On the non-existence of -uniform finite difference methods on uniform meshes for semilinear two-point boundary value problems

In this paper fitted finite difference methods on a uniform mesh with internodal spacing , are considered for a singularly perturbed semilinear two-point boundary value problem. It is proved that a scheme of this type with a frozen fitting factor cannot converge -uniformly in the maximum norm to the solution of the differential equation as the mesh spacing goes to zero. Numerical experiments are presented which show that the same result is true for a number of schemes with variable fitting factors.

     

Ultrafast dynamics of photochemical radical formation from

The excited-state dynamics and photochemistry of [Re(R)(CO)3(dmb)] (R=Me, Et); dmb=4,4'-dimethyl-2,2'-bipyridine) in CH2Cl2 have been studied by time-resolved visible absorption spectroscopy on a broad time scale ranging from approximately 400 fs to a few microseconds, with emphasis on the femtosecond and picosecond dynamics. It was found that the optically prepared Franck-Condon 1MLCT (singlet metal-to-ligand charge transfer) excited state of [Re(R)(CO)3(dmb)] undergoes femtosecond branching between two pathways (< or =400 fs for R=Me; approximately 800 fs for R=Et). For both methyl and ethyl complexes, evolution along one pathway leads to homolysis of the Re-R bond via a 3SBLCT (triplet sigma-bond-to-ligand charge transfer) excited state, from which [Re(S)(CO)3(dmb)]* and R* radicals are formed. The other pathway leads to an inherently unreactive 3MLCT state. For [Re(Me)(CO)3(dmb)], the 3MLCT state lies lowest in energy and decays exclusively to the ground state with a lifetime of approximately 35 ns, thereby acting as an excitation energy trap. The reactive 3SBLCT state is higher in energy. The quantum yield (0.4 at 293 K) of the radical formation is determined by the branching ratio between the two pathways. [Re(Et)(CO)3(dmb)] behaves differently: branching of the Franck-Condon state between two pathways still occurs, but the 3MLCT excited state lies above the dissociative 3SBLCT state and can decay into it. This shortens the 3MLCT lifetime to 213 ps in CH2Cl2 or 83 ps in CH3CN. Once populated, the 3SBLCT state evolves toward radical photoproducts [Re(S)(CO)3(dmb)]* and Et*. Thus, population of the 3MLCT excited state of [Re(Et)(CO)3(dmb)] provides a second, delayed pathway to homolysis. Hence, the quantum yield is unity. The photochemistry and excited-state dynamics of [Re(R)(CO)3(dmb)] (R=Me, Et) complexes are explained in terms of the relative ordering of the Franck-Condon, 3MLCT, and 3SBLCT states in the region of vertical excitation and along the Re-R reaction coordinate. A qualitative potential energy diagram is proposed.     

Hydrogenation of citral on Ir/SiO2 catalysts. Effect of the addition of Nb2O5 on surface and catalytic properties

Hydrogenation of citral over Ir supported on SiO₂, Nb₂O₅ and Ir/Nb₂O₅-SiO₂ catalysts reduced at 473 K (LT) and 773 K (HT) was studied. High selectivity to unsaturated alcohol was found, the main reaction products being geraniol and nerol. The LT catalysts show higher conversion levels, the one with a higher Nb content displays highest conversion.     

Spectroscopic analysis of single-walled carbon nanotubes and semiconjugated polymer composites

Interactions between arc discharge single-walled carbon nanotubes within polymer composites have been well documented. Here hybrid systems of the conjugated organic polymer poly(p-phenylene vinylene-co-2,5-dioctyloxy-m-phenylene vinylene) (PmPV) and HiPco SWNTs are explored using UV/vis/NIR and Raman spectroscopy at 514.5 and 632.8 nm to determine specific interactions. An examination of the radial breathing modes at 514.5 nm shows similar tube diameters of 1.28 and 1.35 nm selected for both the arc discharge and HiPco composites. The corresponding G lines of both composites show no specific type of tubes being selected. At 514.5 nm, the G line of the HiPco composite (1% mass fraction) shows contributions from semiconducing and metallic tubes, and the arc discharge composite (1% mass fraction) is dominated by semiconducting nanotubes. At 632.8 nm, the G line of the HiPco composite (1% mass fraction) is dominated by semiconducting tubes, and the arc discharge composite (1% mass fraction) shows strong contributions from metallic tubes. This finding is a strong indication that the selection process is dependent on tube diameter rather than backbone structure. The solubility limits of both composites are determined by investigating the G lines of both composites and have been found to be greater than 1% mass fraction by weight for the arc discharge composite and greater than 0.1% mass fraction by weight for the HiPco composite.     

