Singularities in cascade models of the Euler equation

The formation of singularities in the three-dimensional Euler equation is investigated. This is done by restricting the number of Fourier modes to a set which allows only for local interactions in wave number space. Starting from an initial large-scale energy distribution, the energy rushes towards smaller scales, forming a universal front independent of initial conditions. The front results in a singularity of the vorticity in finite time, and has scaling form as function of the time difference from the singularity. Using a simplified model, we compute the values of the exponents and the shape of the front analytically. The results are in good agreement with numerical simulations.     

Characterisation of adsorbed layers on sulphide minerals by photoelectron spectroscopy

The systems galena/2-mercaptobenzothiazole (MBT) and pyrite/MBT have been studied using synchrotron radiation excited photoelectron spectroscopy (SRXPS). The chemisorption of MBT and the multilayer formation of 2,2′-dithiobis(benzothiazole) (BBTD) are evidenced by additional structures, observed beside the substrate signals, in the S2p-spectra of cleaved mineral surfaces after adsorption of MBT. The amount of the complex remains constant at concentrations as high as 10^–5 mol/L whereas the amount of BBTD increases. From the dependence of the adsorbate intensities on the excitation energy the conclusion can be drawn that an overlayer of BBTD on a chemisorbed layer of MBT is formed. The very weak adsorption of MBT on pyrite in alkaline solutions may explain the selective flotation of galena from pyrite in alkaline media.     

Substituierte 2-(Thiazol-4-yl)-phenole als Liganden und potentielle Extraktionsmittel für Kupfer(II)

Substituted 2-(Thiazol-4-yl)-phenols as Ligands and Potential Extractants for Copper (II) Substituted 2-(thiazol-4-yl)-phenols are obtained by the HANTZSCH synthesis. Their solubility in toluene is higher than in n-octane depending on the position, the chain length, and the polarity of the substituents. From alcoholic solutions complexes of the type CuL₂ⁿ are precipitated. According to the substituents their structure is distorted octahedral (CuL₂², CuL₂³) or distorted tetrahedral (CuL₂⁸, CuL₂⁹). The new complexes are nearly insoluble in toluene and aliphatic hydrocarbons, but CuL₂⁸ and CuL₂⁹ are soluble in chloroform. Therefore copper(II) may be extracted by HL⁸ and HL⁹ using chloroform as a diluent.     

Extraktion von 3d-Metallionen mit zweizähligen Sulfonamiden. I. Liganden mit Schwefel bzw. heterocyclisch gebundenem Stickstoff als zweitem Haftatom

Extraction of 3d-Metal Ions by Bidendate Sulfonamides. I. Ligands with Sulfur or Heterocyclic Nitrogen as a Second Donor Atom The properties of 2-acetylpyridine-p-toluensulfonylhydrazone (APSH - H), arensulfonylthioureas (I), and the esters of arensulfonylmonothiocarbamic acid (II) or arensulfonyldithiocarbamic acid (III) as extractants for the late 3d-metal ions are proved. APSH-H is comparable to the proprietary extractant LIX 34. But, because of the special structure of the corresponding 1,2-chelates, the pH_1/2-values of nickel(II) and cobalt(II) are ≈2 units lower. The pK_s-values, measured in dioxane-water mixtures (75 per cent v/v), increase in the order III < II < I. In aqueous solutions compounds of type III are acids of medium strength. In the case of compounds of type I the substituents of the non-sulfonated nitrogen have a strong influence on the pK_s-values (ΔpK_s = 4.6). Among the late 3d-elements, the ligands II and III extract only copper(II) (pH_1/2 ～2.7 or ～1.6), the ligands I extract zinc(II), cobalt(II), and nickel(II) as well, but not iron(II) and iron(III). The reasons of this unique behaviour are discussed.     

Thermodynamische Untersuchungen zur Chelatbildung zwischen Aminoterephthalsäure-N,N-diessigsäure und 3 d- bzw. Erdalkalimetallionen. Eine Betrachtung zum Einfluß einer koordinativ inaktiven Carboxylgruppe auf die komplexe Bindung von Metallionen durch Aminopolycarbonsäuren

N-(2-Carboxyphenyl)iminodiacetic acid (H₃A) and N-(2,5-dicarboxyphenyl)iminodiacetic acid (H₄B) are tetradentate ligands and form complexes of the composition MA- and MB^2? with M^II ions. These compounds differ by the additional charge of the second carboxylic group only, which is fixed to the benzene nucleus and which is unable for coordination for steric reasons. Using an anisothermal calorimeter ΔH values for the formation of the complexes MA- and MB^2? in aqueous solution have been measured at an ionic strength 0.1 m KNO₃. From these data, and from the stability constants of the complexes, entropy changes ΔS have been calculated. In all cases investigated (M^m+ = H⁺, Mg²⁺, Ca²⁺, Sr²⁺, Co²⁺, Ni²⁺, Cu²⁺, Zn²⁺) the ΔH values are more negative for the complexes MA^m-3 than for complexes MB^m-4, whereas the ΔS values are greater for complexes MB^m-4. Using a simple model for the molecules of the complexes MB^m-4 and empirically determined dielectric constants of the medium between the central ions and the noncoordinated ionized carboxylic group, the electrostatic attraction between these charges was calculated. Basing on these results the influence of the noncoordinated carboxylic group on the central atom by the mesomeric and inductive effect is discussed.     

