Der nichtlineare Ausgleich in der Röntgenspektrometrie

The hyperbolic approximation of non-linear relationships between intensities and concentrations can be reduced to a linear regression for two constants, being carried out with a modern non-programmable scientific desk or pocket calculator. The approximation is independent on dead-time losses and ensures good results also in cases of unknown background.     

Zur Praxis der Matrixkorrektur in der R?ntgenspektrometrie

Zusammenfassung Für die Auswertung von Meßergebnissen gibt es zwei korrekte Ansätze (1) und (2). Ein dritter Ansatz (3), dessen theoretische Inkorrektheit gezeigt wird, erweist sich auch in der praktischen Anwendung als den anderen Ansätzen unterlegen, weil er auf größere Analysenfehler führt.Gelegentlich wird vorgeschlagen, anstelle der klassischen Regressionsrechnung mit absoluten Fehlern eine Methode mit gewichteten Fehlern zu verwenden. Eine Überprüfung der gewichteten Regression hatte zum Ergebnis, daß durch diese Methode der Analysenfehler vergrößert wurde.

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Practice of matrix correction in X-ray spectrometry

Summary There are two correct eqs. (1) and (2) for the evaluation of measuring results. A third eq. (3) whose theoretical incorrectness was shown proved to be inferior to the other equations by leading to larger analysis errors.Occasionally a regression method is proposed which is using weighted errors instead of absolute errors as used in the classical method. Testing of this method resulted in a clear increase of analysis errors.

     

Carbonylation of epoxides to substituted 3-hydroxy-delta-lactones

Substituted 3-hydroxy-delta-lactones (3HLs) are valuable intermediates in the synthesis of pharmaceuticals and other biologically active natural products. Herein we report the first example of the catalytic carbonylation of substituted homoglycidols to 3HLs using HCo(CO)4. Upon optimization of the catalyst and reaction conditions, a functionally diverse set of 3HLs was prepared. Mechanistic insight was gained by observation of the carbonylation reaction using in situ IR spectroscopy, and we propose a mechanism that is consistent with previously studied epoxide carbonylation systems.     

Selection of Conditions for Cellulase and Xylanase Extraction from Switchgrass Colonized by <Emphasis Type="Italic">Acidothermus cellulolyticus</Emphasis>

Solid-state fermentation has been widely used for enzyme production. However, secreted enzymes often bind to the solid substrate preventing their detection and recovery. A series of screening studies was performed to examine the role of extraction buffer composition including NaCl, ethylene glycol, sodium acetate buffer, and Tween 80, on xylanase and cellulase recovery from switchgrass. Our results indicated that the selection of an extraction buffer is highly dependent on the nature and source of the enzyme being extracted. While a buffer containing 50 mM sodium acetate at pH 5 was found to have a positive effect on the recovery of commercial fungal-derived cellulase and xylanase amended to switchgrass, the same buffer had a significant negative effect on enzyme extraction from solid fermentation samples colonized by the bacterium Acidothermus cellulolyticus. Xylanase activity was more affected by components in the extraction buffers compared to cellulase. This study demonstrated that extraction followed by diafiltration is important for assessing enzyme recovery from solid fermentation samples. Reduction in activity due to compounds present in the switchgrass extracts is reversible when the compounds are removed via diafiltration.     

On the propagation rate constants of cationic polymerizations

The concepts employed to explain polymerizations by ionizing radiations are used for a critical examination of the concepts involved in interpreting the kinetics of chemically initiated cationic polymerizations. It is explained how the interactions of the propagating carbenium ions with the solvent, monomer, and anion can result in the formation of up to six distinct unpaired species and several kinds of ion pairs; therefore, the consumption of the monomer can be governed simultaneously by many rate constants. Only one of these can have any general theoretical use, and suggestions are made for how it can be measured. For the first time, it is shown that the ion‐pairing process must involve a ligand displacement and so resembles the amination of the Ag⁺ ion, for example, in an aqueous solution by NH₃, rather than an association of inert ions of unchanging identity. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2537–2544, 2002     

