Bonds Intersecting Cycles In A Graph

Let G be a k-connected graph G having circumference c ≥ 2k. It is shown that for k ≥ 2, then there is a bond B which intersects every cycle of length c-k + 2 or greater.     

Measurement of time histories of stable intermediates during first stage ignition of n-heptane and its two isomers in a shock tube

We report the first shock tube measurements of formaldehyde (CH₂O) during the first stage ignition of n-heptane, 2-methylhexane and 3,3-dimethylpentane, in highly diluted fuel/oxygen mixtures in the pressure range of 7–10 atm and temperature range of 700–880 K. Combined time histories of all carbonyl (–C = O) species, CO and fuel were also measured simultaneously in an effort to study the impact of fuel structure on the concentration and the rate of evolution of first stage ignition products. Of the three isomers studied in this work, n-heptane was found to be the fastest, while 3,3-dimethylpentane was found to be the slowest. The differences in the time scale of formation, and plateau concentration of the intermediates between the isomers across the entire range of test conditions suggests a strong dependency of the measured time histories to fuel structure. These species therefore act as markers of the Negative Temperature Coefficient (NTC) behavior of fuels and can be used as targets for developing semi-empirical, hybrid chemistry models of complex, multi-component petroleum derived gasoline and jet fuels. The time histories reported in this work should prove very useful in the refinement of detailed kinetic models of n-heptane, and development of rate rules for branched alkane isomers.     

Mass spectroscopic investigation of bis-1,3-urea calix[4]arenes and their ability to complex N-protected α-amino acids

We report the ability of urea’s appended onto the upper-rim of conformationally locked ‘cone’ calix[4]arenes to show a preference for binding specific N-protected α-amino acids. Superior complexation (as judged by mass spectroscopy) between N-protected α-amino results and bis-1,3-N-benzylureas calix[4]arenes was observed when methylene bridges were present between the calix[4]arene ‘host’ and the urea motif. Interestingly we also demonstrate that subjecting mixtures of structurally diverse N-Fmoc-α-amino acids to a single bis-1,3-N-benzylurea derived calix[4]arene allows, in some cases, the calix[4]arene ‘host’ to selectively ‘pick out’ and complex a specific N-Fmoc amino acid from the mixture.     

Insights into metal borohydride and aluminohydride bonding: X-ray and neutron diffraction structures and a DFT and charge density study of [Na(15-crown-5)][EH(4)] (E = B, Al)

The neutron and X-ray structures of [Na(15-crown-5)][BH(4)] and [Na(15-crown-5)][AlH(4)], respectively, are reported, along with a topological analysis of their DFT-computed charge densities that explores the bonding between the anionic complex hydride [EH(4)](-) (E = B, Al) and the counterion [Na(15-crown-5)](+). In each case, the interaction is weak and mainly electrostatic in nature; however, notable differences are observed in the manner in which [BH(4)](-) and [AlH(4)](-) bind to the metal, which explains their different coordination modes. A range of unconventional E-H···H-C contacts is revealed to play an important role in the overall bonding and crystal packing of both complexes. These interactions can be classified as weak dihydrogen bonds based on the atoms in molecules approach.     

Synthesis and characterization of two novel organic–inorganic hybrid solids from Keggin ions and metal coordination complexes

Two new hybrid compounds, [Co(4,4′-bpy)₂(H₂O)₄][(4,4′-bpyH₂]₂[CoW₁₂O₄₀]·8H₂O (1) and [Fe(2,2′-bpy)₃]₃[H₂W₁₂O₄₀]·6H₂O (2), (4,4′-bpy = 4,4′-bipyridine, 2,2′-bpy = 2,2′-bipyridine) have been hydrothermally synthesized. These solids were characterized by elemental analysis, thermogravimetric analysis, UV–Vis spectroscopy and X-ray diffraction. The hydrogen-bonding interactions in 1 lead to the formation of a three dimensional network consisting of [CoW₁₂O₄₀]⁶⁻ anionic clusters, [Co(4,4′-bpy)₂(H₂O)₄]²⁺ cations and lattice water molecules, while the discrete Keggin ion [H₂W₁₂O₄₀]⁶⁻ in compound 2 is surrounded by 14 [Fe(2,2′-bpy)₃]²⁺ complexes through CH?O interactions (2.24–2.56 Å).     

Synthesis and complexation properties of novel triazoyl-based ferrocenyl ligands

Two new ligand derivatives of ferrocene, namely N-4-[3,5-di-(2-pyridyl)-1,2,4-triazoyl]ferrocene carbimine (L1) and N-4-[3,5-di-(2-pyridyl)-1,2,4-triazoyl]ferrocene carbamide (L2), were synthesised in good yields by reacting the known compound 3,5-di-pyridine-2-yl-[1,2,4]triazol-4-ylamine (1) with ferrocenecarbaldehyde and chlorocarbonyl ferrocene, respectively. The structures of L1 and L2 were determined by X-ray crystallography. The complexation of L1 and L2 with Cu^I, Ag^I, Zn^II and Cd^II was studied by NMR and UV-vis spectroscopies, as well as by electrochemistry, with titrations used to determine metal:ligand stoichiometries. The cyclic voltammograms of L1 and L2 and their respective complexes indicated reversible one-electron transfers corresponding to the Fc^0/+ redox couple (Fc = ferrocene), with formal electrode potentials shifting to more positive values upon metal complexation.     

Direct measurement of the friction between and shear moduli of shells of carbon nanotubes

We report measurements of the shear modulus of each shell and the friction between the two shells of double-shell carbon nanotubes in single nanotube-based nanoelectromechanical devices operated in a transmission electron microscope. In situ nanobeam electron diffraction is applied to obtain the chiral indices of each shell of the nanotube and it allows us to establish a quantitative correlation between the atomic structure and properties of the nanotube under investigation.     

Modeling and simulation of titanium dioxide nanoparticle synthesis with finite-rate sintering in planar jets

Numerical simulations of titanium dioxide nanoparticle synthesis in planar, non-premixed diffusion flames are performed. Titania is produced by the oxidation of titanium tetrachloride using a methane–air flame. The flow field is obtained using the two-dimensional Navier–Stokes equations. The methane–air flame and oxidation of titanium tetrachloride are modeled via one-step reactions. Evolution of the particle field is obtained via a nodal method which accounts for nucleation, condensation, coagulation, and coalescence with finite-rate sintering. The modeling of finite-rate sintering is accomplished via the use of uniform primary-particle size distribution. Simulations are performed at two different jet-to-co-flow velocity ratios as well as with finite-rate and instantaneous sintering models. In doing so we elucidate the effect of fluid mixing and finite-rate sintering on the particle field. Results show that highly agglomerated particles are found on the periphery of the eddies, where the collisions leading to nanoparticle coagulation occur faster than nanoparticle coalescence.