Numerical method and models for anti-plane strain of a system with a thin elastic wedge

The paper presents a general method to find asymptotics for a (multi-)wedge system containing a thin wedge. It employs separation of the symmetric and anti-symmetric parts of the boundary displacements and tractions of the wedge. The method is applicable when the angle of the thin wedge turns to zero. A physical interpretation of the derived equations is obtained by using power expansions of non-polynomial functions, which appear after the Mellin transform. We establish that the first term in the expansion of the symmetric part corresponds to shear, while the first term of the anti-symmetric part describes deflection of the wedge axis. Numerical experiments, performed by using a code developed on the basis of the theory, show that using only the first terms of the expansions insignificantly influence accuracy: the approximate results coincide with the exact values of roots to the third significant digit even for the wedge angle of 30°.     

Effects of alcohols on micellization and on the reaction methyl 4‐nitrobenzenesulfonate + Br− in cetyltrimethylammonium bromide aqueous micellar solutions

The effects of n‐hexanol, n‐pentanol, and n‐butanol on the critical micelle concentration (cmc), on the micellar ionization degree (α), and on the rate of the reaction methyl 4‐nitrobenzenesulfonate + Br^? have been investigated in cetyltrimethylammonium bromide (CTAB) aqueous solutions. An increase in the alcohol concentration present in the solution produces a decrease in the cmc and an increase in the micellar ionization degree. Kinetic data show that the observed rate constant decreases as alcohol concentration increases. This result was rationalized by considering variations in the equilibrium binding constant of the methyl 4‐nitrobenzenesulfonate molecules to the micelles, variations in the interfacial bromide ion concentration, and variations in the characteristics of the water–alcohol bulk phase provoked by the presence of alcohols. When these operative factors are considered, kinetic data in this and other works show that the second‐order rate constants in the micellar pseudophases of water–alcohol micellar solutions are quite similar to those estimated in the absence of alcohols. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 36: 634–641, 2004     

Metallocene copolymers of propene and 1‐hexene: The influence of the comonomer content and thermal history on the structure and mechanical properties

The relationships between the structure and properties have been established for copolymers of propylene and 1‐hexene synthesized with an isotactic metallocene catalyst system. The most important factor affecting the structure and properties of these copolymers is the comonomer content. The thermal treatment, that is, the rate of cooling from the melt, is also important. These factors affect the thermal properties, the degree of crystallinity, and therefore the structural parameters and the viscoelastic behavior. A slow cooling from the melt favors the formation of the γ phase instead of the α modification. Regarding the viscoelastic behavior, the β relaxation, associated with the glass‐transition temperature, is shifted to lower temperatures and its intensity is increased as the 1‐hexene content raises. The microhardness values are correlated with those of the storage modulus deduced from dynamic mechanical thermal analysis curves, and good linear relations have been obtained between these parameters. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1253–1267, 2006     

Aluminum(III) complexes containing O,O chelating ligand

The stoichiometric reactions of trimethylaluminum with 2,6‐(MeOCH₂)₂C₆H₃OH (LH) revealed compounds L₃Al ( 1 ) and L₂AlMe ( 2 ). On the other hand reaction of 1 equiv. of LH with trimethylaluminum did not lead to the formation of complex LAlMe₂ ( 3 ), rather 2 together with Me₃Al were observed as a result of a disproportionation of 3 . Compounds 1 and 2 were characterized by elemental analysis, ¹H and ¹³C NMR spectroscopy and in the case of 1 by X‐ray diffraction. Derivative 2 underwent transmetalation with Ph₃SnOH, giving LSnPh₃ ( 4 ) as the result of a migration of ligand L from the aluminum to the tin atom. The identity of 4 was established by elemental analysis, ¹H, ¹³C and ¹¹⁹Sn NMR spectroscopy and ¹H, ¹¹⁹Sn HMBC experiments. The system 2 and B(C₆F₅)₃ in a 1:1 molar ratio was shown to be active in the polymerization of propylene oxide and ε‐caprolactone. Copyright © 2007 John Wiley & Sons, Ltd.     

Asymmetry and magnetism in bis(oximato)-bridged heterobimetallic compounds: a computational approach

A density functional study of exchange coupling was carried out for a series of heterobinuclear oximato-bridged transition metal complexes. Model calculations were used to examine the influence of the electronic configuration of the metal atoms on the coupling constants. This analysis was complemented by a study of the variation of the coupling constant with the most usual structural distortions within this family of compounds. The influence of the nature of the terminal ligands as well as that of the symmetry on the bridge were also investigated.     

PPP-Berechnungen und Vergleich der Elektronenspektren von iso-π-elektronischen Sauerstoff-, Stickstoff-, Schwefel- und Selenheterocyclen

Zusammenfassung 42 Heterocyclen, die sich formal von alternierenden und nichtalternierenden Kohlenwasserstoffen durch Ersatz einer Doppelbindung durch die Heteroatome Sauerstoff, Stickstoff, Schwefel und Selen ableiten, werden nach dem Pariser-Parr-Pople-Verfahren berechnet und ihre Spektren im nahen Ultraviolett und Sichtbaren beschrieben. Schwefel und Selen werden dabei im LCAO-MO-Verfahren nach dem p-Modell behandelt. In den meisten Fällen können die Berechnungen nicht nur die spektralen Charakteristika gut wiedergeben, sondern auch Beziehungen in den Spektren iso--elektronischer Verbindungen gleicher Struktur verständlich machen. Berechnungen an kationischen Stickstoffheterocyclen führten dann zu falschen Ergebnissen, wenn die Stickstoffparameter vom Pyrroltyp übernommen werden.

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PPP-calculations and comparison of electronic spectra of iso--electronic oxygen, nitrogen, sulfur, and selenium heterocycles

42 heterocyclic compounds, formally derived from alternant or nonalternant hydrocarbons by replacing a C=C group by an oxygen, nitrogen, sulfur or selenium atom, are studied by the Pariser-Parr-Pople-type of calculation. By means of these results the near ultraviolet and visible spectra are described. The sulfur and the selenium atoms are treated in the LCAO-MO-method using the p-model. In most cases spectral features are not only well reproduced, but interrelations of the spectra of iso--electronic compounds, possessing analogous structures are interpreted, too. On calculating cationic nitrogen heterocycles using parameters of pyrrol type nitrogen results are unsatisfactory.

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Résumé 42 composés hétérocycliques, formellement dérivés d'hydrocarbures alternants ou non alternants par remplacement d'un groupement C=C par un atome d'oxygène, d'azote, de soufre ou de sélénium, sont étudiés par la méthode de Pariser-Parr-Pople. Les résultats obtenus permettent de décrire le spectre U.V. proche et visible. Soufre et sélénium sont traités en utilisant le modèle p. Dans la plupart des cas les caractères spectraux sont non seulement correctement reproduits, mais les relations entre les spectres des composés iso--électroniques à structures analogues peuvent être interprétées. Les calculs concernant les heterocycles à azote cationique sont insatisfaisants lorsqu'ils sont effectués avec des paramètres de l'azote du type pyrrole.

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Anmerkung: Die Arbeit wurde in dem von Prof. Dr. R. Mayer geleiteten Schwefelarbeitskreis der TU Dresden durchgeführt.