I. Efforts toward the synthesis of aliphatic iodonium salts. II. Flourine-19 nuclear magnetic resonance spectroscopy of cyclic and bicyclic systems

The synthesis of iodonium salts of the general formula [C₆H₅IR]⁺X^-, where R is an alkyl group and x- is a stabilizing anion, was attempted. For the choice of R three groups were selected, whose derivatives are known to be sluggish in S_N1 and S_N2 substitutions: cyclopropyl, 7, 7 -dimethyl-1-norbornyl, and 9 -triptycyl. The synthetic routes followed along classical lines which have been exploited in recent years by Beringer and students. Ultimately, the object of the present study was to study the reactions of the above salts with nucleophiles. In none of the three cases, however, was it possible to isolate a stable salt. A thermodynamic argument suggests that this must be due to kinetic instability rather than thermodynamic instability. Only iodocyclopropane and 1-iodoapocamphane formed isolable iododichlorides.

Several methylated 2, 2-difluoronorbornanes were prepared with the intent of correlating fluorine -19 chemical shifts with geometric features in a rigid system. The effect of a methyl group on the shielding of a β -fluorine is dependent upon the dihedral angle; the maximum effect (an upfield shift of the resonance) occurs at 0° and 180°, whereas almost no effect is felt at a dihedral angle of 120°. The effect of a methyl group on a γ -fluorine is to strongly shift the resonance downfield when fluorine and methyl group are in a 1, 3 - diaxial-like relationship. Molecular orbital calculations of fluorine shielding in a variety of molecules were carried out using the formalism developed by Pople; the results are, at best, in modest agreement with experiment.

Generalized modal identification of linear and nonlinear dynamic systems

This dissertation is concerned with the problem of determining the dynamic characteristics of complicated engineering systems and structures from the measurements made during dynamic tests or natural excitations. Particular attention is given to the identification and modeling of the behavior of structural dynamic systems in the nonlinear hysteretic response regime. Once a model for the system has been identified, it is intended to use this model to assess the condition of the system and to predict the response to future excitations.

A new identification methodology based upon a generalization of the method of modal identification for multi-degree-of-freedom dynaimcal systems subjected to base motion is developed. The situation considered herein is that in which only the base input and the response of a small number of degrees-of-freedom of the system are measured. In this method, called the generalized modal identification method, the response is separated into "modes" which are analogous to those of a linear system. Both parametric and nonparametric models can be employed to extract the unknown nature, hysteretic or nonhysteretic, of the generalized restoring force for each mode.

In this study, a simple four-term nonparametric model is used first to provide a nonhysteretic estimate of the nonlinear stiffness and energy dissipation behavior. To extract the hysteretic nature of nonlinear systems, a two-parameter distributed element model is then employed. This model exploits the results of the nonparametric identification as an initial estimate for the model parameters. This approach greatly improves the convergence of the subsequent optimization process.

The capability of the new method is verified using simulated response data from a three-degree-of-freedom system. The new method is also applied to the analysis of response data obtained from the U.S.-Japan cooperative pseudo-dynamic test of a full-scale six-story steel-frame structure.

The new system identification method described has been found to be both accurate and computationally efficient. It is believed that it will provide a useful tool for the analysis of structural response data.

The interplay of localization and interactions in quantum many-body systems

Disorder and interactions both play crucial roles in quantum transport. Decades ago, Mott showed that electron-electron interactions can lead to insulating behavior in materials that conventional band theory predicts to be conducting. Soon thereafter, Anderson demonstrated that disorder can localize a quantum particle through the wave interference phenomenon of Anderson localization. Although interactions and disorder both separately induce insulating behavior, the interplay of these two ingredients is subtle and often leads to surprising behavior at the periphery of our current understanding. Modern experiments probe these phenomena in a variety of contexts (e.g. disordered superconductors, cold atoms, photonic waveguides, etc.); thus, theoretical and numerical advancements are urgently needed. In this thesis, we report progress on understanding two contexts in which the interplay of disorder and interactions is especially important.

The first is the so-called “dirty” or random boson problem. In the past decade, a strong-disorder renormalization group (SDRG) treatment by Altman, Kafri, Polkovnikov, and Refael has raised the possibility of a new unstable fixed point governing the superfluid-insulator transition in the one-dimensional dirty boson problem. This new critical behavior may take over from the weak-disorder criticality of Giamarchi and Schulz when disorder is sufficiently strong. We analytically determine the scaling of the superfluid susceptibility at the strong-disorder fixed point and connect our analysis to recent Monte Carlo simulations by Hrahsheh and Vojta. We then shift our attention to two dimensions and use a numerical implementation of the SDRG to locate the fixed point governing the superfluid-insulator transition there. We identify several universal properties of this transition, which are fully independent of the microscopic features of the disorder.

