In Part I of the thesis an account is given of the basic algebra of extension fields which is required for the understanding of Galois theory. The fundamental theorem states the relationships of the subgroups of a permutation group of the root field of an equation to the subfields which are left invariant by these subgroups. Extensions of the basic theorem conclude Part I. In part II the solvability of equations by radicals is discussed, for fields of characteristic zero. A discussion of finite fields and primitive roots leads to a criterion for the solvability by radicals of equations over fields of prime characteristic. Finally, a method for determining the Galois group of any equation is discussed. Most of the material in the introductory chapters is taken from Artin's: Galois Theory (cf. p. 120). / Thesis / Master of Arts (MA)

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The effect of steric strain on the esr hyperfine coupling constants of several free-radical adducts of perfluoropropene and perfluoro-2-butene were investigated. Silyl, hydroxyalkyl, thiyl and alkoxy free radicals, which were generated by photo-irradiation, reacted with these olefins to form free-radical adducts. Trends in the esr hfs were then looked for in each class of adducts. The thiyl and alkoxy radicals were found to be unsuitable for this type of study due to the low degree of steric strain produced by these species in the adducts. Trends toward higher a-Fβ/CF₃ hfs and lower a^Fα hfs were observed for the silyl and hydroxyalkyl radical adducts as the steric strain in the adduct was increased. The ratio of the ^Fα to a-Fβ/CF₃ hfs was shown to be a good measure of the degree of steric strain in these radical adducts. The possibility that the (Me₃Si)₂CHC(SiMe₃)₂ free radical, which has been reported to contain an "esr invisible" β-H, might be misidentified was investigated. Our conclusion was that the β-H is present and has not been replaced by a t-butoxy group. / Ph. D.

The results of our studies demonstrate a link between selectivity in free radical brominations and the internal pressure of solvent. The study encompassed l8 solvents and/or mixtures over which the rate constant ratio for SH2 ring opening of cyclopropylbenzene (kC) vs hydrogen abstraction from toluene (kH) by bromine atom was found to vary by nearly a factor of twenty as a function of solvent. The observed rate constant ratios correlate with the cohesive energy density of the solvent, which is approximately equal to the internal pressure (kC/kH is found to increase with increasing solvent pressure) for the solvents used in this study. A similar competition pitting cyclopropylbenzene against p-chlorotoluene shows the same solvent effect. It is suggested that the observed variation in selectivity "with solvent pressure occurs because the volume of activation with kC is more negative than for kH by about 20 cm3/mol. / Master of Science

The rotational spectra of the 2-cyano-2-propyl and d⁶-2·cyano-2-propyl radicals were observed using a Stark modulated spectrometer. The radicals were generated in the gas phase by UV irradiation of sublimed azoisobisbutyronitrile. They were detectable in the cell for approximately one hour. Thirty-three transitions were assigned for (CH₃)₂CCN and twenty-one for (CD₃)₂CCN. The rigid rotor rotational constants determined by calculation of the hypothetical unsplit rotational transitions are A=8276.7, B=3919.7, C=2751.5Mhz for (CH₃)₂CCN and A=6241.3, B=3490.7, C=2372.6Mhz for (CD₃)₂CCN. A program to calculate the fine splittings and hyperfine splittings due to the ¹⁴N nucleus and six protons was written. The spin rotation constants determined for the two species were E_aa=-69.9, E_bb=-36.1, E_cc=2.7Mhz and E_aa=-55.4, E_bb=-32.6 Mhz for (CH₃)₂CCN and (CD₃)₂CCN respectively. The hyperfine coupling constants for ¹⁴N are identical for both isotopic species and were found to be T_aa=-17.2, T_bb=-17.1 and T_cc=34.4 Mhz. The proton and deuteron hyperfine splittings were not resolved. The structural parameters determined from an <r₀> fit of the moments are r_CN=1.18A, r_CC=1.42A, r_CMe=1.50A and CCMe=119.3°. The C₄N skeletal framework was found to be planar. / Ph. D.