Model studies of Ziegler-Natta olefin polymerization using group 3 and group 4 metallocenes

Evidence for the stereochemical isomerization of a variety of ansa metallocene compounds is presented. For the scandocene allyl derivatives described here, we have established that the process is promoted by a variety of salts in both ether and hydrocarbon solvents and is not accelerated by light. A plausible mechanism based on an earlier proposal by Marks, et al., is offered as an explanation of this process. It involves coordination of anions and/or donor solvents to the metal center with cation assistance to encourage metalcyclopentadienyl bond heterolysis, rotation about the Si-Cp bond of the detached cyclopentadienide and recoordination of the opposite face. Our observations in some cases of thermodynamic racemic:meso ratios under the reaction conditions commonly used for the synthesis of the metallocene chlorides suggests that the interchange is faster than metallation, such that the composition of the reaction mixture is determined by thermodynamic, not kinetic, control in these cases.

Two new ansa-scandocene alkenyl compounds react with olefins resulting in the formation of η³-allyl complexes. Kinetics and labeling experiments indicate a tuck-in intermediate on the reaction pathway; in this intermediate the metal is bound to the carbon adjacent to the silyllinker in the rear of the metallocene wedge. In contrast, reaction of permethylscandocene alkenyl compounds with olefins results, almost exclusively, in vinylic C-H bond activation. It is proposed that relieving transition state steric interactions between the cyclopentadienyl rings and the olefin by either linking the rings together or using a larger lanthanide metal may allow for olefin coordination, stabilizing the transition state for allylic σ-bond metathesis.

A selectively isotopically labeled propylene, CH₂CD(¹³CH₃), was synthesized and its polymerization was carried out at low concentration in toluene solution using isospecific metallocene catalysts. Analysis of the NMR spectra (¹³C, ¹H, and ²H) of the resultant polymers revealed that the production of stereoerrors through chain epimerization proceeds exclusively by the tertiaryalkyl mechanism. Additionally, enantiofacial inversion of the terminally unsaturated polymer chain occurs by a non-dissociative process. The implications of these results on the mechanism of olefin polymerization with these catalysts is discussed.

Continuous stochastic processes

A general review of stochastic processes is given in the introduction; definitions, properties and a rough classification are presented together with the position and scope of the author's work as it fits into the general scheme.

The first section presents a brief summary of the pertinent analytical properties of continuous stochastic processes and their probability-theoretic foundations which are used in the sequel.

The remaining two sections (II and III), comprising the body of the work, are the author's contribution to the theory. It turns out that a very inclusive class of continuous stochastic processes are characterized by a fundamental partial differential equation and its adjoint (the Fokker-Planck equations). The coefficients appearing in those equations assimilate, in a most concise way, all the salient properties of the process, freed from boundary value considerations. The writer’s work consists in characterizing the processes through these coefficients without recourse to solving the partial differential equations.

First, a class of coefficients leading to a unique, continuous process is presented, and several facts are proven to show why this class is restricted. Then, in terms of the coefficients, the unconditional statistics are deduced, these being the mean, variance and covariance. The most general class of coefficients leading to the Gaussian distribution is deduced, and a complete characterization of these processes is presented. By specializing the coefficients, all the known stochastic processes may be readily studied, and some examples of these are presented; viz. the Einstein process, Bachelier process, Ornstein-Uhlenbeck process, etc. The calculations are effectively reduced down to ordinary first order differential equations, and in addition to giving a comprehensive characterization, the derivations are materially simplified over the solution to the original partial differential equations.

In the last section the properties of the integral process are presented. After an expository section on the definition, meaning, and importance of the integral process, a particular example is carried through starting from basic definition. This illustrates the fundamental properties, and an inherent paradox. Next the basic coefficients of the integral process are studied in terms of the original coefficients, and the integral process is uniquely characterized. It is shown that the integral process, with a slight modification, is a continuous Markoff process.

The elementary statistics of the integral process are deduced: means, variances, and covariances, in terms of the original coefficients. It is shown that an integral process is never temporally homogeneous in a non-degenerate process.

