ON THE CONVERGENCE OF THE PARABOLIC APPROXIMATION OF A CONSERVATION LAW IN SEVERAL SPACE DIMENSIONS

1.IntrodnctionWegiveaproofofthestrongconvergenceinofthesolutionoftheparabolicapproximationtowardstheentropicsolutiontothescalarconservationlawwhereuo(RN),udenotessomeapproximationofuosuchthatandthefluxfsatisfiesTheconvergenceoftheapproximatesolutions...     

Germanium

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Sterically bulky tris(triazolyl)borate ligands as water-soluble analogues of tris(pyrazolyl)borate

The recently synthesized 3-tert-butyl-5-methyl-1,2,4-triazole reacted with KBH4 to give the new potassium tris(3-tert-butyl-5-methyl-1,2,4-triazolyl)borate K(Ttz(tBu,Me)) ligand. Ttz(tBu,Me) formed a four-coordinate (Ttz(tBu,Me))CoCl complex and five-coordinate (Ttz(tBu,Me))CoNO3 and (Ttz(tBu,Me))ZnOAc complexes. When these complexes were compared to their Tp(tBu,Me) analogues, it was found that Ttz(tBu,Me) resulted in negligible steric differences. K(Ttz(tBu,Me)) is more water-soluble than K(Tp(tBu,Me)), so bulky tris(triazolyl)borate ligands should lead to functional models for enzyme active sites in an aqueous environment and the creation of water-soluble analogues of Tp catalysts.     

Synthesis of zinc, copper, nickel, cobalt, and iron complexes using tris(pyrazolyl)methane sulfonate ligands: a structural model for N,N,O binding in metalloenzymes

Ligands of intermediate steric bulk were designed to mimic metalloenzymes with histidine and carboxlyate binding sites. The reaction between tris(3-isopropylpyrazolyl)methane and butyllithium followed by SO3NMe3 in THF yielded the new ligand lithium tris(3-isopropylpyrazolyl)methane sulfonate (LiTpmsiPr). Various metal salts reacted with LiTpmsiPr to give the octahedral complexes M(TpmsiPr)2 (M = Zn, Cu, Ni, Co, Fe) in which each ligand has N,N,O binding to the metal. In the reaction between LiTpmsiPr and ZnCl2, in addition to the major product Zn(TpmsiPr)2, [LiTpmsiPrZnCl2].2THF was also formed as a minor product with a tetrahedral zinc atom coordinated to either N,N,Cl,Cl in the solid phase or N,N,N,Cl in acetonitrile solution. Although TpmsiPr is coordinatively flexible and can act as a bipodal or tripodal ligand, it appears to favor the formation of octahedral L2M complexes.     

Kinetics and thermodynamics of H. transfer from (eta5-C5R5)Cr(CO)3H (R = Ph,Me, H) to methyl methacrylate and styrene

The rates of H/D exchange have been measured between (a) the activated olefins methyl methacrylate-d(5) and styrene-d(8), and (b) the Cr hydrides (eta(5)-C(5)Ph(5))Cr(CO)(3)H (2a), (eta(5)-C(5)Me(5))Cr(CO)(3)H (2b), and (eta(5)-C(5)H(5))Cr(CO)(3)H (2c). With a large excess of the deuterated olefin the first exchange goes to completion before subsequent exchanges begin, at a rate first order in olefin and in hydride. (Hydrogenation is insignificant except with styrene and CpCr(CO)(3)H; in most cases, the radicals arising from the first H. transfer are too hindered to abstract another H. .) Statistical corrections give the rate constants k(reinit) for H. transfer to the olefin from the hydride. With MMA, k(reinit) decreases substantially as the steric bulk of the hydride increases; with styrene, the steric bulk of the hydride has little effect. At longer times, the reaction of MMA or styrene with 2a gives the corresponding metalloradical 1a as termination depletes the concentration of the methyl isobutyryl radical 3 or the alpha-methylbenzyl radical 4; computer simulation of [1a] as f(t) gives an estimate of k(tr), the rate constant for H. transfer from 3 or 4 back to Cr. These rate constants imply a DeltaG (50 degrees C) of +11 kcal/mol for H. transfer from 2a to MMA, and a DeltaG (50 degrees C) of +10 kcal/mol for H. transfer from 2a to styrene. The CH(3)CN pK(a) of 2a, 11.7, implies a BDE for its Cr-H bond of 59.6 kcal/mol, and DFT calculations give 58.2 kcal/mol for the Cr-H bond in 2c. In combination the kinetic DeltaG values, the experimental BDE for 2a, and the calculated DeltaS values for H. transfer imply a C-H BDE of 45.6 kcal/mol for the methyl isobutyryl radical 3 (close to the DFT-calculated 49.5 kcal/mol), and a C-H BDE of 47.9 kcal/mol for the alpha-methylbenzyl radical 4 (close to the DFT-calculated 49.9 kcal/mol). A solvent cage model suggests 46.1 kcal/mol as the C-H BDE for the chain-carrying radical in MMA polymerization.     

Sonolysis induced decomposition of metal carbonyls: kinetics and product characterization

The decomposition kinetics of Fe(CO)₅ and Mo(CO)₆ induced by sonolysis in hexadecane solvent was studied as a function of temperature (303–343 K) under an inert atmosphere. The decomposition data, obtained over at least two half lives in most of the runs, yielded first-order rate constant (k) values with correlation co-efficient (R²)>0.95. The products were characterized by various spectroscopic techniques. The transmission electron microscopy (TEM) yielded images from which the mean particle diameter (MPD) of 10 nm for Fe and <3 nm for Mo were estimated. The generation of amorphous Fe and semi-crystalline Mo particles was determined from line broadening and corresponding d-spacing values in the X-ray diffraction (XRD) spectra. The XAFS/XANES data were consistent with the production of Fe(0) metal but carbided Mo (Mo₂C). The one-step production of high-yield pyrophoric products demonstrated the applicability of sonolysis to effectively produce gram-quantity of zero-valent metals.