Stick-slip transition at the nanometer scale

We report the first observation of a stick-slip transition of surfactant solution flow through nanopores. From the experimental data, we were able to determine both the slip length and the critical wall shear stress from which slip occurs. Whereas the latter is found to increase linearly with the concentration, the former remains constant and approximately equal to 20 nm over the studied range of concentrations. We model slip to occur in the surfactant bilayer adsorbed at the nanopore wall. The stick-slip transition is then related to a reorganization of the surfactant bilayer from an entangled structure into independent layers flowing past one another, as evidenced by independent surface plasmon resonance experiments. We conclude from our analysis that surfactant solutions are always slipping in larger tubes. However, the larger the tube diameter, the smaller the relative slip contribution to the total flow.     

An external theorem on divisors of a number

Main result: Let ? be a collection of divisors of N = pe11?penn (e1 = minei for all i? {1,…, n}) such that if any two numbers in ? are coprime then their common multiple is N and maximal with respect to this condition, i.e. there is no other collection satisfying this condition which properly contains ?. We prove that ? consists of at least $\text{e}{}_1\text{П}{}^{\mathrm{n}}{}_{\mathrm{i\; =\; 2}}\text{(e}{}_{\mathrm{i}}\text{+ 1)?(e}{}_1\text{? 2)}$ elements.     

Temperature dependence of the conformation of isotactic polystyrene in toluene

In order to obtain information about a possible helix–coil transition of isotactic polystyrene (i-PS) at 80°C in toluene, as has been reported in other solvents, solution properties were examined at temperatures between 10 and 110°C. Use was made of viscometry, high-resolution nuclear magnetic resonance, infrared spectroscopy, calorimetry, and light scattering. No distinct transition was found at 80°C but rather a second-order transition between 62 and 65°C. A similar transition occurred in toluene solutions of atactic polystyrene. The transition may be attributed to a sudden change in the mobility of the phenyl side-group of the polymer. From this study it is concluded that i-PS has a helical conformation in toluene, the mean helix length decreasing smoothly with increasing temperature.     

Die oxydative Kopplung von 2,6-Xylenol durch polymere Cu-Komplexe. 1. Mitt. Kinetische Untersuchung der Katalyse de Cu(II)-Komplexes von partiell aminiertem Polystyrol

Ohne Zusammenfassung     

Kinetik der oxidativen Dimerisation von Äthynylbenzol mit den Cu-Komplexen von 2-Phenylpyridin und von einem polymeren Pyridin-Derivat als Katalysatoren

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Crystallization of isotactic polystyrene from dilute solutions

The overall rate of crystallization of isotactic polystyrene from dilute solutions, 1% by weight, in trans-decalin and benzyl alcohol was studied as a function of temperature using dilatometry. These solvents were chosen because the dissolution temperatures of crystalline isotactic polystyrene are practically the same in both solvents. The overall rate of crystallization as a function of crystallization temperature showed a maximum in both solvents at about 50°C. At lower crystallization temperatures the rate of crystallization is much lower. The overall rate of crystallization of isotactic polystyrene in benzyl alcohol is far larger than in trans-decalin at the same undercooling throughout the temperature range, which is in apparent contradiction to present crystallization theories. At very large undercooling (T_c lower than about 0°C) the solutions of isotactic polystyrene in both solvents quickly become “rigid” gels. Surface replicas of freeze-etched gels indicate that a fringed micelle type of crystallization takes place at these low temperatures. The transition from folded chain crystallization to fringed micelle crystallization may be due to a stiffening of the polymer chain below about 50°C, with a reduced rotational mobility of the phenyl groups on the chain. If very dilute solutions, below 0.5% by weight, are crystallized at these low temperatures no gels were formed but fibrous crystals are produced which could be observed under the polarizing microscope.     

Die oxidative Kopplung von 2,6-Xylenol mit polymeren Komplexen von Cu. 2. Mitt. Physikochemische Untersuchung an den Cu(II)-Komplexen mit partiell dimethylaminomethyliertem Polystyrol

Ohne Zusammenfassung