Particle fluid mechanics in shear flows, acoustic waves, and shock waves

Three different categories of flow problems of a fluid containing small particles are being considered here. They are: (i) a fluid containing small, non-reacting particles (Parts I and II); (ii) a fluid containing reacting particles (Parts III and IV); and (iii) a fluid containing particles of two distinct sizes with collisions between two groups of particles (Part V).

Part I

A numerical solution is obtained for a fluid containing small particles flowing over an infinite disc rotating at a constant angular velocity. It is a boundary layer type flow, and the boundary layer thickness for the mixture is estimated. For large Reynolds number, the solution suggests the boundary layer approximation of a fluid-particle mixture by assuming W = W<sub>psub>. The error introduced is consistent with the Prandtl’s boundary layer approximation. Outside the boundary layer, the flow field has to satisfy the “inviscid equation” in which the viscous stress terms are absent while the drag force between the particle cloud and the fluid is still important. Increase of particle concentration reduces the boundary layer thickness and the amount of mixture being transported outwardly is reduced. A new parameter, β = 1/Ω τ<sub>vsub>, is introduced which is also proportional to μ. The secondary flow of the particle cloud depends very much on β. For small values of β, the particle cloud velocity attains its maximum value on the surface of the disc, and for infinitely large values of β, both the radial and axial particle velocity components vanish on the surface of the disc.

Part II

The “inviscid” equation for a gas-particle mixture is linearized to describe the flow over a wavy wall. Corresponding to the Prandtl-Glauert equation for pure gas, a fourth order partial differential equation in terms of the velocity potential ϕ is obtained for the mixture. The solution is obtained for the flow over a periodic wavy wall. For equilibrium flows where λ<sub>vsub> and λ<sub>Tsub> approach zero and frozen flows in which λ<sub>vsub> and λ<sub>Tsub> become infinitely large, the flow problem is basically similar to that obtained by Ackeret for a pure gas. For finite values of λ<sub>vsub> and λ<sub>Tsub>, all quantities except v are not in phase with the wavy wall. Thus the drag coefficient C<sub>Dsub> is present even in the subsonic case, and similarly, all quantities decay exponentially for supersonic flows. The phase shift and the attenuation factor increase for increasing particle concentration.

Part III

Using the boundary layer approximation, the initial development of the combustion zone between the laminar mixing of two parallel streams of oxidizing agent and small, solid, combustible particles suspended in an inert gas is investigated. For the special case when the two streams are moving at the same speed, a Green’s function exists for the differential equations describing first order gas temperature and oxidizer concentration. Solutions in terms of error functions and exponential integrals are obtained. Reactions occur within a relatively thin region of the order of λ<sub>Dsub>. Thus, it seems advantageous in the general study of two-dimensional laminar flame problems to introduce a chemical boundary layer of thickness λ<sub>Dsub> within which reactions take place. Outside this chemical boundary layer, the flow field corresponds to the ordinary fluid dynamics without chemical reaction.

Part IV

The shock wave structure in a condensing medium of small liquid droplets suspended in a homogeneous gas-vapor mixture consists of the conventional compressive wave followed by a relaxation region in which the particle cloud and gas mixture attain momentum and thermal equilibrium. Immediately following the compressive wave, the partial pressure corresponding to the vapor concentration in the gas mixture is higher than the vapor pressure of the liquid droplets and condensation sets in. Farther downstream of the shock, evaporation appears when the particle temperature is raised by the hot surrounding gas mixture. The thickness of the condensation region depends very much on the latent heat. For relatively high latent heat, the condensation zone is small compared with Ʌ<sub>Dsub>.

For solid particles suspended initially in an inert gas, the relaxation zone immediately following the compression wave consists of a region where the particle temperature is first being raised to its melting point. When the particles are totally melted as the particle temperature is further increased, evaporation of the particles also plays a role.

The equilibrium condition downstream of the shock can be calculated and is independent of the model of the particle-gas mixture interaction.

Part V

For a gas containing particles of two distinct sizes and satisfying certain conditions, momentum transfer due to collisions between the two groups of particles can be taken into consideration using the classical elastic spherical ball model. Both in the relatively simple problem of normal shock wave and the perturbation solutions for the nozzle flow, the transfer of momentum due to collisions which decreases the velocity difference between the two groups of particles is clearly demonstrated. The difference in temperature as compared with the collisionless case is quite negligible.

Solubility and Diffusivity of Water in Lunar Basalt, and Chemical Zonation in Olivine-Hosted Melt Inclusions

I report the solubility and diffusivity of water in lunar basalt and an iron-free basaltic analogue at 1 atm and 1350 °C. Such parameters are critical for understanding the degassing histories of lunar pyroclastic glasses. Solubility experiments have been conducted over a range of fO<sub>2sub> conditions from three log units below to five log units above the iron-wüstite buffer (IW) and over a range of pH<sub>2sub>/pH<sub>2sub>O from 0.03 to 24. Quenched experimental glasses were analyzed by Fourier transform infrared spectroscopy (FTIR) and secondary ionization mass spectrometry (SIMS) and were found to contain up to ~420 ppm water. Results demonstrate that, under the conditions of our experiments: (1) hydroxyl is the only H-bearing species detected by FTIR; (2) the solubility of water is proportional to the square root of pH<sub>2sub>O in the furnace atmosphere and is independent of fO<sub>2sub> and pH<sub>2sub>/pH<sub>2sub>O; (3) the solubility of water is very similar in both melt compositions; (4) the concentration of H<sub>2sub> in our iron-free experiments is <3 ppm, even at oxygen fugacities as low as IW-2.3 and pH<sub>2sub>/pH<sub>2sub>O as high as 24; and (5) SIMS analyses of water in iron-rich glasses equilibrated under variable fO<sub>2sub> conditions can be strongly influenced by matrix effects, even when the concentrations of water in the glasses are low. Our results can be used to constrain the entrapment pressure of the lunar melt inclusions of Hauri et al. (2011).

Diffusion experiments were conducted over a range of fO<sub>2sub> conditions from IW-2.2 to IW+6.7 and over a range of pH<sub>2sub>/pH<sub>2sub>O from nominally zero to ~10. The water concentrations measured in our quenched experimental glasses by SIMS and FTIR vary from a few ppm to ~430 ppm. Water concentration gradients are well described by models in which the diffusivity of water (D^*<sub>watersub>) is assumed to be constant. The relationship between D^*<sub>watersub> and water concentration is well described by a modified speciation model (Ni et al. 2012) in which both molecular water and hydroxyl are allowed to diffuse. The success of this modified speciation model for describing our results suggests that we have resolved the diffusivity of hydroxyl in basaltic melt for the first time. Best-fit values of D^*<sub>watersub> for our experiments on lunar basalt vary within a factor of ~2 over a range of pH<sub>2sub>/pH<sub>2sub>O from 0.007 to 9.7, a range of fO<sub>2sub> from IW-2.2 to IW+4.9, and a water concentration range from ~80 ppm to ~280 ppm. The relative insensitivity of our best-fit values of D^*<sub>watersub> to variations in pH<sub>2sub> suggests that H<sub>2sub> diffusion was not significant during degassing of the lunar glasses of Saal et al. (2008). D^*<sub>watersub> during dehydration and hydration in H<sub>2sub>/CO<sub>2sub> gas mixtures are approximately the same, which supports an equilibrium boundary condition for these experiments. However, dehydration experiments into CO<sub>2sub> and CO/CO<sub>2sub> gas mixtures leave some scope for the importance of kinetics during dehydration into H-free environments. The value of D^*<sub>watersub> chosen by Saal et al. (2008) for modeling the diffusive degassing of the lunar volcanic glasses is within a factor of three of our measured value in our lunar basaltic melt at 1350 °C.

