On linear-fractional relations and images of angular operators

For plus-operators in a Banach indefinite space, we consider a linear-fractional relation. The classes of operators with the empty domain of definition for such a relation are described. The sufficient (and necessary, in some meaning) conditions for the chain rule to be valid are given.     

Eigenvalue estimates for Schrödinger operators on metric trees

We consider Schrödinger operators on radial metric trees and prove Lieb–Thirring and Cwikel–Lieb–Rozenblum inequalities for their negative eigenvalues. The validity of these inequalities depends on the volume growth of the tree. We show that the bounds are valid in the endpoint case and reflect the correct order in the weak or strong coupling limit.     

Determination of Diaryliodonium Species by Reverse Iodometric Titration with Ascorbic Acid

Diaryliodonium salts are used in organic chemistry, materials science and pharmaceutical chemistry. For the quantitative analysis of diaryliodonium salts, only instrumentally demanding techniques requiring highly skilled operators are available. Surprisingly, no titration method taking advantage of the oxidising ability of diaryliodonium is available in the literature. In the present work, a titration method for the determination of diaryliodonium salts is presented. It is based on the reaction of diaryliodonium species with ascorbic acid, whose excess is subsequently determined by means of iodometric potentiometric titration. Application of the protocol to various diaryliodonium salts revealed the scope and limitations of the method.     

X-ray structure and UV spectroscopic studies of (adenmato-N9)triethylphosphinegold(I)

The preparation, characterization, and X-ray structure analysis of (adeninatoN9)triethylphosphinegold(I) is reported. The crystal structure consists of discrete molecules, the adeninate anion coordinates via the N(9) atom with a Au-N(9) bond distance of 2.057(5) Å and the linear geometry about the Au atom is completed by the P atom of a disordered Et₃P ligand; the Au-P(1) bond distance is 2.238(2) Å and the N(9)-Au-P(1) bond angle is 178.8(2)°. The crystals are orthorhombic, space groupPbca, with unit cell dimensionsa=8.528(1),b=17.797(3),c=18.526(2) Å andZ=8. The structure was refined by a full-matrix least-squares procedure to finalR=0.030 andR _w =0.033 for 1749 reflections withI>2.5a(I). The electronic spectrum of the complex dissolved in water in the near ultraviolet is consistent with essentially separate -electron systems of the adenine and phosphinegold moieties; a conclusion which corroborates the X-ray structural results.     

Thin SiC<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> layers prepared by hybrid laser–magnetron deposition

Thin SiC _x films were fabricated by hybrid laser–magnetron deposition system. KrF excimer laser was used for deposition of carbon and magnetron at the same time for sputtering of Si species. Films were fabricated in argon/hydrogen ambient with and without additional RF discharge. The substrate temperature was changed up to 700°C. Films topology, crystallinity, composition, chemical bonds and optical emission spectra were studied. Films were smooth and amorphous. Films of thickness 400–1000 nm were fabricated. Adhesion moved from 8 to 14 N, depending on deposition conditions.     

Ozonolysis of oleic acid adsorbed to polar and nonpolar aerosol particles

Single-particle kinetic studies of the reaction between oleic acid and O 3 have been conducted on two different types of core particles: polystyrene latex (PSL) and silica. Oleic acid was found to adsorb to both particle types in multilayer islands that resulted in an adsorbed layer of a total volume estimated to be less than one monolayer. The rate of the surface reaction between surface-adsorbed oleic acid and O 3 has been shown for the first time to be influenced by the composition of the aerosol substrate in a mixed organic/inorganic particle. A Langmuir-Hinshelwood mechanism was applied to the observed dependence of the pseudo-first-order rate constant with [O 3], and the resulting fit parameters for the ozone partition coefficient ( K O 3 ) and maximum first order rate constant ( k 1,max ) suggest that the reaction proceeded faster on the less polar PSL core at lower [O 3] due to the increased residence time of O 3 on the PSL surface, but the reaction was ultimately more efficient on the silica surface at high [O 3]. Values for the uptake coefficient, gamma oleic , for reaction of oleic acid on PSL spheres decrease from 2.5 x 10 (-5) to 1 x 10 (-5) with increasing [O 3] from 4 to 25 ppm and overlap at high [O 3] with the estimated values for gamma oleic on silica, which decrease from 1.6 x 10 (-5) to 1.3 x 10 (-5). The relationship between gamma oleic and the more common expression for gamma O 3 is discussed.     

