Synthetic, kinetic and mechanistic studies in early transition metal systems. I. α- and β-hydrogen elimination reactions in derivatives of permethyltitanocene, -zirconocene, and -hafnocene. II. The reactions of aluminum alkyls with derivatives of permethylniobocene

The thermal decomposition of Cp*Ti(CH_3)_2 (Cp*≡ ƞ^5-C_5Me_5) toluene solution follows cleanly first-order kinetics and produces a single titanium product Cp*(C_5Me_4CH_2)Ti(CH_3) concurrent with the evolution of one equivalent of methane. Labeling studies using Cp*_2Ti- (CD_3)_2 and (Cp*-d_(15))_2Ti(CH_3)_2 show the decomposition to be intramolecular and the methane to be produced by the coupling of a methyl group with a hydrogen from the other TiCH_3 group. Activation parameters, ΔH^‡ and ΔS^‡, and kinetic deuterium isotope effects have been measured. The alternative decomposition pathways of α-hydrogen abstraction and a-hydrogen elimination, both leading to a titanium-methylidene intermediate, are discussed.

The insertion of unactivated acetylenes into the metal-hydride bonds of Cp*_2MH_2 (M = Zr, Hf) proceeds rapidly at low temperature to form monoand/ or bisinsertion products, dependent upon the steric bulk of the acetylene substituents. Cp*_2M(H)(C(Me)=CHMe), Cp*_2M(H)(CH=CHCMe_3), Cp*_2M(H)-(CH=CHPh), Cp*_2M(CH=CHPh)_2, Cp*_2M(CH=CHCH_3)_2 and Cp*_2Zr- (CH=CHCH_2CH_3)_2 have been isolated and characterized. To extend the study of unsaturated-carbon ligands, Cp*_2M(C≡CCH_3)_2 have been prepared by treating Cp*_2MCl_2 with LiC≡CCH_3. The reactivity of many of these complexes with carbon monoxide and dihydrogen is surveyed. The mono(2- butenyl) complexes Cp*_2M(H)(C(Me)=CHMe) rearrange at room temperature, forming the crotyl-hydride species Cp*_2M(H)(ƞ^3-C_4H_7). The bis(propenyl) and bis(l-butenyl) zirconium complexes Cp*_2Zr(CH=CHR)_2 (R = CH_3, CH_2CH_3) also rearrange, forming zirconacyclopentenes. Labeling studies, reaction chemistry, and kinetic measurements, including deuterium isotope effects, demonstrate that the unusual 6-hydrogen elimination from an sp^2-hybridized carbon is the first step in these latter rearrangements but is not observed in the former. Details of these mechanisms and the differences in reactivity of the zirconium and hafnium complexes are discussed.

The reactions of hydride- and alkyl-carbonyl derivatives of permethylniobocene with equimolar amounts of trialkylaluminum reagents occur rapidly producing the carbonyl adducts Cp*_2Nb(R)(COAlR'_3) (R = H, CH_3, CH_2CH_3, CH_2CH_2Ph, C(Me)=CHMe; R' = Me, Et). The hydride adduct Cp*_2NbH_3•AlEt_3 has also been formed. In solution, each of these compounds exists in equilibrium with the uncomplexed species. The formation constants for Cp*_2Nb(H)(COA1R'_R) have been measured. They indicate the steric bulk of the Cp* ligands plays a deciding factor in the isolation of the first example of an aluminum Lewis acid bound to a carbonyl-oxygen in preference to a metalhydride. Reactions of Cp*_2Nb(H)CO with other Lewis acids and of the one:one adducts with H_2, CO and C_2H_4 are also discussed.

Cp*_2Nb(H)(C_2H_4) also reacts with equimolar amounts of trialkylaluminum reagents, forming a one:one complex that ^1H NMR spectroscopy indicates contains a Nb-CH_2CH_2-Al bridge. This adduct also exists in equilibrium with the uncomplexed species in solution. The formation constant for Cp*_2N+/b(H)(CH_2CH_2ĀlEt_3) has been measured. Reactions of Cp*_2Nb(H)(C_2H_4) with other Lewis acids and the reactions of Cp*_2N+b(H)- (CH_2CH_2ĀlEt_3) with CO and C_2H_4 are described, as are the reactions of Cp_*2Nb(H)(CH_2=CHR) (R = Me, Ph), Cp*_2Nb(H)(CH_3C≡CCH_3) and Cp*_2Ti-(C_2H_4) with AlEt_3.

Selectivity, activity, and stability of ruthenium-carbene based olefin metathesis initiators

The olefin metathesis reaction has found many applications in polymer synthesis and more recently in organic synthesis. The use of single component late metal olefin metathesis catalysts has expanded the scope of the reaction to many new applications and has allowed for detailed study of the catalytic species.

