Size‐Tunable Micron‐Bubbles Based on Fluorous–Fluorous Interactions of Perfluorinated Dendritic Polyglycerols

This paper describes the behavior of various generations of polyglycerol dendrimers that contain a perfluorinated shell. The aggregation in organic solvents is based on supramolecular fluorous–fluorous interactions, which can be described by means of ¹⁹F NMR spectroscopy. In order to study the interaction and aggregation phenomena of dendrimers with perfluorinated shell and perfluoro‐tagged guest molecules we investigated [G3.5]‐dendrimer with a perfluorinated shell in the presence of perfluoro‐tagged disperse red. Noteworthy, the interaction intensities varied in an unexpected manner depending on the equivalents of perfluoro‐tagged guest molecules added to the dendrimers in solution which then formed supramolecular complexes based on fluorous–fluorous interactions. We found that these complexes aggregated around residual air in the solvent to form stable micron‐sized bubbles. Their sizes correlated with the interaction intensities measured for certain dendrimer–guest molecule ratios. Degassing of the solutions led to a quasi phase separation between organic and fluorous phase, whereby the dendrimers formed the fluorous phases. Regassing the sample with air afforded bubbles of the initial size again.     

Rotating black holes in dilatonic Einstein-Gauss-Bonnet theory

We construct generalizations of the Kerr black holes by including higher-curvature corrections in the form of the Gauss-Bonnet density coupled to the dilaton. We show that the domain of existence of these Einstein-Gauss-Bonnet-dilaton (EGBD) black holes is bounded by the Kerr black holes, the critical EGBD black holes, and the singular extremal EGBD solutions. The angular momentum of the EGBD black holes can exceed the Kerr bound. The EGBD black holes satisfy a generalized Smarr relation. We also compare their innermost stable circular orbits with those of the Kerr black holes and show the existence of differences which might be observable in astrophysical systems.     

Variable angle NMR spectroscopy and its application to the measurement of residual chemical shift anisotropy

The successful measurement of anisotropic NMR parameters like residual dipolar couplings (RDCs), residual quadrupolar couplings (RQCs), or residual chemical shift anisotropy (RCSA) involves the partial alignment of solute molecules in an alignment medium. To avoid any influence of the change of environment from the isotropic to the anisotropic sample, the measurement of both datasets with a single sample is highly desirable. Here, we introduce the scaling of alignment for mechanically stretched polymer gels by varying the angle of the director of alignment relative to the static magnetic field, which we call variable angle NMR spectroscopy (VA-NMR). The technique is closely related to variable angle sample spinning NMR spectroscopy (VASS-NMR) of liquid crystalline samples, but due to the mechanical fixation of the director of alignment no sample spinning is necessary. Also, in contrast to VASS-NMR, VA-NMR works for the full range of sample inclinations between 0° and 90°. Isotropic spectra are obtained at the magic angle. As a demonstration of the approach we measure 13C-RCSA values for strychnine in a stretched PDMS/CDCl? gel and show their usefulness for assignment purposes. In this context special care has been taken with respect to the exact calibration of chemical shift data, for which three approaches have been derived and tested.     

Neutron depolarisation imaging: Stress measurements by magnetostriction effects in Ni foils

In this article we present first proof-of-principle neutron depolarization imaging measurements on Ni foils under mechanical stress. The magnetostrictive effect in Ni leads to a reorientation of the magnetic domains in the material depending on the applied force. This in turn leads to a change of the depolarization a neutron beam suffers from transmission of the sample. We propose to use this method as a new technique for the spatially resolved measurement of mechanical stress.     

Halogenation of Dibenzoselenophene and Dibenzo[1,2]diselenine

The syntheses of the selenium containing heterocycles dibenzoselenophene ( 1 ≡ biphenSe) and dibenzo[1,2]diselenine ( 2 ≡ biphenSe₂) were optimized. The halogenation reactions of 1 and 2 with XeF₂, SO₂Cl₂, Br₂ and I₂ were performed and the corresponding products characterized. In the case of 1 , the selenium(IV) dihalogenides, biphenSeF₂ ( 3 ), biphenSeCl₂ ( 4 ), biphenSeBr₂ ( 5 ), and the adduct biphenSe·I₂ ( 6 ), were isolated and identified. The extremely sensitive selenium(IV) difluoride 3 slowly formed significant amounts of an adduct with HF of the corresponding selenium(IV) oxide biphenSeO·HF ( 3a ) upon storage in glass vessels at low temperatures. In the case of 2 , the selenium(IV) trihalogenides, biphen(SeHal₃)₂ (Hal = F, Cl, Br), were found to be extremely labile (Hal = F) or not detectable (Hal = Cl, Br). Instead, as decomposition products, the selenium chloride species Se₂Cl₂, SeCl₄ and 1 were detected. In the case of Hal = I, the stable adduct biphenSe₂·I₂ ( 7 ) was isolated. In addition to characterization by multinuclear NMR spectroscopy, several molecular structures of biphen‐selenium substituted halogenides were determined.     

Analytical Polarization and Coherence Transfer Functions for Three Dipolar Coupled Spins

Analytical polarization and coherence transfer functions are presented for a spin system consisting of three dipolar coupled homonuclear spins under energy matched conditions. Based on these transfer functions, optimal durations of Hartmann–Hahn mixing periods can be determined for arbitrary dipolar coupling constants D₁₂, D₁₃, and D₂₃. In addition, the dependence of the transfer efficiency on the relative size of the dipolar coupling constants is illustrated.     

On Angles and The Fundamental Theorems of Metric Geometry

In this paper we investigate the abstract angle measure for affine metric spaces. Common features and differences between orthogonal angles and angles with measure ≠ 0 are examined. It turns out that an affine collineation which maps angles with a certain fixed measure α ≠ 0,4 to angles with another fixed measure β is already a metric collineation in nearly all cases (fundamental theorem). An analogous result is stated for projective metric spaces. Some applications concerning minimal conditions for metric collineations are given.