1. Astronomical photometry at wavelengths of 8.5, 10.5, and 11.6 µm. 2. Infrared emission from asteroids at wavelengths of 8.5, 10.5, and 11.6 µm

The purpose of this thesis is to present new observations of thermal-infrared radiation from asteroids. Stellar photometry was performed to provide standards for comparison with the asteroid data. The details of the photometry and the data reduction are discussed in Part 1. A system of standard stars is derived for wavelengths of 8.5, 10.5 and 11.6 µm and a new calibration is adopted. Sources of error are evaluated and comparisons are made with the data of other observers.

The observations and analysis of the thermal-emission observations of asteroids are presented in Part 2. Thermal-emission lightcurve and phase effect data are considered. Special color diagrams are introduced to display the observational data. These diagrams are free of any model-dependent assumptions and show that asteroids differ in their surface properties.

On the basis of photometric models, (4) Vesta is thought to have a bolometric Bond albedo of about 0.1, an emissivity greater than 0.7 and a true radius that is close to the model value of 300^(+50)_(-30)km. Model albedos and model radii are given for asteroids 1, 2, 4, 5, 6, 7, 15, 19, 20, 27, 39, 44, 68, 80, 324 and 674. The asteroid (324) Bamberga is extremely dark with a model (~bolometric Bond) albedo in the 0.01 - 0.02 range, which is thought to be the lowest albedo yet measured for any solar-system body. The crucial question about such low-albedo asteroids is their number and the distribution of their orbits.

Theoretical and experimental investigations of the flocculation of charged particles in aqueous solutions by polyelectrolytes of opposite charge

An electrostatic mechanism for the flocculation of charged particles by polyelectrolytes of opposite charge is proposed. The difference between this and previous electrostatic coagulation mechanisms is the formation of charged polyion patches on the oppositely charged surfaces. The size of a patch is primarily a function of polymer molecular weight and the total patch area is a function of the amount of polymer adsorbed. The theoretical predictions of the model agree with the experimental dependence of the polymer dose required for flocculation on polymer molecular weight and solution ionic strength.

A theoretical analysis based on the Derjaguin-Landau, Verwey- Overbeek electrical double layer theory and statistical mechanical treatments of adsorbed polymer configurations indicates that flocculation of charged particles in aqueous solutions by polyelectrolytes of opposite charge does not occur by the commonly accepted polymerbridge mechanism.

A series of 1, 2-dimethyl-5 -vinylpyridinium bromide polymers with a molecular weight range of 6x10^3 to 5x10^6 was synthesized and used to flocculate dilute polystyrene latex and silica suspensions in solutions of various ionic strengths. It was found that with high molecular weight polymers and/or high ionic strengths the polymer dose required for flocculation is independent of molecular weight. With low molecular weights and/or low ionic strengths, the flocculation dose decreases with increasing molecular weight.

Nanophotonic Light Trapping In Thin Solar Cells

Over the last several decades there have been significant advances in the study and understanding of light behavior in nanoscale geometries. Entire fields such as those based on photonic crystals, plasmonics and metamaterials have been developed, accelerating the growth of knowledge related to nanoscale light manipulation. Coupled with recent interest in cheap, reliable renewable energy, a new field has blossomed, that of nanophotonic solar cells.

In this thesis, we examine important properties of thin-film solar cells from a nanophotonics perspective. We identify key differences between nanophotonic devices and traditional, thick solar cells. We propose a new way of understanding and describing limits to light trapping and show that certain nanophotonic solar cell designs can have light trapping limits above the so called ray-optic or ergodic limit. We propose that a necessary requisite to exceed the traditional light trapping limit is that the active region of the solar cell must possess a local density of optical states (LDOS) higher than that of the corresponding, bulk material. Additionally, we show that in addition to having an increased density of states, the absorber must have an appropriate incoupling mechanism to transfer light from free space into the optical modes of the device. We outline a portfolio of new solar cell designs that have potential to exceed the traditional light trapping limit and numerically validate our predictions for select cases.

We emphasize the importance of thinking about light trapping in terms of maximizing the optical modes of the device and efficiently coupling light into them from free space. To further explore these two concepts, we optimize patterns of superlattices of air holes in thin slabs of Si and show that by adding a roughened incoupling layer the total absorbed current can be increased synergistically. We suggest that the addition of a random scattering surface to a periodic patterning can increase incoupling by lifting the constraint of selective mode occupation associated with periodic systems.

