I. Electron spin relaxation studies of manganese(II) complexes in acetonitrile. II. Nuclear spin relaxation studies of bromine in tetrabromomanganese(II) in acetonitrile

Magnetic resonance techniques have given us a powerful means for investigating dynamical processes in gases, liquids and solids. Dynamical effects manifest themselves in both resonance line shifts and linewidths, and, accordingly, require detailed analyses to extract desired information. The success of a magnetic resonance experiment depends critically on relaxation mechanisms to maintain thermal equilibrium between spin states. Consequently, there must be an interaction between the excited spin states and their immediate molecular environment which promote changes in spin orientation while excess magnetic energy is coupled into other degrees of freedom by non-radiative processes. This is well known as spin-lattice relaxation. Certain dynamical processes cause fluctuations in the spin state energy levels leading to spin-spin relaxation and, here again, the environment at the molecular level plays a significant role in the magnitude of interaction. Relatively few electron spin relaxation studies of solutions have been conducted and the present work is addressed toward the extension of our knowledge in this area and the retrieval of dynamical information from line shape analyses on a time scale comparable to diffusion controlled phenomena.

Specifically, the electron spin relaxation of three Mn⁺²3d⁵ complexes, Mn(CH₃CN)₆⁺², MnCl₄^-2 in acetonitrile has been studied in considerable detail. The effective spin Hamiltonian constants were carefully evaluated under a wide range of experimental conditions. Resonance widths of these Mn⁺² complexes were studied in the presence of various excess ligand ions and as a function of concentration, viscosity, temperature and frequency (X-band, ~9.5 Ԍ Hz and K-band, ~35 Ԍ Hz).

A number of interesting conclusions were drawn from these studies. For the Et₄NCl-₄^-2 system several relaxation mechanisms leading to resonance broadening were observed. One source appears to arise through spin-orbit interactions caused by modulation of the ligand field resulting from transient distortions of the complex imparted by solvent fluctuations in the immediate surroundings of the paramagnetic ion. An additional spin relaxation was assigned to the formation of ion pairs [Et₄N⁺…MnCl₄^-2] and it was possible to estimate the dissociation constant for this specie in acetonitrile.

The Bu₄NBr-MnBr₄^-2 study was considerably more interesting. As in the former case, solvent fluctuations and ion-pairing of the paramagnetic complex [Bu₄N⁺…MnBr₄^-2] provide significant relaxation for the electronic spin system. Most interesting, without doubt, is the onset of a new relaxation mechanism leading to resonance broadening which is best interpreted as chemical exchange. Thus, assuming that resonance widths were simply governed by electron spin state lifetimes, we were able to extract dynamical information from an interaction in which the initial and final states are the same

MnBr₄^-2 + Br^- = MnBr₄^-2 + Br^-.

The bimolecular rate constants were obtained at six different temperatures and their magnitudes suggested that the exchange is probably diffusion controlled with essentially a zero energy of activation. The most important source of spin relaxation in this system stems directly from dipolar interactions between the manganese 3d⁵ electrons. Moreover, the dipolar broadening is strongly frequency dependent indicating a deviation between the transverse and longitudinal relaxation times. We are led to the conclusion that the 3d⁵ spin states of ion-paired MnBr₄^-2 are significantly correlated so that dynamical processes are also entering the picture. It was possible to estimate the correlation time, ^Td, characterizing this dynamical process.

In Part II we study nuclear magnetic relaxation of bromine ions in the MnBr4-2-Bu4NBr-acetonitrile system. Essentially we monitor the 79Br and 81Br linewidths in response to the [MnBr4-2]/[Br-] ratio with the express purpose of supporting our contention that exchange is occurring between "free" bromine ions in the solvent and bromine in the first coordination sphere of the paramagnetic anion. The complexity of the system elicited a two-part study: (1) the linewidth behavior of Bu4NBr in anhydrous CH3CN in the absence of MnBr4-2 and (2) in the presence of MnBr4-2. It was concluded in study (1) that dynamical association, Bu4NBr k1= Bu4N+ + Br-, was modulating field-gradient interactions at frequencies high enough to provide an estimation of the unimolecular rate constant, k1. A comparison of the two isotopic bromine linewidth-mole fraction results led to the conclusion that quadrupole interactions provided the dominant relaxation mechanism. In study (2) the "residual" bromine linewidths for both 79Br and 81Br are clearly controlled by quadrupole interactions which appear to be modulated by very rapid dynamical processes other than molecular reorientation. We conclude that the "residual" linewidth has its origin in chemical exchange and that bromine nuclei exchange rapidly between a "free" solvated ion and the paramagnetic complex, MnBr4-2.