In Chapter 4 of this thesis, I document significant zonation in major, minor, trace, and volatile elements in naturally glassy olivine-hosted melt inclusions from the Siqueiros Fracture Zone and the Galapagos Islands. Components with a higher concentration in the host olivine than in the melt (MgO, FeO, Cr<sub>2sub>O<sub>3sub>, and MnO) are depleted at the edges of the zoned melt inclusions relative to their centers, whereas except for CaO, H<sub>2sub>O, and F, components with a lower concentration in the host olivine than in the melt (Al<sub>2sub>O<sub>3sub>, SiO<sub>2sub>, Na<sub>2sub>O, K<sub>2sub>O, TiO<sub>2sub>, S, and Cl) are enriched near the melt inclusion edges. This zonation is due to formation of an olivine-depleted boundary layer in the adjacent melt in response to cooling and crystallization of olivine on the walls of the melt inclusions concurrent with diffusive propagation of the boundary layer toward the inclusion center.

Concentration profiles of some components in the melt inclusions exhibit multicomponent diffusion effects such as uphill diffusion (CaO, FeO) or slowing of the diffusion of typically rapidly diffusing components (Na<sub>2sub>O, K<sub>2sub>O) by coupling to slow diffusing components such as SiO<sub>2sub> and Al<sub>2sub>O<sub>3sub>. Concentrations of H2O and F decrease towards the edges of some of the Siqueiros melt inclusions, suggesting either that these components have been lost from the inclusions into the host olivine late in their cooling histories and/or that these components are exhibiting multicomponent diffusion effects.

A model has been developed of the time-dependent evolution of MgO concentration profiles in melt inclusions due to simultaneous depletion of MgO at the inclusion walls due to olivine growth and diffusion of MgO in the melt inclusions in response to this depletion. Observed concentration profiles were fit to this model to constrain their thermal histories. Cooling rates determined by a single-stage linear cooling model are 150–13,000 °C hr^-1 from the liquidus down to ~1000 °C, consistent with previously determined cooling rates for basaltic glasses; compositional trends with melt inclusion size observed in the Siqueiros melt inclusions are described well by this simple single-stage linear cooling model. Despite the overall success of the modeling of MgO concentration profiles using a single-stage cooling history, MgO concentration profiles in some melt inclusions are better fit by a two-stage cooling history with a slower-cooling first stage followed by a faster-cooling second stage; the inferred total duration of cooling from the liquidus down to ~1000 °C is 40 s to just over one hour.

Based on our observations and models, compositions of zoned melt inclusions (even if measured at the centers of the inclusions) will typically have been diffusively fractionated relative to the initially trapped melt; for such inclusions, the initial composition cannot be simply reconstructed based on olivine-addition calculations, so caution should be exercised in application of such reconstructions to correct for post-entrapment crystallization of olivine on inclusion walls. Off-center analyses of a melt inclusion can also give results significantly fractionated relative to simple olivine crystallization.

All melt inclusions from the Siqueiros and Galapagos sample suites exhibit zoning profiles, and this feature may be nearly universal in glassy, olivine-hosted inclusions. If so, zoning profiles in melt inclusions could be widely useful to constrain late-stage syneruptive processes and as natural diffusion experiments.

Studies of dinucleoside monophosphates and monomer-polynucleotide interactions by proton magnetic resonance

The nature of the intra- and intermolecular base-stacking interactions involving several dinucleoside monophosphates in aqueous solution have been investigated by proton magnetic resonance spectrosocopy, and this method has been applied to a study of the interaction of polyuridylic acid with purine and adenosine monomers.

The pmr spectra of adenylyl (3' → 5') cytidine (ApC) and cytidylyl (3' → 5') adenosine (CpA) have been studied as a function of concentration and temperature. The results of these studies indicate that the intramolecular base-stacking interactions between the adenine and cytosine bases of these dinucleoside monophosphates are rather strong, and that the stacking tendencies are comparable for the two sequence isomers. The chemical shifts of the cytosine H<sub>5sub> and adenine H<sub>2sub> protons, and their variations with temperature, were shown to be consistent with stacked conformations in which both bases of the dinucleoside monophosphates are preferentially oriented in the anti conformation as in similar dApdC, and dCpdA (dA = deoxyadenosine; dC = deoxycytidine) segments in double helical DNA. The intramolecular stacking interaction was found to have a pronounced effect on the conformations of the ribose moieties, and these conformational changes are discussed. The concentration studies indicate extensive self-association of these dinucleoside monophosphates, and analysis of the concentration data facilitated determination of the dimerization constant for the association process as well as the nature of the intermolecular complexes.

The dependence of the ribose conformation upon the extent of intramolecular base-stacking was used to demonstrate that the base-base interaction in cytidylyl (3' → 5') cytidine (CpC) is rather strong, while there appears to be little interaction between the two uracil bases of uridylyl (3' → 5') uridine (UpU).

Studies of the binding of purine to several ribose and deoxyribose dinucleoside monophosphates show that the mode of interaction is base-stacking, and evidence for the formation of a purine-dinucleoside monophosphate intercalated complex is presented. The purine proton resonances are markedly broadened in this complex, and estimates of the purine linewidths in the complex and the equilibrium constant for purine intercalation are obtained.

A study of the interaction of unsubstitued purine with polyuridylic acid at 29°C by pmr indicated that purine binds to the uracil bases of the polymer by base-stacking. The severe broadening of the purine proton resonances observed provides strong evidence for the intercalation of purine between adjacent uracil bases of poly U. This interaction does not result in a more rigid or ordered structure for the polymer.

Investigation of the interaction between adenosine and polyuridylic acid revealed two modes of interaction between the monomer and the polymer, depending on the temperature. At temperatures above 26°C or so, monomeric adenosine binds to poly U by noncooperative A-U base stacking. Below this temperature, a rigid triple-stranded 1A:2U complex is formed, presumably via cooperative hydrogen-bonding as has previously been reported.

These results clearly illustrate the importance of base-stacking in non-specific interactions between bases, nucleosides and nucleotides, and also reveal the important role of the base-stacking interactions in cooperatively for med structures involving specific base-pairing where both types of interaction are possible.

