Atomistic packing models for experimentally investigated swelling states induced by CO2 in glassy polysulfone and poly(ether sulfone)

Atomistic packing models have been created, which help to better understand the experimentally observed swelling behavior of glassy polysulfone and poly (ether sulfone), under CO₂ gas pressures up to 50 bar at 308 K. The experimental characterization includes the measurement of the time‐dependent volume dilation of the polymer samples after a pressure step and the determination of the corresponding gas concentrations by gravimetric gas‐sorption measurements. The models obtained by force‐field‐based molecular mechanics and molecular dynamics methods allow a detailed atomistic analysis of representative swelling states of polymer/gas systems, with respect to the dilation of the matrix. Also, changes of free volume distribution and backbone mobility are accessible. The behavior of gas molecules in unswollen and swollen polymer matrices is characterized in terms of sorption, diffusion, and plasticization. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1874–1897, 2006     

Passivation of an Al acceptor in silicon by hydrogen or muonium

We report on calculations of the electric field gradient at the site of the Al nucleus in the Si-H-Al complex in silicon. As a model for the surroundings of the complex we used a cluster consisting of 43 silicon and one aluminum atoms. The geometry of this cluster was fully optimized at the Hartree-Fock level. To discuss the dependence of our results on the level of theory, we studied a subcluster of four silicon and one aluminum atoms at the Hartree-Fock and CASSCF level.     

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.