Collapsing successors of singulars

Let be a singular cardinal in , and let be a model such that for some -cardinal with . We apply Shelah's pcf theory to study this situation, and prove the following results. 1) is not a -c.c generic extension of . 2) There is no ``good scale for ' in , so in particular weak forms of square must fail at . 3) If then and also . 4) If then .

     

Electrophoresis of ssDNA through nanoelectrode gaps from molecular dynamics: impact of gap width and chain length

Molecular dynamics simulations were performed to study the translocation of single-stranded (ss) DNA through the nanoscale gap between the nanoscale electrodes of a proposed genomic sequencing device. An applied electric field forces the ssDNA to move in the direction of the nanoscale gap in platinum electrodes. A series of simulations utilizing eight different nanoscale gap distances as well as seven different nucleotide chain lengths were performed to determine the impact of these variables on the overall design of the sequencing device and the translocation behavior of ssDNA. The results clearly indicate a threshold value of the gap width below which the ssDNA will readily enter and traverse the nanoscale gap. Translocation velocities obtained for various chain lengths were consistent with simulated bulk data; however, successful translocation was inconsistent, possibly related to the sample's affinity for the metal electrodes. An attempt at overcoming this barrier was made through the implementation of shaped electrodes as well as pre-threading of the ssDNA sample.     

Underpotential surface reduction of mesoporous CeO<Subscript>2</Subscript> nanoparticle films

The formation of variable-thickness CeO₂ nanoparticle mesoporous films from a colloidal nanoparticle solution (approximately 1–3-nm-diameter CeO₂) is demonstrated using a layer-by-layer deposition process with small organic binder molecules such as cyclohexanehexacarboxylate and phytate. Film growth is characterised by scanning and transmission electron microscopies, X-ray scattering and quartz crystal microbalance techniques. The surface electrochemistry of CeO₂ films before and after calcination at 500 °C in air is investigated. A well-defined Ce(IV/III) redox process confined to the oxide surface is observed. Beyond a threshold potential, a new phosphate phase, presumably CePO₄, is formed during electrochemical reduction of CeO₂ in aqueous phosphate buffer solution. The voltammetric signal is sensitive to (1) thermal pre-treatment, (2) film thickness, (3) phosphate concentration and (4) pH. The reversible ‘underpotential reduction’ of CeO₂ is demonstrated at potentials positive of the threshold. A transition occurs from the reversible ‘underpotential region’ in which no phosphate phase is formed to the irreversible ‘overpotential region’ in which the formation of the cerium(III) phosphate phase is observed. The experimental results are rationalised based on surface reactivity and nucleation effects.     

Direct measurement of the rate of interconversion of zirconaaziridine enantiomers

The insertion of enantiopure C2-symmetric diphenylethylene carbonate into the Zr-C bonds of zirconaaziridines leads to the asymmetric synthesis of amino acid methyl esters. Because the zirconaaziridine enantiomers interconvert, the reaction is a dynamic kinetic resolution (DKR). The efficiency of the DKR (the ratio of the two diastereomeric products) is determined by the balance between the rate of enantiomer interconversion and the rate of insertion; slow addition of the inserting enantiopure carbonate is often required to maximize the stereoselectivity. For a case when enantiomer interconversion is fast, its rate constant kinv has been determined by NMR line broadening; for a case when interconversion is slow, k(inv) has been determined by computer simulation of the formation of the diastereomeric products as a function of time; for several intermediate cases, k(inv) has been determined by making the zirconaaziridine enantioenriched and monitoring its racemization by CD spectroscopy. The observed k(inv) is independent of [THF], implying that interconversion occurs with THF coordinated. Interconversion presumably occurs via an achiral intermediate, either a rapidly inverting (via an eta1-N structure) eta3-azaallyl hydride or an eta1-imine. As addition of THF slows insertion without affecting enantiomer interconversion, it produces a more efficient DKR without slow addition of the enantiopure carbonate.     

The Strongest Acid: Protonation of Carbon Dioxide

The strongest carborane acid, H(CHB₁₁F₁₁), protonates CO₂ while traditional mixed Lewis/Brønsted superacids do not. The product is deduced from IR spectroscopy and calculation to be the proton disolvate, H(CO₂)₂⁺. The carborane acid H(CHB₁₁F₁₁) is therefore the strongest known acid. The failure of traditional mixed superacids to protonate weak bases such as CO₂ can be traced to a competition between the proton and the Lewis acid for the added base. The high protic acidity promised by large absolute values of the Hammett acidity function (H₀) is not realized in practice because the basicity of an added base is suppressed by Lewis acid/base adduct formation.     

