Phase Equilibria and Critical Curves of Binary Ammonia–Hydrocarbon Mixtures

Liquid or dense supercritical ammonia has been suggested as an extraction fluid. It is indeed good solvent for very different classes of compounds, as can be seen from phase diagrams. Such diagrams for binary systems of ammonia and hydrocarbons are presented and discussed on the basis of their critical curves. Apparatus and methods for the measurement of phase equilibria and equation of state data of fluid mixtures at high pressure are described.     

Notiz zur quantitativen Bestimmung von Si-H- und Si-Si-Gruppen

Zusammenfassung Eine einfache und genaue Methode zur Bestimmung von Si-H- und Si-Si-Gruppen wird vorgeschlagen, die auf alkalischer Hydrolyse der Substanz in einem verschlossenen und evakuierten Kolben und AuswÄgen des dem entwickelten Wasserstoff entsprechenden Wasservolumens beruht. Bei H-Gehalten von 1–2% betrÄgt die Genauigkeit ± 0,03% (abs.).

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Note on the quantitative determination of Si-H- and Si-Si-groups

A simple, robust and surprisingly exact method for the quantitative determination of Si-H- or Si-Si-groups is based on alkaline hydrolysis of the Si-H- or Si-Si-containing substances in a sealed and evacuated vessel and weighing of the volume of water equivalent to the developed volume of hydrogen. The accuracy is ± 0.03% (abs.) with H contents of 1–2%.

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Herrn Prof. Dr. E. Asmus zum 60. Geburtstag gewidmet.     

High-pressure structural trends of Group 15 elements: simple packed structures versus complex host-guest arrangements

The Group 15 elements P, As, Sb, and Bi all have layered structures consisting of six-membered rings under ambient conditions and attain the body-centered cubic (bcc) structure at the highest pressures applied. In the intermediate pressure region, however, phosphorus and its heavier congeners behave profoundly differently. In this region P first attains the open packed simple cubic (sc) structure for a wide range of pressures and then transforms into the rarely observed simple hexagonal (sh) structure. For the heavier congeners complex, incommensurately modulated host-guest structures emerge as intermediate pressure structures. We investigated the high-pressure behavior of P and As by ab initio density functional calculations in which pseudopotentials and a plane wave basis set were employed. The incommensurately modulated high-pressure structure of As was approximated by a supercell. Our calculations reproduced the experimentally established pressure stability ranges of the sc and sh structures for P and the host-guest structure for As very well. We found that the sc and especially the sh structure are decisively stabilized by the admixture of d states in the occupied levels of the electronic structure. This admixture releases s-s antibonding states above the Fermi level (s-d mixing). With pressure, s-d mixing increases rapidly for P, whereas it remains at a low level for As. As a consequence, the band energy contribution to the total energy determines the structural stability for P in the intermediate pressure region, giving rise to simple packed structures. On the other hand, in the intermediate pressure region of the heavier Group 15 elements, a delicate interplay between the electrostatic Madelung energy and the band energy leads to the formation of complex structures.     

How to synthesize macrocycles efficiently by using virtual combinatorial libraries

The selection of different diimines 4 a-c by alkaline earth ions from a virtual combinatorial library (VCL) is described. The products were stabilized by reduction to the diamines 6 a-c; this allowed easy analysis. The library can be directed toward different target molecules 6 a-c upon addition of alkaline earth ions with different radii. Competition experiments show the possibility of synthesizing the macrocycles 6 a, 6 b, and 6 c simultaneously when using Mg(2+), Ca(2+), and Ba(2+) as template ions. The scope of this thermodynamically controlled, reversible approach for macrocycle syntheses is illustrated.     

Curvature estimates for minimal hypersurfaces in singular spaces

We here prove pointwise curvature estimates for minimal hypersurfaces in singular spaces, using the integral curvature estimate and a generalized Simons inequality which were established recently. A further basic ingredient is a new Sobolev type inequality for stationary hypersurfaces.Oblatum 19-IX-1994This research was supported by the Deutsche Forschungsgemeinschaft through a Heisenberg award. Part of the work described here was carried out during visits to Dipartimento Matematica Applicata, University of Firenze and Department of Mathematics, Stanford University. The author would like to express his gratitude to both institutions for their kind hospitality and support. Also it is a pleasure to thank the referee for his useful comments concerning the formulation of the main theorem.     

Smooth projective translation planes

A projective plane is called smooth if both the point space and the line space are smooth manifolds such that the geometric operations are smooth. We prove that every smooth projective translation plane is isomorphic to one of the classical planes over , , or .Dedicated to Professor Dr. H. Salzmann on the occasion of his 65th birthday