Smooth titania nanotubes: Self-organization and stabilization of anatase phase

We present transmission electron microscopy and Raman scattering measurements showing that niobium inhibits the processes of nucleation and growth of anatase crystallites in the initial amorphous titania nanotubes and thus shifts the temperature of the complete amorphous-to-anatase phase transition to higher values up to 550 °C. Niobium dopants stabilize the anatase phase in titania nanotubes up to 650 °C. The size of anatase crystallites can reach 30–50 nm. Excess niobium atoms which are pulled off from the volume of anatase crystallite form polymeric or monomeric Ti–O–NbO groups at the interface area. Slight shift and broadening of E_g (144 cm^?1), A_1g (515 cm^?1) and E_g (630 cm^?1) modes in Raman spectra can be explained by niobium insertion into the anatase structure.     

Gauge Gravitational Field in a Fractal Space-Time

Considering the fractal structure of space-time, the scale relativity theory in the topological dimension DT = 2 is built. In such a conjecture, the geodesics of this space-time imply the hydrodynamic model of the quantum mechanics. Subsequently, the gauge gravitational field on a fractal space-time is given. Then, the gauge group, the gauge-covariant derivative, the strength tensor of the gauge field, the gauge-invariant Lagrangean, the field equations of the gauge potentials and the gauge energy-momentum tensor are determined. Finally, using this model, a Reissner- Nordstrom type metric is obtained.     

Wechselwirkungen in Kristallen, 176. Mitteilung,Redox‐Reaktionen von Hexahydropyren: Kristallstrukturen seiner Radikalanion‐Salze sowie von Trihydropyrenylium‐tetrachloroaluminat und Dichtefunktionaltheorie‐Berechnungen

Redox Reactions of Hexahydropyrene: Crystal Structures of Its Radical‐Anion Salts as well as of Trihydropyrenylium Tetrachloroaluminate and Density‐Functional‐Theory Calculations Hexahydropyrene 1 , a doubly propane‐1,3‐diyl‐bridged peri‐naphthalene derivative wtih 10 π‐electrons allows both oxidation to its cation as well as reduction to its radical‐anion salts, which could be crystallized and structurally characterized – a rather rare case for small unsaturated hydrocarbons. The unexpected formally threefold dehydrogenation by the oxidizing system AlCl₃/H₂CCl₂ (Bock's reagent) generated the hitherto unknown 1,2,3‐trihydropyrene cation in two polymorphic crystals, which contain 12 π‐electrons delocalized over three anellated six‐membered rings comprising 13 π‐centers. Structural comparison of the altogether four crystallized redox products [K⁺_solv][M^.−] 2a , [K⁺_solv][M^.−]_∞ 2b , [Na⁺_solv][M^.−] 2c , and [(M−3 H)⁺][AlCl⁻₄] 3 with the neutral hydrocarbon 1 reveals only small differences in bond lengths and angles, but establishes solvation contacts, π(η⁶)⋅⋅⋅K⁺ coordination in the polymer 2b , the flattening of one molecular half in the trihydropyren cation of 3 and ten H‐bonds CH⋅⋅⋅Cl to the AlCl₄⁻ counter anion of 3 . DFT/NBO Charge distributions, calculated based on the experimental structural parameters, show charge accumulation in the propanediyl bridges as well as in the peripheral naphthalene C−C bonds of the radical anions. The largest changes result expectedly for the formally triply dehydrogenated 1 , i.e. the trihydropyren cation of 3 , with two slightly positive and partly considerably less negative π‐centers.     

Equal treatment without large numbers

We provide a necessary and sufficient condition under which core allocations of arbitrary TU-games treat substitute players equally. The core satisfies the equal treatment property if and only if no player needs the participation of all of her substitutes to attain her core payoffs. We show how, without the requirement of a large number of players, this condition generalizes and unifies other sufficient conditions proposed in the literature (in the context of large games and economies) and it helps derive new results for particular classes of games.     

