Efficient Collocation Schemes for Singular Boundary Value Problems

We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point.     

Deposition of boron nitride on graphite at 1300 K

A method for the deposition of BN onto graphite and other substrates is described. Boron trichloride (BCl₃) and ammonia (NH₃) diluted with Ar were used as reacting gases. The deposition process was carried out at 1300 K as well as lower temperatures in an open system at pressures of 1 atm. The consequences of the introduction of hydrogen to the system were considered. It was demonstrated that the replacement of argon with hydrogen increases the efficiency of the process as well as the theoretical rate of BN deposition. However, the acceleration of the deposition seems to be unprofitable, because the resulting supersaturation leads to the formation of an amorphous phase. The modification of the experimental conditions were proposed.Dedicated to Professor Dr. rer. nat. Dr. h.c. Hubertus Nickel on the occasion of his 65th birthday     

Determination of Emodin and Phenolic Acids in the Petioles of Rheum undulatum and Rheum rhaponticum

JPC – Journal of Planar Chromatography – Modern TLC - Emodin and twelve phenolic acids (ellagic, gallic, protocatechuic, homoprotocatechuic, caffeic, p-hydroxybenzoic, p-coumaric,...     

Chemically modified proton‐conducting membranes based on sulfonated polyimides: Improved water stability and fuel‐cell performance

A series of branched/crosslinked sulfonated polyimide (B/C‐SPI) membranes were prepared and evaluated as proton‐conducting ionomers based on the new concept of in situ crosslinking from sulfonated polyimide (SPI) oligomers and triamine monomers. Chemical branching and crosslinking in SPI oligomers with 1,3,5‐tris(4‐aminophenoxy)benzene as a crosslinker gave the polymer membranes very good water stability and mechanical properties under an accelerated aging treatment in water at 130 °C, despite their high ion‐exchange capacity (2.2–2.6 mequiv g^?1). The resulting polymer electrolytes displayed high proton conductivities of 0.2–0.3 S cm^?1 at 120 °C in water and reasonably high conductivities of 0.02–0.03 S cm^?1 at 50% relative humidity. In a single H₂/O₂ fuel‐cell system at 90 °C, they exhibited high fuel‐cell performances comparable to those of Nafion 112. The B/C‐SPI membranes also displayed good performances in a direct methanol fuel cell with methanol concentrations as high as 50 wt % that were superior to those of Nafion 112. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3751–3762, 2006     

Sensitised decomposition of microcystin-LR using UV radiation

UV radiation was applied to degrade cyanobacterial hepatotoxin, microcystin-LR in the presence of phycocyanin as a model natural sensitiser. The concentrations of both the toxin and the pigment used in the experiments were higher by several orders of magnitude than found in the environment. The photoreaction parameters were optimised. The process was found to be of limited use for water treatment due to its low efficacy. Additionally, pronounced UV-induced bleaching of the pigment significantly reducing the photoreaction rates of the toxin was observed for the highest UV radiation intensities applied.     

Thermochromic and solvatochromic zinc biladienones: dynamic equilibria of a metal complex having a flexible framework sensitive to environment

Dehydration of zinc biladienone was catalyzed by zinc acetate, while the reverse reaction was catalyzed by triethylamine. The transformation can be performed thermally without catalyst, and the ratio of the hydrated form to the dehydrated form depended on the solvents: the dehydrated form is favored in CHCl₃ and CH₂Cl₂, while the hydrated form is favored in hexane, pyridine, and DMF. Kinetic studies on the thermal transformation of zinc biladienone from its hydrated blue form to the dehydrated yellow-brown form were performed in toluene and THF. The rate law was half order with respect to the zinc biladienone concentration in toluene, while first order in THF, leading to a slow transformation in concentrated solution in toluene.     

Study on the electroreduction of In(III) ions at gold from acidic bromide solutions by the rotating ring-disc electrode technique

The mechanism of the indium electrodeposition on gold from acidic KBr solutions has been investigated by means of the rotating ring-disc electrode technique. The measurements showed that the overall electrode reaction In(III) + 3 e In consists of two successive charge transfer steps, i.e. In(III) + 2 e In(I) and In(I) + e In, with soluble monovalent indium as an intermediate. The current efficiency for In(I) generation under steady-state conditions is 100% in the case of low disc current densities. The disproportionation of In(I) in the bulk of solution occurs in slightly acidified solutions,pH=2, in addition to the In(I) electrochemical reduction. Based on the ring current transients, it was established that the two-electron transfer step is preceded by the formation of a thin passive film of indium metal.

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Untersuchung der elektrochemischen Reduktion von In(III)-Ionen an Gold in sauren Bromidlösungen mit der rotierenden Ring-Scheiben-Elektrode

Zusammenfassung Mit Hilfe der rotierenden Ring-Scheiben-Elektrode wurde der Mechanismus der kathodischen Abscheidung von Indium auf Gold in sauren KBr-Lösungen untersucht. Aus den Messungen folgt, daß die Bruttoreaktion In(III) + 3e In über zwei aufeinanderfolgende Durchtrittsreaktionen, In(III) + 2 e In(I) und In(I) + e In, mit löslichem einwertigem Indium als Zwischenprodukt abläuft. Bei kleinen Stromdichten werden die In(I)-Ionen mit 100%iger Stromausbeute erzeugt. In schwächer sauren Lösungen (pH=2) konnte außer der elektrochemischen Reduktion von In(I) zusätzlich dessen Disproportionierung innerhalb der Lösung ermittelt werden. Auf Grund der Ringstrom-Zeit-Kurven wurde auch festgestellt, daß die Bildung von einer dünnen In-Metallschicht, die ein passives Verhalten aufweist, dem Zweielektronenübergang vorangegangen ist.

