Über zahlentheoretische Funktionen II

Ohne Zusammenfassung     

Design of pi-conjugated organic materials for one-dimensional energy transport in nanochannels

Various end-substituted distyrylbenzenes have been synthesized to serve as guest molecules in inclusion compounds to promote efficient energy transport along one-dimensional channels. Their optical and photophysical properties have been characterized at both experimental and theoretical levels. All molecules display a large transition dipole moment between the ground state and lowest excited state and hence a short radiative lifetime (on the order of 1-2 ns). They also exhibit a large spectral overlap between the emission and absorption spectra, which enables efficient energy transport between molecules arranged in a head-to-tail configuration in nanochannels. Hopping rates on the order of 10(12) s(-1) are calculated at a full quantum-chemical level; this is much larger than the radiative lifetimes and opens the way for energy migration over large distances. Changes in the nature of the terminal substituents are found to modulate the optical properties weakly but to impact significantly the energy transfer rates.     

Unusual dependence of particle architecture on surfactant concentration in partially fluorinated decylpyridinium templated silica

A series of porous silica particles is prepared with different concentrations of the fluorinated cationic surfactant 1-(3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,10)-heptadecafluorodecyl)pyridinium chloride (HFDePC) to trace the changes in pore structure and particle morphology as the surfactant concentration increases. At the lowest concentration studied (1.5 mmol/L), the product consists of small round particles with close-packed cylindrical mesopores. As the HFDePC concentration increases, macroporous voids are introduced to create multi-chambered hollow particles with mesoporous walls. With a still higher concentration of HFDePC the macropore volume decreases, and elongated, tactoid-like nanoparticles are formed with random mesh-phase pores oriented with silica layers perpendicular to the main axis of the particles. Further increasing the concentration of HFDePC eventually leads to the formation of round particles with disordered pores. These changes are consistent with increasing HFDePC concentration favoring increasingly oblate or disklike micelles. The process of forming the elongated particles with random mesh-phase structure is investigated by TEM of chilled and dried samples. The results indicate that the oriented tactoid-like structure forms spontaneously within 2 min by co-assembly of silica and HFDePC rather than by preferred growth perpendicular to the layers. The particle shape and layer orientation are consistent with what would be expected for a liquid-crystal particle with orientation-dependent surface tension. Finally, we compare samples prepared with a high HFDePC and with good or poor mixing. With inadequate mixing, a gel layer forms at the top of the sample which is composed of elongated mesoporous particles with a thick coating of microporous silica. The lower particulate phase contains small disordered particles similar to those obtained in a well-mixed sample. Presumably, the structure of the upper layer results from initial immiscibility of the precursor and slow diffusion of silicates out of the gel.     

Self-organization of gold atoms on a polar FeO(111) surface

The spatial distribution of single Au atoms on a thin FeO film has been investigated by low-temperature scanning tunneling microscopy and spectroscopy. The adatoms preferentially adsorb on distinct sites of the Moiré cell formed by the oxide layer and the Pt(111) support and arrange into a well-ordered hexagonal superlattice with 25 angstroms lattice constant. The self-organization is the consequence of an inhomogeneous surface potential within the FeO Moiré cell and substantial electrostatic repulsion between the adatoms.     

Pythagoras’s oxen revisited

it is said that when Pythagoras discovered his famous theorem, in a right-angled triangle the squares of the smaller sides sum up to the square of the hypoteneuse, he sacrificed a hundred oxen to thank the gods.