ROBUSTNESS OF AN UPWIND FINITE DIFFERENCE SCHEME FOR SEMILINEAR CONVECTION-DIFFUSION PROBLEMS WITH BOUNDARY TURNING POINTS

We consider a singularly perturbed semilinear convection-diffusion problem with a boundary layer of attractive turning-point type. It is shown that its solution can be decomposed into a regular solution component and a layer component. This decomposi-tion is used to analyse the convergence of an upwinded finite difference scheme on Shishkin meshes.     

Analysis of a finite-difference scheme for a singularly perturbed problem with two small parameters

We study a model linear convection-diffusion-reaction problem where both the diffusion term and the convection term are multiplied by small parameters ε_d and ε_c, respectively. Depending on the size of the parameters the solution of the problem may exhibit exponential layers at both end points of the domain. Sharp bounds for the derivatives of the solution are derived using a barrier-function technique. These bounds are applied in the analysis of a simple upwind-difference scheme on Shishkin meshes. This method is established to be almost first-order convergent, independently of the parameters ε_d and ε_c.     

Synthesis,Vibrational Spectrum and Structure of the Tetracyanoborate K[B(CN)4]·CH3CN

The new tetracyanoborate K[B(CN)₄]·CH₃CN was synthesized by dissolution of the solvent‐free K[B(CN)₄] in acetonitrile and subsequent careful crystallization. The crystal structure has been determined by single‐crystal X‐ray diffraction. It crystallizes in the orthorhombic space group P2₁2₁2₁ with Z = 4. Some comparisons with related structures are made, and the vibrational spectrum is discussed.     

Rhodium and palladium β-diketonate determination with on-line supercritical fluid extraction-high performance liquid chromatography via solid phase extraction

 An on-line system of supercritical fluid extraction (SFE) and high performance liquid chromatography (HPLC) via solid phase extraction (SPE) is described for the determination of palladium and rhodium 2,2,6,6-tetramethyl-3,5-heptanedione-(thd) as well as rhodium-acetylacetonate-(acac) and benzylacetonate-(bzac) chelates. The chelates were extracted with supercritical CO₂ from sand and humic acid, concentrated on SPE cartridges and analysed with HPLC. Two cartridge materials were tested and compared to off-line trapping. The percentage of the breakthrough and cartridge retained material were measured in liquid dichloromethane. The SFE conditions could be optimized to separate metal chelates during the extraction. The supercritical fluid (SF) behaviour of different ligands on rhodium were investigated. Received: 19 July 1996/Revised: 11 December 1996/Accepted: 14 December 1996     

Synthesis and properties of crosslinked polyvinylformamide and polyvinylamine hydrogels in conjunction with silica particles

Polyvinylamine hydrogels with silica particles encapsulated (PVAm/silica) were produced by a two‐step synthesis. In the first step, polyvinylformamide/silica (PVFA/silica) hybrids were synthesized from vinylformamide (VFA) and 1,3‐divinylimidazolidin‐2‐one (1,3‐bisvinylethyleneurea, BVU), as the crosslinker, by radical copolymerization in silica/water suspensions using different compositions of VFA/BVU. The target product PVAm/silica was obtained by acidic hydrolysis of the PVFA/silica hydrogels in a second step. The chemical structures of both hydrogels, PVFA/silica and PVAm/silica, respectively, were revealed by solid‐state ¹³C(¹H) cross‐polarity/magic‐angle spinning NMR spectroscopy. Both hydrogels swelled significantly in water. The swelling capacity of the two systems was characterized by the correlation length ξ (or hydrodynamic blob size) of the network meshes with small‐angle neutron scattering experiments. ξ is significantly larger for PVAm/silica than for PVFA/silica, which corresponds to the observed higher swelling capacity of this polyelectrolyte material. Furthermore, the swelling behavior of the hybrid hydrogels was quantitatively described in terms of free swell capacity, centrifuge‐retention capacity, adsorption against pressure, and free swell rate as compared with values of the corresponding copolymer hydrogels. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3144–3152, 2002     

Regiospecific alkylation of tetronic acids : Formation of 4-alkoxy-5H-furan-2-ones and 2-alkoxy-5H-furan-4-ones

2-Alkoxy-5$\text{H}$-furan-4-ones (7,8) and 4-alkoxy-5$\text{H}$-furan-2-ones (4,5) were prepared regiospecifically and in high yields from tetronic acids (4-hydroxy-5$\text{H}$-furan-2-ones) (2) in the first case by acetylating the 4-OH group and then reacting with trialkyloxonium tetrafluoroborate, and in the second case by alkylating tetrabutylammonium tetronates with dialkyl sulfate, respectively. Direct alkylation of tetronic acids with trialkyloxonium tetrafluoroborate gave in four cases regiospecific 2-O-alkylation, in one case 4-O-alkylation and in two other cases mixtures of 2- and 4-alkoxy derivatives.     