Finally, in terms of the original class of admissible coefficients, the statistics of the integral process are explicitly presented, and the integral process of all known continuous processes are specified.

I. Quantal effects in biochemical cooperativity and a proposed mechanism for the differentiation of calcium signaling in synaptic plasticity. II. Evolutionary algorithms for the optimization of methods in computational chemistry

In Part 1 of this thesis, we propose that biochemical cooperativity is a fundamentally non-ideal process. We show quantal effects underlying biochemical cooperativity and highlight apparent ergodic breaking at small volumes. The apparent ergodic breaking manifests itself in a divergence of deterministic and stochastic models. We further predict that this divergence of deterministic and stochastic results is a failure of the deterministic methods rather than an issue of stochastic simulations.

Ergodic breaking at small volumes may allow these molecular complexes to function as switches to a greater degree than has previously been shown. We propose that this ergodic breaking is a phenomenon that the synapse might exploit to differentiate Ca$^{2+}$ signaling that would lead to either the strengthening or weakening of a synapse. Techniques such as lattice-based statistics and rule-based modeling are tools that allow us to directly confront this non-ideality. A natural next step to understanding the chemical physics that underlies these processes is to consider \textit{in silico} specifically atomistic simulation methods that might augment our modeling efforts.

In the second part of this thesis, we use evolutionary algorithms to optimize \textit{in silico} methods that might be used to describe biochemical processes at the subcellular and molecular levels. While we have applied evolutionary algorithms to several methods, this thesis will focus on the optimization of charge equilibration methods. Accurate charges are essential to understanding the electrostatic interactions that are involved in ligand binding, as frequently discussed in the first part of this thesis.

Part I: The abortive infection of bacteriophage øx174 at low temperatures. Part II: The early stages in the process of infection by bacteriophage øx174

Part I

The infection of E. coli by ΦX174 at 15°C is abortive; the cells are killed by the infection but neither mature phage nor SS (single-stranded) DNA are synthesized. Parental RF (replicative form) is formed and subsequently replicated at 15°C. The RF made at 15°C shows normal infectivity and full competence to act as precursor to progeny SS DNA after an increase in temperature to 37°C. The investigations suggest that all of the proteins required for SS DNA synthesis and phage maturation are present in the abortive infection at 15°C.

Three possible causes are suggested for the abortive infection at 15°C: (a) A virus-coded protein whose role is essential to the infection is made at 15°C and assumes its native conformation, but its rate of activity is too low at this temperature to sustain the infection process. (b) Virus maturation may involve the formation of a DNA-protein complex and conformational changes which have an energy threshold infrequently reached at 15°C. (c) A host-coded protein present in uninfected cells, and whose activity is essential to the infection at all temperatures, but not to the host at 15°C, is inactive at 15°C. An hypothesis of this type is offered which proposes that the temperature-limiting factor in SS DNA synthesis in vivo may reflect a temperature-dependent property of the host DNA polymerase.

Part II

Three distinct stages are demonstrated in the process whereby ΦX174 invades its host: (1) Attachment: The phage attach to the cell in a manner that does not irreversibly alter the phage particle and which exhibits "single-hit" kinetics. The total charge on the phage particle is demonstrated to be important in determining the rate at which stable attachment is effected. The proteins specified by ΦX cistrons II, III and VII play roles, which may be indirect, in the attachment reaction. (2) Eclipse: 'The attached phage undergo a conformational change. Some of the altered phage particles spontaneously detach from the cell (in a non-infective form) while the remainder are more tightly bound to the cell. The altered phage particles detached (spontaneously or chemically) from such complexes have at least 40% of their DNA extruded from the phage coat. It is proposed that this particle is, or derives from, a direct intermediate in the penetration of the viral DNA.

The kinetics for the eclipse of attached phage particles are first-order with respect to phage concentration and biphasic; about 85% of the phage eclipse at one rate (k = 0.86 min^-1) and the remainder do so at a distinctly lesser rate (k = 0.21 min^-1).

The eclipse event is very temperature-dependent and has the relatively high Arrhenius activation energy of 36.6 kcal/mole, indicating the cooperative nature of the process. The temperature threshold for eclipse is 17 to 18°C.