Design, Synthesis, and Study of Novel Platforms for Iron-N2 Chemistry and Photoinduced, Copper-mediated C-N Bond Formation

Several new ligand platforms designed to support iron dinitrogen chemistry have been developed. First, we report Fe complexes of a tris(phosphino)alkyl (CP^iPr<sub>3sub>) ligand featuring an axial carbon donor intended to conceptually model the interstitial carbide atom of the nitrogenase iron-molybdenum cofactor (FeMoco). It is established that in this scaffold, the iron center binds dinitrogen trans to the C<sub>alkylsub> anchor in three structurally characterized oxidation states. Fe-C<sub>alkylsub> lengthening is observed upon reduction, reflective of significant ionic character in the Fe-C<sub>alkylsub> interaction. The anionic (CP^iPr<sub>3sub>)FeN<sub>2sub>^- species can be functionalized by a silyl electrophile to generate (CP^iPr<sub>3sub>)Fe-N<sub>2sub>SiR<sub>3sub>. This species also functions as a modest catalyst for the reduction of N<sub>2sub> to NH<sub>3sub>. Next, we introduce a new binucleating ligand scaffold that supports an Fe(μ-SAr)Fe diiron subunit that coordinates dinitrogen (N<sub>2sub>-Fe(μ-SAr)Fe-N<sub>2sub>) across at least three oxidation states (Fe^IIFe^II, Fe^IIFe^I, and Fe^IFe^I). Despite the sulfur-rich coordination environment of iron in FeMoco, synthetic examples of transition metal model complexes that bind N<sub>2sub> and also feature sulfur donor ligands remain scarce; these complexes thus represent an unusual series of low-valent diiron complexes featuring thiolate and dinitrogen ligands. The (N<sub>2sub>-Fe(μ-SAr)Fe-N<sub>2sub>) system undergoes reduction of the bound N<sub>2sub> to produce NH<sub>3sub> (~50% yield) and can efficiently catalyze the disproportionation of N<sub>2sub>H<sub>4sub> to NH<sub>3sub> and N<sub>2sub>. The present scaffold also supports dinitrogen binding concomitant with hydride as a co-ligand. Next, inspired by the importance of secondary-sphere interactions in many metalloenzymes, we present complexes of iron in two new ligand scaffolds ([SiP^NMe<sub>3sub>] and [SiP^iPr<sub>2sub>P^NMe]) that incorporate hydrogen-bond acceptors (tertiary amines) which engage in interactions with nitrogenous substrates bound to the iron center (NH<sub>3sub> and N<sub>2sub>H<sub>4sub>). Cation binding is also facilitated in anionic Fe(0)-N<sub>2sub> complexes. While Fe-N<sub>2sub> complexes of a related ligand ([SiP^iPr<sub>3sub>]) lacking hydrogen-bond acceptors produce a substantial amount of ammonia when treated with acid and reductant, the presence of the pendant amines instead facilitates the formation of metal hydride species.

Additionally, we present the development and mechanistic study of copper-mediated and copper-catalyzed photoinduced C-N bond forming reactions. Irradiation of a copper-amido complex, ((m-tol)<sub>3sub>P)<sub>2sub>Cu(carbazolide), in the presence of aryl halides furnishes N-phenylcarbazole under mild conditions. The mechanism likely proceeds via single-electron transfer from an excited state of the copper complex to the aryl halide, generating an aryl radical. An array of experimental data are consistent with a radical intermediate, including a cyclization/stereochemical investigation and a reactivity study, providing the first substantial experimental support for the viability of a radical pathway for Ullmann C-N bond formation. The copper complex can also be used as a precatalyst for Ullmann C-N couplings. We also disclose further study of catalytic C<sub>alkylsub>-N couplings using a CuI precatalyst, and discuss the likely role of [Cu(carbazolide)<sub>2sub>]^- and [Cu(carbazolide)<sub>3sub>]^- species as intermediates in these reactions.

Finally, we report a series of four-coordinate, pseudotetrahedral P<sub>3sub>Fe^II-X complexes supported by tris(phosphine)borate ([PhBP<sub>3sub>Fe^R]^-) and phosphiniminato X-type ligands (-N=PR'<sub>3sub>) that in combination tune the spin-crossover behavior of the system. Low-coordinate transition metal complexes such as these that undergo reversible spin-crossover remain rare, and the spin equilibria of these systems have been studied in detail by a suite of spectroscopic techniques.

I. Site effects and exciton structure in molecular crystals - Benzene. II. The first and second triplet states of solid benzene

The effect of intermolecular coupling in molecular energy levels (electronic and vibrational) has been investigated in neat and isotopic mixed crystals of benzene. In the isotopic mixed crystals of C<sub>6sub>H<sub>6sub>, C<sub>6sub>H<sub>5sub>D, m-C<sub>6sub>H<sub>4sub>D<sub>2sub>, p-C<sub>6sub>H<sub>4sub>D<sub>2sub>, sym-C<sub>6sub>H<sub>3sub>D<sub>3sub>, C<sub>6sub>D<sub>5sub>H, and C<sub>6sub>D<sub>6sub> in either a C<sub>6sub>H<sub>6sub> or C<sub>6sub>D<sub>6sub> host, the following phenomena have been observed and interpreted in terms of a refined Frenkel exciton theory: a) Site shifts; b) site group splittings of the degenerate ground state vibrations of C<sub>6sub>H<sub>6sub>, C<sub>6sub>D<sub>6sub>, and sym-C<sub>6sub>H<sub>3sub>D<sub>3sub>; c) the orientational effect for the isotopes without a trigonal axis in both the ¹B<sub>2usub> electronic state and the ground state vibrations; d) intrasite Fermi resonance between molecular fundamentals due to the reduced symmetry of the crystal site; and e) intermolecular or intersite Fermi resonance between nearly degenerate states of the host and guest molecules. In the neat crystal experiments on the ground state vibrations it was possible to observe many of these phenomena in conjunction with and in addition to the exciton structure.

To theoretically interpret these diverse experimental data, the concepts of interchange symmetry, the ideal mixed crystal, and site wave functions have been developed and are presented in detail. In the interpretation of the exciton data the relative signs of the intermolecular coupling constants have been emphasized, and in the limit of the ideal mixed crystal a technique is discussed for locating the exciton band center or unobserved exciton components. A differentiation between static and dynamic interactions is made in the Frenkel limit which enables the concepts of site effects and exciton coupling to be sharpened. It is thus possible to treat the crystal induced effects in such a fashion as to make their similarities and differences quite apparent.

A calculation of the ground state vibrational phenomena (site shifts and splittings, orientational effects, and exciton structure) and of the crystal lattice modes has been carried out for these systems. This calculation serves as a test of the approximations of first order Frenkel theory and the atom-atom, pair wise interaction model for the intermolecular potentials. The general form of the potential employed was V(r) = Be^-Cr - A/r⁶ ; the force constants were obtained from the potential by assuming the atoms were undergoing simple harmonic motion.

