THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

Effect of film thickness and supercooling on the performance of cholesteryl cinnamate liquid crystal capillary columns

Improved separations of the isomers of olefinic aliphatic insect pheromones were obtained on cholesteryl cinnamate glass capillary columns by operating in the supercooled temperature range of the liquid crystal. Capillary columns were prepared with varying film thickness of the stationary phase; choice of the correct film thickness ensured optimum retention for a wide range of compounds within the most effective temperature range of the liquid crystal. The deactivation procedures described made the liquid crystal columns suitable for separation of the geometric isomers of polar and nonpolar compounds.     

Cation recognition by new diester- and diamide-calix[4]arenediquinones and a diamide-benzo-15-crown-5-calix[4]arene

The synthesis, metal, ammonium and alkyl ammonium cation coordination chemistry and electrochemical recognition studies of new diester-and diamide-calix[4]arenediquinone receptors are described. In addition the synthesis and coordination properties of a novel diamide benzo-15-crown-5-calix[4]arene molecule is reported.This paper is dedicated to the commemorative issue on the 50th anniversary of calixarenes.     

Mixed-metal cluster chemistry. 19. Crystallographic, spectroscopic, electrochemical, spectroelectrochemical, and theoretical studies of systematically varied tetrahedral group 6-iridium clusters

A systematically varied series of tetrahedral clusters involving ligand and core metal variation has been examined using crystallography, Raman spectroscopy, cyclic voltammetry, UV-vis-NIR and IR spectroelectrochemistry, and approximate density functional theory, to assess cluster rearrangement to accommodate steric crowding, the utility of metal-metal stretching vibrations in mixed-metal cluster characterization, and the possibility of tuning cluster electronic structure by systematic modification of composition, and to identify cluster species resultant upon electrochemical oxidation or reduction. The 60-electron tetrahedral clusters MIr(3)(CO)(11-x)(PMe(3))(x)(eta(5)-Cp) [M = Mo, x = 0, Cp = C(5)H(4)Me (5), C(5)HMe(4) (6), C(5)Me(5) (7); M = W, Cp = C(5)H(4)Me, x = 1 (13), x = 2 (14)] and M(2)Ir(2)(CO)(10-x)(PMe(3))(x)(eta(5)-Cp) [M = Mo, x = 0, Cp = C(5)H(4)Me (8), C(5)HMe(4) (9), C(5)Me(5) (10); M = W, Cp = C(5)H(4)Me, x = 1 (15), x = 2 (16)] have been prepared. Structural studies of 7, 10, and 13 have been undertaken; these clusters are among the most sterically encumbered, compensating by core bond lengthening and unsymmetrical carbonyl dispositions (semi-bridging, semi-face-capping). Raman spectra for 5, 8, WIr(3)(CO)(11)(eta(5)-C(5)H(4)Me) (11), and W(2)Ir(2)(CO)(10)(eta(5)-C(5)H(4)Me)(2) (12), together with the spectrum of Ir(4)(CO)(12), have been obtained, the first Raman spectra for mixed-metal clusters. Minimal mode-mixing permits correlation between A(1) frequencies and cluster core bond strength, frequencies for the A(1) breathing mode decreasing on progressive group 6 metal incorporation, and consistent with the trend in metal-metal distances [Ir-Ir < M-Ir < M-M]. Cyclic voltammetric scans for 5-15, MoIr(3)(CO)(11)(eta(5)-C(5)H(5)) (1), and Mo(2)Ir(2)(CO)(10)(eta(5)-C(5)H(5))(2) (3) have been collected. The [MIr(3)] clusters show irreversible one-electron reduction at potentials which become negative on cyclopentadienyl alkyl introduction, replacement of molybdenum by tungsten, and replacement of carbonyl by phosphine. These clusters show two irreversible one-electron oxidation processes, the easier of which tracks with the above structural modifications; a third irreversible oxidation process is accessible for the bis-phosphine cluster 14. The [M(2)Ir(2)] clusters show irreversible two-electron reduction processes; the tungsten-containing clusters and phosphine-containing clusters are again more difficult to reduce than their molybdenum-containing or carbonyl-containing analogues. These clusters show two one-electron oxidation processes, the easier of which is reversible/quasi-reversible, and the more difficult of which is irreversible; the former occur at potentials which increase on cyclopentadienyl alkyl removal, replacement of tungsten by molybdenum, and replacement of phosphine by carbonyl. The reversible one-electron oxidation of 12 has been probed by UV-vis-NIR and IR spectroelectrochemistry. The former reveals that 12(+) has a low-energy band at 8000 cm(-1), a spectrally transparent region for 12, and the latter reveals that 12(+) exists in solution with an all-terminal carbonyl geometry, in contrast to 12 for which an isomer with bridging carbonyls is apparent in solution. Approximate density functional calculations (including ZORA scalar relativistic corrections) have been undertaken on the various charge states of W(2)Ir(2)(CO)(10)(eta(5)-C(5)H(5))(2) (4). The calculations suggest that two-electron reduction is accompanied by W-W cleavage, whereas one-electron oxidation proceeds with retention of the tetrahedral core geometry. The calculations also suggest that the low-energy NIR band of 12(+) arises from a sigma(W-W) --> sigma*(W-W) transition.