At present no specific ΦX cistron is identified as affecting the eclipse process. (3) DNA penetration: A fraction of the attached, eclipsed phage particles corresponding in number to the plaque-forming units complete DNA penetration. The penetrated DNA is found in the cell as RF, and the empty phage protein coat remains firmly attached to the exterior of the cell. This step is inhibited by prior irradiation of the phage with relatively high doses of UV light and is insensitive to the presence of KCN and NaN₃. Temporally excluded superinfecting phages do not achieve DNA penetration.

Both eclipsed phage particles and empty phage protein coats may be dissociated from infected cells; some of their properties are described.

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_max, is linearly scaled with initial projectile energy per unit cross-section area, e_s , when targets are intact after impact. Based on the experimental data on the mortar targets, the relation is P_max(mm) 1.15e_s (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_max, increases slowly with e_s and does not depend on projectile radius approximately, the dependence of t_max on projectile length is suggested to be described by t_max(μs) = 2.08e_s (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_max, and normalized penetration time, t/t_max, as P/P_max = f(t/t_max, where f is a function of t/t_max. After f(t/t_max 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_f/σ⁰_f = exp(0.0905(log(έ/έ_0) ^1.14, in the strain rate range of 10^-7/s to 10³/s (σ⁰_f 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 GeO₂ 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 GeO₂ 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 ρ₀ = 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 GeO₂ occurs in the pressure range of 4 to 15 ± 1 GPa under planar shock loading. Comparison of the shock loading data for fused SiO₂ to that on vitreous GeO₂ demonstrates that transformation to the rutile structure in both media are similar. The Hugoniots of vitreous GeO₂ and fused SiO₂ are found to coincide approximately if pressure in fused SiO₂ is scaled by the ratio of fused SiO₂to vitreous GeO₂ density. This result, as well as the same structure, provides the basis for considering vitreous Ge0₂ as an analogous material to fused SiO₂ under shock loading. Experimental results from the spherical projectile impact demonstrate: (1) The supported elastic shock in fused SiO₂ decays less rapidly than a linear elastic wave when elastic wave stress amplitude is higher than 4 GPa. The supported elastic shock in vitreous GeO₂ decays faster than a linear elastic wave; (2) In vitreous GeO₂ , 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 SiO₂ and vitreous GeO₂ is predictable on the base of the compressibility variation with stress under one-dimensional strain condition in the two materials.

Social saliency : visual psychophysics and single-neuron recordings in humans

My thesis studies how people pay attention to other people and the environment. How does the brain figure out what is important and what are the neural mechanisms underlying attention? What is special about salient social cues compared to salient non-social cues? In Chapter I, I review social cues that attract attention, with an emphasis on the neurobiology of these social cues. I also review neurological and psychiatric links: the relationship between saliency, the amygdala and autism. The first empirical chapter then begins by noting that people constantly move in the environment. In Chapter II, I study the spatial cues that attract attention during locomotion using a cued speeded discrimination task. I found that when the motion was expansive, attention was attracted towards the singular point of the optic flow (the focus of expansion, FOE) in a sustained fashion. The more ecologically valid the motion features became (e.g., temporal expansion of each object, spatial depth structure implied by distribution of the size of the objects), the stronger the attentional effects. However, compared to inanimate objects and cues, people preferentially attend to animals and faces, a process in which the amygdala is thought to play an important role. To directly compare social cues and non-social cues in the same experiment and investigate the neural structures processing social cues, in Chapter III, I employ a change detection task and test four rare patients with bilateral amygdala lesions. All four amygdala patients showed a normal pattern of reliably faster and more accurate detection of animate stimuli, suggesting that advantageous processing of social cues can be preserved even without the amygdala, a key structure of the “social brain”. People not only attend to faces, but also pay attention to others’ facial emotions and analyze faces in great detail. Humans have a dedicated system for processing faces and the amygdala has long been associated with a key role in recognizing facial emotions. In Chapter IV, I study the neural mechanisms of emotion perception and find that single neurons in the human amygdala are selective for subjective judgment of others’ emotions. Lastly, people typically pay special attention to faces and people, but people with autism spectrum disorders (ASD) might not. To further study social attention and explore possible deficits of social attention in autism, in Chapter V, I employ a visual search task and show that people with ASD have reduced attention, especially social attention, to target-congruent objects in the search array. This deficit cannot be explained by low-level visual properties of the stimuli and is independent of the amygdala, but it is dependent on task demands. Overall, through visual psychophysics with concurrent eye-tracking, my thesis found and analyzed socially salient cues and compared social vs. non-social cues and healthy vs. clinical populations. Neural mechanisms underlying social saliency were elucidated through electrophysiology and lesion studies. I finally propose further research questions based on the findings in my thesis and introduce my follow-up studies and preliminary results beyond the scope of this thesis in the very last section, Future Directions.