In part II the location and identification of the benzene first and second triplet states (³B<sub>1usub> and ³E<sub>1usub>) is given.

I. Nickel-Exchanged Zincosilicate Catalysts for the Oligomerization of Propylene and II. Organic SDA-Free Catalysts for the Methanol-to-Olefins Reaction

Nickel-containing catalysts are developed to oligomerize light olefins. Two nickel-containing zincosilicates (Ni-CIT-6 and Ni-Zn-MCM-41) and two nickel-containing aluminosilicates (Ni-HiAl-BEA and Ni-USY) are synthesized as catalysts to oligomerize propylene into C<sub>3nsub> (C<sub>6sub> and C<sub>9sub>) products. All catalysts oligomerize propylene, with the zincosilicates demonstrating higher average selectivities to C<sub>3nsub> products, likely due to the reduced acidity of the Zn heteroatom.

To test whether light alkanes can be incorporated into this oligomerization reaction, a supported homogeneous catalyst is combined with Ni-containing zincosilicates. The homogeneous catalyst is included to provide dehydrogenation/hydrogenation functions. When this tandem catalyst system is evaluated using a propylene/n-butane feed, no significant integration of alkanes are observed.

Ni-containing zincosilicates are reacted with 1-butene and an equimolar propylene/1-butene mixture to study other olefinic feeds. Further, other divalent metal cations such as Mn²⁺, Co²⁺, Cu²⁺, and Zn²⁺ are exchanged onto CIT-6 samples to investigate stability and potential use for other reactions. Co-CIT-6 oligomerizes propylene, albeit less effectively than Ni-CIT-6. The other M-CIT-6 samples, while not able to oligomerize light olefins, may be useful for other reactions, such as deNO<sub>xsub>.

Molecular sieves are synthesized, characterized, and used to catalyze the methanol-to-olefins (MTO) reaction. The Al concentration in SSZ-13 samples is varied to investigate the effect of Al number on MTO reactivity when compared to a SAPO-34 sample with only isolated Si Brønsted acid sites. These SSZ-13 samples display reduced transient selectivity behavior and extended reaction lifetimes as Si/Al increases; attributable to fewer paired Al sites. MTO reactivity for the higher Si/Al SSZ-13s resembles the SAPO-34 sample, suggesting that both catalysts owe their stable reaction behavior to isolated Brønsted acid sites.

Zeolites CHA and RHO are prepared without the use of organic structure-directing agents (OSDAs), dealuminated by steam treatments (500°C-800°C), and evaluated as catalysts for the MTO reaction. The effects of temperature and steam partial pressure during steaming are investigated. X-ray diffraction (XRD) and Ar physisorption show that steaming causes partial structural collapse of the zeolite, with degradation increasing with steaming temperature. ²⁷Al MAS NMR spectra of steamed materials reveal the presence of tetrahedral, pentacoordinate, and hexacoordinate aluminum.

Proton forms of as-synthesized CHA (Si/Al=2.4) and RHO (Si/Al=2.8) rapidly deactivate under MTO testing conditions (400°C, atmospheric pressure). CHA samples steamed at 600°C performed best among samples tested, showing increased olefin selectivities and catalyst lifetime. Acid washing these steamed samples further improved activity. Reaction results for RHO were similar to CHA, with the RHO sample steamed at 800°C producing the highest light olefin selectivities. Catalyst lifetime and C<sub>2sub>-C<sub>3sub> olefin selectivities increase with increasing reaction temperature for both CHA-type and RHO-type steamed samples.

I. Rigid body penetration into brittle materials. II. Phase change effect on shock wave propagation

Part I.

We have developed a technique for measuring the depth time history of rigid body penetration into brittle materials (hard rocks and concretes) under a deceleration of ~ 10⁵ g. The technique includes bar-coded projectile, sabot-projectile separation, detection and recording systems. Because the technique can give very dense data on penetration depth time history, penetration velocity can be deduced. Error analysis shows that the technique has a small intrinsic error of ~ 3-4 % in time during penetration, and 0.3 to 0.7 mm in penetration depth. A series of 4140 steel projectile penetration into G-mixture mortar targets have been conducted using the Caltech 40 mm gas/ powder gun in the velocity range of 100 to 500 m/s.

We report, for the first time, the whole depth-time history of rigid body penetration into brittle materials (the G-mixture mortar) under 10⁵ g deceleration. Based on the experimental results, including penetration depth time history, damage of recovered target and projectile materials and theoretical analysis, we find:

1. Target materials are damaged via compacting in the region in front of a projectile and via brittle radial and lateral crack propagation in the region surrounding the penetration path. The results suggest that expected cracks in front of penetrators may be stopped by a comminuted region that is induced by wave propagation. Aggregate erosion on the projectile lateral surface is < 20% of the final penetration depth. This result suggests that the effect of lateral friction on the penetration process can be ignored.

2. Final penetration depth, P<sub>maxsub>, is linearly scaled with initial projectile energy per unit cross-section area, e<sub>ssub> , when targets are intact after impact. Based on the experimental data on the mortar targets, the relation is P<sub>maxsub>(mm) 1.15e<sub>ssub> (J/mm² ) + 16.39.

3. Estimation of the energy needed to create an unit penetration volume suggests that the average pressure acting on the target material during penetration is ~ 10 to 20 times higher than the unconfined strength of target materials under quasi-static loading, and 3 to 4 times higher than the possible highest pressure due to friction and material strength and its rate dependence. In addition, the experimental data show that the interaction between cracks and the target free surface significantly affects the penetration process.

4. Based on the fact that the penetration duration, t<sub>maxsub>, increases slowly with e<sub>ssub> and does not depend on projectile radius approximately, the dependence of t<sub>maxsub> on projectile length is suggested to be described by t<sub>maxsub>(μs) = 2.08e<sub>ssub> (J/mm² + 349.0 x m/(πR²), in which m is the projectile mass in grams and R is the projectile radius in mm. The prediction from this relation is in reasonable agreement with the experimental data for different projectile lengths.

5. Deduced penetration velocity time histories suggest that whole penetration history is divided into three stages: (1) An initial stage in which the projectile velocity change is small due to very small contact area between the projectile and target materials; (2) A steady penetration stage in which projectile velocity continues to decrease smoothly; (3) A penetration stop stage in which projectile deceleration jumps up when velocities are close to a critical value of ~ 35 m/s.

6. Deduced averaged deceleration, a, in the steady penetration stage for projectiles with same dimensions is found to be a(g) = 192.4v + 1.89 x 10⁴, where v is initial projectile velocity in m/s. The average pressure acting on target materials during penetration is estimated to be very comparable to shock wave pressure.