The metathesis of terminal olefins of different steric bulk, different geometry as well as electronically different para-substituted styrenes was studied with the ruthenium based metathesis initiators, trans-(PCy₃)₂Cl₂Ru=CHR, of different carbene substituents. Increasing olefin bulk was found to slow the rate of reaction and trans internal olefins were found to be slower to react than cis internal olefins. The kinetic product of a11 reactions was found to be the alkylidene, rather than the methylidene, suggesting the intermediacy of a 2,4-metallacycle. The observed effects were used to explain the mechanism of ring opening cross metathesis and acyclic diene metathesis polymerization. No linear electronic effects were observed.

In studying the different carbene ligands, a series of ester-carbene complexes was synthesized. These complexes were found to be highly active for the metathesis of olefinic substrates, including acrylates and trisubstituted olefins. In addition, the estercarbene moiety is thermodynamically high in energy. As a result, these complexes react to ring-open cyclohexene by metathesis to alleviate the thermodynamic strain of the ester-carbene ligand. However, ester-carbene complexes were found to be thermolytically unstable in solution.

Thermolytic decomposition pathways were studied for several ruthenium-carbene based olefin metathesis catalysts. Substituted carbenes were found to decompose through bimolecular pathways while the unsubstituted carbene (the methylidene) was found to decompose unimolecularly. The stability of several derivatives of the bis-phosphine ruthenium based catalysts was studied for its implications to ring-closing metathesis. The reasons for the activity and stability of the different ruthenium-based catalysts is discussed.

The difference in catalyst activity and initiation is discussed for the bis-phosphine based and mixed N-heterocyclic carbene/phosphine based ruthenium olefin metathesis catalysts. The mixed ligand catalysts initiate far slower than the bis-phosphine catalysts but are far more metathesis active. A scheme is proposed to explain the difference in reactivity between the two types of catalysts.

Preparation, characterization and intramolecular electron-transfer studies of ruthenium-modified cytochromes c

Redox-active ruthenium complexes have been covalently attached to the surface of a series of natural, semisynthetic and recombinant cytochromes c. The protein derivatives were characterized by a variety of spectroscopic techniques. Distant Fe^(2+) - Ru^(3+) electronic couplings were extracted from intramolecular electron-transfer rates in Ru(bpy)_2(im)HisX (where X= 33, 39, 62, and 72) derivatives of cyt c. The couplings increase according to 62 (0.0060) < 72 (0.057) < 33 (0.097) < 39 (0.11 cm^(-1)); however, this order is incongruent with histidine to heme edge-edge distances [62 (14.8) > 39 (12.3) > 33 (11.1) > =72 (8.4 Å)]. These results suggest the chemical nature of the intervening medium needs to be considered for a more precise evaluation of couplings. The rates (and couplings) correlate with the lengths of a-tunneling pathways comprised of covalent bonds, hydrogen bonds and through-space jumps from the histidines to the heme group. Space jumps greatly decrease couplings: one from Pro71 to Met80 extends the σ-tunneling length of the His72 pathway by roughly 10 covalent bond units. Experimental couplings also correlate well with those calculated using extended Hiickel theory to evaluate the contribution of the intervening protein medium.

Two horse heart cyt c variants incorporating the unnatural amino acids (S)-2- amino-3-(2,2'-bipyrid-6-yl)-propanoic acid (6Bpa) and (S)-2-amino-3-(2,2'-bipyrid-4-yl)propanoic acid ( 4Bpa) at position 72 have been prepared using semisynthetic protocols. Negligible perturbation of the protein structure results from this introduction of unnatural amino acids. Redox-active Ru(2,2'-bipyridine)_2^(2+) binds to 4Bpa72 cyt c but not to the 6Bpa protein. Enhanced ET rates were observed in the Ru(bpy)_2^(2+)-modified 4Bpa72 cyt c relative to the analogous His72 derivative. The rapid (< 60 nanosecond) photogeneration of ferrous Ru-modified 4Bpa72 cyt c in the conformationally altered alkaline state demonstrates that laser-induced ET can be employed to study submicrosecond protein-folding events.

Reactions of platinum(II) complexes with dioxygen: progress toward alkane functionalization

Whereas stoichiometric activation of C-H bonds by complexes of transition metals is becoming increasingly common, selective functionalization of alkanes remains a formidable challenge in organometallic chemistry. The recent advances in catalytic alkane functionalization by transition-metal complexes are summarized in Chapter I.