Progress in numerical modeling of non-premixed combustion

Progress is made on the numerical modeling of both laminar and turbulent non-premixed flames. Instead of solving the transport equations for the numerous species involved in the combustion process, the present study proposes reduced-order combustion models based on local flame structures.

For laminar non-premixed flames, curvature and multi-dimensional diffusion effects are found critical for the accurate prediction of sooting tendencies. A new numerical model based on modified flamelet equations is proposed. Sooting tendencies are calculated numerically using the proposed model for a wide range of species. These first numerically-computed sooting tendencies are in good agreement with experimental data. To further quantify curvature and multi-dimensional effects, a general flamelet formulation is derived mathematically. A budget analysis of the general flamelet equations is performed on an axisymmetric laminar diffusion flame. A new chemistry tabulation method based on the general flamelet formulation is proposed. This new tabulation method is applied to the same flame and demonstrates significant improvement compared to previous techniques.

For turbulent non-premixed flames, a new model to account for chemistry-turbulence interactions is proposed. %It is found that these interactions are not important for radicals and small species, but substantial for aromatic species. The validity of various existing flamelet-based chemistry tabulation methods is examined, and a new linear relaxation model is proposed for aromatic species. The proposed relaxation model is validated against full chemistry calculations. To further quantify the importance of aromatic chemistry-turbulence interactions, Large-Eddy Simulations (LES) have been performed on a turbulent sooting jet flame. %The aforementioned relaxation model is used to provide closure for the chemical source terms of transported aromatic species. The effects of turbulent unsteadiness on soot are highlighted by comparing the LES results with a separate LES using fully-tabulated chemistry. It is shown that turbulent unsteady effects are of critical importance for the accurate prediction of not only the inception locations, but also the magnitude and fluctuations of soot.

Seismic structure along transitions from flat to normal subduction: central Mexico, southern Peru, and southwest Japan

The fine-scale seismic structure of the central Mexico, southern Peru, and southwest Japan subduction zones is studied using intraslab earthquakes recorded by temporary and permanent regional seismic arrays. The morphology of the transition from flat to normal subduction is explored in central Mexico and southern Peru, while in southwest Japan the spatial coincidence of a thin ultra-slow velocity layer (USL) atop the flat slab with locations of slow slip events (SSEs) is explored. This USL is also observed in central Mexico and southern Peru, where its lateral extent is used as one constraint on the nature of the flat-to-normal transitions.

In western central Mexico, I find an edge to this USL which is coincident with the western boundary of the projected Orozco Fracture Zone (OFZ) region. Forward modeling of the 2D structure of the subducted Cocos plate using a finite-difference algorithm provides constraints on the velocity and geometry of the slab’s seismic structure in this region and confirms the location of the USL edge. I propose that the Cocos slab is currently fragmenting into a North Cocos plate and a South Cocos plate along the projection of the OFZ, by a process analogous to that which occurred when the Rivera plate separated from the proto-Cocos plate 10 Ma.

