Higher dimensional Apollonian packings,revisited

The Apollonian circle and sphere packings are well known objects that have attracted the attention of mathematicians throughout the ages. The historically natural generalization of the procedure for generating the packing breaks down in higher dimensions, as it leads to overlapping hyperspheres. There is, however, an alternative interpretation that allows one to extend the concept to higher dimensions and in a unique way. For relatively small dimensions (2 through at least 8), those packings can be thought of as ample cones for classes of K3 surfaces. We describe the packings in some detail for dimensions 4 (with plenty of pictures), 5, and 6.     

Chemoselective vinylation of aminophenols with acetylene catalyzed by sodium aminophenolates in aqueous DMSO

1. Download : Download high-res image (41KB)
2. Download : Download full-size image

     

Electrochemical sensing of heavy metals in biological media: A review

Trace metals are required in the body as they play a significant role in several biochemical processes. Moreover, certain heavy metals are beneficial at appropriate levels. Copper (Cu), for example, is essential for red blood cell formation, bone strength, and infant growth. Despite these fundamental roles, Cu can become toxic at high levels. Other heavy metals such as lead (Pb), cadmium (Cd), manganese (Mn), and mercury (Hg), have been identified to cause acute and chronic health complications. For these reasons, rapid, real-time quantification of such metals in biological media is of interest to improving human health outcomes. Electrochemical methods offer numerous advantages, such as portability, capability to be miniaturized, low cost, and ease-of-use. In this review, we examine recent developments in electrochemical sensing for the detection of heavy metals in biological media. To meet the requirements for inclusion in this review, the electrochemical sensor must have been evaluated in biological media (blood, serum, sweat, saliva, urine, brain tissue/cells). Several applications are explored to examine recent advancements in electrochemical sensing within these matrices. Addressing the challenges through materials, device, and system innovations, it is expected that electrochemical sensing of heavy metals in biological media will facilitate future diagnoses and treatments in healthcare.     

The Reaction of Cs2[Tc(NO)F5] with BF3 in Acetonitrile: Formation and Structure of [{Tc(NO)(CH3CN)4}2(μ‐F)](BF4)3

The deep blue, paramagnetic Cs₂[Tc^II(NO)F₅] is formed during reactions of pertechnetate, acetohydroxamic acid, and CsF in aqueous HF. A reaction of Cs₂[Tc(NO)F₅] with BF₃ · MeOH in acetonitrile gives yellow blocks of the fluorido‐bridged dimer [{Tc^I(NO)(CH₃CN)₄}₂F](BF₄)₃. The compound is stable as solid and in acetonitrile solutions. The complex cation contains a bent μ‐F^– ligand and two linear nitrosyl groups.     

Chromatographic separation of thulium from erbium for neutron capture cross section measurements—Part I: Trace scale optimization of ion chromatography method with various complexing agents

The impact of various ion chromatography parameters on the separation of trace amounts of thulium from erbium was examined to address the need for the preparation of a ¹⁷¹Tm target for neutron capture cross section measurements. The following optimal operation parameters for analytical scale separations with cation exchange resin were established based on a modified separation resolution: 0.046 M α-HIB^? as eluent with a flow rate of 1.2 mL min^?1 at 25 °C. Different carboxylic acids with varying pH were also investigated, which reaffirmed the use of α-hydroxyisobutyrate as the most suitable complexant for the separation of these neighboring lanthanides.     

Poly(Pyridinium Salt)s Containing 2,7-Diamino-9,9′-Dioctylfluorene Moieties with Various Organic Counterions Exhibiting Both Lyotropic Liquid-Crystalline and Light-Emitting Properties

A series of poly(pyridinium salt)s-fluorene main-chain ionic polymers with various organic counterions were synthesized by using ring-transmutation polymerization and metathesis reactions. Their chemical structures were characterized by Fourier Transform Infrared (FTIR), proton (¹H), and fluorine 19 (¹⁹F) nuclear magnetic resonance (NMR) spectrometers. These polymers showed a number-average molecular weight (M_ns) between 96.5 and 107.8 kg/mol and polydispersity index (PDI) in the range of 1.12–1.88. They exhibited fully-grown lyotropic phases in polar protic and aprotic solvents at different critical concentrations. Small-angle X-ray scattering for one polymer example indicates lyotropic structure formation for 60–80% solvent fraction. A lyotropic smectic phase contains 10 nm polymer platelets connected by tie molecules. The structure also incorporates a square packing motif within platelets. Thermal properties of polymers were affected by the size of counterions as determined by differential scanning calorimetry and thermogravimetric analysis measurements. Their ultraviolet-visible (UV-Vis) absorption spectra in different organic solvents were essentially identical, indicating that the closely spaced π-π* transitions occurred in their conjugated polymer structures. In contrast, the emission spectra of polymers exhibited a positive solvatochromism on changing the polarity of solvents. They emitted green lights in both polar and nonpolar organic solvents and showed blue light in the film-states, but their λ_em peaks were dependent on the size of the counterions. They formed aggregates in polar aprotic and protic solvents with the addition of water (v/v, 0–90%), and their λ_em peaks were blue shifted.     

Fluorescence and absorbance spectroscopy of the uranyl ion in nitric acid for process monitoring applications

Near real time process monitoring of the uranium content in an aqueous fuel recycling plant is a desired component of an advanced safeguards suite; Ultraviolet–Visible spectroscopy and Time Resolved Laser induced Fluorescence Spectroscopy can contribute to this technology gap. This work presents the observation of the spectroscopic parameters (molar absorptivities, fluorescent response) of the uranyl ion across the range of conditions expected in reprocessing chemistry. From this data, a monitor using the ratio of the absorbance of the uranyl ion at 403 and 426 nm has been developed. This technique can determine the nitrate solution concentration and can be coupled with a condition appropriate molar absorptivity to determine the uranyl concentration. This method provides a reliable technique for online, real time process monitoring of the uranyl and nitrate concentration under a wide range of solution compositions.