Thesis (Ph. D.)--University of Wisconsin--Madison, 1952. / Typescript. Includes abstract and vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 91-93).

N. Fatica's Thesis--University of Michigan. / "Reprinted from Chemical engineering progress, November, 1949."

Thesis (PH.D.) -- Syracuse University, 2006 / "Publication number AAT 3251759."

Thesis (PH.D.) -- Syracuse University, 2006 / "Publication number AAT 3251776."

The effects of salts on the behavior of polyelectrolyte systems were investigated. The phase behavior of polyelectrolyte solutions in the presence of added salt was calculated by combining the free energies due to Flory-Huggins mixing and Debye-Huckel electrostatics, with both terms modified for our polyelectrolyte solutions. Using the calculated phase diagrams, we found that most results give a typical polymer-solvent-nonsolvent phase diagram, with the solvent acting as a “nonsolvent” (since we assume that the polymer-solvent interaction parameter, χ, is positive) and the dissociated salt acting as a “solvent”. However, for high charges of the salt ions, we found a completely different phase diagram, one which can be explained by a “salting out effect” where the addition of salt over a certain concentration threshold causes complete phase separation over all concentrations of polymer and solvent. Also, the density and repulsive force profiles for a system comprised of two parallel, planar, uncharged surfaces uniformly covered with poly electrolyte brushes in an electrolyte solution was calculated using a computational enumeration of a one-dimensional random walk model. For large surface separations, we found three different density profiles: a Gaussian regime when κ is large, a stretched regime when κ is intermediate in value, and a “pancake” regime, with chains collapsed onto their grafted surface, when κ is small. For small surface separations, the first two regimes are replaced with an interpenetrating regime, where the density is essentially uniform across the entire region between the surfaces. For intermediate surface separations, the repulsive force scales as exp[special characters omitted] unlike what is expected using Gouy-Chapman theory.

A generic scenario of a crossover between weak-coupling and strong-coupling limits of a many-body quantum system is studied. Powerful numerical methods of investigating the strongly correlated regime are developed and applied to answering a number of important questions of the strongly correlated fermions physics. The internal structure of an exciton in an insulating medium is studied throughout the crossover between the (analytically solvable) strong- and weak-coupling limits. In the intermediate regime, accurate results for the exciton ground state are obtained and used to establish the limits of applicability of the corresponding limiting cases for the first time. A novel combination of the diagrammatic determinant Monte Carlo and the worm algorithm is developed and used for investigating the unitarity regime of the BEC-BCS crossover via simulating the dilute Fermi-Hubbard model. Superfluid phase transition and thermodynamic properties of the normal state are characterized for both lattice fermions and continuum unitary Fermi gas. The relation to current experiments with trapped ultracold quantum gases is discussed.

This thesis will review my experimental efforts in measuring charge transport using on-chip and scanning probe techniques at the nanometer size scale, as well as numerical investigations into the charge transport of a single molecular C60 transistor [H. Park et al., Nature (London) 407, 57 (2000)]. Experimentally, I report on efforts to utilize on-chip and scanning probe electronic interfacing for chemical and biological systems for which we expect charge transport measurements to reveal interesting and technologically relevant information. Theoretically, I show how the microscopic force fields in nanostructures can influence their electronic dynamics using the example calculations of a molecular single electron transistor (SET) with a single mode, linearly coupled vibrational environment. These calculations predict a novel negative differential conductance (NDC) effect due to the Franck-Condon quantum dynamics of charged, "vibrating" SET islands in a mechanically soft potential well.

When a water-soluble polyelectrolyte is combined with an oppositely-charged surfactant solution at a stoichiometric charge ratio, self-assembly into a highly ordered, water-insoluble complex can occur. These materials exhibit phase structures which are analogous to their pure surfactant components, and significant effort has been made in the past several decades to characterize, predict, and control the various morphologies observed in these systems. However, a truly comprehensive understanding of the phase behavior of these systems is lacking. The purpose of this project is to establish general phase diagrams for self-assembled, stoichiometric poly(acrylate-co-acrylamide)-cetyltrimethylammonium halide (PAAm-CTAX) complexes by studying phase structure as a function of ionic strength, salt type, polyelectrolyte charge density, temperature, and applied osmotic pressure with small-angle X-ray scattering (SAXS). By developing a deeper understanding of the phase behavior and energetics of such a model system, it is hoped that general trends can be extrapolated to other polyelectrolyte-surfactant systems, such as polysaccharide-surfactant systems, which may provide the means to template desired structures in nanoporous, biocompatible matrices. Materials such as these may be attractive targets for drug delivery and nanoscale separation applications.

We study the superfluid transition of weakly interacting Bose gases, classical fields and related systems in two dimensions, where it is a Berezinskii-Kosterlitz-Thouless transition, and in three dimensions, where it is a U(1) transition accompanied by the onset of Bose-Einstein condensation. We show that for small interaction strength U, these systems can be described by a :Ψ:4 model based on classical complex fields and we establish universal behavior among systems of different microscopical details, such as classical and quantum, continuous and lattice. By numerical simulations of the classical lattice field, using Worm Algorithm, we solve all relevant thermodynamical functions of this system, which are density, condensate density (in 3D), superfluid density and quasi-condensate. Through universality considerations, we can translate these results to all systems which can be described by a :Ψ:4 model based on a classical complex field. Our results cover the fluctuation region and extend into mean field and critical region, where we connect them to results of mean field theory and renormalization group theory respectively. We also establish that the quasicondensate, which exists in two and three dimensions, is a basis for a more accurate mean field theory treatment than the condensate, which exists only in three dimensions.

The fact that two-dimensional interacting trapped systems do not undergo Bose-Einstein Condensation (BEC) in the thermodynamic limit, though rigorously proved, is somewhat mysterious because all relevant limiting cases (zero temperature, small atom numbers, noninteracting particles) suggest otherwise. We study the possibility of condensation in finite trapped two-dimensional systems. We first consider the ideal gas, which incorporates the inhomogeneity and finite size of experimental systems and can be solved exactly. A semiclassical self-consistent approximation gives us a feel for the temperature scales; diagonalization of the one-body density matrix confirms that the condensation is into a single state. We squeeze a three-dimensional system and see how it crosses over into two dimensions. Mean-field theory, our main tool for the study of interacting systems, prescribes coupled equations for the condensate and the thermal cloud: the condensate receives a full quantum-mechanical treatment, while the noncondensate is described by different schemes of varying sophistication. We analyze the T = 0 case and its approach to the thermodynamic limit, finding a criterion for the dimensionality crossover and obtaining the coupling constant of the two-dimensional system that results from squeezing a three-dimensional trap. We next apply a semiclassical Hartree-Fock approximation to purely two-dimensional finite gases and find that they can be described either with or without a condensate; this continues to be true in the thermodynamic limit. The condensed solutions have a lower free energy at all temperatures but neglect the presence of phonons within the system and cease to exist when we allow for this possibility. The uncondensed solutions, in turn, are valid under a more rigorous scheme but have consistency problems of their own. Path-integral Monte Carlo simulations provide an essentially exact description of finite interacting gases and enable us to study highly anisotropic systems at finite temperature. We find that our two-dimensional Hartree-Fock solutions accurately mimic the surface density profile and predict the condensate fraction of these systems; the equivalent interaction parameter is smaller than that dictated by the T = 0 analysis. We conclude that, in two-dimensional isotropic finite trapped systems and in highly compressed three-dimensional gases, there is a phenomenon resembling a condensation into a single state.