Nuclear reactions leading to energy levels of Ar37 and K37

In view of recent interest in the Cl³⁷ (ʋ solar’^e-)Ar³⁷ reaction cross section, information on some aspects of mass 37 nuclei has been obtained using the K³⁹ (d, ∝) Ar³⁷ and Cl³⁵ (He³, p) Ar³⁷ reactions. Ar³⁷ levels have been found at 0, 1.41, 1.62, 2.22, 2.50, 2.80, 3.17, 3.27, 3.53, 3.61, 3.71, (3.75), (3.90), 3.94, 4.02, (4.21), 4.28, 4.32, 4.40, 4.45, 4.58, 4.63, 4.74, 4.89, 4.98, 5.05, 5.10, 5.13, 5.21, 5.35, 5.41, 5.44, 5.54, 5.58, 5.67, 5.77, and 5.85 MeV (the underlined values correspond to previously tabulated levels). The nuclear temperature calculated from the Ar³⁷ level density is 1.4 MeV. Angular distributions of the lowest six levels with the K³⁹ (d, ∝) Ar³⁷ reaction at E_d = 10 MeV indicate a dominant direct interaction mechanism and the inapplicability of the 2I + 1 rule of the statistical model. Comparison of the spectra obtained with the K³⁹ (d, ∝) Ar³⁷ and Cl³⁵ (He³, p) Ar³⁷ reactions leads to the suggestion that the 5.13-MeV level is the T = 3/2 Cl³⁷ ground state analog. The ground state Q-value of the Ca⁴⁰ (p, ∝) K³⁷ reaction has been measured: -5179 ± 9 keV. This value implies a K³⁷ mass excess of -24804 ± 10 keV. Description of a NMR magnetometer and a sixteen-detector array used in conjunction with a 61-cm double-focusing magnetic spectrometer are included in appendices.

Entrainment of fine sediments by turbulent flows

A study was made of the means by which turbulent flows entrain sediment grains from alluvial stream beds. Entrainment was considered to include both the initiation of sediment motion and the suspension of grains by the flow. Observations of grain motion induced by turbulent flows led to the formulation of an entrainment hypothesis. It was based on the concept of turbulent eddies disrupting the viscous sublayer and impinging directly onto the grain surface. It is suggested that entrainment results from the interaction between fluid elements within an eddy and the sediment grains.

A pulsating jet was used to simulate the flow conditions in a turbulent boundary layer. Evidence is presented to establish the validity of this representation. Experiments were made to determine the dependence of jet strength, defined below, upon sediment and fluid properties. For a given sediment and fluid, and fixed jet geometry there were two critical values of jet strength: one at which grains started to roll across the bed, and one at which grains were projected up from the bed. The jet strength K, is a function of the pulse frequency, ω, and the pulse amplitude, A, defined by

K = Aω^-s

Where s is the slope of a plot of log A against log ω. Pulse amplitude is equal to the volume of fluid ejected at each pulse divided by the cross sectional area of the jet tube.

Dimensional analysis was used to determine the parameters by which the data from the experiments could be correlated. Based on this, a method was devised for computing the pulse amplitude and frequency necessary either to move or project grains from the bed for any specified fluid and sediment combination.

Experiments made in a laboratory flume with a turbulent flow over a sediment bed are described. Dye injection was used to show the presence, in a turbulent boundary layer, of two important aspects of the pulsating jet model and the impinging eddy hypothesis. These were the intermittent nature of the sublayer and the presence of velocities with vertical components adjacent to the sediment bed.

A discussion of flow conditions, and the resultant grain motion, that occurred over sediment beds of different form is given. The observed effects of the sediment and fluid interaction are explained, in each case, in terms of the entrainment hypothesis.

The study does not suggest that the proposed entrainment mechanism is the only one by which grains can be entrained. However, in the writer’s opinion, the evidence presented strongly suggests that the impingement of turbulent eddies onto a sediment bed plays a dominant role in the process.