7. A similarity of penetration process is found to be described by a relation between normalized penetration depth, P/P<sub>maxsub>, and normalized penetration time, t/t<sub>maxsub>, as P/P<sub>maxsub> = f(t/t<sub>maxsub>, where f is a function of t/t<sub>maxsub>. After f(t/t<sub>maxsub> is determined using experimental data for projectiles with 150 mm length, the penetration depth time history for projectiles with 100 mm length predicted by this relation is in good agreement with experimental data. This similarity also predicts that average deceleration increases with decreasing projectile length, that is verified by the experimental data.

8. Based on the penetration process analysis and the present data, a first principle model for rigid body penetration is suggested. The model incorporates the models for contact area between projectile and target materials, friction coefficient, penetration stop criterion, and normal stress on the projectile surface. The most important assumptions used in the model are: (1) The penetration process can be treated as a series of impact events, therefore, pressure normal to projectile surface is estimated using the Hugoniot relation of target material; (2) The necessary condition for penetration is that the pressure acting on target materials is not lower than the Hugoniot elastic limit; (3) The friction force on projectile lateral surface can be ignored due to cavitation during penetration. All the parameters involved in the model are determined based on independent experimental data. The penetration depth time histories predicted from the model are in good agreement with the experimental data.

9. Based on planar impact and previous quasi-static experimental data, the strain rate dependence of the mortar compressive strength is described by σ<sub>fsub>/σ⁰<sub>fsub> = exp(0.0905(log(έ/έ_0) ^1.14, in the strain rate range of 10^-7/s to 10³/s (σ⁰<sub>fsub> and έ are reference compressive strength and strain rate, respectively). The non-dispersive Hugoniot elastic wave in the G-mixture has an amplitude of ~ 0.14 GPa and a velocity of ~ 4.3 km/s.

Part II.

Stress wave profiles in vitreous GeO<sub>2sub> were measured using piezoresistance gauges in the pressure range of 5 to 18 GPa under planar plate and spherical projectile impact. Experimental data show that the response of vitreous GeO<sub>2sub> to planar shock loading can be divided into three stages: (1) A ramp elastic precursor has peak amplitude of 4 GPa and peak particle velocity of 333 m/s. Wave velocity decreases from initial longitudinal elastic wave velocity of 3.5 km/s to 2.9 km/s at 4 GPa; (2) A ramp wave with amplitude of 2.11 GPa follows the precursor when peak loading pressure is 8.4 GPa. Wave velocity drops to the value below bulk wave velocity in this stage; (3) A shock wave achieving final shock state forms when peak pressure is > 6 GPa. The Hugoniot relation is D = 0.917 + 1.711u (km/s) using present data and the data of Jackson and Ahrens [1979] when shock wave pressure is between 6 and 40 GPa for ρ<sub>0sub> = 3.655 gj cm³ . Based on the present data, the phase change from 4-fold to 6-fold coordination of Ge⁺⁴ with O^-2 in vitreous GeO<sub>2sub> occurs in the pressure range of 4 to 15 ± 1 GPa under planar shock loading. Comparison of the shock loading data for fused SiO<sub>2sub> to that on vitreous GeO<sub>2sub> demonstrates that transformation to the rutile structure in both media are similar. The Hugoniots of vitreous GeO<sub>2sub> and fused SiO<sub>2sub> are found to coincide approximately if pressure in fused SiO<sub>2sub> is scaled by the ratio of fused SiO<sub>2sub>to vitreous GeO<sub>2sub> density. This result, as well as the same structure, provides the basis for considering vitreous Ge0<sub>2sub> as an analogous material to fused SiO<sub>2sub> under shock loading. Experimental results from the spherical projectile impact demonstrate: (1) The supported elastic shock in fused SiO<sub>2sub> decays less rapidly than a linear elastic wave when elastic wave stress amplitude is higher than 4 GPa. The supported elastic shock in vitreous GeO<sub>2sub> decays faster than a linear elastic wave; (2) In vitreous GeO<sub>2sub> , unsupported shock waves decays with peak pressure in the phase transition range (4-15 GPa) with propagation distance, x, as α 1/x^-3.35 , close to the prediction of Chen et al. [1998]. Based on a simple analysis on spherical wave propagation, we find that the different decay rates of a spherical elastic wave in fused SiO<sub>2sub> and vitreous GeO<sub>2sub> is predictable on the base of the compressibility variation with stress under one-dimensional strain condition in the two materials.

Searches for new symmetries in pp collisions with the razor kinematic variables at √s = 7 TeV

The construction and LHC phenomenology of the razor variables M<sub>Rsub>, an event-by-event indicator of the heavy particle mass scale, and R, a dimensionless variable related to the transverse momentum imbalance of events and missing transverse energy, are presented.  The variables are used  in the analysis of the first proton-proton collisions dataset at CMS  (35 pb^-1) in a search for superpartners of the quarks and gluons, targeting indirect hints of dark matter candidates in the context of supersymmetric theoretical frameworks. The analysis produced the highest sensitivity results for SUSY to date and extended the LHC reach far beyond the previous Tevatron results.  A generalized inclusive search is subsequently presented for new heavy particle pairs produced in √s = 7 TeV proton-proton collisions at the LHC using 4.7±0.1 fb^-1 of integrated luminosity from the second LHC run of 2011.  The selected events are analyzed in the 2D razor-space of M<sub>Rsub> and R and the analysis is performed in 12 tiers of all-hadronic, single and double leptons final states in the presence and absence of b-quarks, probing the third generation sector using the event heavy-flavor content.   The search is sensitive to generic supersymmetry models with minimal assumptions about the superpartner decay chains. No excess is observed in the number or shape of event yields relative to Standard Model predictions. Exclusion limits are derived in the CMSSM framework with  gluino masses up to 800 GeV and squark masses up to 1.35 TeV excluded at 95% confidence level, depending on the model parameters. The results are also interpreted for a collection of simplified models, in which gluinos are excluded with masses as large as 1.1 TeV, for small neutralino masses, and the first-two generation squarks, stops and sbottoms are excluded for masses up to about 800, 425 and 400 GeV, respectively.

With the discovery of a new boson by the CMS and ATLAS experiments in the γ-γ and 4 lepton final states, the identity of the putative Higgs candidate must be established through the measurements of its properties. The spin and quantum numbers are of particular importance, and we describe a method for measuring the J^PC of this particle using the observed signal events in the H to ZZ^* to 4 lepton channel developed before the discovery. Adaptations of the razor kinematic variables are introduced for the H to WW^* to 2 lepton/2 neutrino channel, improving the resonance mass resolution and increasing the discovery significance. The prospects for incorporating this channel in an examination of the new boson J^PC is discussed, with indications that this it could provide complementary information to the H to ZZ^* to 4 lepton final state, particularly for measuring CP-violation in these decays.