In eastern central Mexico, observations of a sharp transition in slab dip near the abrupt end of the Trans Mexican Volcanic Belt (TMVB) suggest a possible slab tear located within the subducted South Cocos plate. The eastern lateral extent of the USL is found to be coincident with these features and with the western boundary of a zone of decreased seismicity, indicating a change in structure which I interpret as evidence of a possible tear. Analysis of intraslab seismicity patterns and focal mechanism orientations and faulting types provides further support for a possible tear in the South Cocos slab. This potential tear, together with the tear along the projection of the OFZ to the northwest, indicates a slab rollback mechanism in which separate slab segments move independently, allowing for mantle flow between the segments.

In southern Peru, observations of a gradual increase in slab dip coupled with a lack of any gaps or vertical offsets in the intraslab seismicity suggest a smooth contortion of the slab. Concentrations of focal mechanisms at orientations which are indicative of slab bending are also observed along the change in slab geometry. The lateral extent of the USL atop the horizontal Nazca slab is found to be coincident with the margin of the projected linear continuation of the subducting Nazca Ridge, implying a causal relationship, but not a slab tear. Waveform modeling of the 2D structure in southern Peru provides constraints on the velocity and geometry of the slab’s seismic structure and confirms the absence of any tears in the slab.

In southwest Japan, I estimate the location of a possible USL along the Philippine Sea slab surface and find this region of low velocity to be coincident with locations of SSEs that have occurred in this region. I interpret the source of the possible USL in this region as fluids dehydrated from the subducting plate, forming a high pore-fluid pressure layer, which would be expected to decrease the coupling on the plate interface and promote SSEs.

Suspension mechanics: I. Inertial and non-Newtonian migration of neutrally buoyant rigid spheres in two-dimensional unidirectional flows; II. The effect of viscoelasticity on the creeping motion of a train of neutrally buoyant Newtonian drops through a circular tube

The lateral migration of neutrally buoyant rigid spheres in two-dimensional unidirectional flows was studied theoretically. The cases of both inertia-induced migration in a Newtonian fluid and normal stress-induced migration in a second-order fluid were considered. Analytical results for the lateral velocities were obtained, and the equilibrium positions and trajectories of the spheres compared favorably with the experimental data available in the literature. The effective viscosity was obtained for a dilute suspension of spheres which were simultaneously undergoing inertia-induced migration and translational Brownian motion in a plane Poiseuille flow. The migration of spheres suspended in a second-order fluid inside a screw extruder was also considered.

The creeping motion of neutrally buoyant concentrically located Newtonian drops through a circular tube was studied experimentally for drops which have an undeformed radius comparable to that of the tube. Both a Newtonian and a viscoelastic suspending fluid were used in order to determine the influence of viscoelasticity. The extra pressure drop due to the presence of the suspended drops, the shape and velocity of the drops, and the streamlines of the flow were obtained for various viscosity ratios, total flow rates, and drop sizes. The results were compared with existing theoretical and experimental data.

Photochemical electron transfer at fixed distance : a synthetic model of the photosynthetic primary process

A series of meso-phenyloctamethylporphyrins covalently bonded at the 4'phenyl position to quinones via rigid bicyclo[2.2.2]octane spacers were synthesized for the study of the dependence of electron transfer reaction rate on solvent, distance, temperature, and energy gap. A general and convergent synthesis was developed based on the condensation of ac-biladienes with masked quinonespacer-benzaldehydes. From picosecond fluorescence spectroscopy emission lifetimes were measured in seven solvents of varying polarity. Rate constants were determined to vary from 5.0x10⁹sec^-1 in N,N-dimethylformamide to 1.15x10¹⁰ Sec^-1 in benzene, and were observed to rise at most by about a factor of three with decreasing solvent polarity. Experiments at low temperature in 2-MTHF glass (77K) revealed fast, nearly temperature-independent electron transfer characterized by non-exponential fluorescence decays, in contrast to monophasic behavior in fluid solution at 298K. This example evidently represents the first photosynthetic model system not based on proteins to display nearly temperature-independent electron transfer at high temperatures (nuclear tunneling). Low temperatures appear to freeze out the rotational motion of the chromophores, and the observed nonexponential fluorescence decays may be explained as a result of electron transfer from an ensemble of rotational conformations. The nonexponentiality demonstrates the sensitivity of the electron transfer rate to the precise magnitude of the electronic matrix element, which supports the expectation that electron transfer is nonadiabatic in this system. The addition of a second bicyclooctane moiety (15 Å vs. 18 Å edge-to-edge between porphyrin and quinone) reduces the transfer rate by at least a factor of 500-1500. Porphyrinquinones with variously substituted quinones allowed an examination of the dependence of the electron transfer rate constant κ_ET on reaction driving force. The classical trend of increasing rate versus increasing exothermicity occurs from 0.7 eV≤ |ΔG^0'(R)| ≤ 1.0 eV until a maximum is reached (κ_ET = 3 x 10⁸ sec^-1 rising to 1.15 x 10¹⁰ sec^-1 in acetonitrile). The rate remains insensitive to ΔG⁰ for ~ 300 mV from 1.0 eV≤ |ΔG^0’(R)| ≤ 1.3 eV, and then slightly decreases in the most exothermic case studied (cyanoquinone, κ_ET = 5 x 10⁹ sec^-1).