The second focus of this thesis is the interplay of localization and interactions in systems with high energy density (i.e., far from the usual low energy limit of condensed matter physics). Recent theoretical and numerical work indicates that localization can survive in this regime, provided that interactions are sufficiently weak. Stronger interactions can destroy localization, leading to a so-called many-body localization transition. This dynamical phase transition is relevant to questions of thermalization in isolated quantum systems: it separates a many-body localized phase, in which localization prevents transport and thermalization, from a conducting (“ergodic”) phase in which the usual assumptions of quantum statistical mechanics hold. Here, we present evidence that many-body localization also occurs in quasiperiodic systems that lack true disorder.

Theoretical studies of novel organic systems : biradicals, polyradicals, and conducting polymers

Chapter 1

Cyclobutanediyl has been studied in both its singlet and triplet states by ab initio electronic structure theory. The triplet, which is the ground state of the molecule, exists in both C_(2h) and C_(2v) forms, which interconvert via a C_s transition state. For the singlet, only a C_(2h) form is found. It passes, via a C_s transition state, onto the C_(2v) surface on which bicyclobutane is the only minimum. The ring-flipping (inversion) process in bicyclobutane includes the singlet biradical as an intermediate, and involves a novel, nonleast motion pathway. Semiclassical periodic orbit theory indicates that the various minima on both the singlet and triplet surfaces can interconvert via quantum mechanical tunneling.

Chapter 2

The dimethylenepolycyclobutadienes (n) are the non-Kekulé analogues of the classical acenes. Application of a variety of theoretical methods reveals several novel features of such structures. Most interesting is the emergence of a parity rule. When n is even, n is predicted to be a singlet, with n disjoint NBMOs. When n is odd, theory predicts a triplet ground state with (n+1) NBMOs that are not fully disjoint.

Chapter 3

Bi(cyclobutadienyl) (2), the cyclobutadiene analogue of biphenyl, and its homologues tri- (3) and tetra(cyclobutadienyl) (4) have been studied using electronic structure theory. Ab initio calculations on 2 reveal that the central bond is a true double bond, and that the structure is best thought of as two allyl radicals plus an ethylene. The singlet and triplet states are essentially degenerate. Trimer 3 is two allyls plus a dimethylenecyclobutanediyl, while 4 is two coplanar bi(cyclobutadienyl) units connected by a single bond. For both 3 and 4, the quintet, triplet, and singlet states are essentially degenerate, indicating that they are tetraradicals. The infinite polymer, polycyclobutadiene, has been studied by HMO, EHCO, and VEH methods. Several geometries based on the structures of 3 and 4 have been studied, and the band structures are quite intriguing. A novel crossing between the valence and conduction bands produces a small band gap and a high density of states at the Fermi level.

Chapter 4

At the level of Hückel theory, polyfulvene has a HOCO-LUCO degeneracy much like that seen in polyacetylene. Higher levels of theory remove the degeneracy, but the band gap (E_g) is predicted to be significantly smaller than analogous structures such as polythiophene and polypyrrole at the fulvenoid geometry. An alternative geometry, which we have termed quinoid, is also conceivable for polyfulvene, and it is predicted to have a much larger E_g. The effects of benzannelation to produce analogues of polyisothianaphthene have been evaluated. We propose a new model for such structures based on conventional orbital mixing arguments. Several of the proposed structures have quite interesting properties, which suggest that they are excellent candidates for conducting polymers.

Chapter 5

Theoretical studies of polydimethylenecyclobutene and polydiisopropylidene- cyclobutene reveal that, because of steric crowding, they cannot achieve a planar, fully conjugated structure in either their undoped or doped states. Rather, the structure consists of essentially orthogonal hexatriene units. Such a structure is incompatible with conventional conduction mechanisms involving polarons and bipolarons.

Microwave dynamics of quasiparticles and critical fields in superconducting films

The microwave response of the superconducting state in equilibrium and non-equilibrium configurations was examined experimentally and analytically. Thin film superconductors were mostly studied in order to explore spatial effects. The response parameter measured was the surface impedance.

For small microwave intensity the surface impedance at 10 GHz was measured for a variety of samples (mostly Sn) over a wide range of sample thickness and temperature. A detailed analysis based on the BCS theory was developed for calculating the surface impedance for general thickness and other experimental parameters. Experiment and theory agreed with each other to within the experimental accuracy. Thus it was established that the samples, thin films as well as bulk, were well characterised at low microwave powers (near equilibrium).