The studies of the displacement of pentafluoropyridine in [(tmeda)Pt(CH_3)(NC_5F_5)][BAr^f_4] (1) with γ- tetrafluoropicoline, a very poor nucleophile, are reported in Chapter II. The ligand substitution occurs by a dissociative interchange mechanism. This result implies that dissociative loss of pentafluoropyridine is the rate-limiting step in the C-H activation reactions of 1.

Oxidation of dimethylplatinum(II) complexes (N-N)Pt(CH_3)_2 (N-N = tmeda(1), α-diimines) by dioxygen is described in Chapter III. Mechanistic studies suggest a two-step mechanism. First, a hydroperoxoplatinum(IV) complex is formed in a reaction between (N-N)Pt(CH_3)_2 and dioxygen. Next, the hydroperoxy complex reacts with a second equivalent of (N-N)Pt(CH_3)_2 to afford the final product, (N-N)Pt(OH)(OCH_3)(CH_3)_2. The hydroperoxy intermediate, (tmeda)Pt(OOH)(OCH_3)(CH_3)_2 (2), was isolated and characterized. The reactivity of 2 with several dime thylplatinum(II) complexes is reported.

The studies described in Chapter IV are directed toward the development of a platinum(II)-catalyzed oxidative alkane dehydrogenation. Stoichiometric conversion of alkanes (cyclohexane, ethane) to olefins (cyclohexene, ethylene) is achieved by C-H activation with [(N-N)Pt(CH_3)(CF_3CH_2OH)]BF_4 (1, N-N is N,N'-bis(3,5-di-t- butylphenyl)-1,4-diazabutadiene) which results in the formation of olefin hydride complexes. The first step in the C-H activation reaction is formation of a platinum(II) alkyl which undergoes β-hydrogen elimination to afford the olefin hydride complex. The cationic ethylplatinum(II) intermediate can be generated in situ by treating diethylplatinum(II) compounds with acids. Treatment of (phen)PtEt_2 with [H(OEt_2)_2]Bar^f_4 at low temperatures resulted in the formation of a mixture of [(phen)PtEt(OEt_2)]Bar^f_4 (8) and [(phen)Pt(C_2H_4)H] Bar^f_4 (7). The cationic olefin complexes are unreactive toward dioxygen or hydrogen peroxide. Since the success of the overall catalytic cycle depends on our ability to oxidize the olefin hydride complexes, a series of neutral olefin complexes of platinum(II) with monoanionic ligands (derivatives of pyrrole-2-carboxyaldehyde N-aryl imines) was prepared. Unfortunately, these are also stable to oxidation.

Structure-, stereochemistry-, and metal-regulated DNA binding/cleaving molecules

In the cell, the binding of proteins to specific sequences of double helical DNA is essential for controlling the processes of protein synthesis (at the level of DNA transcription) and cell proliferation (at the level of DNA replication). In the laboratory, the sequence-specific DNA binding/cleaving properties of restriction endonuclease enzymes (secreted by microorganisms to protect them from foreign DNA molecules) have helped to fuel a revolution in molecular biology. The strength and specificity of a protein:DNA interaction depend upon structural features inherent to the protein and DNA sequences, but it is now appreciated that these features (and therefore protein:DNA complexation) may be altered (regulated) by other protein:DNA complexes, or by environmental factors such as temperature or the presence of specific organic molecules or inorganic ions. It is also now appreciated that molecules much smaller than proteins (including antibiotics of molecular weight less than 2000 and oligonucleotides) can bind to double-helical DNA in sequence-specific fashion. Elucidation of structural motifs and microscopic interactions responsible for the specific molecular recognition of DNA leads to greater understanding of natural processes and provides a basis for the design of novel sequence-specific DNA binding molecules. This thesis describes the synthesis and DNA binding/cleaving characteristics of molecules designed to probe structural, stereochemical, and environmental factors that regulate sequence-specific DNA recognition.