Neue Redoxserien auf der Basis von Übergangsmetallkomplexen heterocyclischer Arensulfonylhydrazone

New Redox Series Based on Transition Metal Complexes of Heterocyclic Arenesulfonylhydrazones Heterocyclic bidentate arenesulfonylhydrazones (2-acetylpyridine-p-toluenesulfonylhydrazone ? APSH? H, 2-acetylquinoline-p-toluenesulfonylhydrazone ? ACSH? H) with transition metal ions afford tetrahedral 1,2-complexes M^II(APSH)₂ and M^II(ACSH)₂. In most cases the E-isomers of APSH^? and ACSH^? are coordinated, five-membered chelate rings are formed with the pyridine and hydrazone nitrogen atoms as donor atoms. In the complexes Zn(APSH)₂ and Cu(APSH)₂ probably the Z-isomer of APSH^? is present with the pyridine and the sulfonylamide nitrogen atoms as a donor set, yielding a six-membered chelate ring. These proposals are based on the magnetic moments, the ligand field spectra, and the binding energies (ESCA). Normally the complexes M^II(APSH)₂ and M^II(ACSH)₂ are reduced in two reversible steps. For Fe(APSH)₂ and Fe(ACSH)₂ a third anodic wave, but for Cu(APSH)₂ only one wave is observed. Relations between redox properties and structure of the new complexes are discussed, and the redox series are compared with that of the M(dipy)₃ⁿ⁺-type complexes.     

Reaktionen von π-Organokomplexen des Nickels mit tertiären Phosphanen

Reactions of π-Organonickel Complexes with Tertiary Phosphanes In a hexane solution Ni(C₅H₅)₂ reacts with PBu₃ or Ph₂PBu forming the nickel(O) complexes Ni(PBu3)₄ or Ni(Ph₂PBu)₄ (A). Under the same conditions only one cyclopentadienyl ligand is substituted by PhPBu₂ and the nickel(I) compound (C₅H₅)Ni (PhPBu₂)₂ (B) is obtained. Products of the reactions between B and α,α′-dipyridyl, hydrogen chlorid in ether, or Ni(PhPBu₂),Cl₂ are Ni(dipy)₂, [PhPHBu₂]₂[NiCl₄], or (C₅H₅) Ni(PhPBu₂)₂Cl. By the reaction with HgCl₂ a cyclopentadienyl compound of an unknown structur is formed. The compound Ni(PhPBu₂)₄ which is analogous to A is synthesized by the reduction of bis(acety1acetonato)-nickel with Et₂AlOEt in the presence of PhPBu₂ or by the reaction of bis (cyclooctadiene-1,5)-nickel with PhPBu₂.     

Zur Synthese von Siloxanen auf der Basis von Silyltriflat-Derivaten

Synthesis of Siloxanes on the Basis of Silyltriflates The reaction of silyltriflates with silanols leads to the formation of siloxanes. This method is of importance if the synthesis of silyltriflates is more simply and selectively than the preparation of the corresponding chlorosilanes. This is observed in the case of functional substituted silyltriflates or triflate derivatives of oligosilanes. The synthetic potential of these compounds for the preparation of siloxanes is shown on selected examples.     

Zur Synthese und Reaktivität Triflatsubstituierter Siloxanderivate

Synthesis and Reactivity of Triflate Substituted Siloxane Derivatives The reaction of amino substituted siloxane derivatives with trifluoromethanesulfonic acid leads under elimination of ammonium trifluoromethanesulfonate to the formation of siloxanyl triflates. The compounds are characterised by NMR-spectroscopy (²⁹Si, ¹³C, ¹H). The synthetic potential of these siloxanes is shown on selected examples. One interesting point of view is the synthesis of silicon containing oligo- and polymeres, in which siloxane and silylenealkine units are combined.     

Zum komplexchemischen Verhalten von potentiell vier- und fünfzähligen Bis(salicylidenamino)-Liganden gegenüber Ionen der 3d-Elemente

Studies on the Coordinative Behaviour of Potentially Four and Fivedentate Bis(salicylidene amino)-Ligands with Ions of the 3d-Elements. Fourdentate bis(salicylidene amino)-ligands (^?ONΦCH₂ΦNO^? and ^?ONΦOΦNO^?, meaning of the abbreviations see text) with the centres of donor atoms connected by rigid, bifunctional residues, form polymeric complexes Me^II(ONΦCH₂ΦNO) and Me^II(ONΦOΦNO) with cobalt(II), nickel(II), and copper(II). Among the cobalt(II) chelates the structure is uniformly tetrahedral, but the nickel(II) and copper(II) complexes contain square planar central atoms and such with a higher coordination number side by side. The potential fivedentate ligands ^～ON3PPh3NO^?, ^?ON2O2NO^?, and ^?ON2S2NO^? differ as to their coordinative behaviour. The coordination number of the complexes Ni(ON3PPh3NO) and Co(ON3PPh3NO) is five. On the other hand the compounds Co(ON2S2NO) and Co(ON2O2NO) are tetrahedral. No coordination of the ether or sulfide group is observed. Ni(ON2O2NO) has an octahedral structure which is produced by coordination polymerisation and possibly by coordination of the ether group. The new complexes are compared with the transition metal complexes of simple salicylaldimines.