The Design and Synthesis of Transition Metal Complexes Supported by Non-innocent Ligand Scaffolds for Small Molecule Activation

This dissertation focuses on the incorporation of non-innocent or multifunctional moieties into different ligand scaffolds to support one or multiple metal centers in close proximity. Chapter 2 focuses on the initial efforts to synthesize hetero- or homometallic tri- or dinuclear metal carbonyl complexes supported by para-terphenyl diphosphine ligands. A series of [M₂M’(CO)₄]-type clusters (M = Ni, Pd; M’ = Fe, Co) could be accessed and used to relate the metal composition to the properties of the complexes. During these studies it was also found that non-innocent behavior was observed in dinuclear Fe complexes that result from changes in oxidation state of the cluster. These studies led to efforts to rationally incorporate central arene moieties capable managing both protons and electrons during small molecule activation.

Chapter 3 discusses the synthesis of metal complexes supported by a novel para-terphenyl diphosphine ligand containing a non-innocent 1,4-hydroquinone moiety as the central arene. A Pd⁰-hydroquinone complex was found to mediate the activation of a variety of small molecules to form the corresponding Pd⁰-quinone complexes in a formal two proton ⁄ two electron transformation. Mechanistic investigations of dioxygen activation revealed a metal-first activation process followed by subsequent proton and electron transfer from the ligand. These studies revealed the capacity of the central arene substituent to serve as a reservoir for a formal equivalent of dihydrogen, although the stability of the M-quinone compounds prevented access to the PdII-quinone oxidation state, thus hindering of small molecule transformations requiring more than two electrons per equivalent of metal complex.

Chapter 4 discusses the synthesis of metal complexes supported by a ligand containing a 3,5-substituted pyridine moiety as the linker separating the phenylene phosphine donors. Nickel and palladium complexes supported by this ligand were found to tolerate a wide variety of pyridine nitrogen-coordinated electrophiles which were found to alter central pyridine electronics, and therefore metal-pyridine π-system interactions, substantially. Furthermore, nickel complexes supported by this ligand were found to activate H-B and H-Si bonds and formally hydroborate and hydrosilylate the central pyridine ring. These systems highlight the potential use of pyridine π-system-coordinated metal complexes to reversibly store reducing equivalents within the ligand framework in a manner akin to the previously discussed 1,4-hydroquinone diphosphine ligand scaffold.

Chapter 5 departs from the phosphine-based chemistry and instead focuses on the incorporation of hydrogen bonding networks into the secondary coordination sphere of [Fe₄(μ₄-O)]-type clusters supported by various pyrazolate ligands. The aim of this project is to stabilize reactive oxygenic species, such as oxos, to study their spectroscopy and reactivity in the context of complicated multimetallic clusters. Herein is reported this synthesis and electrochemical and Mössbauer characterization of a series of chloride clusters have been synthesized using parent pyrazolate and a 3-aminophenyl substituted pyrazolate ligand. Efforts to rationally access hydroxo and oxo clusters from these chloride precursors represents ongoing work that will continue in the group.

