) in the orthogonal direction. It was found that the random motion reduced the efficiency of the sinusoidal tracking. However, the sinusoidal tracking was only slightly dependent on the bandwidth of the random motion. Thus the system should be thought of as consisting of two independent channels with a small amount of mutual cross-talk.

These target motions were then rotated to discover whether or not the system is capable of recognizing the two-component nature of the target motion. That is, the sinusoid was presented along an oblique line (neither vertical nor horizontal) with the random motion orthogonal to it. The system did not simply track the vertical and horizontal components of motion, but rotated its frame of reference so that its two tracking channels coincided with the directions of the two target motion components. This recognition occurred even when the two orthogonal motions were both random, but with different bandwidths.

In the second section, time delays, prediction and power spectra were examined. Time delays were calculated in response to various periodic signals, various bandwidths of narrow-band Gaussian random motions and sinusoids. It was demonstrated that prediction occurred only when the target motion was periodic, and only if the harmonic content was such that the signal was sufficiently narrow-band. It appears as if general periodic motions are split into predictive and non-predictive components.

For unpredictable motions, the relationship between the time delay and the average speed of the retinal image was linear. Based on this I proposed a model explaining the time delays for both random and periodic motions. My experiments did not prove that the system is sampled data, or that it is continuous. However, the model can be interpreted as representative of a sample data system whose sample interval is a function of the target motion.

It was shown that increasing the bandwidth of the low-pass filtered Gaussian random motion resulted in an increase of the eye movement bandwidth. Some properties of the eyeball-muscle dynamics and the extraocular muscle "active state tension" were derived.