Gas Chromatographic Separation of Enantiomers on Cyclodextrin Derivatives

In investigations concerned with the phenomenon of molecular chirality, the use of gas chromatography for the enantiomeric analysis of stable, volatile compounds is a technique of steadily growing importance. ^[1] In the last three years an important breakthrough in gas-chro-matographic separation of enantiomers has been achieved by using alkylated cyclodextrins (α, β, and γ) as chiral stationary phases in high-resolution capillary columns. In academic and commercial practice two different and complementary strategies have been adopted up to now. In the first, alkylated cyclodextrins are diluted with polysiloxanes and coated on glass or fused silica capillary columns. In the second, lipophilic per-n-pentylcyclodextrins and hydrophilic di-n-pentyl- and hydroxyalkylpermethylcyclodextrins are coated directly in the form of liquid phases onto suitably pretreated glass or fused silica surfaces. These techniques permit enantiomer separations not only for polar diols and alcohols, derivatized hydroxycarboxylic acids, amino acids, sugars, and alkyl halides, but also for nonpolar alkenes, cyclic saturated hydrocarbons, and metal π complexes. An important aspect for practical applications is that in many cases the enantiomers can be separated without previous derivatization. Whereas the resolution of racemates of unfunctionalized hydrocarbons is attributed to an enantioselective host–guest inclusion complex, some observations indicate that for polar guest molecules additional enantioselective interactions are also involved. The new chiral stationary phases can be used over a wide range of temperatures (25 to 250°C). The technique described is likely to become widely adopted as a simple, accurate and highly sensitive method for the enantiomeric analysis of chiral compounds that can be vaporized without decomposition. It will also stimulate future research aimed at finding universal cyclodextrin phases and elucidating the mechanisms of enantioselectivity.     

Ebene absolute geometrie über Euklidischen Körpern

We give a set of seven postulates for plane absolute geometry based on the geometric notions points and lines and show that every absolute plane is — up to isomorphisms — either a Euclidean or a hyperbolic plane over a Euclidean field.     

Convergence of finite element approximations of large eddy motion

Fluid motion in many applications occurs at higher Reynolds numbers. In these applications dealing with turbulent flow is thus inescapable. One promising approach to the simulation of the motion of the large structures in turbulent flow is large eddy simulation in which equations describing the motion of local spatial averages of the fluid velocity are solved numerically. This report considers “numerical errors” in LES. Specifically, for one family of space filtered flow models, we show convergence of the finite element approximation of the model and give an estimate of the error. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 689–710, 2002; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/num.10027.     

Chemical Analysis of Synthetic Fibers

The analytical characterization of synthetic fibers has not kept pace with their development and production. Whereas the “second-generation” fibers have already conquered the market, the chemical investigation methods used until now for the three classical fiber polymers of the polyester, polyamide, and polyacrylonitrile types are still frequently unsatisfactory. Though they satisfy the requirements of production supervision and quality control, they do not supply enough information to enable us to understand and to explain the degradation of and damage to the polymers under hydrolytic, thermal, or thermooxidative influences. This report presents methods of chemical analysis that open up new possibilities for investigations of this nature on synthetic fibers. The results reported for commercial products must not be taken as an assessment of quality. They are simply intended to show the diversity to be expected in the chemical properties and to emphasize the practical basis of the chemical analysis of synthetic fibers.     

Zur Approximation auf dünnen Mengen im ℂ2

Ohne ZusammenfassungHerrn Professor Tietz zum 60. Geburtstag     

Dielektrische „Hysterese“ von Wasser in mikroporösen Systemen

Zusammenfassung Die an mikroporösen Aluminiumoxid/Wassersystemen festgestellten dielektrischen Hystereseerscheinungen nach Abkühlen unter –20 C (2) lassen sich durch eine dichtere Packung der Molekeln infolge einer Abnahme des Schwingungsvolumens beim Abkühlen unter die Me\temperatur erklären. Diese dichtere Anordnung ist möglich, weil die starren Porenwände nur eine relativ lockere Gruppierung der Molekeln in den Kapillaren zulassen, so da\ ein gro\es freies Volumen vorhanden ist. Infolge dieser sterisch bedingten, als Verunreinigung wirkenden Löcher wird das Erstarren des Wassers zu tieferen Temperaturen hin verschoben. Man kann auch sagen, da\ das Wasser weniger assoziiert ist als im normal-flüssigen Zustand. Der Verteilung der Porenradien entspricht eine Verteilung der Löcherkonzentration, so da\ die glasartig-amorphe oder zumindest parakristalline Erstarrung des Kapillarwassers in einem breiten Temperaturintervall erfolgt.Die dielektrische Hysterese kommt dadurch zustande, da\ man bei ansteigender Temperatur die dichter gepackten und damit jetzt energieärmeren Molekeln auf höhere Temperatur bringen mu\, zum ihnen die einem bestimmten- und tan-Wert entsprechende Beweglichkeit wiederzugeben.Herrn Prof. Dr.F. H. Müller und Herrn Priv.-Dozent Dr.H. Kilian habe ich für anregende Diskussionen zu danken. Au\erdem bin ich der Deutschen Forschungsgemeinschaft für die gro\zügige Unterstützung unserer Arbeiten sehr zu Dank verpflichtet.