Hamiltonian evolution and quantization for extremal black holes

We present and contrast two distinct ways of including extremal black holes in a Lorentzian Hamiltonian quantization of spherically symmetric Einstein-Maxwell theory. First, we formulate the classical Hamiltonian dynamics with boundary conditions appropriate for extremal black holes only. The Hamiltonian contains no surface term at the internal infinity, for reasons related to the vanishing of the extremal hole surface gravity, and quantization yields a vanishing black hole entropy. Second, we give a Hamiltonian quantization that incorporates extremal black holes as a limiting case of nonextremal ones, and examine the classical limit in terms of wave packets. The spreading of the packets, even the ones centered about extremal black holes, is consistent with continuity of the entropy in the extremal limit, and thus with the Bekenstein-Hawking entropy even for the extremal holes. The discussion takes place throughout within Lorentz-signature spacetimes.     

Ruthenium Trichloride,Tricyclohexyl- phosphane, 1-Alkynes,Magnesium, Hydrogen,and Water—Ingredients of an Efficient One-Pot Synthesis of Ruthenium Catalysts for Olefin Metathesis

An active role is played by MgCl₂ during the conversion of the vinylidene precursor 2 into carbenes 3 (R=H, Ph; L=P(C₆H₁₁)₃). These complexes can be prepared in a convenient and very efficient one-pot synthesis and have a catalytic activity in metathesis comparable to that of Grubbs compound (Ph instead of CH₂R).     

Isocyanate-Based Dendritic Building Blocks: Combinatorial Tier Construction and Macromolecular-Property Modification

Used individually or combinatorially , unique isocyanate-based dendritic monomers generate homo- and heterofunctional materials (the sketch shows schematically a molecule with a heterofunctional surface). Tier construction by combinatorial monomer addition offers new avenues to macromolecular architectural design and the control of physical properties.     

Justus Liebig trifft Georg Büchner: Sturm und Dung — eine fiktive Begegnung

In a fictitious meeting between the chemist and agricultural reformer Justus Liebig and the poet and social revolutionary Georg Büchner alternative paths of historical development in the early 19^th century as well as current developments in food engeneering are discussed.     

Large scale particle image velocimetry with helium filled soap bubbles

The application of Particle Image Velocimetry (PIV) to measurement of flows on large scales is a challenging necessity especially for the investigation of convective air flows. Combining helium filled soap bubbles as tracer particles with high power quality switched solid state lasers as light sources allows conducting PIV on scales of the order of several square meters. The technique was applied to mixed convection in a full scale double aisle aircraft cabin mock-up for validation of Computational Fluid Dynamics simulations.     

Metalloporphyrin heterodimers,molecular bilayer fibers and monolayer leaflets

Amphiphilic metalloporphyrins assemble in water to form supramolecular fibers, which have been characterized by transmission electron microscopy. Loose octopus porphyrin fibers can be doped with hydrophobic electron acceptors, metalloporphyrin monomolecular sheets are crystalline. Charge separation occurs in amino porphyrin fibers without added electron acceptors. Bolaamphiphilic porphyrins with four pyridinyl or methyl pyridinium groups in β-pyrrolic positions have been synthesized. The regioisomer mixture is very soluble in water (≌ 0.1 M) and is ideally suited to form heterodimers with negatively charged ms-tetrasubstituted porphyrins. Bimetallic porphyrinate pairs are described. The zinc complex is stable down to pH 1.0. Regioisomer II forms well-defined molecular monolayer leaflets in bulk water at pH 2.5. The surface structure of such monolayers is discussed. It consists of a large cationic plane and hydrophobic edges. Possible applications are discussed shortly.     

Swimming against the Stream? A Discussion of the Bonding in d6 and d8 Fluoro Complexes and Its Consequences for Catalytic Applications

Fluoride has recently found increasing application as coligand both in complexes of late transition metals and as a reagent in asymmetric catalysis. In recent papers, this topic was reviewed, with emphasis on the role played by so‐called ‘push‐pull interactions' between the fluoro ligand and a π acid in the stabilization of fluoro complexes with a d⁶ or d⁸ electron configuration. This picture has led to the concept that fluoride is the strongest π‐donor in the halide series. Herein, the latter concept is discussed and criticized. In particular, the effect of the ionicity of the metal‐fluoride bond is proposed as an alternative explanation to most of the observations that show a ‘reversed' halide order. The ionic character of the M F bond also accounts for its intrinsic reactivity and suggests some strategies for the stabilizatioin of fluoro complexes, including the use of coordinative unsaturation. The scope and limitations of the application of d⁶ and d⁸ fluoro complexes in catalysis are also discussed. The most promising application is the use of 16‐electron fluoro complexes in the metal‐promoted formation of the C F bond.     

Strukturen von planaren und tetraedrischen TetrafulminatoMetallkomplexen: [N(C3H7)4]2 [Ni(CNO)4], [N(C3H7)4]2 [Pt(CNO)4] und [N(C3H7)4]2 [Zn(CNO)4]

Pseudohalogeno Metal Compounds. LXXVIII. Structures of Planar and Tetrahedral Tetrafulminato Metal Complexes: [N(C₃H₇)₄]₂ [Ni(CNO)₄], [N(C₃H₇)₄]₂ [Pt(CNO)₄], and [N(C₃H₇)₄]₂ [Zn(CNO)₄] The crystals contain the tetrafulminatometallates of an ideal square planar structure ([Ni(CNO)₄]^2–, [Pt(CNO)₄]^2–) with D_4h symmetry at the nickel and platinum atom and a tetrahedron ([Zn(CNO)₄]^2–) with perfect T_d symmetry at the zinc atom and with linear C≡N–O ligands. The metal carbon bonds (Ni–C: 187 pm, Pt–C: 200 pm, Zn–C: 201 pm) of the metal fulminates are very close to those of the corresponding cyano complexes. In the crystals the anions ([Ni(CNO)₄]^2–, [Pt(CNO)₄]^2–, [Zn(CNO)₄]^2–) are separated by the cations ([N(C₃H₇)₄]⁺) which explains the thermal stability of these compounds.