Lastly, through experiment and simulation, we investigate a potential high efficiency solar cell architecture that can be improved with the nanophotonic light trapping concepts described in this thesis. Optically thin GaAs solar cells are prepared by the epitaxial liftoff process by removal from their growth substrate and addition of a metallic back reflector. A process of depositing large area nano patterns on the surface of the cells is developed using nano imprint lithography and implemented on the thin GaAs cells.

I. Quantum mechanics of one-dimensional two-particle models. II. A quantum mechanical treatment of inelastic collisions

Part I

Solutions of Schrödinger’s equation for system of two particles bound in various stationary one-dimensional potential wells and repelling each other with a Coulomb force are obtained by the method of finite differences. The general properties of such systems are worked out in detail for the case of two electrons in an infinite square well. For small well widths (1-10 a.u.) the energy levels lie above those of the noninteresting particle model by as much as a factor of 4, although excitation energies are only half again as great. The analytical form of the solutions is obtained and it is shown that every eigenstate is doubly degenerate due to the “pathological” nature of the one-dimensional Coulomb potential. This degeneracy is verified numerically by the finite-difference method. The properties of the square-well system are compared with those of the free-electron and hard-sphere models; perturbation and variational treatments are also carried out using the hard-sphere Hamiltonian as a zeroth-order approximation. The lowest several finite-difference eigenvalues converge from below with decreasing mesh size to energies below those of the “best” linear variational function consisting of hard-sphere eigenfunctions. The finite-difference solutions in general yield expectation values and matrix elements as accurate as those obtained using the “best” variational function.

The system of two electrons in a parabolic well is also treated by finite differences. In this system it is possible to separate the center-of-mass motion and hence to effect a considerable numerical simplification. It is shown that the pathological one-dimensional Coulomb potential gives rise to doubly degenerate eigenstates for the parabolic well in exactly the same manner as for the infinite square well.

Part II

A general method of treating inelastic collisions quantum mechanically is developed and applied to several one-dimensional models. The formalism is first developed for nonreactive “vibrational” excitations of a bound system by an incident free particle. It is then extended to treat simple exchange reactions of the form A + BC →AB + C. The method consists essentially of finding a set of linearly independent solutions of the Schrödinger equation such that each solution of the set satisfies a distinct, yet arbitrary boundary condition specified in the asymptotic region. These linearly independent solutions are then combined to form a total scattering wavefunction having the correct asymptotic form. The method of finite differences is used to determine the linearly independent functions.

The theory is applied to the impulsive collision of a free particle with a particle bound in (1) an infinite square well and (2) a parabolic well. Calculated transition probabilities agree well with previously obtained values.

Several models for the exchange reaction involving three identical particles are also treated: (1) infinite-square-well potential surface, in which all three particles interact as hard spheres and each two-particle subsystem (i.e. BC and AB) is bound by an attractive infinite-square-well potential; (2) truncated parabolic potential surface, in which the two-particle subsystems are bound by a harmonic oscillator potential which becomes infinite for interparticle separations greater than a certain value; (3) parabolic (untruncated) surface. Although there are no published values with which to compare our reaction probabilities, several independent checks on internal consistency indicate that the results are reliable.

Dynamic response of hysteretic systems with application to a system containing limited slip

A general class of single degree of freedom systems possessing rate-independent hysteresis is defined. The hysteretic behavior in a system belonging to this class is depicted as a sequence of single-valued functions; at any given time, the current function is determined by some set of mathematical rules concerning the entire previous response of the system. Existence and uniqueness of solutions are established and boundedness of solutions is examined.

An asymptotic solution procedure is used to derive an approximation to the response of viscously damped systems with a small hysteretic nonlinearity and trigonometric excitation. Two properties of the hysteresis loops associated with any given system completely determine this approximation to the response: the area enclosed by each loop, and the average of the ascending and descending branches of each loop.

The approximation, supplemented by numerical calculations, is applied to investigate the steady-state response of a system with limited slip. Such features as disconnected response curves and jumps in response exist for a certain range of system parameters for any finite amount of slip.

To further understand the response of this system, solutions of the initial-value problem are examined. The boundedness of solutions is investigated first. Then the relationship between initial conditions and resulting steady-state solution is examined when multiple steady-state solutions exist. Using the approximate analysis and numerical calculations, it is found that significant regions of initial conditions in the initial condition plane lead to the different asymptotically stable steady-state solutions.