Hydrogenation of citral over pt and pt-fe/sio2 catalysts

Summary Pt/SiO₂ and Pt-Fe/SiO₂ catalysts having a Pt loading ranging from 0.5 to 3.0 wt.% and a fixed amount of Fe in the bimetallic series, 1.0 wt.% have been prepared by the impregnation procedure, followed by calcinations and reduction in H₂ flow at 773 K. The samples were characterized by N₂ adsorption at 77 K, H₂ chemisorption at 298 K, TEM, TPR and XPS. The hydrogenation of citral at 363 K and 8.3 bar over a series of Pt/SiO₂ and Pt-Fe/SiO₂ catalysts was studied. Thus, the selectivity towards the unsaturated alcohol (geraniol + nerol) decreases at high loads of monometallic Pt. An effect of polarization of the C=O bond due to the presence of Fe³⁺ species leads to catalysts active and highly selective to the hydrogenation of the carbonyl bond. Characterization results showed that Pt is present as Pt^o and Fe mainly asFe³⁺.     

Catalytic combustion of ethyl acetate over ceria-promoted platinum supported on Al2O3 and ZrO2 catalysts

Platinum-supported catalysts prepared by impregnation of mixed CeO₂/Al₂O₃ and CeO₂/ZrO₂ oxides using the sol-gel method were characterized and used in the combustion of ethyl acetate. In each series, the effect of CeO₂ loading (3 and 5 wt%) was studied. Characterization data from the studied catalysts (specific area measurements, hydrogen chemisorption, programmed temperature reduction (TPR), X-ray diffraction (XRD), photoelectron spectra (XPS) and transmission electron microscopy (TEM)) revealed significant changes in porosity and metal dispersion in each series. The catalytic activity of the solids, evaluated in the total combustion of ethyl acetate, exhibited a positive effect with the addition of Ce in the zirconia series whereas no significant changes was observed in the alumina series.     

Preparation of ferrocene-containing phosphinamine ligands possessing central and planar chirality and their application in palladium-catalyzed asymmetric allylic alkylation

The preparation of [2-(S(p))-[(trans-(2R,5R)-2,5-dialkylpyrrolidinyl)methyl]]ferrocenyldiphenyl phosphines, new ferrocenylphosphinamine ligands possessing one site of planar and two stereogenic centers, is described. trans-(2R,5R)-2,5-Dialkyl-1-(ferrocenylmethyl)pyrrolidines were diastereoselectively lithiated and quenched with chlorodiphenylphosphine. For the dimethyl ligand, chemical yields of up to 65% and des of up to 90% were obtained whereas the diethyl ligand afforded lower chemical yields (10%) and des of 78%. Diastereomerically pure material was obtained in both cases after a single recrystallization from ethanol. (S)-Planar chirality was confirmed by X-ray crystallographic analysis of the dimethyl ligand. The palladium complexes of the new ligands were applied in the allylic alkylation of 1,3-diphenylprop-2-enyl acetate with reasonable chemical yields and moderate ees of up to 36% and 38% when dimethyl malonate and dimethyl methyl malonate were employed as nucleophiles, respectively. Importantly, it was found that the new ligands possessing the combination of planar and central chirality gave the opposite enantiomeric alkylation products compared to ligands which possess only the central chirality of the trans-2,5-dimethylpyrrolidinyl moiety. Solution NMR studies of the 1,3-diphenylallyl palladium complex of the dimethyl ligand revealed the presence of only the exo-configured allyl diastereomer.     

Synthesis and characterization of a helical step‐ladder polyarylene

A helical step‐ladder polyarylene incorporating chiral (R)‐2,2′‐dioctoxy‐1,1′‐binaphthyl units was synthesized for the first time. The first step involved the preparation of a precursor poly(arylene ketone) via a palladium‐mediated Suzuki‐type cross‐coupling reaction with the aid of microwave heating. Two polymer‐analog reaction steps, the reduction of the keto groups to tertiary alcohol functionalities and subsequent intramolecular Friedel–Crafts cyclization, gave a step‐ladder polymer ( 6 ) in good yields with reasonable mean average molecular weights greater than 13,000. The regioselective cyclization pattern in the α position of the naphthalene core was confirmed by a comparison of the NMR data of the polymer with those of the corresponding model ladder oligomers, 12 and 13 , and also a single‐crystal structure of 13 . The optical spectra of the oligomers and polymers indicated that there was little electronic interaction across the binaphthyl units. The circular dichroism spectrum of 6 exhibited a strong bisignate Cotton effect in the π–π* absorption region of the planar chromophores, which reflected the strong exciton coupling within the helical polymer chain. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5533–5545, 2006     

Synthesis,thermal reactivity,and kinetics of stabilized phosphorus ylides,part 2: [(Arylcarbamoyl)(cyano)methylene]triphenylphosphoranes and their thiocarbamoyl analogues

A series of five cyano(arylcarbamoyl) phosphorus ylides 2 and five cyano(arylthiocarbamoyl) phosphorus ylides 3 are prepared and fully characterized. Pyrolytic reaction products of a representative example of each type obtained by flash vacuum pyrolysis technique show that they undergo thermal extrusion of Ph₃PO or Ph₃PS. Kinetic study of the gas‐phase pyrolysis of each ylide by static method shows that these reactions are unimolecular and first order with no significant substituent effect, but the thiocarbamoyl ylides 3 react 40–65 times more rapidly than their carbamoyl analogues 2 . © 2006 Wiley Periodicals, Inc. Int J Chem Kinet 38: 496–502, 2006