Resonant oscillations in open tubes

Summary The problem of a gas-filled tube excited by sinusoidal piston motion at one end and open at the other end is reinvestigated.It is shown that the key idea for the solution of the problem is a suitable combination of the usual amplitude nonlinearity and distortion effects. The main consequence of this is that the solution cannot be expressed in terms of a hierarchy associated with an expansion in the Mach number. Nevertheless an equation can be constructed which describes the behaviour of the flow in the limit of small Mach numbers. At the open end shock waves appear in the solution within a well-defined frequency band at each resonant frequency. Two different models which have been proposed by Wijngaarden and Jimenez respectively are used to define the boundary condition. It is seen that some basic properties of the resonant oscillations are independent of the boundary condition. Wijngaarden's model leads to very good agreement with results from several different experimenters. In this case, the width of the frequency interval where shocks occur is of the orderO(M); the width of the resonance band is of the orderO(M ^1/2), just as for the closed end tube.

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Zusammenfassung Betrachtet wird ein mit Gas gefülltes Rohr, welches an einem Ende offen ist und am andern Ende von einem harmonisch schwingenden Kolben angetrieben wird. Der Schlüssel zur Lösung dieses Problems ist eine geeignete Kombination der üblichen Amplitudennichtlinearität mit den Dispersionseffekten. Dies führt auf die grundlegende Konsequenz, dass es nicht möglich ist, die Lösung im Rahmen einer Hierarchie auszudrücken, welche aus einer Entwicklung in der Machzahl hervorgeht. Es ist gleichwohl möglich, eine Gleichung zu konstruieren, welche die Gasschwingungen für kleine Machzahlen beschreibt. Am offenen Ende treten innerhalb eines wohldefinierten Frequenzbandes (bei jeder Resonanzfrequenz) Stosswellen auf. Zur Definition der Randbedingung am offenen Ende werden zwei Modelle benützt, die (beziehungsweise) von Wijngaarden und Jimenez vorgeschlagen wurden. Einige der grundlegenden Eigenschaften der Lösungen sind unabhängig von der Randbedingung. Wijngaardens Modell führt auf sehr gute Übereinstimmung mit typischen Experimenten. In diesem Fall ist die Breite des Intervalls, in welchen Stösse auftreten, von der Ordnung O(M); die Breite des Resonanzbandes ist (in Übereinstimmung mit den Ergebnissen vom geschlossenen Rohr) von der OrdnungO(M ^1/2).

     

Nonlinear acoustic resonances in shock tubes with varying cross-sectional area

Summary Second-order resonance effects in closed tubes with varying cross-sectional area are investigated. It is seen that for tubes with cross-sectional areasA(x)x ^–2 solutions for the pressure disturbances can be found, as was done by W. Chester in case of tubes with constant cross-sectional area.

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Zusammenfassung Es werden Resonanzeffekte zweiter Ordnung in Rohren mit veränderlicher Querschnittsfläche betrachtet. Ist die QuerschnittsflächeA(x)x ^–2, so können die Druckstörungen in Analogie zu Chesters Theorie analytisch berechnet werden.

     

Assessment of supporting electrolyte contributions in electrochemically modulated liquid chromatography

This paper reports the results of an investigation on the role of the supporting electrolyte in separations using electrochemically modulated liquid chromatography (EMLC) with a porous graphitic carbon stationary phase. With respect to the identity of the supporting electrolyte, the elution strength of the electrolyte anion increased as F- < OH- < BF4- < ClO4- < PF6- for injections of negatively charged aromatic molecules, whereas a 10-fold increase in electrolyte concentration induced a 60% change in retention for the same solutes. Furthermore, both the concentration and composition of the supporting electrolyte affected retention in a manner that varied with the charge of the analyte and applied potential. This behavior is explained using Gouy-Chapman diffuse double layer theory, coupled with comparisons of this theory with closely related models for ion-pair chromatography. Insights into the retention mechanism reveal that an ion-exchange mechanism controls the retention of negatively charged solutes at applied potentials removed from the potential of zero charge (PZC). At potentials close to the PZC, the electrostatic model is less effective with the predominant retention mechanism likely involving hydrophobic interactions with the carbonaceous stationary phase. The combined effects of these findings are demonstrated by using a temporal gradient in supporting electrolyte concentration to optimize an EMLC separation.     