Short and stereoselective synthesis of C-glycosylated glycine derivatives from glycals by radical addition and reduction

Only three steps are required for the convenient synthesis of 2-C-branched glyco-amino acids from glycals with good yields and stereoselectivities.     

Ultrafast proton-coupled electron-transfer dynamics in pyrene-modified pyrimidine nucleosides: model studies towards an understanding of reductive electron transport in DNA.

5-(Pyren-1-yl)-2'-deoxyuridine (PydU) and 5-(Pyren-1-yl)-2'-deoxycytidine (PydC) were used as model nucleosides for DNA-mediated reductive electron transport (ET) in steady-state fluorescence and femtosecond time-resolved transient absorption spectroscopy studies. Excitation of the pyrene moiety in PydU and PydC leads to an intramolecular electron transfer that yields the pyrenyl radical cation and the corresponding pyrimidine radical anion (dU.- and dC.-. By comparing the excited state dynamics of PydC and PydU, we derived information about the energy difference between the two pyrimidine radical anion states. To determine the influence of protonation on the rates of photoinduced intramolecular ET, the spectroscopic investigations were performed in acetonitrile, MeCN, and in water at different pH values. The results show a significant difference in the basicity of the generated pyrimidine radical anions and imply an involvement of proton transfer during electron hopping in DNA. Our studies revealed that the radical anion dC.- is being protonated even in basic aqueous solution on a picosecond time scale (or faster). These results suggest that protonation of dC.- may also occur in DNA. In contrast, efficient ET in PydU could only be observed at low pH values (< 5). In conclusion, we propose--based on the free energy differences and the different basicities--that only dT.- but not dC.- can participate as an intermediate charge carrier for excess electron migration in DNA.     

Separation of (Z)- and (E)-isomers of thioxanthene and dibenz[b,e]oxepin derivatives with calixarenes and resorcinarenes as additives in nonaqueous capillary electrophoresis

Five acidic calix[4]arenes with carboxylic or sulfonic groups at either the upper or lower rim of the cavity and one resorc[4]arene were investigated to separate three thioxanthenes (flupentixol, clopenthixol, chlorprothixene) and a dibenz[b,e]oxepin derivative (doxepin) with cis-/trans-isomerism by nonaqueous capillary electrophoresis (NACE). Partial filling of the capillary with the UV-absorbing selectors led to a low detection limit and an advantageous signal-to-noise ratio (S/N). A sufficient electrophoretic mobility of the calixarenes towards the anode was necessary to outweigh the oppositely directed electroosmotic flow (EOF). This depended from the functional groups, the dissociation and the hydrodynamic radius of the cyclophanes. In contrast, the resorcinarene was useable only by addition of sodium dodecyl sulfate (SDS) because only the complex of the two selectors had an anodic apparent electrophoretic mobility. p-Sulfonyl-calix[4]arene (ss-a1) was the most capable selector for all E/Z-isomers with maximal alpha-values ranging from 1.056 for doxepin to 1.224 for chlorprothixene. This was due to the sufficient migration in reversed direction to the EOF even at low pH* values of 3.0. Otherwise, electrostatic as well as hydrophobic interactions with the positively charged isomers seem to contribute to a superior recognition. Increasing the concentration up to 15 mM ss-a1 and using acidic media (pH* 5.0) led to high separation efficiency. Changing the organic solvent provides a powerful tool to improve selectivity with N,N-dimethylformamide-methanol (DMF-MeOH)-mixtures for thioxanthenes. Further electrophoretic parameters were optimized, such as the concentration of the electrolytes, the addition of SDS, the kind of electrolytes and the voltage. Distinct differences in selectivities were found between the derivatives with thioxanthene and dibenzo[b,e]oxepin ring system, respectively. Further, the different basic side chain was responsible for the different selectivity at higher pH* values. In contrast, the substitution at position 2 of the thioxanthenes played a secondary role. Based on the studies of single parameters a method for a simultaneous separation of the four pairs of isomers within 13 min was developed.