Molecular dynamics simulations of stretched gold nanowires: the relative utility of different semiempirical potentials

The mechanical elongation of a finite gold nanowire has been studied by molecular dynamics simulations using different semiempirical potentials for transition metals. These potentials have been widely used to study the mechanical properties of finite metal clusters. Combining with density functional theory calculations along several atomic-configuration trajectories predicted by different semiempirical potentials, the authors conclude that the second-moment approximation of the tight-binding scheme (TB-SMA) potential is the most suitable one to describe the energetics of finite Au clusters. They find that for the selected geometries of Au wires studied in this work, the ductile elongation of Au nanowires along the [001] direction predicted by the TB-SMA potential is largely independent of temperature in the range of 0.01-298 K. The elongation leads to the formation of monatomic chains, as has been observed experimentally. The calculated force-versus-elongation curve is remarkably consistent with available experimental results.     

Aggregation of POSS monomers in liquid hexane: a molecular-simulation study

Polyhedral oligomeric silsesquioxanes (POSS) are multifunctional molecules that can be employed as building blocks to develop nanocomposite materials whose mechanical properties often improve upon those of traditional polymeric materials. We report here molecular simulation results for the effective potential of mean force between octamethyl POSS monomers and between POSS monomers in which one methyl group has been substituted by a linear alkane chain of nine carbon atoms in liquid normal hexane at 300 and 400 K. The results are discussed and compared to available data for the effective interactions between octamethyl POSS monomers in normal hexadecane. Our results show that the effective short-ranged POSS-POSS attraction is significantly weaker in hexane than it is in hexadecane, perhaps explaining why normal hexane is often the solvent of choice for the preparation of POSS-containing materials. Additionally, we provide results for the radial distribution functions between selected sites in the POSS monomers that can be used both to understand the association between POSS monomers in solution and to parametrize coarse-grained simulation models. Such models will be used to study the formation of POSS-containing supramolecular structures such as lamellae or micelles that are currently not accessible by atomistic simulation and can be compared to experimental observations.     

T3P-Promoted Synthesis of a Series of 2-Aryl-3-phenyl-2,3-dihydro-4H-pyrido[3,2-e][1,3]thiazin-4-ones and Their Activity against the Kinetoplastid Parasite Trypanosoma brucei

A series of fourteen 2-aryl-3-phenyl-2,3-dihydro-4H-pyrido[3,2-e][1,3]thiazin-4-ones was prepared at room temperature by T3P-mediated cyclization of N-phenyl-C-aryl imines with thionicotinic acid, two difficult substrates. The reactions were operationally simple, did not require specialized equipment or anhydrous solvents, could be performed as either two or three component reactions, and gave moderate–good yields as high as 63%. This provides ready access to N-phenyl compounds in this family, which have been generally difficult to prepare. As part of the study, the first crystal structure of neutral thionicotinic acid is also reported, and showed the molecule to be in the form of the thione tautomer. Additionally, the synthesized compounds were tested against T. brucei, the causative agent of Human African Sleeping Sickness. Screening at 50 µM concentration showed that five of the compounds strongly inhibited growth and killed parasites.     

Effective Rheology of Two-Phase Flow in Three-Dimensional Porous Media: Experiment and Simulation

We present an experimental and numerical study of immiscible two-phase flow of Newtonian fluids in three-dimensional (3D) porous media to find the relationship between the volumetric flow rate (Q) and the total pressure difference (\(\Delta P\)) in the steady state. We show that in the regime where capillary forces compete with the viscous forces, the distribution of capillary barriers at the interfaces effectively creates a yield threshold (\(P_t\)), making the fluids reminiscent of a Bingham viscoplastic fluid in the porous medium. In this regime, Q depends quadratically on an excess pressure drop (\(\Delta P-P_t\)). While increasing the flow rate, there is a transition, beyond which the overall flow is Newtonian and the relationship is linear. In our experiments, we build a model porous medium using a column of glass beads transporting two fluids, deionized water and air. For the numerical study, reconstructed 3D pore networks from real core samples are considered and the transport of wetting and non-wetting fluids through the network is modeled by tracking the fluid interfaces with time. We find agreement between our numerical and experimental results. Our results match with the mean-field results reported earlier.     

Characterization of sealed radioactive sources: uncertainty analysis to improve detection methods

A radioactive ¹³⁷Cs source has been analyzed for the radioactive parent ¹³⁷Cs and stable decay daughter ¹³⁷Ba. The ratio of the daughter to parent atoms is used to estimate the date when Cs was purified prior to source encapsulation (an “age” since purification). The isotopes were analyzed by inductively coupled plasma mass spectrometry (ICP-MS) after chemical separation. In addition, Ba was analyzed by isotope dilution ICP-MS (ID-ICP-MS). A detailed error analysis of the mass spectrometric work has been undertaken to identify areas of improvement, as well as quantifying the effect the errors have on the “age” determined. This paper reports an uncertainty analysis to identifying areas of improvement and alternative techniques that may reduce the uncertainties. In particular, work on isotope dilution using ICP-MS for the “age” determination of sealed sources is presented. The results will be compared to the original work done using external standards to calibrate the ICP-MS instrument.