Na5AlF2(PO4)2: Darstellung,Kristallstruktur und Ionenleitfähigkeit

Na₅AlF₂(PO₄)₂: Synthesis, Crystal Structure and Ionic Conductivity Two different procedures (precipitation from aqueous solution and solid state reaction) for the synthesis of hitherto unknown Na₅AlF₂(PO₄)₂ were optimized. The crystal structure was determined using diffractometer data (P3 , a = b = 10.483(1), c = 6.607(1) Å, MoKα, 1080 independent reflections, R_w = 0.025). PO₄-tetrahedra and AlO₄F₂-“octahedra” are connected via common vertices forming a twodimensionally extended heteropolyanion. Sodium is located in interconnected spacings of the [AlF₂(PO₄)₂]-part of the structure. Ionic conductivity as expected because of these structural features was affirmed experimentally.     

Existence theorem for solitary waves on lattices

In this article we give an existence theorem for localized travelling wave solutions on one-dimensional lattices with Hamiltonian $$H = \sum\limits_{n \in \mathbb{Z}} {\left( {\tfrac{1}{2}p_n^2 + V(q_{n + 1} - q_n )} \right)} ,$$ whereV(·) is the potential energy due to nearest-neighbour interactions. Until now, apart from rare integrable lattices like the Toda latticeV(φ)=ab ^?1(e ^?bφ+bφ?1), the only evidence for existence of such solutions has been numerical. Our result in particular recovers existence of solitary waves in the Toda lattice, establishes for the first time existence of solitary waves in the (nonintegrable) cubic and quartic latticesV(φ)= 1/2φ ² + 1/3aφ ³,V(φ) = 1/2φ ² + 1/4bφ ⁴, thereby confirming the numerical findings in [1] and shedding new light on the recurrence phenomena in these systems observed first by Fermi, Pasta and Ulam [2], and shows that contrary to widespread belief, the presence of exact solitary waves is not a peculiarity of integrable systems, but “generic” in this class of nonlinear lattices. The approach presented here is new and quite general, and should also be applicable to other forms of lattice equations: the travelling waves are sought as minimisers of a naturally associated variational problem (obtained via Hamilton's principle), and existence of minimisers is then established using modern methods in the calculus of variations (the concentration-compactness principle of P.-L. Lions [3]).     

A domino copper-catalyzed C-O coupling-Claisen rearrangement process

A practical method for the diastereoselective generation of two adjacent quarternary stereocenters by combining a copper-catalyzed C-O coupling reaction with a subsequent Claisen rearrangement in a one-pot domino process is described. Furthermore, an experimentally simple method for the stereoselective synthesis of a variety of different types of vinyl ethers is delineated using the same catalyst system.     

Effect of surfactants on the stability of thin liquid film flow on a rotating disk

The effect of surfactants on surface instabilities of thin liquid film flow on a rotating disk was studied at different flow rates Q (0.5相似文献   

Synthese und Charakterisierung neuer intramolekular stickstoffstabilisierter Organoaluminium‐ und Organogalliumalkoxide

Synthesis and Characterization of New Intramolecularly Nitrogen‐stabilized Organoaluminium‐ and Organogallium Alkoxides The intramolecularly nitrogen stabilized organoaluminium alkoxides [Me₂Al{μ‐O(CH₂)₃NMe₂}]₂ ( 1a ), Me₂AlOC₆H₂(CH₂NMe₂)₃‐2,4,6 ( 2a ), [(S)‐Me₂Al{μ‐OCH₂CH(i‐Pr)NH‐i‐Pr}]₂ ( 3a ) and [(S)‐Me₂Al{μ‐OCH₂CH(i‐Pr)NHCH₂Ph}]₂ ( 4 ) are formed by reacting equimolar amounts of AlMe₃ and Me₂N(CH₂)₃OH, C₆H₂[(CH₂NMe₂)₃‐2,4,6]OH, (S)‐i‐PrNHCH(i‐Pr)CH₂OH, or (S)‐PhCH₂NHCH(i‐Pr)CH₂OH, respectively. An excess of AlMe₃ reacts with Me₂N(CH₂)₂OH, Me₂N(CH₂)₃OH, C₆H₂[(CH₂NMe₂)₃‐2,4,6]OH, and (S)‐i‐PrNHCH(i‐Pr)CH₂OH producing the “pick‐a‐back” complexes [Me₂AlO(CH₂)₂NMe₂](AlMe₃) ( 5 ), [Me₂AlO(CH₂)₃NMe₂](AlMe₃) ( 1b ), [Me₂AlOC₆H₂(CH₂NMe₂)₃‐2,4,6](AlMe₃)₂ ( 2b ), and [(S)‐Me₂AlOCH₂CH(i‐Pr)NH‐i‐Pr](AlMe₃) ( 3b ), respectively. The mixed alkyl‐ or alkenylchloroaluminium alkoxides [Me(Cl)Al{μ‐O(CH₂)₂NMe₂}]₂ ( 6 ) and [{CH₂=C(CH₃)}(Cl)Al{μ‐O(CH₂)₂NMe₂}]₂ ( 8 ) are to obtain from Me₂AlCl and Me₂N(CH₂)₂OH and from [Cl₂Al{μ‐O(CH₂)₂NMe₂}]₂ ( 7 ) and CH₂=C(CH₃)MgBr, respectively. The analogous dimethylgallium alkoxides [Me₂Ga{μ‐O(CH₂)₃NMe₂}]₂ ( 9 ), [(S)‐Me₂Ga{μ‐OCH₂CH(i‐Pr)NH‐i‐Pr}]_n ( 10 ), [(S)‐Me₂Ga{μ‐OCH₂CH(i‐Pr)NHCH₂Ph}]_n ( 11 ), [(S)‐Me₂Ga{μ‐OCH₂CH(i‐Pr)N(Me)CH₂Ph}]_n ( 12 ) and [(S)‐Me₂Ga{μ‐OCH₂(C₄H₇NHCH₂Ph)}]_n ( 13 ) result from the equimolar reactions of GaMe₃ with the corresponding alcohols. The new compounds were characterized by elemental analyses, ¹H‐, ¹³C‐ and ²⁷Al‐NMR spectroscopy, and mass spectrometry. Additionally, the structures of 1a , 1b , 2a , 2b , 3a , 5 , 6 and 8 were determined by single crystal X‐ray diffraction.