Outer-Sphere Electron Transfer in Methylene Chloride: Concentration, Salt, and Temperature Dependences of the Oxidation of beta-Re(2)X(4)(cis-1,2-bis(diphenylphosphino)ethylene)(2) (X = Cl, Br) by [Co(dimethylglyoximate)(3)(BF)(2)]BF(4) and the Oxidation of Re(2)Br(4)(PMe(2)Ph)(4) by [Co(1,2-cyclohexanedione dioximate)(3)(BBu)(2)]BF(4)

The kinetics of the oxidation of beta-Re(2)X(4)(cis-1,2-bis(diphenylphosphino)ethylene)(2) (X = Cl, Br) by the cobalt clathrochelate [Co(dimethylglyoximate)(3)(BF)(2)]BF(4) and the oxidation of Re(2)Br(4)(PMe(2)Ph)(4) by the cobalt clathrochelate [Co(1,2-cyclohexanedione dioximate)(3)(BBu)(2)]BF(4) have been studied by the stopped-flow method as a function of temperature (-85 to -19 degrees C), added Bu(4)NBF(4) (0-0.100 M), and reactant concentration in the low dielectric solvent methylene chloride. For each reaction, approximately 100 different conditions were studied. The observed rate constants were well fit by a mechanism involving separate paths for free ion and the ion-paired Co(III) oxidant. The analysis yielded values for DeltaH() and DeltaS() for each path of each reaction and consistent DeltaH degrees and DeltaS degrees values for the ion-pairing of the cationic reactant and the electrolyte. In addition, temperature-dependent electrochemical measurements in 0.10 M Bu(4)NBF(4) yielded DeltaH degrees and DeltaS degrees for the electron transfer process. This is the first measurement of the homogeneous electron transfer reactivity of the dirhenium complexes, and they showed the expected high reactivity. The most notable result is a very high inhibition (ca. 700-fold) by added salt of only the [Co(dmg)(3)(BF)(2)]BF(4) reactions. We attribute this to a change of rate-controlling step, for the ion-paired path, to one involving anion migration. This appears only to occur when the magnitude of ion-pairing free energy is significantly greater than the magnitude of the free energy change for the electron transfer process.     

Characterization of an actively linearized ultrabroadband chirped laser with a fiber-laser optical frequency comb

The optical frequency sweep of an actively linearized, ultrabroadband, chirped laser source is characterized through optical heterodyne detection against a fiber-laser frequency comb. Frequency sweeps were measured over approximately 5 THz bandwidths from 1530 nm to 1570 nm. The dominant deviation from linearity resulted from the nonzero dispersion of the fiber delay used as a reference for the sweep linearization. Removing the low-order dispersion effects, the residual sweep nonlinearity was less than 60 kHz rms, corresponding to a constant chirp with less than 15 ppb deviation across the 5 THz sweep.     

An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

Modification of galvannealed steel through aluminum addition

Aluminum is believed to modify and to some extent control the coating characteristics of commercially produced galvanneal sheet steel. These include mechanical, chemical, and aesthetic properties. Whereas the aluminum added to the molten zinc bath is known to form intermetallics before the steel is annealed, our research is primarily concerned with the effect aluminum has on suppression or enhancement of the particular iron--zinc alloy phases in the coating during galvannealing. The microstructure of four commercially important iron--zinc intermetallic phases containing varying aluminum content between 0--1.5 weight percent has been studied. It is also believed that an iron--aluminum alloy, known as the inhibition layer, forms on the steel surface following hot dipping and prior to annealing. Transmission and scattering Mössbauer spectroscopy as well as X-ray diffraction have been used to identify iron--zinc and iron--aluminum alloys present in the coatings. Discussion will be presented on the effect aluminum has on phase suppression for Fe--Zn alloys prepared in commercially produced galvanneal.     

Self-adjoint subspace extensions of nondensely defined symmetric operators

The self-adjoint subspace extensions of a possibly nondensely defined symmetric operator in a Hilbert space are characterized in terms of “generalized boundary conditions.”     

Direct-comb molecular spectroscopy with accurate, resolved comb teeth over 43 THz

We demonstrate a dual-comb spectrometer using stabilized frequency combs spanning 177 to 220 THz (1360 to 1690 nm) in the near infrared. Comb-tooth-resolved measurements of amplitude and phase generate over 4×10(5) individually resolved spectral elements at 100 MHz point spacing and kilohertz-level resolution and accuracy. The signal-to-noise ratio is 100 to 3000 per comb tooth. Doppler-broadened phase and amplitude spectra of CO(2), CH(4), C(2)H(2), and H(2)O in a 30 m multipass cell agree with established spectral parameters, achieving high-resolution measurements with optical bandwidth generally associated with blackbody sources.