“Surface water” and “strong-bonded water” in cyclodextrins: a Karl Fischer titration approach

Cyclodextrins are some of the most used carriers for bioactive compounds (as host–guest complex) and many factors influence the association–dissociation of this complex, some of them being related to hydrophobicity. In the solid state, cyclodextrins contain two types of water molecules: “surface” water molecules (especially close to the crystal surface) and “strong-bonded” water molecules (especially from the cyclodextrin cavity), but the classification is hard to do, and the concentration of these water molecules are relatively difficult to estimate by simple methods. In the present study we used the volumetric Karl Fischer titration to estimate these types of water molecules in cyclodextrins by means of the rate of water reaction (related to diffusion from cyclodextrin crystals). “Surface” water molecules are titrated with rates between 1.8–2.8 mM/s for α-cyclodextrin, while for β-cyclodextrin these rates are little bit higher (2.9–3.4 mM/s). The rates corresponding to “strong-bonded” water molecules are approximately tens fold lower (0.05–0.3 mM/s for α-cyclodextrin and 0.15–0.33 mM/s for β-cyclodextrin). The approximate ratio between “surface” and “strong-bonded” water molecules could also be estimated by this simple and rapid method.     

On Parameter Depending Differential Systems Under Carathéodory Conditions

For every λ in a complex domain G, consider on some interval I the initial value problem y′(λ,x) = A(λ,x)y(λ,x) + b(λ,x), y(λ,x₀) - y₀. If this problem satisfies the Carathéodory conditions for every A, then there exist locally absolutely continuous and almost everywhere differentiable solutions y(λ,· ) of the initial value problem. In general, the union N of the exceptional sets N _λ ? I where y(λ, ·) is not differentiate or does not fulfill the differential equation, is not of Lebesgue measure zero. It will be shown that N is of Lebesgue measure zero provided that A and b are holomorphic with respect to λ and their integrals with respect to x are locally bounded on G × I.     

Zum Satz vom abgeschlossenen Graphen in topologischen Gruppen

Ohne Zusammenfassung     

Untersuchung von Stossvorgängen mittels eines Laser-Interferometers

Zusammenfassung Während sich die experimentellen Untersuchungen des Stosses deformierbarer Körper bisher im wesentlichen auf den Anfangs- und den Endzustand beschränkten, untersucht die vorliegende Arbeit den zeitlichen Verlauf der Bewegung während des Stosses bei zwei zentral aufeinander treffenden Kugeln. Als Messgerät diente ein Laser-Interferometer, das räumliche Messpunktabstände von weniger als 200 Å und eine zeitliche Auflösung von weit unter einer Mikrosekunde zulässt, Es wurden als Beispiele ein elastischer und ein unelastischer Stoss vermessen, wobei der elastische Übereinstimmung mit der Hertzschen Theorie zeigte.

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Summary Hitherto, experimental studies of the collision process between deformable bodies mainly concerned the difference between the initial and the final state of the shape at the beginning and at the end of the contact interval. In comparison with this method, the present note deals with an experimental analysis of the deformation process itself during the contact period. The measuring device consists essentially of an optical Michelson type interferometer fed by a He-Ne-gas Laser. It allows a spatial resolution of the timedisplacement history of the event of less than 200 Å, whereas the time resolution is much better than one microsecond. Typical experimental results of elastic and non-elastic collision processes between spheres are discussed, leading in the former case to the conclusion of a good agreement with the classical theory of Hertz.

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Résumé Les études expérimentales de la mécanique des chocs entre des corps déformables visaient jusqu'ici à connaître essentiellement les différences entre leurs états au début et à la fin du phénomène. Par contre, la présente note concerne les variations dans le temps de la déformation de deux sphères pendant leur phase de contact lors d'un choc droit. L'installation de mesure comprenant un interféromètre du type Michelson associée à un laser à gaz fournit une solution meilleure que 200 Å dans la courbe espace-temps du déplacement relatif des deux objets. Ceci co rrespond à une solution dans le temps très inférieure à la microseconde. Comme exemple type de cette méthode, on discute les résultats obtenus pour des chocs droits élastiques et non-élastiques. Il en résulte dans le premier cas une bonne concordance avec la theorie classique de Hertz.

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Vom Ernst-Mach-Institut, Weil am Rhein, gemeinnütziges Institut der Fraunhofergesellschaft, zum ISL abgeordnet.     

Zermelo and the Heidelberg Congress 1904

At the Third International Congress of Mathematicians Julius König gave a flawed refutation of Cantor's continuum hypothesis and the well-ordering theorem. A newly discovered postcard of Zermelo to Max Dehn supports the view that Zermelo quickly detected the gap in König's argument. This is in contrast to more recent views that attribute this role exclusively to Hausdorff.     

Karl Fischer titration at elevated temperatures

The determination of the water content is one of the most frequent analyses. This is particularly true in the field of foodstuffs, where the water content influences many technological, physical, microbiological and sensory properties and is important for the shelf life, logistic and legal aspects.Although drying methods (above all oven drying, also in infrared or microwave dryers) are the most commonly used technique, they can principally not yield the water content as result. On the one hand strongly bound water may not be detected. On the other hand not only water is driven out by the process, but all the substances volatile under the drying conditions, even those produced by the process itself. So these results are a question of definition, because they depend on the employed conditions. For nearly no foodstuff a really stable mass in the course of a drying process can be obtained.The by far most widespread procedure to determine the true water content is Karl Fischer titration which is based on a specific chemical reaction. It may also serve to calibrate indirect methods like nuclear magnetic resonance spectroscopy, near infrared spectroscopy or microwave techniques.In some cases a problem may arise because the water must get in direct contact with the reagents. We dispose, however, of several measures to provide for a liberation of practically all the water contained in samples that are not soluble in the working medium. One of these measures is the titration at elevated temperatures. The positive effect of this parameter (also in combination with others) is shown for several examples of foodstuffs.     

Metal-oxide interfacial reactions: encapsulation of Pd on TiO2 (110)

The model system Pd/TiO2 (110) was used to evaluate the correlation between metal encapsulation and electronic structure of TiO2 crystals. We observed encapsulation of Pd clusters supported on TiO2 crystals, which were heavily Ar+ sputtered, Nb-doped, or reduced by vacuum annealing. In contrast, encapsulation was not observed on unreduced, undoped, or slightly sputtered TiO2 crystals. Our results indicate a strong dependence of the encapsulation process on the electron density in the conduction band of TiO2 and on the space charge formed at Pd/TiO2 interfaces. This behavior is controlled by the initial position of the Fermi energy level (EF) of the metal and the oxide before contact is established. We proved that encapsulation reactions are favored by n-type doping of the oxide and a large work function of the metal. On the basis of this mechanism, we conclude on general trends controlling encapsulation reactions of oxide-supported metal clusters and the strong metal-support interaction (SMSI).