Chapter One introduces the DNA minor groove binding antibiotics Netropsin and Distamycin A, which are di- and tri(N-methylpyrrolecarboxamide) peptides, respectively. The method of DNA affinity cleaving, which has been employed to determine DNA binding properties of designed synthetic molecules is described. The design and synthesis of a series of Netropsin dimers linked in tail-to-tail fashion (by oxalic, malonic, succinic, or fumaric acid), or in head-to-tail fashion (by glycine, β-alanine, and γ-aminobutanoic acid (Gaba)) are presented. These Bis(Netropsin)s were appended with the iron-chelating functionality EDTA in order to make use of the technique of DNA affinity cleaving. Bis(Netropsin)-EDTA compounds are analogs of penta(N-methylpyrrolecarboxamide)-EDTA (P5E), which may be considered a head-to-tail Netropsin dimer linked by Nmethylpyrrolecarboxamide. Low- and high-resolution analysis of pBR322 DNA affinity cleaving by the iron complexes of these molecules indicated that small changes in the length and nature of the linker had significant effects on DNA binding/cleaving efficiency (a measure of DNA binding affinity). DNA binding/cleaving efficiency was found to decrease with changes in the linker in the order β-alanine > succinamide > fumaramide > N-methylpyrrolecarboxamide > malonamide >glycine, γ-aminobutanamide > oxalamide. In general, the Bis(Netropsin)-EDTA:Fe compounds retained the specificity for seven contiguous A:T base pairs characteristic of P5E:Fe binding. However, Bis(Netropsin)Oxalamide- EDTA:Fe exhibited decreased specificity for A:T base pairs, and Bis(Netropsin)-Gaba-EDT A:Fe exhibited some DNA binding sites of less than seven base pairs. Bis(Netropsin)s linked with diacids have C₂-symmmetrical DNA binding subunits and exhibited little DNA binding orientation preference. Bis(Netropsin)s linked with amino acids lack C₂-symmetrical DNA binding subunits and exhibited higher orientation preferences. A model for the high DNA binding orientation preferences observed with head-to-tail DNA minor groove binding molecules is presented.

Chapter Two describes the design, synthesis, and DNA binding properties of a series of chiral molecules: Bis(Netropsin)-EDTA compounds with linkers derived from (R,R)-, (S,S)-, and (RS,SR)-tartaric acids, (R,R)-, (S,S)-, and (RS,SR)-tartaric acid acetonides, (R)- and (S)-malic acids, N ,N-dimethylaminoaspartic acid, and (R)- and (S)-alanine, as well as three constitutional isomers in which an N-methylpyrrolecarboxamide (P1) subunit and a tri(N-methylpyrrolecarboxamide)-EDTA (P3-EDTA) subunit were linked by succinic acid, (R ,R)-, and (S ,S)-tartaric acids. DNA binding/cleaving efficiencies among this series of molecules and the Bis(Netropsin)s described in Chapter One were found to decrease with changes in the linker in the order β-alanine > succinamide > P1-succinamide-P3 > fumaramide > (S)-malicamide > N-methylpyrrolecarboxamide > (R)-malicamide > malonamide > N ,N-dimethylaminoaspanamide > glycine = Gaba = (S,S)-tartaramide = P1-(S,S)-tanaramide-P3 > oxalamide > (RS,SR)-tartaramide = P1- (R,R)-tanaramide-P3 > (R,R)-tartaramide (no sequence-specific DNA binding was detected for Bis(Netropsin)s linked by (R)- or (S)-alanine or by tartaric acid acetonides). The chiral molecules retained DNA binding specificity for seven contiguous A:T base pairs. From the DNA affinity cleaving data it could be determined that: 1) Addition of one or two substituents to the linker of Bis(Netropsin)-Succinamide resulted in stepwise decreases in DNA binding affinity; 2) molecules with single hydroxyl substituents bound DNA more strongly than molecules with single dimethylamino substituents; 3) hydroxyl-substituted molecules of (S) configuration bound more strongly to DNA than molecules of (R) configuration. This stereochemical regulation of DNA binding is proposed to arise from the inherent right-handed twist of (S)-enantiomeric Bis(Netropsin)s versus the inherent lefthanded twist of (R)-enantiomeric Bis(Netropsin)s, which makes the (S)-enantiomers more complementary to the right-handed twist of B form DNA.