Ternäre Thallium-Indium-Sulfide: Eine Zusammenfassung

Ternary Thallium Indium Sulfides: A Summary Combined thermal and X-Ray analyses in the ternary system Thallium—Indium—Sulfur show, that the two binary sections Tl₂S? In₂S₃ and TlS? InS contain ternary compounds with unique crystal structures. The chemical formulas of these ternary solids are TlIn₅S₈, TlIn₃S₅, TlInS₂ and Tl₃InS₃ for the section Tl₂S? In₂S₃ and TlIn₅S₆ as well as Tl₃In₅S₈ (metastable high temperature phase) for the section TlS? InS respectively. With TlIn₅S₇ an additional ternary solid could be detected, which is located outside the two sections. It is derived from the binary mixed valence compound In₆S₇ by complete substitution of In⁺ by Tl⁺. The following ionic formulations make the mixed valence character of the ternary Thallium—Indium-Sulfides reasonable: TlIn₅S₈ = Tl⁺(In³⁺)₅(S^2?)₈, TlIn₃S₅ = Tl⁺ (In³⁺)₃(S^2?)₅, TlInS₂ = Tl⁺In³⁺(S^2?)₂, Tl₃InS₃ = (Tl⁺)₃In³⁺ · (S^2?)₃, TlIn₅S₆ = Tl⁺([In₂]⁴⁺)₂In³⁺ (S^2?)₆, Tl₃In₅S₈ = 4 × [(Tl⁺)_0,75 · (In⁺)_0,25In³⁺(S^2?)₂], TlIn₅S₇ = Tl⁺[In₂]⁴⁺ (In³⁺)₃(S^2?)₇. All compounds contain Tl⁺-ions in a characteristic “lone pair coordination” of S^2? ions. Indium atoms however occur with the oxidation numbers +2 (formal, In₂ dumb bells with covalent In? In bonding) and +3 (with In³⁺ in tetrahedral and octahedral coordination of S^2?). Chemical preparation, crystal chemistry and general properties of the ternary solids are discussed, summarized and compared to each other.     

Sodium Taurocholate-Induced Lamellar-Micellar Phase Transitions of DPPC

The thermotropic transitions of 1,2-dipalmitoylphosphatidylcholine (DPPC) and the structural changes of its lamellar phases have been studied between 0 and 50°C by both DSC and synchrotron small angle X-ray diffraction/scattering as a function of temperature (XRDT) and sodium taurocholate concentration [TC] in the 0–40 mM range ([DPPC]=50 mM) at pH 7.4. The existence of multiple phase transitions (up to 5 peaks within a 5°C interval) in a narrow domain of temperature between 25 and 42°C depending on the [TC]/[lipid] ratio was observed in the DSC curves. XRDT showed that at low ratios they might correspond to transitions between lamellar phases, the structural characteristics of which are given. At higher ratios a lamellar to micellar transition was observed, and the temperature at which it was observed decreased as a function of the TC content. The relationships with DPPC vesicle bilayer permeabilization and solubilization are discussed.     

In Situ Study of the Surface Oxidation of FeCr Alloys Using Grazing Incidence X‐ray Absorption Spectroscopy (GIXAS)

The surface oxidation of FeCr alloys with 18, 28, and 43 mass‐% Cr was investigated in situ using grazing‐incidence X‐ray absorption spectroscopy (GIXAS) at the chromium and iron K‐edges. Oxidation in air was monitored in situ in the temperature range from 290 K to 680 K. The standard GIXAS data analysis is extended for the treatment of a single layer model in order to estimate the chromium concentrations of the oxide layer and of the near‐interface substrate as well as the oxide layer thickness. XANES analysis shows transitions from b.c.c. Fe to corundum type Fe₂O₃ and from b.c.c. Cr to corundum type Cr₂O₃. The initial oxide layers are 1.1‐1.4 nm thick and contain 60‐90 mass‐% chromium, while the near‐interface substrate is depleted in Cr. During heating, iron oxide growth dominates up to 560‐600 K. Then the chromium oxide layer loses its passivation effect and Cr oxidation sets in.     