Catalytic conversion of nitrogen to ammonia by an iron model complex

Threefold symmetric Fe phosphine complexes have been used to model the structural and functional aspects of biological N<sub>2sub> fixation by nitrogenases. Low-valent bridging Fe-S-Fe complexes in the formal oxidation states Fe(II)Fe(II), Fe(II)/Fe(I), and Fe(I)/Fe(I) have been synthesized which display rich spectroscopic and magnetic behavior. A series of cationic tris-phosphine borane (TPB) ligated Fe complexes have been synthesized and been shown to bind a variety of nitrogenous ligands including N<sub>2sub>H<sub>4sub>, NH<sub>3sub>, and NH<sub>2sub>-. These complexes are all high spin S = 3/2 and display EPR and magnetic characteristics typical of this spin state. Furthermore, a sequential protonation and reduction sequence of a terminal amide results in loss of NH<sub>3sub> and uptake of N<sub>2sub>. These stoichiometric transformations represent the final steps in potential N<sub>2sub> fixation schemes.

Treatment of an anionic FeN<sub>2sub> complex with excess acid also results in the formation of some NH<sub>3sub>, suggesting the possibility of a catalytic cycle for the conversion of N<sub>2sub> to NH<sub>3sub> mediated by Fe. Indeed, use of excess acid and reductant results in the formation of seven equivalents of NH<sub>3sub> per Fe center, demonstrating Fe mediated catalytic N<sub>2sub> fixation with acids and protons for the first time. Numerous control experiments indicate that this catalysis is likely being mediated by a molecular species.

A number of other phosphine ligated Fe complexes have also been tested for catalysis and suggest that a hemi-labile Fe-B interaction may be critical for catalysis. Additionally, various conditions for the catalysis have been investigated. These studies further support the assignment of a molecular species and delineate some of the conditions required for catalysis.

Finally, combined spectroscopic studies have been performed on a putative intermediate for catalysis. These studies converge on an assignment of this new species as a hydrazido(2-) complex. Such species have been known on group 6 metals for some time, but this represents the first characterization of this ligand on Fe. Further spectroscopic studies suggest that this species is present in catalytic mixtures, which suggests that the first steps of a distal mechanism for N<sub>2sub> fixation are feasible in this system.

Chain-forming zintl antimonides as novel thermoelectric materials

Zintl phases, a subset of intermetallic compounds characterized by covalently-bonded "sub-structures," surrounded by highly electropositive cations, exhibit precisely the characteristics desired for thermoelectric applications. The requirement that Zintl compounds satisfy the valence of anions through the formation of covalent substructures leads to many unique, complex crystal structures. Such complexity often leads to exceptionally low lattice thermal conductivity due to the containment of heat in low velocity optical modes in the phonon dispersion. To date, excellent thermoelectric properties have been demonstrated in several Zintl compounds. However, compared with the large number of known Zintl phases, very few have been investigated as thermoelectric materials.

From this pool of uninvestigated compounds, we selected a class of Zintl antimonides that share a common structural motif: anionic moieties resembling infinite chains of linked MSb<sub>4sub> tetrahedra, where $M$ is a triel element. The compounds discussed in this thesis (A<sub>5sub>M<sub>2sub>Sb<sub>6sub> and A<sub>3sub>MSb<sub>3sub>, where A = Ca or Sr and M = Al, Ga and In) crystallize as four distinct, but closely related "chain-forming" structure types. This thesis describes the thermoelectric characterization and optimization of these phases, and explores the influence of their chemistry and structure on the thermal and electronic transport properties. Due to their large unit cells, each compound exhibits exceptionally low lattice thermal conductivity (0.4 - 0.6 W/mK at 1000 K), approaching the predicted glassy minimum at high temperatures. A combination of Density Functional calculations and classical transport models were used to explain the experimentally observed electronic transport properties of each compound. Consistent with the Zintl electron counting formalism, A<sub>5sub>M<sub>2sub>Sb<sub>6sub> and A<sub>3sub>MSb<sub>3sub> phases were found to have filled valence bands and exhibit intrinsic electronic properties. Doping with divalent transition metals (Zn²⁺ and Mn²⁺) on the M³⁺ site, or Na¹⁺ on the A³⁺ site allowed for rational control of the carrier concentration and a transition towards degenerate semiconducting behavior. In optimally-doped samples, promising peak zT values between 0.4 and 0.9 were obtained, highlighting the value of continued investigations of complex Zintl phases.

I. Spectroscopic evidence for slow vibrational relaxation in excited electronic states of diatomics in rare gas solids. II. Static crystal field effects in the electronic spectra of isotopically mixed benzene crystals

Part I

Studies of vibrational relaxation in excited electronic states of simple diatomic molecules trapped in solid rare-gas matrices at low temperatures are reported. The relaxation is investigated by monitoring the emission intensity from vibrational levels of the excited electronic state to vibrational levels of the ground electronic state. The emission was in all cases excited by bombardment of the doped rare-gas solid with X-rays.

The diatomics studied and the band systems seen are: N<sub>2sub>, Vegard-Kaplan and Second Positive systems; O<sub>2sub>, Herzberg system; OH and OD, A ²Σ⁺ - X²II<sub>isub> system. The latter has been investigated only in solid Ne, where both emission and absorption spectra were recorded; observed fine structure has been partly interpreted in terms of slightly perturbed rotational motion in the solid. For N<sub>2sub>, OH, and OD emission occurred from v' > 0, establishing a vibrational relaxation time in the excited electronic state of the order, of longer than, the electronic radiative lifetime. The relative emission intensity and decay times for different v' progressions in the Vegard-Kaplan system are found to depend on the rare-gas host and the N<sub>2sub> concentration, but are independent of temperature in the range 1.7°K to 30°K.

Part II

Static crystal field effects on the absorption, fluorescence, and phosphorescence spectra of isotopically mixed benzene crystals were investigated. Evidence is presented which demonstrate that in the crystal the ground, lowest excited singlet, and lowest triplet states of the guest deviate from hexagonal symmetry. The deviation appears largest in the lowest triplet state and may be due to an intrinsic instability of the ³B<sub>1usub> state. High resolution absorption and phospho- rescence spectra are reported and analyzed in terms of site-splitting of degenerate vibrations and orientational effects. The guest phosphorescence lifetime for various benzene isotopes in C<sub>6sub>D<sub>6sub> and sym-C<sub>6sub>H<sub>3sub>D<sub>3sub> hosts is presented and discussed.

