Chromatic thresholds in sparse random graphs

The chromatic threshold of a graph H with respect to the random graph G (n, p ) is the infimum over d > 0 such that the following holds with high probability: the family of H‐free graphs with minimum degree has bounded chromatic number. The study of was initiated in 1973 by Erd?s and Simonovits. Recently was determined for all graphs H . It is known that for all fixed , but that typically if Here we study the problem for sparse random graphs. We determine for most functions when , and also for all graphs H with © 2017 Wiley Periodicals, Inc. Random Struct. Alg., 51, 215–236, 2017     

Nitrene Insertion into C?C and C?H Bonds of Diamide Diimine Ligands Ligated to Chromium and Iron

The impact of redox non‐innocence (RNI) on chemical reactivity is a forefront theme in coordination chemistry. A diamide diimine ligand, [{‐CHN(1,2‐C₆H₄)NH(2,6‐iPr₂C₆H₃)}₂]ⁿ (n=0 to −4), (dadi)ⁿ, chelates Cr and Fe to give [(dadi)M] ([ 1 Cr(thf)] and [ 1 Fe]). Calculations show [ 1 Cr(thf)] (and [ 1 Cr]) to have a d⁴ Cr configuration antiferromagnetically coupled to (dadi)²⁻*, and [ 1 Fe] to be S=2. Treatment with RN₃ provides products where RN is formally inserted into the C C bond of the diimine or into a C H bond of the diimine. Calculations on the process support a mechanism in which a transient imide (imidyl) aziridinates the diimine, which subsequently ring opens.     

Methodological advances for measuring low-level radium isotopes in seawater

A new approach for quantifying radium isotopes in seawater was developed in advance of the international GEOTRACES program, which has the goal of identifying processes and quantifying fluxes that control the distribution of trace elements and isotopes (TEIs) in the ocean. High-resolution water column samples were collected via a commercially available in situ pump modified to accept multiple filter media including a manganese-oxide (MnO₂) impregnated acrylic cartridge for extracting dissolved radionuclides from seawater. The modifications mitigated prefilter clogging and allowed for up to 1,800 L filtrations in 4 h of pumping. Different MnO₂ cartridge preparation methods were investigated to achieve maximum radium (Ra) extraction efficiency under high sample flow rates. Full-ocean depth profiles were measured for short-lived radium isotopes (²²³Ra and ²²⁴Ra) in shipboard laboratories using a delayed coincidence alpha scintillation counter (RaDeCC). Samples were reanalyzed 4 weeks and 2 months after collection for ²²⁸Th and ²²⁷Ac to correct for supported ²²⁴Ra and ²²³Ra, respectively. Finally, the cartridges were measured on a gamma-ray spectrometer for the long-lived radium isotopes (²²⁶Ra and ²²⁸Ra). Parallel 20 L samples at each pumping depth were collected from Niskin bottles and analyzed via alpha scintillation for ²²⁶Ra to determine radium extraction efficiencies for the cartridges. These modified methods will allow for increased sample throughput, and hence higher spatial resolution for radium isotopes in the ocean. Such resolution will greatly improve the determination of oceanic vertical and horizontal mixing rates over small and large scales, which in turn can be used to calculate fluxes of TEIs into the ocean.     

Work Hardening Effects in Gellan Gum Gels1

Abstract

Gellan gum is a bacterial polysaccharide that is marketed as a broad spectrum gelling agent. The shear and Young's moduli, and the fracture strength of gellan gels increase with increasing ionic strength, pass through maxima and then decrease to zero at higher ionic strength. The position of the maxima depend on the valency of added counterions and are virtually independent of polymer concentration. At low ionic strength the measured rheological parameters show small variability but these values become increasingly variable with increasing ionic strength. Stress relaxation experiments were carried out in order to examine the mechanical behaviour of gellan gels and to explain these effects. At low ionic strength the gels approximate to elastic solids whereas at high ionic strength the increased stress relaxation is colloid-like in behaviour. However, unlike colloidal dispersions, the magnitude of the stress relaxation decreases on successive applications of stress and the relaxation modulus increases. The gels work harden. Such behaviour is attributed to a heterogeneous structure within the gel.     

Some Reactions of α-Allenic Boronates

α-Allenic boronates, readily available in high yield from gem-borazirconcene alkanes, react with iodine to give diiodo adducts that when treated with sodium acetate provide 2-iodo-1,3-butadienes. Alternatively, hydrozirconation of the α-allenic boronates followed by treatment with D₂O occurs regioselectively to place deuterium in the allylic position.     

Soft-graphoepitaxy using nanoimprinted polyhedral oligomeric silsesquioxane substrates for the directed self-assembly of PS-b-PDMS

We report here the fabrication of periodic sub-25 nm diameter size cylinder structures using block copolymer (BCP) directed self-assembly on nanoimprinted topographically patterned substrates. Tailored polyhedral oligomeric silsesquioxanes (POSSs) films were spin coated onto silicon substrates and were patterned by nanoimprint lithography to produce topographies commensurable with the BCP domain spacing. The chemistry of the POSS was tuned to control the alignment and orientation of the BCP films. The substrates were used to direct the microphase separation (following toluene solvent annealing) of a hexagonal structure forming polystyrene-block-polydimethylsiloxane (PS-b-PDMS) having a domain spacing of 42.6 nm and PDMS cylinder widths of 23.7 nm. On more hydrophilic POSS substrates the cylinders were obtained parallel to the substrate plane and aligned with the topography. In contrast, in more hydrophobic POSS patterns, the cylinders align perpendicular to the substrate plane. The use of these methods for the nanofabrication of vias, nanofluidic devices or interconnect structures of sub-25 nm feature size is discussed.     

A model for the stability of films stabilized by randomly packed spherical particles

Particle stabilized thin films occur in a range of industrial applications where their properties affect the efficiency of the process concerned. However, due to their dynamic and unstable nature they are difficult to observe experimentally. As such, a tractable way of gaining insight into the fundamental aspects of this complicated system is to use computer simulations of particles at interfaces. This paper presents modeling results of the effect of nonuniform packing of spherical particles on the stability of thin liquid films. Surface Evolver was used to model cells containing up to 20 particles, randomly packed in a thin liquid film. The capillary pressure required to rupture the film for a specific combination of particle arrangement, packing density, and contact angle was identified. The data from the periodic, randomly packed models has been used to find a relationship between particle packing density, contact angle, and critical capillary pressure which is refined to a simple equation that depends on the film loading and contact angle of the particles it contains. The critical capillary pressure for film rupture obeys the same trends observed for particles in regular 2D and 3D packing arrangements. The absolute values of P*(crit), however, are consistently lower than those for regular packing. This is due to the irregular arrangement of the particles, which allows for larger areas of free film to exist, lowering the critical capillary pressure required to rupture the film.