Channel activity of a viral transmembrane peptide in micro-BLMs: Vpu(1-32) from HIV-1

We report for the first time on pore-suspending lipid bilayers, which we call micro-black lipid membranes (micro-BLMs), based on a highly ordered macroporous silicon array. Micro-BLMs were established by first functionalizing the backside porous silicon surface with gold and then chemisorbing 1,2-dipalmitoyl-sn-glycero-3-phosphothioethanol followed by spreading 1,2-diphytanoyl-sn-glycero-3-phosphocholine dissolved in n-decane. Impedance spectroscopy revealed the formation of single lipid bilayers confirmed by a mean specific capacitance of 0.6 +/- 0.2 microF/cm2. Membrane resistances were in the G omega-regime and beyond. The potential of the system for single channel recordings was demonstrated by inserting the transmembrane domain of the HIV-1 accessory peptide Vpu(1-32), which forms helix bundles with characteristic opening states. We elucidated different amilorides as potential drugs to inhibit channel activity of Vpu.     

AES investigations on starting powders for high performance ceramics

AES depth profiles on ceramic powders (untreated/hydrolyzed/oxidized/ (Al, Y)₂O₃ coated Si₃N₄, [BaO, SiO₂] coated Al₂O₃) are feasible on thin, homogeneous layers or m sized agglomerations prepared on an Au foil. By means of the depth profiles one can qualitatively characterize the coating around the particles. Factor analysis of the depth profiles on the differently treated Si₃N₄ powders suggests the existence of an Si₂N₂O phase on the oxidized sample.Dedicated to Professor Günther Tölg on the occasion of his 60th birthday     

Shape resonances in photoionization of diatomic molecules: An example in thed inner shell ionization of the hydrogen halides

A classification of the shape resonances in the photoionization of diatomic molecules into two types is proposed: the well known molecular shape resonances which appear in the σ _u channel for the photoionization of the σ _g shells of light molecules like 3σ _g in N₂ or in O₂, and the atomic-like shape resonances. To illustrate this last class of shape resonances, calculations in the frozen core static exchange approximation of thed inner shell photoionization cross sections, σ, and of the angular distribution parameters, β, are performed for both HBr and HI. In our model, the σ and β curves look roughly like that of the isoelectronic Kr and Xe rare gases, but in order to obtain quantitative agreement with experiment, an approach including interchannel interactions, i.e. similar to that used for the halogen atoms would be probably necessary.     

Macro lattice from segregated amorphous phases of a three block copolymer

Summary Extruded plugs of the styrene-butadiene-styrene amorphous copolymer Kraton 102 were found to exhibit discrete X-ray reflections in the low angle region such as are characteristic of an individual single crystal. This crystal lattice is hexagonal, with a lateral lattice spacing of 300 and an infinite period along the hexagonal axis which coincides with the extrusion direction. Annealing improved the crystal perfection, in fact a large portion of the macroscopic sample could become a single crystal. The orientation of the lattice could be influenced by deformation procedures in a consistent fashion. The diffraction effects are consistent with the styrene phase being in the form of cylinders. The cylinder diameter was estimated both from the lattice spacing coupled with the known molecular composition, and from missing reflections: both methods gave a diameter of close to 150 . Some suggestions are made on the molecular origin of this remarkable ordering phenomenon, together with pointing out some of the possible further consequences of such an order.

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Zusammenfassung Extrudierte pfropfenartige Proben von einem amorphen Block-Copolymeren Styrol-butadien-styrol (Kraton 102) ergaben diskrete Röntgenreflexe im Kleinwinkelbereich, wie sie im Weitwinkelbereich für Einzelkristalle charakteristisch sind. Das Kristallgitter ist hexagonal, lateraler Gitterabstand 300 , unendliche Periode entlang der hexagonalen Achse, die mit der Extrusionsrichtung zusammenfällt. Tempern verbesserte die Güte des Kristalls, so daß tatsächlich große Teile einer makroskopischen Probe sich zum Einzelkristall formen. Die Orientierung des Gitters kann auch durch Deformationsprozesse in konsistenter Weise beeinflußt werden. Die Beugungseffekte lassen sich deuten, wenn man für die Styrolphase Anordnungen zylindrischer Form annimmt. Der Durchmesser der Zylinder wurde geschätzt aus den Gitterabständen und den bekannten Molekulargewichtszusammensetzungen, sowie aus den fehlenden Reflexionen. Beide ergeben den Wert von ungefähr 150 . Einige Vorschläge werden über den molekularen Ursprung dieses bemerkenswerten Ordnungsphänomens gebracht, zusammen mit weiteren möglichen Konsequenzen einer solchen Ordnung.

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With 5 figures in 9 details