I. Nuclear spin-internal-rotation-coupling. II. Fluorine spin-rotation interaction and magnetic shielding in fluorobenzene

Part I.

The interaction of a nuclear magnetic moment situated on an internal top with the magnetic fields produced by the internal as well as overall molecular rotation has been derived following the method of Van Vleck for the spin-rotation interaction in rigid molecules. It is shown that the Hamiltonian for this problem may be written

H_SR = Ῑ · M · Ĵ + Ῑ · M” · Ĵ”

Where the first term is the ordinary spin-rotation interaction and the second term arises from the spin-internal-rotation coupling.

The F¹⁹ nuclear spin-lattice relaxation time (T₁) of benzotrifluoride and several chemically substituted benzotrifluorides, have been measured both neat and in solution, at room temperature by pulsed nuclear magnetic resonance. From these experimental results it is concluded that in benzotrifluoride the internal rotation is crucial to the spin relaxation of the fluorines and that the dominant relaxation mechanism is the fluctuating spin-internal-rotation interaction.

Part II.

The radiofrequency spectrum corresponding to the reorientation of the F¹⁹ nuclear moment in flurobenzene has been studied by the molecular beam magnetic resonance method. A molecular beam apparatus with an electron bombardment detector was used in the experiments. The F¹⁹ resonance is a composite spectrum with contributions from many rotational states and is not resolved. A detailed analysis of the resonance line shape and width by the method of moments led to the following diagonal components of the fluorine spin-rotational tensor in the principal inertial axis system of the molecule:

F/Caa = -1.0 ± 0.5 kHz

F/Cbb = -2.7 ± 0.2 kHz

F/Ccc = -1.9 ± 0.1 kHz

From these interaction constants, the paramagnetic contribution to the F¹⁹ nuclear shielding in C₆H₅F was determined to be -284 ± ppm. It was further concluded that the F¹⁹ nucleus in this molecule is more shielded when the applied magnetic field is directed along the C-F bond axis. The anisotropy of the magnetic shielding tensor, σ_” - σ_⊥, is +160 ± 30 ppm.

The rate and mechanism of the partial oxidation of acetaldehyde by PPM concentrations of nitrogen dioxide

The thermal reaction between nitrogen dioxide and acetaldehyde in the gas phase was investigated at room temperature and atmospheric pressure. The initial rate of disappearance of nitrogen dioxide was 1.00 ± 0.03 order with respect to nitrogen dioxide and 1.00 ± 0.07 order with respect to acetaldehyde. An initial second order rate constant of (8.596 ± 0.189) x 10^-3 1.mole^-1 sec^-1 was obtained at 22.0 ± 0.1 °C and a total pressure of one atmosphere. The activation energy of the reaction was 12,900 cal/mole in the temperature range between 22°C and 122°C.

The products of the reaction were nitric oxide, carbon dioxide, methyl nitrite, nitromethane and a trace amount of trans-dimeric nitrosomethane. The addition of nitric oxide increased the rate of formation of nitromethane and decreased the rate of formation of methyl nitrite. There were no measurable surface effects due to the addition of glass wool or glass beads to the reactor.

Reactants and products were analyzed by gas chromatography. A mechanism was proposed incorporating the principal features of the reaction.

A nonlinear systems model for the control mechanism of free fatty acid-glucose metabolosm in normal humans

A mathematical model is proposed in this thesis for the control mechanism of free fatty acid-glucose metabolism in healthy individuals under resting conditions. The objective is to explain in a consistent manner some clinical laboratory observations such as glucose, insulin and free fatty acid responses to intravenous injection of glucose, insulin, etc. Responses up to only about two hours from the beginning of infusion are considered. The model is an extension of the one for glucose homeostasis proposed by Charette, Kadish and Sridhar (Modeling and Control Aspects of Glucose Homeostasis. Mathematical Biosciences, 1969). It is based upon a systems approach and agrees with the current theories of glucose and free fatty acid metabolism. The description is in terms of ordinary differential equations. Validation of the model is based on clinical laboratory data available at the present time. Finally procedures are suggested for systematically identifying the parameters associated with the free fatty acid portion of the model.