     

Electrochemical studies of Tl(I) crown-ether complexes in nonaqueous media

Summary Complexation equilibria of the Tl(I) ion with 18-crown-6 and dibenzo-18-crown-6 were studied polarographically in 10 nonaqueous solvents. The stability of the complexes is strongly influenced by the nature of solvents and varies with their Lewis basicities. It has been found that the logK _s value (K _s is the stability constant of the complex) can be well described by empirical relation logK _s=a DN+b, whereDN stands for the Gutmann donor number anda andb mark the regression coefficient. Addition of the second explanatory parameter, the acceptor number, is not statistically significant. This result is in agreement with the predominant role of Tl(I) ion solvation.

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Elektrochemische Untersuchungen von Tl(I)-Kronenetherkomplexen in nichtwäßrigen Medien

Zusammenfassung Es wurden die Komplexierungsgleichgewichte des Tl(I)-Ions mit 18-Krone-6 und Dibenzo-18-krone-6 polarographisch in 10 nichtwäßrigen Lösungsmitteln untersucht. Die Stabilität der Komplexe wird sehr stark vom Solvens beeinflußt, wobei eine starke Abhängigkeit von der Lewis-Basizität beobachtet wird. Es wurde festgestellt, daß die logK _s-Werte (K _s ist die Komplexstabilitätskonstante) gut mit der empirischen Beziehung logK _s=a DN+b beschrieben werden können, wobeiDN die Gutmann'sche Donorzahl unda undb die Regressionskonstanten bedeuten. Hinzunahme der Akzeptorzahl als zweiten Parameter bleibt statistisch insignifikant. Dieses Ergebnis stimmt mit dem dominierenden Einfluß der Tl(I)-Ionensolvatation überein.

     

Kinetics and mechanism of the first aquation stage for the [Cr(pic)3]0 and [Cr(pic)2(OH)]2 0 complexes in HClO4 solutions

Aquation of [Cr(pic)₃]⁰ and [Cr(pic)₂(OH)]₂ ⁰ in aqueous HClO₄ solutions leads to formation of the common product – [Cr(pic)₂(H₂O)₂]⁺. The first, reversible stage, the ring opening via Cr—N bond breaking in [Cr(pic)₃]⁰ is followed by the second, rate-determining step – one-end bonded pic ligand liberation. In the case of the [Cr(pic)₂(OH)]₂ ⁰ complex, the first faster stage produces the singly bridged dimer, which undergoes cleavage into the parent monomers in the second, much slower step. The subsequent aquation of [Cr(pic)₂(H₂O)₂]⁺ is extremely slow and leads to [Cr(pic)(H₂O)₄]²⁺ formation, which practically does not undergo further ligand substitution under the conditions applied. Kinetics of the first aquation stage for [Cr(pic)₃]⁰ and of the second step for [Cr(pic)₂(OH)]₂ ⁰ were studied spectrophotometrically in the 0.1–1.0 M HClO₄ range at I = 1.0 M. The observed pseudo-first order rate constant for [Cr(pic)₃]⁰ decreases with [H⁺] increase according to the rate law: k _obs = k ₁ + k _–1 Q ₁/[H⁺], where k ₁ and k _–1 are the rate constants of the forward and the reverse processes in the unprotonated substrate and Q ₁ is the protonation constant of the pyridine nitrogen atom. In the case of the [Cr(pic)₂(OH)]₂ ⁰ complex, the rate for the singly bridged dimer cleavage does not depend on [H⁺]. The activation parameters for the chelate-ring opening in [Cr(pic)₃]⁰ and for the singly bridged dimer cleavage have been determined and discussed. Some kinetic data of the slow, second aquation stage for the [Cr(pic)₃]⁰ complex and of the fast, first aquation stage for the doubly bridged dimer have been studied; for both reactions the rate increases linearly with the increase in [H⁺].     

Creatinine biosensor based on ammonium ion selective electrode and its application in flow-injection analysis

A new, highly sensitive, fast responding and stable potentiometric biosensor for creatinine determination is developed. The biosensor is based on an ammonium ion-selective electrode. Creatinine deiminase (EC 3.5.4.21) is chemically immobilized on the surface of the polymeric ion-sensitive membrane in the form of monomolecular layer using a simple, one-step carbodiimide covalent attachment method. The resulting enzyme electrodes are useful for measurement under flow injection analysis (FIA) conditions. The biosensors exhibit excellent operational and storage stability. The enzyme electrodes retain over 70% of initial sensitivity after ten weeks of work under FIA conditions. The storage stability at 4 °C is longer than half a year without loss of sensitivity. Under optimized conditions near 30 samples per hour can be analyzed and the determination range (0.02-20.0 mmol l⁻¹) fully covers creatinine concentrations important from clinical and biomedical point of view. The simple biosensor/FIA system has been successfully used for determination of creatinine in urine, serum and posthemodialysate samples.