Chapter Three describes the design and synthesis of molecules for the study of metalloregulated DNA binding phenomena. Among a series of Bis(Netropsin)-EDTA compounds linked by homologous tethers bearing four, five, or six oxygen atoms, the Bis(Netropsin) linked by a pentaether tether exhibited strongly enhanced DNA binding/cleaving in the presence of strontium or barium cations. The observed metallospecificity was consistent with the known affinities of metal cations for the cyclic hexaether 18-crown-6 in water. High-resolution DNA affinity cleaving analysis indicated that DNA binding by this molecule in the presence of strontium or barium was not only stronger but of different sequence-specificity than the (weak) binding observed in the absence of metal cations. The metalloregulated binding sites were consistent with A:T binding by the Netropsin subunits and G:C binding by a strontium or barium:pentaether complex. A model for the observed positive metalloregulation and novel sequence-specificity is presented. The effects of 44 different cations on DNA affinity cleaving by P5E:Fe were examined. A series of Bis(Netropsin)-EDTA compounds linked by tethers bearing two, three, four, or five amino groups was also synthesized. These molecules exhibited strong and specific binding to A:T rich regions of DNA. It was found that the iron complexes of these molecules bound and cleaved DNA most efficiently at pH 6.0-6.5, while P5E:Fe bound and cleaved most efficiently at pH 7.5-8.0. Incubating the Bis(Netropsin) Polyamine-EDTA:Fe molecules with K₂PdCl₄ abolished their DNA binding/cleaving activity. It is proposed that the observed negative metalloregulation arises from kinetically inert Bis(Netropsin) Polyamine:Pd(II) complexes or aggregates, which are sterically unsuitable for DNA complexation. Finally, attempts to produce a synthetic metalloregulated DNA binding protein are described. For this study, five derivatives of a synthetic 52 amino acid residue DNA binding/cleaving protein were produced. The synthetic mutant proteins carried a novel pentaether ionophoric amino acid residue at different positions within the primary sequence. The proteins did not exhibit significant DNA binding/cleaving activity, but they served to illustrate the potential for introducing novel amino acid residues within DNA binding protein sequences, and for the development of the tricyclohexyl ester of EDTA as a superior reagent for the introduction of EDT A into synthetic proteins.

Chapter Four describes the discovery and characterization of a new DNA binding/cleaving agent, [SalenMn(III)]OAc. This metal complex produces single- and double-strand cleavage of DNA, with specificity for A:T rich regions, in the presence of oxygen atom donors such as iodosyl benzene, hydrogen peroxide, or peracids. Maximal cleavage by [SalenMn(III)]OAc was produced at pH 6-7. A comparison of DNA singleand double-strand cleavage by [SalenMn(III)]⁺ and other small molecules (Methidiumpropyl-EDTA:Fe, Distamycin-EDTA:Fe, Neocarzinostatin, Bleomycin:Fe) is presented. It was found that DNA cleavage by [SalenMn(III)]⁺ did not require the presence of dioxygen, and that base treatment of DNA subsequent to cleavage by [SalenMn(III)]⁺ afforded greater cleavage and alterations in the cleavage patterns. Analysis of DNA products formed upon DNA cleavage by [SalenMn(III)] indicated that cleavage was due to oxidation of the sugar-phosphate backbone of DNA. Several mechanisms consistent with the observed products and reaction requirements are discussed.

Chapter Five describes progress on some additional studies. In one study, the DNA binding/cleaving specificities of Distamycin-EDTA derivatives bearing pyrrole N-isopropyl substituents were found to be the same as those of derivatives bearing pyrrole N-methyl substituents. In a second study, the design of and synthetic progress towards a series of nucleopeptide activators of transcription are presented. Five synthetic plasmids designed to test for activation of in vitro run-off transcription by DNA triple helix-forming oligonucleotides or nucleopeptides are described.

Chapter Six contains the experimental documentation of the thesis work.

Multipole moments in general relativity and dynamical perturbations of black-hole magnetospheres

This thesis consists of two parts. In Part I, we develop a multipole moment formalism in general relativity and use it to analyze the motion and precession of compact bodies. More specifically, the generic, vacuum, dynamical gravitational field of the exterior universe in the vicinity of a freely moving body is expanded in positive powers of the distance r away from the body's spatial origin (i.e., in the distance r from its timelike-geodesic world line). The expansion coefficients, called "external multipole moments,'' are defined covariantly in terms of the Riemann curvature tensor and its spatial derivatives evaluated on the body's central world line. In a carefully chosen class of de Donder coordinates, the expansion of the external field involves only integral powers of r ; no logarithmic terms occur. The expansion is used to derive higher-order corrections to previously known laws of motion and precession for black holes and other bodies. The resulting laws of motion and precession are expressed in terms of couplings of the time derivatives of the body's quadrupole and octopole moments to the external moments, i.e., to the external curvature and its gradient.

