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Electron spin resonance spectrum of the diphenylcyclobutene anion radical

The anion radical of 1,2-diphenylcyclobutene was studied by electron spin resonance. The hyperfine splittings were found to be 0·47 and 0·74 G for the meta-positions, 2·23 and 2·69 G for the ortho-positions and 4·21 G for the para-positions of the phenyl rings. The methylene proton splittings were 4·27 G, which would imply that the value of Q is 27 G, much lower than that of other cyclobutene anions. It was also estimated that the angle between the axis of the p-orbitals of the ethylene group and that of the phenyl group is about 30°, in agreement with that found for the tetraphenylethylene anion.     

A 200 mJ unstable resonator Nd:YAG oscillator

We have designed and operated a positive branch 6.3 mm diameter rod Nd:YAG unstable resonator oscillator with a 12 nsec, 200 mJ Q-switched output at 10 Hz repetition rate. When followed by a single 9 mm diameter Nd:YAG amplifier output energies up to 750 mJ were obtained with a divergence less than 0.5 mrad.     

Electron spin resonance study of free radicals in the radiation grafting of butadiene to poly(vinyl chloride)

The kinetics of the disappearance of propagating butadiene radicals produced in the grafting of butadiene to poly(vinyl chloride) was followed by electron spin resonance measurements. The radical species observed in the temperature range 213–298°K is the conjugated allylic radical: The reaction conditions were adjusted to provide a highly viscous medium in which the propagation reaction took place. Under these conditions the radicals were stabilized and a precise ESR spectrum was obtained. Arrhenius plots of the second-order decay rate constants yield an activation energy of 5 kcal/mole. This suggests that the bimolecular termination reaction is controlled by the segmental motion of the grafted side chains.     

Depth-first search as a combinatorial correspondence

A depth first search algorithm is used to establish the connection between labeled connected graphs and inversions of trees.     

Electron exchange between alpha-Keggin tungstoaluminates and a well-defined cluster-anion probe for studies in electron transfer

Fully oxidized alpha-AlIIIW12O40(5-) (1ox), and one-electron-reduced alpha-AlIIIW12O40(6-) (1red), are well-behaved (stable and free of ion pairing) over a wide range of pH and ionic-strength values at room temperature in water. Having established this, 27Al NMR spectroscopy is used to measure rates of electron exchange between 1ox (27Al NMR: 72.2 ppm relative to Al(H2O)63+; nu(1/2) = 0.77 Hz) and 1red (74.1 ppm; nu(1/2) = 0.76 Hz). Bimolecular rate constants, k, are obtained from line broadening in 27Al NMR signals as ionic strength, mu, is increased by addition of NaCl at the slow-exchange limit of the NMR time scale. The dependence of k on is plotted using the extended Debye-Hückel equation: log k = log k0 + 2alphaz1z2mu(1/2)/(1 + betarnu(1/2)), where z1 and z2 are the charges of 1ox and 1red, alpha and beta are constants, and r, the distance of closest contact, is fixed at 1.12 nm, the crystallographic diameter of a Keggin anion. Although not derived for highly charged ions, this equation gives a straight line (R2 = 0.996), whose slope gives a charge product, z1z2, of 29 +/- 2, statistically identical to the theoretical value of 30. Extrapolation to mu = 0 gives a rate constant k11 of (6.5 +/- 1.5) x 10(-3) M(-1) s(-1), more than 7 orders of magnitude smaller than the rate constant [(1.1 +/- 0.2) x 10(5) M(-1) s(-1)] determined by 31P NMR for self-exchange between P(V)W12O40(3-) and its one-electron-reduced form, P(V)W12O40(4-). Sutin's semiclassical model reveals that this dramatic difference arises from the large negative charges of 1ox and 1red. These results, including independent verification of k11, recommend 1red as a well-behaved electron donor for investigating outer-sphere electron transfer to molecules or nanostructures in water, while addressing a larger issue, the prediction of collision rates between uniformly charged nanospheres, for which 1ox and 1red provide a working model.     

Equidistributing principles in moving finite element methods

Recently Miller and his co-workers proposed a moving finite element method based on a least squares principle. This was followed by a similar method by the present authors using a Petrov—Galerkin approach. In this paper the two methods are compared. In particular, it is shown that both methods move their nodes according to an approximate equidistributing principle. This observation leads to a criterion for the placement of the nodes. It is also shown that the penalty function designed by Miller may also be used with the Petrov—Galerkin method. Finally, numerical examples are given, illustrating the performance of the two methods.