Monopoly

Mathematische Semesterberichte - Die Spielidee des Monopoly-Spiels ist mehr als 100 Jahre alt. Ein Grund für den beständigen Erfolg ist die Anpassungsfähigkeit der Spielidee....     

Die Doppelbrechung von Seifensolen

Zusammenfassung Zusammengefaßt hat sich ergeben: Seifensole zeigen eine Vorzeichenumkehr der Strömungsdoppelbrechung. Diese Umkehr ist reversibel. Das Vorzeichen der Doppelbrechung beim Strömen hängt ab von der Konzentration der Wasserstoffionen im Dispersionsmittel. Durch H-Ionen wird die Dissoziation der COOH-Gruppe der Fettsäuren zurückgedrängt, dagegen durch OH-Ionen gefördert. Bei starker Dissoziation und hoher Ladung der COOH-Gruppe überwiegt die heteropolare Ionenbindung — die Seifenmoleküle ordnen sich hintereinander an (Stäbchen). Bei geringer Dissoziation der COOH Gruppe überwiegt die homöopolare Nebenvalenzbindung der Paraffinketten — und die Fettsäuremoleküle ordnen sich nebeneinander an (Plättchen).Die verschiedenartigen Mizellen haben ein verschiedenes optisches Verhalten. Im Inversionspunkt ist das Sol isotrop. Dieser Punkt ist wahrscheinlich der Neutralpunkt der Seifen. Die Inversion ist eine Zeitreaktion.Die Änderung des mizellaren Aufbaus der Seife wie auch von Palmitat und Stearat gibt sich gleichzeitig in einer Änderung der Viskosität, der Trübung, der Spinnbarkeit, der Häutchenbildung, der Gelbildung und dem Schaumvermögen zu erkennen.     

Mechanism of enzymatic Birch reduction: stereochemical course and exchange reactions of benzoyl-CoA reductase

Dearomatizing benzoyl-coenzyme A reductases (BCR) from facultatively anaerobic bacteria are key enzymes in the anaerobic degradation of aromatic compounds. They catalyze the ATP-dependent reduction of benzoyl-CoA (BCoA) to cyclohexa-1,5-diene-1-carboxyl-CoA (dienoyl-CoA). A Birch reduction mechanism involving alternate electron transfer and protonation steps has been proposed for BCR. In this work we reacted BCoA in H2O and D2O, and d5-BCoA in H2O with BCR and the second enzyme of the pathway, dienoyl-CoA hydratase (DCH). The 1,4 hydration product formed from the dienoyl-CoA, 6-hydroxycyclohex-1-ene-1-carbonyl-CoA, was analyzed by several NMR techniques. The results obtained indicate that BCR stereoselectively forms the trans-dienoyl-CoA product, and DCH stereoselectively catalyzes a trans-1,4 water addition. Moreover, unexpected proton exchanges at C-2 and C-6 were observed. They indicate that a free radical intermediate with an unusual low pKa is formed during BCR catalysis. This finding provides evidence for the proposed Birch reduction mechanism of BCR and is in agreement with the established radical mechanism of homologous alpha-hydroxyacyl-CoA dehydratases.     

Even-electron ions: a systematic study of the neutral species lost in the dissociation of quasi-molecular ions

The collision-induced dissociations of the even-electron [M + H](+) and/or [M - H](-) ions of 121 model compounds (mainly small aromatic compounds with one to three functional groups) ionized by electrospray ionization (ESI) or atmospheric pressure chemical ionization (APCI) have been studied using an ion trap instrument, and the results are compared with the literature data. While some functional groups (such as COOH, COOCH(3), SO(3)H in the negative ion mode, or NO(2) in both the positive and negative ion modes) generally promote the loss of neutrals that are characteristic as well as specific, other functional groups (such as COOH in the positive ion mode) give rise to the loss of neutrals that are characteristic, but not specific. Finally, functional groups such as OH and NH(2) in aromatic compounds do not lead to the loss of a neutral that reflects the presence of these substituents. In general, the dissociation of [M + H](+) and [M - H](-) ions generated from aliphatic compounds or compounds containing an aliphatic moiety obeys the even-electron rule (loss of a molecule), but deviations from this rule (loss of a radical) are sometimes observed for aromatic compounds, in particular for nitroaromatic compounds. Thermochemical data and ab initio calculations at the CBS-QB3 level of theory provide an explanation for these exceptions. When comparing the dissociation behaviour of the even-electron [M + H](+) and/or [M - H](-) ions (generated by ESI or APCI) with that of the corresponding odd-electron [M](+) ions (generated by electron ionization, EI), three cases may be distinguished: (1) the dissociation of the two ionic species differs completely; (2) the dissociation involves the loss of a common neutral, yielding product ions differing in mass by one Da, or (3) the dissociations lead to a common product ion.     