In part II, we study the interaction of magnetohydrodynamic (MHD) waves in a black-hole magnetosphere with the "dragging of inertial frames" effect of the hole's rotation - i.e., with the hole's "gravitomagnetic field." More specifically: we first rewrite the laws of perfect general relativistic magnetohydrodynamics (GRMHD) in 3+1 language in a general spacetime, in terms of quantities (magnetic field, flow velocity, ...) that would be measured by the ''fiducial observers” whose world lines are orthogonal to (arbitrarily chosen) hypersurfaces of constant time. We then specialize to a stationary spacetime and MHD flow with one arbitrary spatial symmetry (e.g., the stationary magnetosphere of a Kerr black hole); and for this spacetime we reduce the GRMHD equations to a set of algebraic equations. The general features of the resulting stationary, symmetric GRMHD magnetospheric solutions are discussed, including the Blandford-Znajek effect in which the gravitomagnetic field interacts with the magnetosphere to produce an outflowing jet. Then in a specific model spacetime with two spatial symmetries, which captures the key features of the Kerr geometry, we derive the GRMHD equations which govern weak, linealized perturbations of a stationary magnetosphere with outflowing jet. These perturbation equations are then Fourier analyzed in time t and in the symmetry coordinate x, and subsequently solved numerically. The numerical solutions describe the interaction of MHD waves with the gravitomagnetic field. It is found that, among other features, when an oscillatory external force is applied to the region of the magnetosphere where plasma (e⁺e^-) is being created, the magnetosphere responds especially strongly at a particular, resonant, driving frequency. The resonant frequency is that for which the perturbations appear to be stationary (time independent) in the common rest frame of the freshly created plasma and the rotating magnetic field lines. The magnetosphere of a rotating black hole, when buffeted by nonaxisymmetric magnetic fields anchored in a surrounding accretion disk, might exhibit an analogous resonance. If so then the hole's outflowing jet might be modulated at resonant frequencies ω=(m/2) Ω_H where m is an integer and Ω_H is the hole's angular velocity.

Applications of nuclear magnetic resonance spectroscopy to the study of medium-sized rings. I. Conformational properties of cycloheptane. II. Conformational properties of cycloöctane

Conformational equilibrium in medium-sized rings has been investigated by the temperature variation of the fluorine-19 n.m.r. spectra of 1, 1-difluorocycloalkanes and various substituted derivatives of them. Inversion has been found to be fast on the n.m.r. time scale at -180˚ for 1, 1-difluorocycloheptane, but slow for 1, 1-difluoro-4, 4-dimethylcycloheptane at -150˚. At low temperature, the latter compound affords a single AB pattern with a chemical-shift difference of 841 cps. which has been interpreted in terms of the twist-chair conformation with the methyl groups on the axis position and the fluorine atoms in the 4-position. At room temperature, the n.m.r. spectrum of 1, 1-difluoro-4-t-butylcycloheptane affords an AB pattern with a chemical-shift difference of 185 cps. The presence of distinct trans and gauche couplings from the adjacent hydrogens has been interpreted to suggest the existence of a single predominant form, the twist chair with the fluorine atoms on the axis position.

Investigation of 1, 1-difluorocycloöctane and 1, 1, 4, 4-tetrafluorocycloöctane has led to the detection of two kinetic processes both having activation energies of 8-10 kcal./mole but quite different A values. In light of these results eleven different conformations of cycloöctane along with a detailed description of the ways in which they may be interconverted are discussed. An interpretation involving the twist-boat conformation rapidly equilibrating through the saddle and the parallel-boat forms at room temperature is compatible with the results.

New Catalysts for the Renewable Production of Monomers for Bioplastics

Terephthalic acid (PTA) is one of the monomers used for the synthesis of the polyester, polyethylene terephthalate (PET), that is used for the large-scale manufacture of synthetic fibers and plastic bottles. PTA is largely produced from the liquid-phase oxidation of petroleum-derived p-xylene (PX). However, there are now ongoing worldwide efforts exploring alternative routes for producing PTA from renewable, biomass resources.

In this thesis, I present a new route to PTA starting from the biomass-derived platform chemical, 5-hydroxymethylfurfural (HMF). This route utilizes new, selective Diels-Alder-dehydration reactions involving ethylene and is advantageous over the previously proposed Diels-Alder-dehydration route to PTA from HMF via 2,5-dimethylfuran (DMF) since the H₂ reduction of HMF to DMF is avoided. Specifically, oxidized derivatives of HMF are reacted as is, or after etherification-esterification with methanol, with ethylene over solid Lewis acid catalysts that do not contain strong Brønsted acids in order to synthesize intermediates of PTA and its equally important diester, dimethyl terephthalate (DMT). The partially oxidized HMF, 5-(hydroxymethyl)furoic acid (HMFA) is reacted with high pressure ethylene over a pure-silica molecular sieve catalyst containing framework tin (Sn-Beta) to produce the Diels-Alder-dehydration product, 4-(hydroxymethyl)benzoic acid (HMBA), with ~30% selectivity at ~20% yield. If HMFA is protected with methanol to form methyl 5-(methoxymethyl)furan-2-carboxylate (MMFC), MMFC can react with ethylene in the presence of a pure-silica molecular sieve containing framework zirconium (Zr-Beta) to produce methyl 4-(methoxymethyl)benzenecarboxylate (MMBC) with >70% selectivity at >20% yield. HMBA and MMBC can then be oxidized to produce PTA and DMT, respectively. When Lewis acid containing mesoporous silica (MCM-41) and amorphous silica, or Brønsted acid containing zeolites (Al-Beta), are used as catalysts, a significant decrease in selectivity/yield of the Diels-Alder-dehydration product is observed.