Heats of formation of Co(CO)(2)NOPR(3), R = CH(3) and C(2)H(5), and its ionic fragments

A joint threshold photoelectron photoion coincidence spectrometry (TPEPICO) and collision-induced dissociation (CID) study on the thermochemistry of Co(CO)(2)NOPR(3), R = CH(3) (Me) and C(2)H(5) (Et), complexes is presented. Adiabatic ionization energies of 7.36 +/- 0.04 and 7.24 +/- 0.04 eV, respectively, were extracted from scans of the total ion and threshold electron signals. In the TPEPICO study, the following 0 K onsets were determined for the various fragment ions: CoCONOPMe(3)(+), 8.30 +/- 0.05 eV; CoNOPMe(3)(+), 9.11 +/- 0.05 eV; CoPMe(3)(+) 10.80 +/- 0.05 eV; CoCONOPEt(3)(+), 8.14 +/- 0.05 eV; CoNOPEt(3)(+), 8.92 +/- 0.05 eV; and CoPEt(3)(+), 10.66 +/- 0.05 eV. These onsets were combined with the Co(+)-PR(3) (R = CH(3) and C(2)H(5)) bond dissociation energies of 2.88 +/- 0.11 and 3.51 +/- 0.17 eV, obtained from the TCID experiments, to derive the heats of formation of the neutral and ionic species. Thus, the Co(CO)(2)NOPR(3) (R = CH(3) and C(2)H(5)) 0 K heats of formation were found to be -350 +/- 13 and -376 +/- 18 kJ x mol(-)(1), respectively. These heats of formation were combined with the published heat of formation of Co(CO)(3)NO to determine the substitution enthalpies of the carbonyl to phosphine substitution reactions. Room-temperature values of the heats of formation are also given using the calculated harmonic vibrational frequencies. Analysis of the TCID experimental results provides indirectly the adiabatic ionization energies of the free phosphine ligands, P(CH(3))(3) and P(C(2)H(5))(3), of 7.83 +/- 0.03 and 7.50 +/- 0.03 eV, respectively.     

Janus Face All-cis 1,2,4,5-tetrakis(trifluoromethyl)- and All-cis 1,2,3,4,5,6-hexakis(trifluoromethyl)- Cyclohexanes

We report the synthesis of all-cis 1,2,4,5-tetrakis (trifluoromethyl)- and all-cis 1,2,3,4,5,6-hexakis (trifluoromethyl)- cyclohexanes by direct hydrogenation of precursor tetrakis- or hexakis- (trifluoromethyl)benzenes. The resultant cyclohexanes have a stereochemistry such that all the CF₃ groups are on the same face of the cyclohexyl ring. All-cis 1,2,3,4,5,6-hexakis(trifluoromethyl)cyclohexane is the most sterically demanding of the all-cis hexakis substituted cyclohexanes prepared to date, with a barrier (ΔG) to ring inversion calculated at 27 kcal mol⁻¹. The X-ray structure of all-cis 1,2,3,4,5,6-hexakis(trifluoromethyl)cyclohexane displays a flattened chair conformation and the electrostatic profile of this compound reveals a large diffuse negative density on the fluorine face and a focused positive density on the hydrogen face. The electropositive hydrogen face can co-ordinate chloride (K≈10³) and to a lesser extent fluoride and iodide ions. Dehydrofluorination promoted decomposition occurs with fluoride ion acting as a base.