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.     

Divinylsiloxane‐bisbenzocyclobutene‐based polymer modified with polystyrene–polybutadiene–polystyrene triblock copolymers

Divinylsiloxane‐bisbenzocyclobutene (DVS‐bisBCB) polymer has very low dielectric constant and dissipation factor, good thermal stability, and high chemical resistance. The fracture toughness of the thermoset polymer is moderate due to its high crosslink density. A thermoplastic elastomer, polystyrene–polybutadiene–polystyrene triblock copolymer, was incorporated into the matrix to enhance its toughness. The cured thermoset matrix showed different morphology when the elastomer was added to the B‐staged prepolymer or when the elastomer was B‐staged with the DVS‐bisBCB monomer. Small and uniformly distributed elastomer domains were detected by transmission electron micrographs (TEM) in the former case, but TEM did not detect a separate domain in the latter case. A high percentage of the polystyrene–polybutadiene–polystyrene triblock copolymer could be incorporated into the DVS‐bisBCB thermoset matrix by B‐staging the triblock copolymer with the BCB monomer. The elastomer increased the fracture toughness of DVS‐bisBCB polymer as indicated by enhanced elongation at break and increased K1c values obtained by the modified edge‐lift‐off test. Elastomer modified DVS‐bisBCB maintained excellent electrical properties, high T_g and good thermal stability, but showed higher coefficient of linear thermal expansion values. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1591–1599, 2006     

Form fluctuations of carbosilane dendrimers in dilute solution: a study using neutron spin echo spectroscopy

A series of carbosilane dendrimers with perfluorinated end groups has been prepared. The structure of these molecules in dilute solution is studied using small angle neutron scattering. For generations g<3 we find a non-spherical shape of the particles and a tendency for aggregation. This result is supported by the analysis of the diffusion coefficient obtained from photon correlation spectroscopy. The overall shape of the molecules is that of a core-shell particle. The generation 4 molecule is obtained as a compact sphere. Neutron spin echo spectroscopy reveals a relaxation time which is attributed to the form fluctuations of this particle.     

High regio-, chemo-, and stereoselectivity via low-temperature 4 + 3 cycloadditions. Convergent synthesis of multifunctionalized vinylmetals (M = Si, Sn) and S-vinyl benzenecarbothioates

A series of enantiomerically pure 8-oxabicyclo[3.2.1]oct-6-en-3-ones functionalized in the unsaturated two-carbon bridge has been prepared by the title reaction. Carbocation reactivity has been fined-tuned at -95 degrees C and adjusted to diene nucleophilicity. Conventional electrophilic substitution of 3-silylated and 3-stannylated furan is suppressed in favor of the rapid 4 + 3 cycloaddition mode. In the case of cycloadduct 13A, stereoselectivity (17:1) is perfectly matched to regioselectivity (17:1). High stereoselection as well as unprecedented regioselection and chemoselection is attributed to the low-temperature cycloaddition protocol and the design of chiral auxiliary and tether.     

Oxidation of propene in the gas phase

A series of laboratory and modelling experiments on the oxidation of propene in the gas phase has been undertaken to determine conditions which give high yields of propene oxide. The conditions under which the experiments were conducted were 505–549 K and up to 4 bar pressure. It is proposed that propene oxide is formed from propene by reaction with several peroxy radicals including HO₂ and CH₃CO₃. However, one of the more important radicals is hydroxypropylperoxy. Its reaction with propene, under these conditions is more important than concerted decomposition to formaldehyde and acetaldehyde. © 1995 John Wiley & Sons, Inc.     

Bivoltametric titrations using electrodes with innovative geometry

Electrodes with different surface areas were investigated for the determination of reversible, quasireversible, irreversible or electroinactive substrates. Two kinds of electrodes were constructed, a helical electrode with a given asymmetry and a platinum array electrode with a variable area. These electrodes were applied for the cerimetry of ammonium iron(II) sulfate and for the bromatometry of various organic substances. The theoretically derived effects on the shape of the voltametric titration curve are verified experimentally. It is possible to sharpen one side of the peak and to broaden the other side, depending on the system and the side of the peak one is interested in. It is possible to improve the bivoltametric determination of hydroquinone, benzocaine and sulfaguanidine by bromatometry by the directed employment of electrodes of different areas. For the bromatometric determination of electrochemically irreversible substrates the use of the electrode geometries proposed is a way to obtain a sharp bend and a steep decrease of titration curves with low values of the constant current which is a basic requirement for the accuracy.