An investigation to elucidate the reaction network and side products in the conversion of MMFC to MMBC was performed, and the main side products are found to be methyl 4-formylcyclohexa-1,3-diene-1-carboxylate and the ethylene Diels-Alder adduct of this cyclohexadiene. These products presumably form by a different dehydration pathway of the MMFC/ethylene Diels-Alder adduct and should be included when determining the overall selectivity to PTA or DMT since, like MMBC, these compounds are precursors to PTA or DMT.

Fundamental physical and chemical information on the ethylene Diels-Alder-dehydration reactions catalyzed by the Lewis acid-containing molecular sieves was obtained. Madon-Boudart experiments using Zr-Beta as catalyst show that the reaction rates are limited by chemical kinetics only (physical transport limitations are not present), all the Zr⁴⁺ centers are incorporated into the framework of the molecular sieve, and the whole molecular sieve crystal is accessible for catalysis. Apparent activation energies using Zr-Beta are low, suggesting that the overall activation energy of the system may be determined by a collection of terms and is not the true activation energy of a single chemical step.

Micromechanical damage and fracture in elastomeric polymers

This thesis aims at a simple one-parameter macroscopic model of distributed damage and fracture of polymers that is amenable to a straightforward and efficient numerical implementation. The failure model is motivated by post-mortem fractographic observations of void nucleation, growth and coalescence in polyurea stretched to failure, and accounts for the specific fracture energy per unit area attendant to rupture of the material.

Furthermore, it is shown that the macroscopic model can be rigorously derived, in the sense of optimal scaling, from a micromechanical model of chain elasticity and failure regularized by means of fractional strain-gradient elasticity. Optimal scaling laws that supply a link between the single parameter of the macroscopic model, namely the critical energy-release rate of the material, and micromechanical parameters pertaining to the elasticity and strength of the polymer chains, and to the strain-gradient elasticity regularization, are derived. Based on optimal scaling laws, it is shown how the critical energy-release rate of specific materials can be determined from test data. In addition, the scope and fidelity of the model is demonstrated by means of an example of application, namely Taylor-impact experiments of polyurea rods. Hereby, optimal transportation meshfree approximation schemes using maximum-entropy interpolation functions are employed.

Finally, a different crazing model using full derivatives of the deformation gradient and a core cut-off is presented, along with a numerical non-local regularization model. The numerical model takes into account higher-order deformation gradients in a finite element framework. It is shown how the introduction of non-locality into the model stabilizes the effect of strain localization to small volumes in materials undergoing softening. From an investigation of craze formation in the limit of large deformations, convergence studies verifying scaling properties of both local- and non-local energy contributions are presented.

Regional variations in upper mantle structure beneath North America

Several types of seismological data, including surface wave group and phase velocities, travel times from large explosions, and teleseismic travel time anomalies, have indicated that there are significant regional variations in the upper few hundred kilometers of the mantle beneath continental areas. Body wave travel times and amplitudes from large chemical and nuclear explosions are used in this study to delineate the details of these variations beneath North America.

As a preliminary step in this study, theoretical P wave travel times, apparent velocities, and amplitudes have been calculated for a number of proposed upper mantle models, those of Gutenberg, Jeffreys, Lehman, and Lukk and Nersesov. These quantities have been calculated for both P and S waves for model CIT11GB, which is derived from surface wave dispersion data. First arrival times for all the models except that of Lukk and Nersesov are in close agreement, but the travel time curves for later arrivals are both qualitatively and quantitatively very different. For model CIT11GB, there are two large, overlapping regions of triplication of the travel time curve, produced by regions of rapid velocity increase near depths of 400 and 600 km. Throughout the distance range from 10 to 40 degrees, the later arrivals produced by these discontinuities have larger amplitudes than the first arrivals. The amplitudes of body waves, in fact, are extremely sensitive to small variations in the velocity structure, and provide a powerful tool for studying structural details.

Most of eastern North America, including the Canadian Shield has a Pn velocity of about 8.1 km/sec, with a nearly abrupt increase in compressional velocity by ~ 0.3 km/sec near at a depth varying regionally between 60 and 90 km. Variations in the structure of this part of the mantle are significant even within the Canadian Shield. The low-velocity zone is a minor feature in eastern North America and is subject to pronounced regional variations. It is 30 to 50 km thick, and occurs somewhere in the depth range from 80 to 160 km. The velocity decrease is less than 0.2 km/sec.