Structure of the hydrated, hydrolysed and solvated zirconium(IV) and hafnium(IV) ions in water and aprotic oxygen donor solvents. A crystallographic, EXAFS spectroscopic and large angle X-ray scattering study

The tetrameric hydrolysis products of zirconium(IV) and hafnium(IV), the zirconyl(IV) and hafnyl(IV) ions, [M(4)(OH)(8)(OH(2))(16)(8+)], often labelled MO(2+).5H(2)O, are in principle the only zirconium(IV) and hafnium(IV) species present in aqueous solution without stabilising ligands and pH larger than zero. These complexes are furthermore kinetically very stable and do not become protonated even after refluxing in concentrated acid for at least a week. The structures of these complexes have been determined in both solid state and aqueous solution by means of crystallography, EXAFS and large angle X-ray scattering (LAXS). Each metal ion in the [M(4)(OH)(8)(OH(2))(16)](8+) complex binds four hydroxide ions in double hydroxo bridges, and four water molecules terminally. The M-O bond distance to the hydroxide ions are markedly shorter, ca. 0.12 A, than to the water molecules. The hydrated zirconium(IV) and hafnium(IV) ions only exist in extremely acidic aqueous solution due to their very strong tendency to hydrolyse. The structure of the hydrated zirconium(IV) and hafnium(IV) ions has been determined in concentrated aqueous perchloric acid by means of EXAFS, with both ions being eight-coordinated, most probably in square antiprismatic fashion, with mean Zr-O and Hf-O bond distances of 2.187(3) and 2.160(12) A, respectively. The dimethyl sulfoxide solvated zirconium(IV) and hafnium(IV) ions are square antiprismatic in both solid state and solution, with mean Zr-O and Hf-O bond distances of 2.193(1) and 2.181(6) A, respectively, in the solid state. Hafnium(IV) chloride does not dissociate in N,N'-dimethylpropyleneurea, dmpu, a solvent with good solvating properties but with a somewhat lower permittivity (epsilon= 36.1) than dimethyl sulfoxide (epsilon= 46.4), and an octahedral HfCl(4)(dmpu)(2) complex is formed.     

New potentiometric microbial biosensor for ethanol determination in alcoholic beverages

A potentiometric oxygen electrode was successfully used to produce a microbial biosensors with an extended response range, based on immobilised yeast cells (Saccharomyces ellipsoideus). The response for ethanol takes ca. 7 min for the steady-state method and 2 min for kinetic measurements. A linear calibration achieved over more than two decades of ethanol concentration. Selective determination of ethanol in the presence of non-volatile compounds was achieved using a second PTFE membrane to cover the biocatalytic layer.     

Mechanism of pyridine protonation in water clusters of increasing size

This work presents a theoretical mechanistic study of the protonation of pyridine in water clusters, at the B3LYP/cc-pVDZ theory level. Clusters from one to five water molecules were used. Starting from previously determined structures, the reaction paths for the protonation process were identified. For complexes of pyridine with water clusters of up to three water molecules just one transition state (TS) links the solvated and protonated forms. It is found that the activation energy decreases with the number of water molecules. For complexes of four and five water molecules two transition states are found. For four water molecules, the first TS links the starting solvated structure with a new, less stable, solvated form through a concerted proton transfer between a ring of water molecules. The second TS links the new solvated structure to the protonated form. Thus, protonation is a two-step process. For the five water molecules cluster, the new solvated structure is more stable than the starting one. This structure exhibits two double hydrogen bonds involving the pyridinic nitrogen and several water molecules. The second TS links the new structure with the protonated form. Now the process occurs in one step. In all cases considered, the proton transfers involve an interconversion between covalent and hydrogen bonds. For four and five water molecules, the second TS is structurally and energetically very close to the protonated form. As evidenced by the vibration frequencies, this is due to a flat potential energy hypersurface in the direction of the reaction coordinate. Determination of DeltaG at 298.15 K and 1 atm shows that the protonation of pyridine needs at least four water molecules to be spontaneous. The complex with five water molecules exhibits a large DeltaG. This value yields a pKa of 2.35, relatively close to the reported 5.21 for pyridine in water.