A uniqueness theorem for weak solutions of the stationary semiconductor equations

In this paper we prove a uniqueness theorem for weak solutions of a mixed boundary-value problem for the stationary semiconductor equations (van Roosbroeck's system) under the assumption that the deviation of the carrier potentials from an equilibrium solution is sufficiently small.     

Einfluß der Abrundung scharfer Eintrittskanten auf den Widerstand von Flügeln

Ohne ZusammenfassungZum Schluß möchte ich Herrn Prof. Dr.A. Betz für die Anregung zu dieser Arbeit und für seine wertvolle Unterstützung bei ihrer Durchführung danken.     

Anomalies in the flow curves of mixtures of butadiene styrene rubber and particulate fillers

Summary The flow curves of SBR-1500 containing increasing amounts of tread powder and of glass powder of different grain sizes were taken by means of aGöttfert High-Pressure-Capillary-Rheometer. Up to a certain extrusion pressure of about 300 bar the flow rate decreases with increasing filler concentration. In this pressure range the characteristic filler influence upon the flow behaviour was estimated from the relative viscosity.At extrusion pressures higher than 300 bar, however, the flow curves intersect and an increase of the flow rate with increasing filler concentration is observed. Possible reasons for this peculiar behaviour are discussed.

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Zusammenfassung Die Fließgeschwindigkeit von SBR-1500, dem steigende Mengen von Reifenmehl oder Glaspulver zugesetzt waren, wurde mit Hilfe desGöttfert-Hochdruck-Kapillar-Rheometers HKR 2000 als Funktion des Extrusionsdruckes bei 120°C ermittelt. Die Fließgeschwindigkeit nahm im Bereich kleiner Extrusionsdrücke mit steigender Füllstoffkonzentration ab. Bei Drücken um 300 bar und höher stieg die Fließgeschwindigkeit mit steigender Füllstoffkonzentration plötzlich an. Die Gründe für dieses unerwartete Verhalten werden diskutiert.

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Paper presented at the Annual Conference of the German Rheologists in Berlin, April 28–30, 1975.

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With 8 figures     

Depletion at solid/liquid interfaces: flowing hexadecane on functionalized surfaces

We present a neutron reflectivity study on interfaces in contact with flowing hexadecane, which is known to exhibit surface slip on functionalized solid surfaces. The single crystalline silicon substrates were either chemically cleaned Si(100) or Si(100) coated by octadecyl-trichlorosilane (OTS), which resulted in different interfacial energies. The liquid was sheared in situ and changes in reflectivity profiles were compared to the static case. For the OTS surface, the temperature dependence was also recorded. For both types of interfaces, density depletion of the liquid at the interface was observed. In the case of the bare Si substrate, shear load altered the structure of the depletion layer, whereas for the OTS covered surface no effect of shear was observed. Possible links between the depletion layer and surface slip are discussed. The results show that, in contrast to water, for hexadecane the enhancement of the depletion layer with temperature and interfacial energy reduces the amount of slip. Thus a density depletion cannot be the origin of surface slip in this system.     

Ionic Liquids: New Perspectives for Inorganic Synthesis?

Ionic liquids are credited with a number of unusual properties. These include a low vapor pressure, a wide liquid‐phase range, weakly coordinating properties, and a high thermal/chemical stability. These properties are certainly of great interest for inorganic synthesis and the creation of novel inorganic compounds. On the other hand, the synthesis repertoire for preparing inorganic compounds has always been broad, ranging from syntheses in solutions and melts to solid‐state reactions, and from crystal growth in the gas phase to high‐pressure syntheses. What new aspects can ionic liquids then add to the synthesis of inorganic compounds? This Minireview uses some early examples to show that the use of ionic liquids indeed provides access to unusual inorganic compounds.     

Prediction of steady-state viscous and elastic properties of polyolefin melts in shear and elongation

The linear and nonlinear steady-state viscosities and elastic compliances were measured in shear and elongational flows for two low-density polyethylenes, a linear polypropylene, and two metallocene catalyzed polyethylenes (one linear and one long-chain branched) by Wolff et al. (Rheol Acta 49:95?C103, 2010) and Resch (dissertation, 2010). Comprehensive data of this type are rarely found in the literature, and comprehensive modeling of both viscous and elastic effects is even rarer. In this contribution, the reliability of a modeling approach proposed by Laun (J Rheol 30(3):459?C501, 1986) and based on the damping function concept is tested. The strain hardening seen for the long-chain branched polymers and its absence in the case of the linear polymer, the stronger decrease of the tensile compliance in comparison to the shear compliance with increasing stress, as well as the extended linear-viscoelastic regime of the shear viscosity in contrast to the shear compliance are correctly modeled. While the modeling of the nonlinear response in shear can be achieved with only one material parameter for most of the polymers considered here, the nonlinear modeling in elongation is achieved with two parameters. The same parameter values are shown to describe viscous as well as elastic properties of the melts, and thus the relations of Laun can be used to test the consistency of viscosity and compliance measurements.