Consideration of the absolute amplitudes indicates that the attenuation due to anelasticity is negligible for 2 hz waves in the upper 200 km along the southeastern and southwestern margins of the Canadian Shield. For compressional waves the average Q for this region is > 3000. The amplitudes also indicate that the velocity gradient is at least 2 x 10^-3 both above and below the low-velocity zone, implying that the temperature gradient is < 4.8°C/km if the regions are chemically homogeneous.

In western North America, the low-velocity zone is a pronounced feature, extending to the base of the crust and having minimum velocities of 7.7 to 7.8 km/sec. Beneath the Colorado Plateau and Southern Rocky Mountains provinces, there is a rapid velocity increase of about 0.3 km/sec, similar to that observed in eastern North America, but near a depth of 100 km.

Complicated travel time curves observed on profiles with stations in both eastern and western North America can be explained in detail by a model taking into account the lateral variations in the structure of the low-velocity zone. These variations involve primarily the velocity within the zone and the depth to the top of the zone; the depth to the bottom is, for both regions, between 140 and 160 km.

The depth to the transition zone near 400 km also varies regionally, by about 30-40 km. These differences imply variations of 250 °C in the temperature or 6 % in the iron content of the mantle, if the phase transformation of olivine to the spinel structure is assumed responsible. The structural variations at this depth are not correlated with those at shallower depths, and follow no obvious simple pattern.

The computer programs used in this study are described in the Appendices. The program TTINV (Appendix IV) fits spherically symmetric earth models to observed travel time data. The method, described in Appendix III, resembles conventional least-square fitting, using partial derivatives of the travel time with respect to the model parameters to perturb an initial model. The usual ill-conditioned nature of least-squares techniques is avoided by a technique which minimizes both the travel time residuals and the model perturbations.

Spherically symmetric earth models, however, have been found inadequate to explain most of the observed travel times in this study. TVT4, a computer program that performs ray theory calculations for a laterally inhomogeneous earth model, is described in Appendix II. Appendix I gives a derivation of seismic ray theory for an arbitrarily inhomogeneous earth model.

Smooth Banach spaces and approximations

If E and F are real Banach spaces let C^p,q(E, F) O ≤ q ≤ p ≤ ∞, denote those maps from E to F which have p continuous Frechet derivatives of which the first q derivatives are bounded. A Banach space E is defined to be C^p,q smooth if C^p,q(E,R) contains a nonzero function with bounded support. This generalizes the standard C^p smoothness classification.

If an L^p space, p ≥ 1, is C^q smooth then it is also C^q,q smooth so that in particular L^p for p an even integer is C^∞,∞ smooth and L^p for p an odd integer is C^p-1,p-1 smooth. In general, however, a C^p smooth B-space need not be C^p,p smooth. C_o is shown to be a non-C^2,2 smooth B-space although it is known to be C^∞ smooth. It is proved that if E is C^p,1 smooth then C_o(E) is C^p,1 smooth and if E has an equivalent C^p norm then c_o(E) has an equivalent C^p norm.

Various consequences of C^p,q smoothness are studied. If f ϵ C^p,q(E,F), if F is C^p,q smooth and if E is non-C^p,q smooth, then the image under f of the boundary of any bounded open subset U of E is dense in the image of U. If E is separable then E is C^p,q smooth if and only if E admits C^p,q partitions of unity; E is C^p,psmooth, p ˂∞, if and only if every closed subset of E is the zero set of some C^P function.

f ϵ C^q(E,F), 0 ≤ q ≤ p ≤ ∞, is said to be C_p,q approximable on a subset U of E if for any ϵ ˃ 0 there exists a g ϵ C^p(E,F) satisfying

sup/xϵU, O≤k≤q ‖ D^k f(x) - D^k g(x) ‖ ≤ ϵ.

It is shown that if E is separable and C^p,q smooth and if f ϵ C^q(E,F) is C_p,q approximable on some neighborhood of every point of E, then F is C_p,q approximable on all of E.

In general it is unknown whether an arbitrary function in C¹(l², R) is C_2,1 approximable and an example of a function in C¹(l², R) which may not be C_2,1 approximable is given. A weak form of C_∞,q, q≥1, to functions in C^q(l², R) is proved: Let {U_α} be a locally finite cover of l² and let {T_α} be a corresponding collection of Hilbert-Schmidt operators on l². Then for any f ϵ C^q(l²,F) such that for all α

sup ‖ D^k(f(x)-g(x))[T_αh]‖ ≤ 1.

xϵU_α,‖h‖≤1, 0≤k≤q