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.     

NADH Electrooxidation Using Bis(1,10-phenanthroline-5,6-dione) (2,2'-bipyridine)ruthenium(II)-Exchanged Zirconium Phosphate Modified Carbon Paste Electrodes

We present a carbon paste electrode (CPE) modified using the electron mediator bis(1,10‐phenanthroline‐5,6‐dione)(2,2′‐bipyridine)ruthenium(II) ([Ru(phend)₂bpy]²⁺) exchanged into the inorganic layered material zirconium phosphate (ZrP). X‐Ray powder diffraction showed that the interlayer distance of ZrP increases upon [Ru(phend)₂bpy]²⁺ intercalation from 10.3 Å to 14.2 Å. The UV‐vis and IR spectroscopies results showed the characteristic peaks expected for [Ru(phend)₂bpy]²⁺. The UV‐vis spectrophotometric results indicate that the [Ru(phend)₂bpy]²⁺ concentration inside the ZrP layers increased as a function of the loading level. The exchanged [Ru(phend)₂bpy]²⁺ exhibited luminescence even at low concentration. Modified CPEs were constructed and analyzed using cyclic voltammetry. The intercalated mediator remained electroactive within the layers (E°′=–38.5 mV vs. Ag/AgCl, 3.5 M NaCl) and electrocatalysis of NADH oxidation was observed. The kinetics of the modified CPE shows a Michaelis–Menten behavior. This CPE was used for the oxidation of NADH in the presence of Bakers' yeast alcohol dehydrogenase. A calibration plot for ethanol is presented.     

Synthesis of Unsubstituted and 4,4′-Substituted Oligobipyridines as Ligand Strands for Helicate Self-Assembly

A general strategy for the synthesis of oligobipyridine ligands 2 – 5 containing from two to five 2,2′-bipyridine subunits, for helical metal complexes is described (sec Scheme). Both the unsubstituted parent strands ( a series) as well as their derivatives bearing fester or amide functions in the 4,4′-positions of the bipyridine moieties ( b – d series) have been obtained.     

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.     

A note on theΠ 2 0 -induction rule

It is well-known (due to C. Parsons) that the extension of primitive recursive arithmeticPRA by first-order predicate logic and the rule of ₂ ⁰ -induction ₂ ⁰ -IR is ₂ ⁰ -conservative overPRA. We show that this is no longer true in the presence of function quantifiers and quantifier-free choice for numbersAC ^0,0-qf. More precisely we show that :=PRA ² + ₂ ⁰ -IR+AC ^0,0-qf proves the totality of the Ackermann function, wherePRA ² is the extension ofPRA by number and function quantifiers and ₂ ⁰ -IR may contain function parameters.This is true even forPRA ² + ₁ ⁰ -IR+ ₂ ⁰ -IR ^–+AC ^0,0-qf, where ₂ ⁰ -IR ^– is the restriction of ₂ ⁰ -IR without function parameters.I am grateful to an anonymous referee whose suggestions led to an improved discussion of our results     

Phase diagram and scattering intensity of binary amphiphilic systems

A Ginzburg-Landau model with a scalar and a vector order parameter, which describe the concentration and orientation of the amphiphile, respectively, is used to study the phase diagram and the scattering intensity of binary amphiphilic systems. With increasing amphiphile concentration, the calculated phase diagram shows the typical sequence of ordered phases observed experimentally, that is micellar liquid cubic micellar hexagonal lamellar cubic bicontinuous invers hexagonal. The scattering intensity in the homogeneous phase is calculated in the oneloop approximation. In the vicinity of a phase transition to an ordered phase, the intensity is found to show a 1/q behavior for not too small wave vectorsq, followed by a small peak, and a 1/q ² decay for large wave vectors, in agreement with experimental observations in theL ₃-(or sponge-)phase.Dedicated to Prof. H. Wagner on the occasion of his 60th birthday