Synthesis and characterization of SiC materials with hierarchical porosity obtained by replication techniques

Porous silicon carbide monoliths were obtained using the infiltration of preformed SiO(2) frameworks with appropriate carbon precursors such as mesophase pitch. The initial SiO(2) monoliths possessed a hierarchical pore system, composed of an interpenetrating bicontinuous macropore structure and 13 nm mesopores confined in the macropore walls. After carbonization, further heat treatment at ca. 1,400 degrees C resulted in the formation of a SiC-SiO(2) composite, which was converted into a porous SiC monolith by post-treatment with ammonium fluoride solution. The resulting porous SiC featured high crystallinity, high chemical purity and showed a surface area of 280 m(2) g(-1) and a pore volume of 0.8 ml g(-1).     

Hybrid integral equation/simulation model for enhancing free energy computations

Integral equation theory is used for extrapolating free energy data from molecular simulations of a reference state with respect to a modification of the interaction potential. The methodology is applied to the correction of artefacts arising from potential shifting and truncation. Corrective contributions for the hydration free energy with respect to the full potential are analysed for the case that both the solute-solvent as well as the solvent-solvent potentials are truncated and modified by a shifted-force term, reaching beyond the range of the dielectric continuum approximation and simple long-range correction expressions. The model systems argon in water and pure water are used as examples for apolar and polar solutes, revealing significant correction contributions even for the short-ranged dispersive interactions and the magnitude of solute-solvent and solvent-solvent components. In comparison with simulation-based extrapolation techniques the integral equation method is shown to be capable of quantitatively predicting truncation artefacts at negligible computational overhead.     

Synthesis and optimization of peptidomimetics as HIV entry inhibitors against the receptor protein CD4 using STD NMR and ligand docking

We recently described the design and synthesis of a novel CD4 binding peptidomimetic as a potential HIV entry inhibitor with a KD value of approximately 35 microM and a high proteolytic stability [A. T. Neffe and B. Meyer, Angew. Chem., Int. Ed., 2004, 43, 2937-2940]. Based on saturation transfer difference (STD) NMR analyses and docking studies of peptidomimetics we now report the rational design, synthesis, and binding properties of 11 compounds with improved binding affinity. Surface plasmon resonance (SPR) resulted in a KD = 10 microM for the best peptidomimetic XI, whose binding affinity is confirmed by STD NMR (KD = 9 microM). The STD NMR determined binding epitope of the ligand indicates a very similar binding mode as that of the lead structure. The binding studies provide structure activity relationships and demonstrate the utility of this approach.     

Adsorption structures of water in NaX studied by DRIFT spectroscopy and neutron powder diffraction

Diffuse reflectance infrared Fourier transform spectroscopic (DRIFTS) measurements (4000-1500 cm(-1)) and the results of neutron powder diffraction have been combined to study the structure of adsorption complexes of water in a NaX zeolite at different water loadings (25, 48, 72, and 120 water molecules per unit cell, respectively). Sharp bands corresponding to non-hydrogen-bonded OH groups of water molecules and broad associate bands due to hydrogen-bonded molecules are observed in the DRIFT spectra. We observe a remarkable downshift of the high-frequency associate band in a narrow temperature interval when the water amount decreases from 120 to 72 molecules per unit cell, which could signify some kind of "phase transition" for the water inside the zeolite cavities. Neutron powder diffraction results show that water molecules are predominantly localized in or near the 12-ring windows. Water molecules with hydrogen-bonded and non-hydrogen-bonded OH groups were found, in agreement with the observation of sharp and broad bands in the DRIFT spectra. We find strong evidence for the formation of cyclic hexamers of water molecules localized in the 12-ring windows, which are further stabilized by hydrogen bonds to framework oxygen atoms.     

A unifying approach to the Margolis–Meakin and Birget–Rhodes group expansion

Let G be a group. We show that the Birget–Rhodes prefix expansion \(G^{Pr}\) and the Margolis–Meakin expansion M(X; f) of G with respect to \(f:X\rightarrow G\) can be regarded as inverse subsemigroups of a common E-unitary inverse semigroup P. We construct P as an inverse subsemigroup of an E-unitary inverse monoid \(U/\zeta \) which is a homomorphic image of the free product U of the free semigroup \(X^+\) on X and G. The semigroup P satisfies a universal property with respect to homomorphisms into the permissible hull C(S) of a suitable E-unitary inverse semigroup S, with \(S/\sigma _S=G\), from which the characterizing universal properties of \(G^{Pr}\) and M(X; f) can be recaptured easily.     

A Single Crystal Study of a Solid-state Polymerization Reaction

Halogenoacetates are known to undergo a solid-state elimination reaction to metal halide and poly(hydroxyacetic acid), polyglycolide. Earlier studies have shown that the reaction takes place exclusively in the solid-state without the occurrence of liquid intermediates. Single crystals of sodium chloroacetate and silver chloroacetate were reacted and studied with X-ray diffractometry, scanning electron microscopy and thermomicroscopy. The results show that the reaction leads from single crystals to a composite of polyglycolide and metal halide. Neither the salt nor the polymer exhibit a preferred crystallographic orientation, therefore it must be concluded that the crystal lattice is not preserved during the reaction.This revised version was published online in November 2005 with corrections to the Cover Date.     

An isoperimetric inequality related to a Bernoulli problem

Given a bounded domain Ω we look at the minimal parameter Λ(Ω) for which a Bernoulli free boundary value problem for the p-Laplacian has a solution minimising an energy functional. We show that amongst all domains of equal volume Λ(Ω) is minimal for the ball. Moreover, we show that the inequality is sharp with essentially only the ball minimising Λ(Ω). This resolves a problem related to a question asked in Flucher et al. (Reine Angew Math 486:165–204, 1997).