Appendix A discusses attempts to access [Fe₃Ni]-type clusters as models of the enzymatic active site of [NiFe] carbon monoxide dehydrogenase. Efforts to construct tetranuclear clusters with an interstitial sulfide proved unsuccessful, although a (μ₃-S) ligand could be installed through non-oxidative routes into triiron clusters. While [Fe₃Ni(μ₄-O)]-type clusters could be assembled, accessing an open heterobimetallic edge site proved challenging, thus prohibiting efforts to study chemical transformations, such as hydroxide attack onto carbon monoxide or carbon dioxide coordination, relevant to the native enzyme. Appendix B discusses the attempts to synthesize models of the full H-cluster of [FeFe]-hydrogenase using a bioinorganic approach. A synthetic peptide containing three cysteine donors was successfully synthesized and found to chelate a preformed synthetic [Fe₄S₄] cluster. However, efforts to incorporate the diiron subsite model complex proved challenging as the planned thioester exchange reaction was found to non-selectively acetylate the peptide backbone, thus preventing the construction of the full six-iron cluster.

Non-Linear Scale Interactions in a Forced Turbulent Boundary Layer

This thesis explores the dynamics of scale interactions in a turbulent boundary layer through a forcing-response type experimental study. An emphasis is placed on the analysis of triadic wavenumber interactions since the governing Navier-Stokes equations for the flow necessitate a direct coupling between triadically consist scales. Two sets of experiments were performed in which deterministic disturbances were introduced into the flow using a spatially-impulsive dynamic wall perturbation. Hotwire anemometry was employed to measure the downstream turbulent velocity and study the flow response to the external forcing. In the first set of experiments, which were based on a recent investigation of dynamic forcing effects in a turbulent boundary layer, a 2D (spanwise constant) spatio-temporal normal mode was excited in the flow; the streamwise length and time scales of the synthetic mode roughly correspond to the very-large-scale-motions (VLSM) found naturally in canonical flows. Correlation studies between the large- and small-scale velocity signals reveal an alteration of the natural phase relations between scales by the synthetic mode. In particular, a strong phase-locking or organizing effect is seen on directly coupled small-scales through triadic interactions. Having characterized the bulk influence of a single energetic mode on the flow dynamics, a second set of experiments aimed at isolating specific triadic interactions was performed. Two distinct 2D large-scale normal modes were excited in the flow, and the response at the corresponding sum and difference wavenumbers was isolated from the turbulent signals. Results from this experiment serve as an unique demonstration of direct non-linear interactions in a fully turbulent wall-bounded flow, and allow for examination of phase relationships involving specific interacting scales. A direct connection is also made to the Navier-Stokes resolvent operator framework developed in recent literature. Results and analysis from the present work offer insights into the dynamical structure of wall turbulence, and have interesting implications for design of practical turbulence manipulation or control strategies.

Experimental studies of weak superconductivity

Experimental investigations were made of the nature of weak superconductivity in a structure having well-defined, controllable characteristics and geometry. Controlled experiments were made possible by using a thin-film structure which was entirely metallic and consisted of a superconducting film with a localized section that was weak in the sense that its transition temperature was depressed relative to the rest of the film. The depression of transition temperature was brought about by underlaying the superconductor with a normal metal.

The DC and AC electrical characteristics of this structure were studied. It was found that this structure exhibited a non-zero, time-average supercurrent at finite voltage to at least .2 mV, and generated an oscillating electric potential at a frequency given by the Josephson relation. The DC V-I characteristic and the amplitude of the AC oscillation were found to be consistent with a two- fluid (normal current-supercurrent) model of weak super-conductivity based on e thermodynamically irreversible process of repetitive phase-slip, and featuring a periodic time dependence in the amplitude of the superconducting order parameter.

The observed linewidth of the AC oscillation could be accounted for by incorporating Johnson noise in the two-fluid model.

Experimentally it was found that the behavior of a short (length on the order of the coherence distance) weak superconductor could be characterized by its critical current and normal-state resistance, and an empirical expression was obtained for the time dependence of the super-current and voltage.

It was found that the results could not be explained on the basis of the theory of the Josephson junction.