Zirconocenes as models for homogeneous Ziegler-Natta olefin polymerization catalysts

Using density functional theory, we studied the fundamental steps of olefin polymerization for zwitterionic and cationic Group IV ansa-zirconocenes and a neutral ansa- yttrocene. Complexes [H<sub>2sub>E(C<sub>5sub>H<sub>4sub>)<sub>2sub>ZrMe]ⁿ (n = 0: E = BH<sub>2sub> (1), BF<sub>2sub> (2), AlH<sub>2sub>(3); n = +: E = CH<sub>2sub>(4), SiH<sub>2sub>(5)) and H<sub>2sub>Si(C<sub>5sub>H<sub>4sub>)<sub>2sub>YMe were used as computational models. The largest differences among these three classes of compounds were the strength of olefin binding and the stability of the β-agostic alkyl intermediate towards β-hydrogen elimination. We investigated the effect of solvent on the reaction energetics for land 5. We found that in benzene the energetics became very similar except that a higher olefin insertion barrier was calculated for 1. The calculated anion affinity of [CH<sub>3sub>BF<sub>3sub>]^- was weaker towards 1 than 5. The calculated olefin binding depended primarily on the charge of the ansa linker, and the olefin insertion barrier was found to decrease steadily in the following order: [H<sub>2sub>C(C<sub>5sub>H<sub>4sub>)<sub>2sub>ZrMe]⁺ > [F<sub>2sub>B(C<sub>5sub>H<sub>4sub>)<sub>2sub>ZrMe] ≈ [H<sub>2sub>B(C<sub>5sub>H<sub>4sub>)<sub>2sub>ZrMe] > [H<sub>2sub>Si(C<sub>5sub>H<sub>4sub>)<sub>2sub>ZrMe]⁺ > [H<sub>2sub>Al(C<sub>5sub>H<sub>4sub>)<sub>2sub>ZrMe].

We prepared ansa-zirconocene dicarbonyl complexes Me<sub>2sub>ECp<sub>2sub>Zr(CO)<sub>2sub> (E = Si, C), and t-butyl substituted complexes (t-BuCp)<sub>2sub>Zr(CO)<sub>2sub>, Me<sub>2sub>E(t-BuCp)<sub>2sub>Zr(CO)<sub>2sub> (E = Si, C), (Me<sub>2sub>Si)<sub>2sub>(t-BuCp)<sub>2sub>Zr(CO)<sub>2sub> as well as analogous zirconocene complexes. Both the reduction potentials and carbonyl stretching frequencies follow the same order: Me<sub>2sub>SiCp<sub>2sub>ZrCl<sub>2sub>> Me<sub>2sub>CCp<sub>2sub>ZrCl<sub>2sub>> Cp<sub>2sub>ZrCl<sub>2sub>> (Me<sub>2sub>Si)<sub>2sub>Cp<sub>2sub>ZrCl<sub>2sub>. This ordering is a result of both the donating abilities of the cyclopentadienyl substituents and the orientation of the cyclopentadiene rings. Additionally, we prepared a series of analogous cationic zirconocene complexes [LZrOCMe<sub>3sub>][MeB(C<sub>6sub>F<sub>5sub>)<sub>3sub>] (L = CP<sub>2sub>, Me<sub>2sub>SiCp<sub>2sub>, Me<sub>2sub>CCP<sub>2sub>, (Me<sub>2sub>Si)<sub>2sub>Cp<sub>2sub>) and studied the kinetics of anion dissociation. We found that the enthalpy of anion dissociation increased from 10.3 kcal•mol^-1 to 17.6 kcal•mol^-1 as exposure of the zirconium center increased.

We also prepared series of zirconocene complexes bearing 2,2-dimethyl-2-sila-4-pentenyl substituents (and methyl-substituted olefin variants). Methide abstraction with B(C<sub>6sub>F<sub>5sub>) results in reversible coordination of the tethered olefin to the cationic zirconium center. The kinetics of olefin dissociation have been examined using NMR methods, and the effects of ligand variation for unlinked, singly [SiMe<sub>2sub>]-linked and doubly [SiMe<sub>2sub>]-linked bis(cyclopentadienyl) arrangements has been compared (ΔG‡ for olefin dissociation varies from 12.8 to 15.6 kcal•mol^-1). Methide abstraction from 1,2-(SiMe<sub>2sub>)<sub>2sub>(η⁵-C<sub>5sub>H<sub>3sub>)<sub>2sub>Zr(CH<sub>3sub>)-(CH<sub>2sub>CMe<sub>2sub>CH<sub>2sub>CH = CH<sub>2sub>) results in rapid β-allyl elimination with loss of isobutene yielding the allyl cation [{1,2-(SiMe<sub>2sub>)<sub>2sub>(η⁵-C<sub>5sub>H<sub>3sub>)<sub>2sub>Zr(η³-CH<sub>2sub>CH=CH<sub>2sub>)]⁺.

Investigations of the origin of stereocontrol in syndiospecific Ziegler-Natta polymerizations

In order to expand our understanding of the mechanism of stereocontrol in syndiospecific α-olefin polymerization, a family of Cs-symmetric, ansa-group 3 metallocenes was targeted as polymerization catalysts. The syntheses of new ansa-yttrocene and scandocene derivatives that employ the doubly [SiMe<sub>2sub>]- bridged ligand array (1,2-SiMe<sub>2sub>)<sub>2sub>{C<sub>5sub>H-3,5-(CHMe<sub>2sub>)<sub>2sub>} (where R = t- butyl, tBuThp; where R = i-propyl, iPrThp) are described. The structures of tBuThpY(µ-Cl)<sub>2sub>K(THF)<sub>2sub>, tBuThpSc(µ-Cl)<sub>2sub>K(Et<sub>2sub>O)<sub>2sub>, tBuThpYCH(SiMe<sub>3sub>)<sub>2sub>, Y<sub>2sub>{µ<sub>2sub>-(tBuThp)<sub>2sub>}(µ<sub>2sub>-H)<sub>2sub>, and tBuThpSc(µ-CH<sub>3sub>)<sub>2sub> have been examined by single crystal X-ray diffraction methods. Ansa-yttrocenes and scandocenes that incorporate the singly [CPh<sub>2sub>]-bridged ligand array (CPh<sub>2sub>)(C<sub>5sub>H<sub>4sub>)(C<sub>13sub>H<sub>8sub>)(where C<sub>5sub>H<sub>4sub> = Cp, cyclopentadienyl; where C<sub>13sub>H<sub>8sub> = Flu, fluourenyl) have also been prepared. Select meallocene alkyl complexes are active single component catalysts for homopolymerization of propylene and 1-pentene. The scandocene tetramethylaluminate complexes generate polymers with the highes molecular weights of the series. Under all conditions examined atactic polymer microstructures are observed, suggesting a chain-end mechanism for stereocontrol.

A series of ansa-tantalocenes have been prepared as models for Ziegler-Natta polymerization catalysts. A singly bridged ansa-tantalocene trimethyl complex, Me<sub>2sub>Si(η⁵-C<sub>5sub>H<sub>4sub>)<sub>2sub>TaMe<sub>3sub>, has been prepared and used for the synthesis of a tantalocene ethylene-methyl complex. Addition of propylene to this ethylene-methyl adduct results in olefin exchange to give a mixture of endo and exo propylene isomers. Doubly-silylene bridged ansa-tantalocene complexes have been prepared with the tBuThp ligand; a tantalocene trimethyl complex and a tantalocene methylidene-methyl complex have been synthesized and characterized by X-ray diffraction. Thermolysis of the methylidene-methyl complex affords the corresponding ethylene-hydride complex. Addition of either propylene or styrene to this ethylene-hydride compound results in olefin exchange. In both cases, only one product isomer is observed. Studies of olefin exchange with ansa-tantalocene olefin-hydride and olefin-methyl complexes have provided information about the important steric influences for olefin coordination in Ziegler-Natta polymerization.

