Geometry in preduals of spaces of 2-homogeneous polynomials on Hilbert spaces

Let H be a (real or complex) Hilbert space. Using spectral theory and properties of the Schatten–Von Neumann operators, we prove that every symmetric tensor of unit norm in HoH is an infinite absolute convex combination of points of the form xox with x in the unit sphere of the Hilbert space. We use this to obtain explicit characterizations of the smooth points of the unit ball of HoH .

Modulating the selectivity for CO and butane oxidation over heterogeneous catalysis through amorphous catalyst coatings

The preparation of porous films directly deposited onto the surface of catalyst particles is attracting increasing attention. We report here for the first time a method that can be carried out at ambient pressure for the preparation of porous films deposited over 3 mm diameter catalyst particles of silica-supported Pt-Fe. Characterization of the sample prepared at ambient pressure (i.e., open air, OA) and its main structural differences as compared with a Na-A (LTA) coated catalyst made using an autoclave-based method are presented. The OA-coated material predominantly exhibited an amorphous film over the catalyst surface with between 4 and 13% of crystallinity as compared with fully crystallized LTA zeolite crystals. This coated sample was highly selective for CO oxidation in the presence of butane with no butane oxidation observed up to 350 degrees C. This indicates, for the first time, that the presence of a crystalline membrane is not necessary for the difference in light off temperature between CO and butane to be achieved and that amorphous films may also produce this effect. An examination of the space velocity dependence and adsorption of Na+ on the catalysts indicates that the variation in CO and butane oxidation activity is not caused by site blocking predominantly, although the Pt activity was lowered by contact with this alkali.

Absolute Atomic Oxygen Density Distributions in the Effluent of a Micro Scale Atmospheric Pressure Plasma Jet

The coplanar microscale atmospheric pressure plasma jet (µ-APPJ) is a capacitively coupled radio frequency discharge (13.56 MHz, ~15W rf power) designed for optimized optical diagnostic access. It is operated in a homogeneous glow mode with a noble gas flow (1.4 slm He) containing a small admixture of molecular oxygen (~0.5%). Ground state atomic oxygen densities in the effluent up to 2 × 1014 cm-3 are measured by two-photon absorption laser-induced fluorescence spectroscopy (TALIF) providing space resolved density maps. The quantitative calibration of the TALIF setup is performed by comparative measurements with xenon. A maximum of the atomic oxygen density is observed for 0.6% molecular oxygen admixture. Furthermore, an increase in the rf power up to about 15W (depending on gas flow and mixture) leads to an increase in the effluent’s atomic oxygen density, then reaching a constant level for higher powers.

The Co-Entrapment of a Homogeneous Catalyst and an Ionic Liquid by a Sol-gel Method: Recyclable Ionogel Hydrogenation Catalysts

Molecular hydrogenation catalysts have been co-entrapped with the ionic liquid [Bmim]NTf(2) inside a silica matrix by a sot-gel method. These catalytic ionogels have been compared to simple catalyst-doped glasses, the parent homogeneous catalysts, commercial heterogeneous catalysts, and Rh-doped mesoporous silica. The most active ionogel has been characterised by transmission electron microscopy, X-ray photoelectron spectroscopy, and solid state NMR before and after catalysis. The ionogel catalysts were found to be remarkably active, recyclable and resistant to chemical change.

Investigating the Mechanism and Electrode Kinetics of the Oxygen vertical bar Superoxide (O-2 vertical bar O-2(center dot-)) Couple in Various Room-Temperature Ionic Liquids at Gold and Platinum Electrodes in the Temperature Range 298-318 K

The reduction of oxygen was studied over a range of temperatures (298-318 K) in n-hexyltriethylammonium bis(trifluoromethanesulfonyl)imide, [N-6,N-2,N-2,N-2][NTf2], and 1-butyl-2,3-methylimidazolium bis(trifluoromethanesulfonyl)imide, [C(4)dmim][NTf2] on both gold and platinum microdisk electrodes, and the mechanism and electrode kinetics of the reaction investigated. Three different models were used to simulate the CVs, based on a simple electron transfer ('E'), an electron transfer coupled with a reversible homogeneous chemical step ('ECrev') and an electron transfer followed by adsorption of the reduction product ('EC(ads)'), and where appropriate, best fit parameters deduced, including the heterogeneous rate constant, formal electrode potential, transfer coefficient, and homogeneous rate constants for the ECrev mechanism, and adsorption/desorption rate constants for the EC(ads) mechanism. It was concluded from the good simulation fits on gold that a simple E process operates for the reduction of oxygen in [N-6,N-2,N-2,N-2][NTf2], and an ECrev process for [C(4)dmim][NTf2], with the chemical step involving the reversible formation of the O-2(center dot-)center dot center dot center dot [C(4)dmim](+) ion-pair. The E mechanism was found to loosely describe the reduction of oxygen in [N-6,N-2,N-2,N-2][NTf2] on platinum as the simulation fits were reasonable although not perfect, especially for the reverse wave. The electrochemical kinetics are slower on Pt, and observed broadening of the oxidation peak is likely due to the adsorption of superoxide on the electrode surface in a process more complex than simple Langmuirian. In [C(4)dmim][NTf2] the O-2(center dot-) predominantly ion-pairs with the solvent rather than adsorbs on the surface, and an ECrev quantitatively describes the reduction of oxygen on Pt also.

Solventless continuous flow homogeneous hydroformylation of 1-octene

The hydroformylation of 1-octene under continuous flow conditions is described. The system involves dissolving the catalyst, made in situ from [ Rh(acac)(CO)(2)] (acacH = 2,4- pentanedione) and [RMIM][TPPMS] ( RMIM = 1-propyl (Pr), 1-pentyl (Pn) or 1-octyl (O)-3-methyl imidazolium, TPPMS = Ph2P(3-C6H4SO3)), in a mixture of nonanal and 1-octene and passing the substrate, 1-octene, together with CO and H-2 through the system dissolved in supercritical CO2 (scCO(2)). [PrMIM][TPPMS] is poorly soluble in the medium so heavy rhodium leaching (as complexes not containing phosphine) occurs in the early part of the reaction. [PnMIM][ PPMS] affords good rates at relatively low catalyst loadings and relatively low overall pressure (125 bar) with rhodium losses <1 ppm, but the catalyst precipitates at higher catalyst loadings, leading to lower reaction rates. [OMIM][ TPPMS] is the most soluble ligand and promotes high reaction rates, although preliminary experiments suggested that rhodium leaching was high at 5-10 ppm. Optimisation aimed at balancing flows so that the level within the reactor remained constant involved a reactor set up based around a reactor fitted with a sight glass and sparging stirrer with the CO2 being fed by a cooled head HPLC pump, 1-octene by a standard HPLC pump and CO/H-2 through a mass flow controller. The pressure was controlled by a back pressure regulator. Using this set up, [OMIM][ TPPMS] as the ligand and a total pressure of 140 bar, it was possible to control the level within the reactor and obtain a turnover frequency of ca. 180 h(-1). Rhodium losses in the optimised system were 100 ppb. Transport studies showed that 1-octene is preferentially transported over the aldehydes at all pressures, although the difference in mol fraction in the mobile phase was less at lower pressures. Nonanal in the mobile phase suppresses the extraction of 1-octene to some extent, so it is better to operate at high conversion and low pressure to optimise the extraction of the products relative to the substrate. CO and H2 in the mobile phase also suppress the extraction effciency by as much as 80%.