Time Domain Impedance Boundary Conditions for a Slip Mean FlowBoundary

In modeling the physical condition of an impedance boundary, the assumption of either particle displacement continuity (PDC) or particle normal velocity continuity (PVC) at the interface between the acoustic treatment and the adjacent fluid needs to be used. Although it is well accepted that the impedance boundary condition derived from the PDC is the appropriate impedance boundary condition when there is a slip mean flow at the liner surface, the time domain impedance boundary condition is however unstable due to the Kelvin‐Helmholtz instability associated with the ”vortex sheet.” In this paper, an effective time domain impedance boundary condition for a slip mean flow boundary is proposed and validated. Several relevant issues related to the PDC and PVC are discussed. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Die Kristallstruktur von Lithiummesitolat [{LiOC6H2-2,4,6-(CH3)3}4(THF)3]

X-Ray Structure of [{LiOC₆H₂-2,4,6-(CH₃)₃}₄(THF)₃] The title compound crystallized from a THF/OEt₂ solution. Its crystal structure (monoclinic, P2₁/c, a = 21.362(3), b = 13.441(2), c = 17.188(2) Å, β = 98.39(1)°, Z = 4, R = 0,0911, wR² = 0,2562) is built up by cuban-like tetrameric units. Three of the four Li cations attain a coordination number of four by binding to an additional THF molecule. Li(4) without THF coordination has a short distance to one ortho-methyl group (Li(4)…C(27) 2.669(10) Å). The Li–O_ph bonding distances vary from 1.869(10) to 2.051(10) Å (average 1.97 Å); the average bonding distance for Li–O_THF is 2.012(10) Å. Averaged bonding angles for Li–O_ph–Li′ and O_ph–Li–O′_ph amount to 84.4(4)° and 95.4(4)°, respectively. The Li…Li distances significantly differ from each other. They range from 2.556(12) to 2.739(11) Å (average 2.65(1) Å).     

On rational approaches to formulate minimal integrity basis for explicit stress closures

Due to their high efficiency and robustness almost all simulations of complex engineering flows rely on turbulence models with explicit stress closures. Focal point of an explicit stress closure is the stress‐strain‐relationship, that couples the Reynolds‐stresses to the velocity field. Mostly linear eddy‐viscosity models are employed, thus, they are based on the hypothesis and assume Reynolds‐stress proportional to the strain‐rate tensor. Therefore, they are easy to implement, but they fail to predict complex flow fields besides two dimensional shear flow such as secondary flow in non‐circular ducts. In contrast to these models, explicit algebraic stress models (EASM) represent the Reynolds‐stress by the integrity basis of the strain‐rate and vorticity tensors. This leads to a more general stress‐strain‐relationship, however, it increases the implementation and computation effort. In this paper the properties of the integrity basis will be discussed and the derivation of a minimal integrity basis will be proposed.     

Monomere und dimere Oxovanadium(IV)-phenolate: Synthese,Struktur und Reaktionen mit reduzierenden und arylierenden Reagenzien

Monomeric and Dimeric Oxovanadium(IV)-phenolate Complexes: Synthesis, Structure, and Reaction with a Reducing and Arylation Agent Reaction of [OVCl₂(THF)₂] with LiOMes yields dimeric [Li(Et₂O)₂OVCl₂(μ-OMes)]₂ ( 1 ) which can be converted with excess LiOMes to the substitution product [Li(THF)₂OV(OMes)₃(THF)] ( 2 ). Treatment of ( 1 ) with LiMes results in the formation of complexes [Li(THF)₃OVMes₃] ( 3 ) and [Li(THF)₃OVMes₂(OMes)] ( 4 ). Complex [{Li(THF)₂OV(OMes)₂(μ-OH)}₂ · 2 THF] ( 6 ) has been isolated as a by-product of an unknown reaction of [OV(OMes)₃] and Li. The structures of 1 , 2 , 3 , and 6 have been determined by X-ray analysis. In 1 (monoclinic, P2₁/c, a = 9.522(1) Å, b = 19.777(2) Å, c = 12.311(1) Å, β = 104.45(1)°, Z = 2) the vanadium atoms which are bridged by the phenolate ligands show a square-pyramidal coordination sphere. The central atom in 2 (monoclinic, P2₁/c, a = 17.755(2) Å, b = 11.629(1) Å, c = 20.956(3) Å, β = 113.98(1)°, Z = 4) has a bipyramidal environment which is realized by coordination of a THF donor molecule. The (THF)₂Li fragment is bound via bridging phenolate ligands. The structure of 3 (orthorhombic, P2₁2₁2₁, a = 15.465(2) Å, b = 15.456(2) Å, c = 15.469(2) Å, Z = 4) is built up by two tetrahedrons linked by the oxo atom. Dimeric 6 (triclinic, P1, a = 10.780(4) Å, b = 11.428(2) Å, c = 13.734(3) Å, α = 77.24(2)°, β = 84.79(2)°, γ = 74.35(2)°, Z = 1) has a structure similar to 1 . The vanadium atoms are bridged by two OH groups while phenolate ligands link the lithium cations with the vanadium atoms.     

Interfacial instabilities driven by chemical reactions

We investigate the interaction of thin films with chemical reactions by using as a model system a horizontal film with a reactive mixture of insoluble surfactants on its free surface. The reaction is modeled by a bistable/excitable FitzHugh-Nagumo (FHN) prototype. The chemical reaction can destabilize the film leading to the propagation of solitary pulses on its free surface.