Structural Diversity of Copper(I)–N‐Heterocyclic Carbene Complexes; Ligand Tuning Facilitates Isolation of the First Structurally Characterised Copper(I)–NHC Containing a Copper(I)–Alkene Interaction

The preparation of a series of imidazolium salts bearing N‐allyl substituents, and a range of substituents on the second nitrogen atom that have varying electronic and steric properties, is reported. The ligands have been coordinated to a copper(I) centre and the resulting copper(I)–NHC (NHC=N‐heterocyclic carbene) complexes have been thoroughly examined, both in solution and in the solid‐state. The solid‐state structures are highly diverse and exhibit a range of unusual geometries and cuprophilic interactions. The first structurally characterised copper(I)–NHC complex containing a copper(I)–alkene interaction is reported. An N‐pyridyl substituent, which forms a dative bond with the copper(I) centre, stabilises an interaction between the metal centre and the allyl substituent of a neighbouring ligand, to form a 1D coordination polymer. The stabilisation is attributed to the pyridyl substituent increasing the electron density at the copper(I) centre, and thus enhancing the metal(d)‐to‐alkene(π*) back‐bonding. In addition, components other than charge transfer appear to have a role in copper(I)–alkene stabilisation because further increases in the Lewis basicity of the ligand disfavours copper(I)–alkene binding.     

Hot dense capsule-implosion cores produced by Z-pinch dynamic Hohlraum radiation

Hot dense capsule implosions driven by Z-pinch x rays have been measured using a approximately 220 eV dynamic Hohlraum to implode 1.7-2.1 mm diameter gas-filled CH capsules. The capsules absorbed up to approximately 20 kJ of x rays. Argon tracer atom spectra were used to measure the T(e) approximately 1 keV electron temperature and the n(e) approximately 1-4 x 10(23) cm(-3) electron density. Spectra from multiple directions provide core symmetry estimates. Computer simulations agree well with the peak emission values of T(e), n(e), and symmetry, indicating reasonable understanding of the Hohlraum and implosion physics.     

Letter: Invariants of the Kerr Vacuum

The Kerr vacuum has two independent invariants derivable from the Riemann tensor without differentiation. Both of these invariants must be examined in order to avoid an erroneous conclusion that the ring singularity of this spacetime is directional.     

Time- and space-resolved spectroscopy of dynamic hohlraum interiors

A dynamic hohlraum is created when an annular z-pinch plasma implodes onto a cylindrical 0.014 g/cc 6-mm-diameter CH₂ foam. The impact launches a radiating shock that propagates toward the axis at 350 μm/ns. The radiation trapped by the tungsten z-pinch plasma forms a 200 eV hohlraum that provides X-rays for indirect drive inertial confinement fusion capsule implosion experiments. We are developing the ability to diagnose the hohlraum interior using emission and absorption spectroscopy of Si atoms added as a tracer to the central portion of the foam. Time- and space-resolved Si spectra are recorded with an elliptical crystal spectrometer viewing the cylindrical hohlraum end-on. A rectangular aperture at the end of the hohlraum restricts the field of view so that the 1D spectrometer resolution corresponds approximately to the hohlraum radial direction. This enables distinguishing between spectra from the unshocked radiation-heated foam and from the shocked foam. Typical spectral lines observed include the Si Lyα with its He-like satellites and the He-like resonance sequence including Heα, Heβ, and Heγ, along with some of their associated Li-like satellites. Work is in progress to infer the hohlraum conditions using collisional–radiative modeling that accounts for the radiation environment and includes both opacity effects and detailed Stark broadening calculations. These 6-mm-scale radiation-heated plasmas might eventually also prove suitable for testing Stark broadening line profile calculations or for opacity measurements.     

Formation of microvias in epoxy-glass composites by laser ablation

Single CO₂ laser pulses, of 10.6μm wavelength, are used to form blind microvias (holes in electronic boards for through-plating conducting paths) in copper-clad epoxy-glass laminates. The microvia dimensions depend on pulse energy and duration, the thicknesses of the epoxy-glass laminate and copper cladding, and the distribution of glass within the epoxy-glass laminate. The useful range of laser parameters, especially pulse energy, is primarily determined by the ability to metallize subsequently the blind microvias. Several conclusions can be drawn from the data. The pulse enegy should be within ±20% of the optimum value in order to form vias with a cylindrical geometry. For 300 μm thick laminates, the thickness of the copper on the bottom should be 18 μm or more. A larger range of pulse energies could be used if the glass fibre density was more uniform and if subsequent copper metallization of the blind vias could be improved.     

Barrier asymmetry and the mm-wave performance of resonant tunnel diodes

The effects of barrier asymmetry in a resonant tunnel diode (RTD) on the frequency response of the negative dynamical resistance are described for (i) DC biasing in the positive differential resistance (PDR) region and (ii) DC biasing in the negative differential resistance (NDR) region. Collector barriers more transparent than emitter barriers enhance performance for NDR DC-biased devices. Asymmetry has no apparent effect for PDR DC-biased devices operating in transit time mode.     

Imaging Endogenous Metal Ions in Living Cells Using a DNAzyme–Catalytic Hairpin Assembly Probe

DNAzymes are a promising platform for metal ion detection, and a few DNAzyme-based sensors have been reported to detect metal ions inside cells. However, these methods required an influx of metal ions to increase their concentrations for detection. To address this major issue, the design of a catalytic hairpin assembly (CHA) reaction to amplify the signal from photocaged Na⁺-specific DNAzyme to detect endogenous Na⁺ inside cells is reported. Upon light activation and in the presence of Na⁺, the NaA43 DNAzyme cleaves its substrate strand and releases a product strand, which becomes an initiator that trigger the subsequent CHA amplification reaction. This strategy allows detection of endogenous Na⁺ inside cells, which has been demonstrated by both fluorescent imaging of individual cells and flow cytometry of the whole cell population. This method can be generally applied to detect other endogenous metal ions and thus contribute to deeper understanding of the role of metal ions in biological systems.     

Tame measures and Raikov systems on the circle

This paper constructs a tame continuous probability measure concentrated on a proper Raikov System on the circle group $\text{T}$.     

A problem concerning infinite graphs

We show that there are graphs G and H which satisfy: (I) for every integer n, H contains n disjoint graphs each isomorphic to G, and (II) H does not contain infinitely many disjoint graphs each isomorphic to G. This answers one of the questions raised by Halin in the Graph Theory Newsletter.