Thin films were perturbed by a small dc supercurrent and the effect on the superconducting order parameter and the quasiparticle response determined by measuring changes in the surface resistance (still at low microwave intensity and independent of it) due to the induced current. The use of fully superconducting resonators enabled the measurement of very small changes in the surface resistance (< 10^-9 Ω/sq.). These experiments yield information regarding the dynamics of the order parameter and quasiparticle systems. For all the films studied the results could be described at temperatures near T_c by the thermodynamic depression of the order parameter due to the static current leading to a quadratic increase of the surface resistance with current.

For the thinnest films the low temperature results were surprising in that the surface resistance decreased with increasing current. An explanation is proposed according to which this decrease occurs due to an additional high frequency quasiparticle current caused by the combined presence of both static and high frequency fields. For frequencies larger than the inverse of the quasiparticle relaxation time this additional current is out of phase (by π) with the microwave electric field and is observed as a decrease of surface resistance. Calculations agree quantitatively with experimental results. This is the first observation and explanation of this non-equilibrium quasiparticle effect.

For thicker films of Sn, the low temperature surface resistance was found to increase with applied static current. It is proposed that due to the spatial non-uniformity of the induced current distribution across the thicker films, the above purely temporal analysis of the local quasiparticle response needs to be generalised to include space and time non-equilibrium effects.

The nonlinear interaction of microwaves arid superconducting films was also examined in a third set of experiments. The surface impedance of thin films was measured as a function of the incident microwave magnetic field. The experiments exploit the ability to measure the absorbed microwave power and applied microwave magnetic field absolutely. It was found that the applied surface microwave field could not be raised above a certain threshold level at which the absorption increased abruptly. This critical field level represents a dynamic critical field and was found to be associated with the penetration of the app1ied field into the film at values well below the thermodynamic critical field for the configuration of a field applied to one side of the film. The penetration occurs despite the thermal stability of the film which was unequivocally demonstrated by experiment. A new mechanism for such penetration via the formation of a vortex-antivortex pair is proposed. The experimental results for the thinnest films agreed with the calculated values of this pair generation field. The observations of increased transmission at the critical field level and suppression of the process by a metallic ground plane further support the proposed model.

I. Proton magnetic resonance of polynucleotides and transfer RNA. II. Electron spin relaxation studies of manganese (II) complexes in acetonitrile

Part I. Proton Magnetic Resonance of Polynucleotides and Transfer RNA.

Proton magnetic resonance was used to follow the temperature dependent intramolecular stacking of the bases in the polynucleotides of adenine and cytosine. Analysis of the results on the basis of a two state stacked-unstacked model yielded values of -4.5 kcal/mole and -9.5 kcal/mole for the enthalpies of stacking in polyadenylic and polycytidylic acid, respectively.

The interaction of purine with these molecules was also studied by pmr. Analysis of these results and the comparison of the thermal unstacking of polynucleotides and short chain nucleotides indicates that the bases contained in stacks within the long chain poly nucleotides are, on the average, closer together than the bases contained in stacks in the short chain nucleotides.

Temperature and purine studies were also carried out with an aqueous solution of formylmethionine transfer ribonucleic acid. Comparison of these results with the results of similar experiments with the homopolynucleotides of adenine, cytosine and uracil indicate that the purine is probably intercalating into loop regions of the molecule.

The solvent denaturation of phenylalanine transfer ribonucleic acid was followed by pmr. In a solvent mixture containing 83 volume per cent dimethylsulf oxide and 17 per cent deuterium oxide, the tRNA molecule is rendered quite flexible. It is possible to resolve resonances of protons on the common bases and on certain modified bases.

Part II. Electron Spin Relaxation Studies of Manganese (II) Complexes in Acetonitrile.

The electron paramagnetic resonance spectra of three Mn⁺² complexes, [Mn(CH₃CN)₆]⁺², [MnCl₄]^-2, and [MnBr₄]^-2, in acetonitrile were studied in detail. The objective of this study was to relate changes in the effective spin Hamiltonian parameters and the resonance line widths to the structure of these molecular complexes as well as to dynamical processes in solution.

Of the three systems studied, the results obtained from the [Mn(CH₃CN)₆]⁺² system were the most straight-forward to interpret. Resonance broadening attributable to manganese spin-spin dipolar interactions was observed as the manganese concentration was increased.

In the [MnCl₄]^-2 system, solvent fluctuations and dynamical ion-pairing appear to be significant in determining electron spin relaxation.

In the [MnBr₄]^-2 system, solvent fluctuations, ion-pairing, and Br- ligand exchange provide the principal means of electron spin relaxation. It was also found that the spin relaxation in this system is dependent upon the field strength and is directly related to the manganese concentration. A relaxation theory based on a two state collisional model was developed to account for the observed behavior.