An image system and surface singularity solutions for potential flow past an elliptical cylinder

The Milne-Thomson circle theorem is extended to give a simplegeneral expression for the image system in an elliptical cylinderintroduced into an otherwise specified unbounded potential flowwhich contains no singularities in the region to be occupiedby the ellipse. This image system is used to obtain an expressionfor the corresponding source-sink surface singularity distributionon the ellipse, thus providing new benchmark test cases forsource-sink solutions as obtained numerically by a panel method.Several typical examples are given to illustrate the generaltheoretical approach.     

A model study of vibrational excitation of carbon dioxide molecule by slow electrons: the role of wave packet sliding from the ridge

The method of an accurate calculation of vibrational excitation cross sections of a two-mode molecule by slow electrons within the framework of the local theory (the ‘boomerang’ model) is applied for a model study of the excitation of the symmetrical stretching vibrational modes of carbon dioxide in the two-mode approximation (i.e., only the symmetrical stretch and bending modes are included in the consideration). It is shown that the 'boomerang’ oscillations in the cross section are strongly suppressed due to the decay of the one-dimensional ‘boomerang' state caused by the anion wave packet sliding from the linear configuration ridge. Consequently, the bending motion in CO₂ molecule should to be taken into account even if only the processes without the final bending excitation are considered. A simple quasi one-dimensional model describing the system sliding from the ridge is put forward which treats this phenomenon as a decay of the initial wave packet via the series of diabatic resonant states related to unstable trajectory.     

Specific Sorption Sites for Nitrogen in Zeolites NaLSX and LiLSX

Specific sorption sites for nitrogen, N₂, in NaLSX and LiLSX zeolites were investigated using a DRIFT spectroscopic method. Sorption of molecular hydrogen, H₂, by NaLSX or LiLSX zeolite at 77 K with DRIFT control of perturbation of sorbed molecules allowed to discriminate two or three different types of specific sorption sites in the respective zeolites. Their H–H stretching frequencies are 4077 and 4081 cm^–1 for NaLSX, and 4061, 4084 and 4129 cm^–1 for LiLSX. With reference to an independent investigation by methods of both sorption thermodynamics and molecular modeling for N₂ sorption on LiLSX, the first two of the corresponding bands were ascribed to H₂ sorption on lithium cations, Li⁺, localized in supercages of the faujasite, FAU, zeolite framework at sites SIII and SIII, while the latter band most likely belongs to H₂ sorption on Li⁺ cations at sites SII, and on hydroxyl groups, OH. Sorption of N₂ by Li⁺ cations at sites SIII and SIII is the strongest, resulting in a decrease of intensity of the corresponding DRIFT bands that stem from subsequent H₂ sorption. Nitrogen sorption by Li⁺ cations at sites SII is much weaker. Sorption of N₂ on Na⁺ cations at sites SIII in NaLSX zeolite is also stronger than by Na⁺ cations at sites SII.     

Intensities of IR stretching bands as a criterion of polarization and initial chemical activation of adsorbed molecules in acid catalysis. Ethane adsorption and dehydrogenation by zinc ions in ZnZSM-5 zeolite

A DRIFT study of ethane adsorbed by zinc cations in ZnZSM-5 prepared by chemical reaction of the hydrogen form of the zeolite with zinc vapor at 770 K, or by wet ion exchange, reveals unusual spectra of adsorbed C2H6 species. In addition to the weakly perturbed narrow bands in the region of C-H stretching vibrations, these spectra exhibit a very intense broad IR band with a frequency that is more than 200 cm(-1) lower than those of the C-H stretching vibrations of gaseous or physically adsorbed ethane. The very high relative intensity of this band indicates a very strong polarizability of the corresponding vibrational mode. It is concluded that these strongly polarized vibrations are closely connected with the subsequent heterolytic dissociation of ethane at moderately elevated temperatures, resulting in the formation of acidic hydroxyl groups and zinc ethyl fragments. At higher temperatures, the zinc ethyl fragments decomposed, resulting in the formation of zinc hydrides and ethylene. The unusual DRIFT spectrum of the molecular form of ethane adsorption by zinc cations represents a first example of anisotropy of polarizability of adsorbed molecules, which may provide a new explanation for selectivity of the acid-catalyzed reactions. In this connection, it is suggested to use the relative intensities of IR bands of adsorbed molecules as a reactivity index that is directly connected with chemical activation of adsorbed molecules via their polarization by the active sites.