Group theoretic properties of Rijndael-like ciphers

We provide conditions for which the round functions of an ?-bit Rijndael-like block cipher generate the alternating group on the set {0,1}^?. These conditions show that the class of Rijndael-like ciphers whose round functions generate the alternating group on their message space is large, and includes both the actual Rijndael and the block cipher used by the compression function of the Whirlpool hash function. The result indicates that there is no trapdoor design for a Rijndael-like cipher based on the imprimitivity of the group action of its proper round functions which is difficult to detect.     

Zur Kristallchemie der tetragonalen Wolframbronze: Ba6FeNb9O30

Solid state reaction of BaCO₃, FeC₂O₄·2H₂O and Nb₂O₅ gave single crystals of Ba₆FeNb₉O₃₀. The crystal structure was solved by X-ray investigations (a=12.597,c=3.990Å, space group P 4 bm-C _4v ² ,Z=1). Ba₆FeNb₉O₃₀ crystallyzes in the tetragonal bronze type with a statistical distribution of Fe³⁺ and Nb⁵⁺ in the octahedral framework. The anisotropic temperature factors of barium are discussed with respect to the oxygen coordination.

     

Selectivity of Calixarene-bonded Silica-phases in HPLC: Description of Special Characteristics with a Multiple Term Linear Equation at Two Different pH-Values

Six different calixarene-bonded phases were characterized by analyzing 36 and 26 solutes at pH 3 and 7, respectively. Dolan and Snyder's multiple term linear equation was used to correlate retention factors k' to parameters of the solutes and columns. The column parameters have been related to molecular properties of the stationary phases and new suggestions were made for the interpretation of steric selectivity. Ionic and polar interactions have been found dependent on pH value, while steric interactions are less dependent and hydrophobic interactions remain unchanged. Distinct differences of the supported interactions were confirmed between the calixarene-bonded and the common alkyl-bonded silicas. By use of the parameters, values of k' can be estimated with an average deviation of 2.50 and 7.92% at low and neutral pH-value, respectively.     

Imines in the Titanium Coordination Sphere – Transformation of Imidoyl Chlorides to Nitrilium Ions

In the reaction of TiCl₄ in benzene as solvent with the imidoyl chloride p‐Tolyl(Cl)C=NPh ( 1 ) the abstraction of the chloride substituent is observed, leading to the nitrilium salt [p‐Tolyl–C≡N–Ph]⁺[Ti₂Cl₉]^– ( 2 ) in quantitative yield. The highly electrophilic salt 2 is characterized by IR‐ and NMR spectroscopy. The observed band for the C≡N stretching mode of 2 clearly indicates the formation of a nitrilium ion. Especially a characteristic line broadening of the ¹³C{¹H}‐NMR signals related to carbon atoms next to the nitrogen is observed. By ¹⁵N,¹H‐HMBC NMR experiments it is shown that the nitrogen signal of 2 is significantly shifted to high‐field in relation to nitriles and imines. The molecular structure of 2 was confirmed by single‐crystal X‐ray diffraction. The C≡N bond length and the linearity of the C–C≡N–C unit in 2 confirm the triple bond character of this bond.     

Activation of Molecular Hydrogen by Bis(η5,η1‐pentafulvene)‐titanium Complexes – Efficient Formation of Titanium(III)hydrides

The synthesis and crystal structures of two dinuclear titanocene hydride complexes are reported. Both complexes, namely bis(η⁵‐(di‐para‐tolylmethyl)cyclopentadienyl)titanium hydride dimer, [(η⁵‐C₂₀H₁₉)₂Ti(μ‐H)]₂ ( 2a ), and bis(η⁵‐2‐adamantylcyclopentadienyl)‐titanium hydride dimer, [(η⁵‐C₁₅H₁₉)₂Ti(μ‐H)]₂ ( 2b ), are formed via activation of molecular hydrogen by the corresponding bis(η⁵,η¹‐pentafulvene)titanium complexes 1a and 1b at ambient temperatures and pressures in high yields. The hydride complexes 2a and 2b exhibit planar [Ti₂H₂] cores and, as a result of the heterolytic cleavage of molecular hydrogen, substituted Cp Ligands were formed during the reaction.     

Hydroxide and hydronium ion adsorption — A survey

The propensity of hydroxide and hydronium ions to accumulate at interfaces is the subject of ongoing scientific debate. Electrokinetic and surface force measurements suggest elevated interfacial concentrations of hydroxide ions across a wide range of pHs. Contrary to this, however, surface-sensitive spectroscopic techniques and molecular dynamic (MD) simulations indicate that hydronium ions have strong surface affinity under similar conditions. Here we review results obtained for gas/water, oil/water and solid/water interfaces. Emphasis is placed on ion adsorption phenomena occurring on polymer films of different hydrophobicity and structure. The results clearly show that asymmetric water ion adsorption is independent of the hydrophobicity of the solid surface. Recently obtained data reveal significant effects of the hydroxide and hydronium ions even on the charging of hydrophobic polymers in the presence of multivalent electrolytes and on the charging of zwitterionic lipid membranes.