Discrete Laplace cycles of period four

We study discrete conjugate nets whose Laplace sequence is of period four. Corresponding points of opposite nets in this cyclic sequence have equal osculating planes in different net directions, that is, they correspond in an asymptotic transformation. We show that this implies that the connecting lines of corresponding points form a discrete W-congruence. We derive some properties of discrete Laplace cycles of period four and describe two explicit methods for their construction.     

The gradient flow of the M?bius energy near local minimizers

In this article we show that for initial data close to local minimizers of the M?bius energy the gradient flow exists for all time and converges smoothly to a local minimizer after suitable reparametrizations. To prove this, we show that the heat flow of the M?bius energy possesses a quasilinear structure which allows us to derive new short-time existence results for this evolution equation and a ?ojasiewicz-Simon gradient inequality for the M?bius energy.     

The Unexpected Formation of a 2,2′-Di( N -ethyl-acetamino)substituted Diphenyl Disulfane on Oxidation of 3-Ethyl-2-methylbenzothiazolium Tetrafluoroborate

Attempts at the oxidation of 3-ethyl-2-methylbenzothiazolium salt 2 with a variety of oxidizing reagents did not lead to the desired isochiral S -oxide 3 or achiral S , S -dioxide 4 , in some cases, however, unexpectedly to the ring-opened dimeric 2,2'-di( N -ethyl-acetamino)substituted diphenyl disulfane 5 , the molecular structure of which was confirmed by x-ray analysis. The synthesis of 2-methylbenzothiazole- S , S -dioxide 14 , reported by Zincke et al. in 1915, turned out to be not reproducible. \centerline{\epsfbox{:art:fig-01.jpg}}     

Temperature-Dependent Surface-Enrichment Effects of Imidazolium-Based Ionic Liquids

We present the first systematic study of the influence of temperature on the degree of surface enrichment of 1-alkyl-3-methylimidazolium-based ionic liquids (ILs). Using angle-resolved X-ray photoelectron spectroscopy, we demonstrate that the degree of surface enrichment strongly decreases with increasing temperature for all the studied ILs. For ILs with the same cation, but different anions, [C₈C₁Im]Br, [C₈C₁Im][TfO] and [C₈C₁Im][Tf₂N], no significant differences of the temperature-induced partial loss of surface enrichment are found. Measurements for [C₄C₁Im][TfO], [C₈C₁Im][TfO] and [C₁₈C₁Im][TfO] indicate a small effect of the chain length. For [C₁₈C₁Im][TfO], a continuous decrease of alkyl surface enrichment is found with increasing temperature, with no abrupt changes at the phase-transition temperature from the smectic A to the isotropic phase, indicating that the surface enrichment is not affected by this phase transition.     

Wet-Chemically Prepared Porphyrin Layers on Rutile TiO2(110)

Porphyrins are large organic molecules that are interesting for different applications, such as photovoltaic cells, gas sensors, or in catalysis. For many of these applications, the interactions between adsorbed molecules and surfaces play a crucial role. Studies of porphyrins on surfaces typically fall into one of two groups: (1) evaporation onto well-defined single-crystal surfaces under well-controlled ultrahigh vacuum conditions or (2) more application-oriented wet chemical deposition onto less well-defined high surface area surfaces under ambient conditions. In this study, we will investigate the wet chemical deposition of 5-(monocarboxyphenyl)-10,15,20-triphenylporphyrin (MCTPP) on well-defined rutile TiO₂(110) single crystals under ambient conditions. Prior to deposition, the TiO₂(110) crystals were also cleaned wet-chemically under ambient conditions, meaning none of the preparation steps were done in ultrahigh vacuum. However, after each preparation step, the surfaces were characterized in ultrahigh vacuum with X-ray photoelectron spectroscopy (XPS) and the result was compared with porphyrin layers prepared in ultrahigh vacuum (UHV) by evaporation. The differences of both preparations when exposed to zinc ion solutions will also be discussed.     

Probing the Roughness of Porphyrin Thin Films with X-ray Photoelectron Spectroscopy

Thin-film growth of molecular systems is of interest for many applications, such as for instance organic electronics. In this study, we demonstrate how X-ray photoelectron spectroscopy (XPS) can be used to study the growth behavior of such molecular systems. In XPS, coverages are often calculated assuming a uniform thickness across a surface. This results in an error for rough films, and the magnitude of this error depends on the kinetic energy of the photoelectrons analyzed. We have used this kinetic-energy dependency to estimate the roughnesses of thin porphyrin films grown on rutile TiO₂(110). We used two different molecules: cobalt (II) monocarboxyphenyl-10,15,20-triphenylporphyrin (CoMCTPP), with carboxylic-acid anchor groups, and cobalt (II) tetraphenylporphyrin (CoTPP), without anchor groups. We find CoMCTPP to grow as rough films at room temperature across the studied coverage range, whereas for CoTPP the first two layers remain smooth and even; depositing additional CoTPP results in rough films. Although, XPS is not a common technique for measuring roughness, it is fast and provides information of both roughness and thickness in one measurement.     

Surface science goes liquid !

Ionic liquids are a new class of materials with most interesting properties. They are liquid at room temperature, but have a negligible vapour pressure. Consequently they can, in contrast to normal liquids, be investigated by all UHV-based methods of surface science. This allows to determine their properties with the same atomic level accuracy that is presently common for solid surfaces and conventional adsorbate systems. Apart from the investigation of the specific properties of ionic liquids, which are relevant for many applications, this also opens the possibility to obtain more detailed insight in the general physical and chemical properties of liquids. In that sense it opens the door to a new chapter of surface science – “Ionic Liquid Surface Science”.