Spectral properties and absolute rate constants for beta-scission of ring-substituted cumyloxyl radicals. A laser flash photolysis study

A laser flash photolysis study of the spectral properties and beta-scission reactions of a series of ring-substituted cumyloxyl radicals has been carried out. All cumyloxyl radicals display a broad absorption band in the visible region of the spectrum, which decays on the microsecond time scale, leading to a strong increase in absorption in the UV region of the spectrum, which is attributed to the corresponding acetophenone formed after beta-scission of the cumyloxyl radicals. The position of the visible absorption band is red-shifted by the presence of electron-donating ring substituents, while a blue-shift is observed in the presence of electron-withdrawing ring substituents, suggesting that + R ring substituents promote charge separation in the excited cumyloxyl radical through stabilization of the partial positive charge on the aromatic ring of an incipient radical zwitterion. Along this line, an excellent Hammett-type correlation between the experimentally measured energies at the visible absorption maxima of the cumyloxyl radicals and sigma(+) substituent constants is obtained. A red-shift is also observed on going from MeCN to MeCN/H(2)O for all cumyloxyl radicals, pointing toward a specific effect of water. The ring substitution does not influence to a significant extent the rate constants for beta-scission of the cumyloxyl radicals, which varies between 7.1 x 10(5) and 1.1 x 10(6) s(-1), a result that suggests that cumyloxyl radical beta-scission is not governed by the stability of the resulting acetophenone. Finally, k(beta) increases on going from MeCN to the more polar MeCN/H(2)O 1:1 for all cumyloxyl radicals, an observation that reflects the increased stabilization of the transition state for beta-scission through increased solvation of the incipient acetophenone product.     

Stereochemical memory in the temperature-dependent photodenitrogenation of bridgehead-substituted DBH-type azoalkanes: inhibition of inverted-housane formation in the diazenyl diradical through the mass effect (inertia) and steric hindrance

The photochemical denitrogenation of the cyclopentene-annelated DBH-type azoalkanes 1 has been examined in solution as a function of bridgehead substitution and temperature. For all derivatives, namely, the unsubstituted 1a(H/H), monomethyl 1b(Me/H) dimethyl 1c(Me/Me), monophenyl 1d(Ph/H), and diphenyl 1e(Ph/Ph), the temperature-dependent ratio of syn and anti housanes 2 provides experimental support for a competition between the singlet (high temperature) and triplet (low temperature) reaction channels in the direct photolysis. The syn/anti ratio of the housanes 2 depends on the extent and type of bridgehead substitution; the amount of the anti diastereomer (retention) follows the order Ph > Me > H, and double substitution is more effective than single. This stereochemical memory is interpreted in terms of the mass effect (inertia) of the substituents and steric interaction (size) between the substituents at the bridgehead and the methylene bridge during the deazetation step of the transient diazenyl diradical conformations (1)DZ (exo-ax) and (1)DZ (exo-eq). These conformers are impulsively generated upon decay of the (1)(n,pi)-excited azoalkane, a trajectory assessed through computational work. The new mechanistic feature disclosed by the unprecedented anti stereoselectivity (retention) is the intervention of a puckered 1,3-cyclopentanediyl singlet diradical (1)DR as product bifurcation step, whose conformational relaxation to the planar species (loss of stereochemical memory) is encumbered by bridgehead substitution.     

Finite element three-dimensional analysis of the vibrational behaviour of the Langevin-type transducer

The vibrational behaviour of the Langevin transducer is usually analysed using 1D Mason model which is valid when the lateral dimensions of the transducer are smaller than a quarter wavelength at the fundamental longitudinal resonance. In this work a 3D finite element analysis of the Langevin transducer's behaviour operating in the underwater sonar range of frequencies (30-140 kHz) is presented. Several samples with total length greater, comparable to, and smaller than the diameter of the transducer are analysed. For each sample, the resonance frequencies in the observed frequency range are computed and compared with those obtained experimentally from the measurements carried out using several in-house built prototypes. For the most important aspect ratios the resonance displacement distributions are presented and discussed. The results obtained permit to gain insight into the coupling phenomenon between thickness-extensional and radial modes and suggest that in practical applications transducers with diameters comparable to or greater than total length of the active stack can also be used. The trade-off between the efficiency and power handling ability for different designs is also discussed.     

Study on Planar Whispering Gallery Dielectric Resonators. I. General Properties

Several basic properties of homogeneous planar Whispering Gallery dielectric resonators are investigated through a general approach. In particular the values for the minimum and maximum allowed radius, defined by irradiation and dielectric losses, respectively, are obtained in terms of the complex dielectric constant of the involved media. The same approach is employed in the analysis of the limit allowed frequencies of a fixed family of mode, leading to the definition of the ideal frequency band. The role of the transverse mode is then discussed, and the effective frequency band is introduced and determined both in simple disc and circular ring resonators. The extension of the effective band is limited at least by a factor 3, in terms of decades, in comparison to the extension of the ideal one; this limitation, due to the presence of transverse modes, can be overcome using suitable designed nonhomogeneous resonators, as discussed in a following companion paper.     

Locally compact unimodular groups with atomic duals

Milan Journal of Mathematics - A locally compact commutative group is compact if and only if its dual group is discrete, in other words if its regular representation is atomic. Nevertheless, there...