Ancillary ligand effects : from zirconium(IV)-catalyzed homogeneous propylene polymerization to platinum(II)-mediated C-H bond activation

A series of C<sub>ssub>- and C<sub>1sub>-symmetric doubly-linked ansa-metallocenes of the general formula {1,1'-SiMe<sub>2sub>-2,2'-E-('ƞ⁵-C<sub>5sub>H<sub>2sub>-4-R¹)-(ƞ⁵-C<sub>5sub>H-3',5'-(CHMe<sub>2sub>)<sub>2sub>)}ZrC<sub>2sub> (E = SiMe<sub>2sub> (1), SiPh<sub>2sub> (2), SiMe<sub>2sub> -SiMe<sub>2sub> (3); R¹ = H, CHMe<sub>2sub>, C<sub>5sub>H<sub>9sub>, C<sub>6sub>H<sub>11sub>, C<sub>6sub>H<sub>5sub>) has been prepared. When activated by methylaluminoxane, these are active propylene polymerization catalysts. 1 and 2 produce syndiotactic polypropylenes, and 3 produces isotactic polypropylenes. Site epimerization is the major pathway for stereoerror formation for 1 and 2. In addition, the polymer chain has slightly stronger steric interaction with the diphenylsilylene linker than with the dimethylsilylene linker. This results in more frequent site epimerization and reduced syndiospecificity for 2 compared to 1.

C<sub>1sub>-Symmetric ansa-zirconocenes [1,1 '-SiMe<sub>2sub>-(C<sub>5sub>H<sub>4sub>)-(3-R-C<sub>5sub>H<sub>3sub>)]ZrCl<sub>2sub> (4), [1,1 '-SiMe<sub>2sub>-(C<sub>5sub>H<sub>4sub>)-(2,4-R<sub>2sub>-C<sub>5sub>H<sub>2sub>)]ZrCl<sub>2sub> (5) and [1,1 '-SiMe<sub>2sub>-2,2 '-(SiMe<sub>2sub>-SiMe<sub>2sub>)-(C<sub>5sub>H<sub>3sub>)-( 4-R-C<sub>5sub>H<sub>2sub>)]ZrCl<sub>2sub> (6) have been prepared to probe the origin of isospecificity in 3. While 4 and 3 produce polymers with similar isospecificity, 5 and 6 give mostly hemi-isotactic-like polymers. It is proposed that the facile site epimerization via an associative pathway allows rapid equilibration of the polymer chain between the isospecific and aspecific insertion sites. This results in more frequent insertion from the isospecific site, which has a lower kinetic barrier for chain propagation. On the other hand, site epimerization for 5 and 6 is slow. This leads to mostly alternating insertion from the isospecific and aspecific sites, and consequently, a hemi-isotactic-like polymers. In comparison, site epimerization is even slower for 3, but enchainment from the aspecific site has an extremely high kinetic barrier for monomer coordination. Therefore, enchainment occurs preferentially from the isospecific site to produce isotactic polymers.

A series of cationic complexes [(ArN=CR-CR=NAr)PtMe(L)]⁺[BF<sub>4sub>]⁺ (Ar = aryl; R = H, CH<sub>3sub>; L = water, trifluoroethanol) has been prepared. They react smoothly with benzene at approximately room temperature in trifluoroethanol solvent to yield methane and the corresponding phenyl Pt(II) cations, via Pt(IV)-methyl-phenyl-hydride intermediates. The reaction products of methyl-substituted benzenes suggest an inherent reactivity preference for aromatic over benzylic C-H bond activation, which can however be overridden by steric effects. For the reaction of benzene with cationic Pt(II) complexes, in which the diimine ligands bear 3,5-disubstituted aryl groups at the nitrogen atoms, the rate-determining step is C-H bond activation. For the more sterically crowded analogs with 2,6-dimethyl-substituted aryl groups, benzene coordination becomes rate-determining. The more electron-rich the ligand, as reflected by the CO stretching frequency in the IR spectrum of the corresponding cationic carbonyl complex, the faster the rate of C-H bond activation. This finding, however, does not reflect the actual C-H bond activation process, but rather reflects only the relative ease of solvent molecules displacing water molecules to initiate the reaction. That is, the change in rates is mostly due to a ground state effect. Several lines of evidence suggest that associative substitution pathways operate to get the hydrocarbon substrate into, and out of, the coordination sphere; i.e., that benzene substitution proceeds by a solvent- (TFE-) assisted associative pathway.

Temperature effects on the activity coefficient of the bicarbonate ion

Natural waters may be chemically studied as mixed electrolyte solutions. Some important equilibrium properties of natural waters are intimately related to the activity-concentration ratios (i.e., activity coefficients) of the ions in solution. An Ion Interaction Model, which is based on Pitzer's (1973) thermodynamic model, is proposed in this dissertation. The proposed model is capable of describing the activity coefficient of ions in mixed electrolyte solutions. The effects of temperature on the equilibrium conditions of natural waters and on the activity coefficients of the ions in solution, may be predicted by means of the Ion Interaction Model presented in this work.

The bicarbonate ion, HCO<sub>3sub>^-, is commonly found in natural waters. This anion plays an important role in the chemical and thermodynamic properties of water bodies. Such properties are usually directly related to the activity coefficient of HCO<sub>3sub>^- in solution. The Ion Interaction Model, as proposed in this dissertation, is used to describe indirectly measured activity coefficients of HCO<sub>3sub>^- in mixed electrolyte solutions.

Experimental pH measurements of MCl-MHCO<sub>3sub> and MCl-H<sub>2sub>CO<sub>3sub> solutions at 25°C (where M = K⁺, Na⁺, NH<sub>4sub>⁺, Ca²⁺ or Mg²⁺) are used in this dissertation to evaluate indirectly the MHCO<sub>3sub> virial coefficients. Such coefficients permit the prediction of the activity coefficient of HCO<sub>3sub>^- in mixed electrolyte solutions. The Ion Interaction Model is found to be an accurate method for predicting the activity coefficient of HCO<sub>3sub>^- within the experimental ionic strengths (0.2 to 3.0 m). The virial coefficients of KHCO<sub>3sub> and NaHCO<sub>3sub> and their respective temperature variations are obtained from similar experimental measurements at 10° and 40°C. The temperature effects on the NH<sub>4sub>HCO<sub>3sub>, Ca(HCO<sub>3sub>)<sub>2sub>, and Mg(HCO<sub>3sub>)<sub>2sub> virial coefficients are estimated based on these results and the temperature variations of the virial coefficients of 40 other electrolytes.

Finally, the Ion Interaction Model is utilized to solve various problems of water chemistry where bicarbonate is present in solution.