Metallo‐supramolecular micelles: Studies by analytical ultracentrifugation and electron microscopy

In aqueous solutions, amphiphilic block copolymers in which a polystyrene (PS) segment is connected to a poly(ethylene oxide) (PEO) block via a bis(2,2′:6′,2″‐ terpyridine ruthenium) complex can form micelles. Such micelles of the protomer type PS₂₀‐[Ru]‐PEO₇₀, according to the preparation procedure representing frozen micelles, were studied by sedimentation velocity and sedimentation equilibrium analysis in an analytical ultracentrifuge and by transmission electron microscopy, with different techniques applied for the sample preparation. The particles obtained were surprisingly multifarious in size. In ultracentrifugation experiments performed at relatively low salt concentrations, the distributions of the sedimentation coefficient s_20,w showed a pronounced peak at 9.6 S and a broad, only partly separated second peak around 14 S. The molar mass of the particles at the peak was around 430,000 g/mol, corresponding to an aggregation number of approximately 85. The average hydrodynamic diameter of the particles in the peak fraction was approximately 13 nm. In electron micrographs of negatively stained samples, spheres of diameters between 10 and 25 nm were the most abundant particles, but larger ones with a wide size range were also visible. The latter particles apparently were composed of smaller ones. The data from both sedimentation analysis and electron microscopy showed that (1) the studied compound formed primary micelles of diameters around 20 nm and (2) the primary micelles had a tendency toward aggregation. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3159–3168, 2003     

Über trigonometrische Reihen mit zahlentheoretischen Koeffizienten

Ohne Zusammenfassung     

Über die Primteiler-Anzahl ω(n)

It is shown by analytical means that, if one assumes the Riemann hypothesis, the asymptotic formula $$\sum\limits_{n \leqslant x} {\omega (n) = x 1n1n } x + B - x\int_l^{x^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } {\frac{{\{ t\} }}{{t^2 (1n x - 1n t)}}dt + O(x^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2} + \varepsilon } )} $$ holds. This improves a result ofB. Saffari, who got a weaker error term by using the Dirichlet “hyperbola method”. The above formula, in turn, implies the Riemann hypothesis.     

Γ-Lakton-cis-anellierung an Δ2- und Δ3- Cholesten

γ-Lactone-cis-annulation to Δ²- and Δ³- Cholestene. From Δ²- and Δ³- cholestene the γ-lactones 11a , 11b , 12a , and 12b are synthesized through the dibromocarbene adducts 3 and 4 , the bromohydrines 5 and 6 , the oxapiropentanes 7 and 8 , and the cyclobutanones 9a , 9b and 10a , 10b , respectively. The ¹³C-NMR.-spectra of 1–8 and 11 as well as the ORD.-spectra of the cyclobutanones 9 and 10 are reported.     

Transition metal nitrosyls as nitrosylation agents : II.Photo-nitrosylation of η5-C5H5V(CO)3L(L = CO,Pz3) by [Co(NO)2Br]2

η⁵-C₅H₅V(NO)₂CO is prepared in 40% yield by the photo-reaction between η⁵-C₅H₅V(CO)₄ and [Co(NO)₂Br]₂.η⁵-C₅H₅V(NO)₂CO reacts by an S_N1 mechanism with various phosphines PZ₃ to yield η⁵-C₅-H₅V(NO)₂PZ₃. The phosphine complexes are also obtained by photo-induced ligand interchange between η⁵-C₅H₅V(CO)₃PZ₃ and [Co(NO)₂Br]₂, or η⁵-C₅H₅V(CO)₄ and Co(NO)₂Br(PZ₃). In all cases, the main cobalt species formed is Co(NO)(CO)₃. While the one-bond vanadiumphosphorus coupling constants of most of the phosphine complexes are virtually the same (ca 410 Hz),the chemical shift values δ(⁵¹V) (?1328 to ?973 ppm rel. VOCl₃) decrease in the order PF₃ > CO > P(OR)₃ > P(alkyl)₃ > PPh₃ > PPh(NEt₂)₂, reflecting the decreasing π-acceptor ability of the ligands. δ(⁵¹V) also decreases in the series of alkylphosphines PR₃ (R = Me, Et, Prⁿ, Buⁱ, Prⁱ, BU^t) as the cone angle of PR₃increases.     

Perfluoralkyljod-verbindungen: Darstellungen und eigenschaften von CF3JO,CF3JOF2 und CF3JO2

Perfluoroalkyl iodine compounds: preparations and properties of CF₃IO, CF₃IOF₂, and CF₃IO₂. The trifluoromethyl iodine compounds CF₃IO, CF₃IOF₂, and CF₃IO₂ are formed from the reactions of CF₃I, CF₃IF₂ or CF₃IF₄ with ozone or silicon dioxide respectively. Their preparartions, properties, ¹⁹F-nmr spectra, and ir spectra are described.