Stereospecific polymerization of isobutyl vinyl ether by AIR3–VCl3·LiCl catalyst. II. Effects of polymerization conditions on polymerization

The effect of polymerization conditions such as aging time of the catalyst, polymerization temperature, polymerization time, monomer concentration, and catalyst concentration on the polymerization of isobutyl vinyl ether was intensively studied by using the VCI₃·LiCl–Al(i-Bu)₃ system at an Al(i-Bu)/VCl₃·LiCl ratio of 6 at which the cationic polymerization by VCl₃·LiCl is sufficiently depressed. About 10 min aging of the catalyst in the presence of monomer yields a fairly stable catalytie system. The optimum polymerization temperature is around 30°C. The conversion increased with increasing monomer concentration, whereas the stereospecificity of polymerization decreased. Unexpectedly, the conversion decreased as total catalyst concentration increased. This phenomenon is explained by considering the deactivation of catalytic sites by the excess of Al(i-Bu)₃. A reasonable mechanism from kinetic considerations is that two molecules of Al(i-Bu)₃ deactivate the catalytic site in an equilibrium reaction. This deactivation is understandable by considering that the coordination of two molecules of Al(i-Bu)₃ will occupy all the coordination positions of vanadium, so that there is no room for coordination of monomer coming to the catalytic site.     

Variabler und konstanter innerer Standard in der R?ntgenspektrometrie

Zusammenfassung Die Dotierung von Standards und unbekannten Proben mit einem inneren Standard ist ein bekanntes Verfahren zur verringerung des Matrixeffekts in der Röntgenspektrometrie. Es werden zwei Ansätze für variable und konstante innere standards theoretisch abgeleitet und an Meßergebnissen mit positivem Ergebnis überprüft. Die Ansätze gelten sowohl für Netto- als auch für Bruttointensitäten.Der Vergleich mit einem früher veröffentlichten Ansatz [5] ergab etwa gleiche Leistungsfähigkeit beider Ansätze.

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Variable and constant internal standard in X-ray spectrometry

Summary The addition of an internal standard to the standards and unknown samples is a well known method of reduction of the interelement effects. Two equations for variable and constant internal standards are theoretically derived and successfully tested with measuring results. They are valid for net and gross intensities.A comparison with a formerly published equation [5] for net intensities resulted in nearly the same efficiency of both equations.

     

Das Polynom dritter Ordnung als Eichkurve der R?ntgenspektrometric

Zusammenfassung Die Methode der quadratischen Optimierung (auch als Methode der kleinsten Quadrate bezeichnet) mit einem Polynomansatz zweiter Ordnung führt zu verschiedenen Eichkurven, je nachdem, ob man die Konzentration als Funktion der Intensität oder die Intensität als Funktion der Konzentration darstellt. Da beide Ansätze mathematisch gleichberechtigt sind, entsteht eine echte Doppeldeutigkeit, die einen systematischen Analysenfehler zur Folge hat.Er wird durch die Anwendung der Interpolationsformel von Newton beseitigt. Da ihre Koeffizienten sehr einfach zu berechnen sind, kann ohne Schwierigkeit mit Polynomen dritter Ordnung gearbeitet werden, die eine bessere Anpassung an die Meßwerte der Standards und damit einen kleineren zufälligen Analysenfehler bewirken.

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The polynomial of third order as calibration curve in X-ray spectrometry

The method of the least squares with a polynomial of second order leads to different calibration curves depending on the choice of either the concentration as a function of the intensity or the intensity as a function of the concentration. Both statements are mathematically equivalent and an uncertainty of the analysis is therefore caused with a systematical error as a consequence.This uncertainty is removed by the application of Newton's interpolation formula the coefficients of which can be calculated very easily. Therefore it is possible to use a polynomial of third order as calibration function which allows a better accomodation to the measurement results of the standards. Further, the random analytical error is reduced and above all it can be directly calculated.