Asymptotic limit-cycle analysis of oscillating chemical reactions

The asymptotic limit-cycle analysis of mathematical models for oscillating chemical reactions is presented. In this work, after a brief presentation of mathematical preliminaries applied to the biased Van der Pol oscillator, we consider a two-dimensional model of the Chlorine dioxide Iodine Malonic-Acid (CIMA) reactions and the three-dimensional and two-dimensional Oregonator models of the Belousov–Zhabotinsky reactions. Explicit analytical expressions are given for the relaxation-oscillation periods of these chemical reactions that are accurate within 5% of their numerical values. In the two-dimensional CIMA and Oregonator models, we also derive critical parameter values leading to canard explosions and implosions in their associated limit cycles.

     

Calorimetric study of the component steps of oscillating chemical reactions

An influence of inorganic compounds (Fe₂O₃, ZnO, PbO, CaCO₃ and K₂CO₃) on the blast furnace coke thermal oxidation in the air and in the CO₂atmosphere was investigated by means of thermal analysis. A catalytic effect showed itself at the oxidation in the air, especially with PbO and K₂CO₃. These compounds bring the oxidation starting temperature and activation energy down and increase the reaction rate constant most distinctly. The PbO and K₂CO₃ actions differ in their mechanisms. K₂CO₃ accelerates particularly the amorphous coke fractions oxidation. In the CO₂ atmosphere an important catalytic effect occurred only with K₂CO₃. The PbO catalytic influence is less distinct. This revised version was published online in July 2006 with corrections to the Cover Date.     

Uncertainty of analytical determinations

Two examples of uncertainty calculation are described for determination of nitrates in solution (APHA method 4500B) and total suspended solids in water (APHA method 2540D).     

New oscillating chemical reactions involving copper and nickel tetraazamacrocyclic complexes

Copper and nickel complexes with tetraazamacrocyclic ligands are shown to act as catalysts in Belousov-Zhabotinskii oscillating reactions. New oscillating reactions, viz. the oxidation of unsaturated macrocyclic complexes of copper and nickel by bromate-ions, have been discovered.

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Analytical assessment of the oscillating chemical reactions by use chemiluminescence detection

This paper introduces the chemiluminescence (CL) detection in oscillating reaction-based determinations using the analyte pulse perturbation technique, a straightforward and expeditious approach to deriving quantitative analytical information from oscillating chemical reactions. The behavior of the H(2)O(2)-KSCN-CuSO(4)-NaOH oscillating system in the presence of luminol was examined by using the proposed detection method and the classical potentiometric technique. Some analytical and practical aspects of both detection systems are discussed. A new analytical method for the determination of vitamin B(6) based on the sequential perturbation produced by different amounts of this substance on the oscillating chemical system was also developed in order to assess the potential of CL detection for routine analyses. The calibration curve thus obtained was linear over the range 0.5-2.0 mumol of vitamin B(6), and the precision and throughput were also quite good (3.04% as RSD and nine samples h(-1), respectively). The proposed method was validated by determining the vitamin in pharmaceutical preparations.     

Fluorescence studies of ternary complexes of Europium and Terbium and their application to analytical determinations

Europium and Terbium were found to form ternary complexes with ethylenediammine tetraacetic acid (EDTA) and ortho-phenanthroline (o-phen) in aqueous solution in the pH range of 6-8. These ternary complexes were found to have 1:1:1 composition and showed strong fluorescence properties. The method is made use of for the determination of these lanthanide ions in presence of excess amounts of other lanthanide ions. The lowest detection limit was calculated as 30 and 65 ng/ml of Tb(3+) and Eu(3+), respectively.     

A boundedness theorem with application to oscillation of autocatalytic chemical reactions

For a class of dynamical systems of the form , we prove boundedness of all solutions in the positive time direction. We discuss the existence of stable limit cycles for the simplest autocatalytic reaction involving two internal and two external reactants, as well as for a number of other models arising in applications.     

The application of ICP-OES to industrial analytical problems

ICP optical emission spectroscopy was introduced for multi-element determinations some 15 years ago. Nowadays, its field of application covers the analysis of widely differing materials at every stage of industrial activity.     

Wavelet frequency spectrum and its application in analyzing an oscillating chemical system

Based on the continuous wavelet transform (CWT), three types frequency spectra, wavelet frequency spectrum (WFS), point frequency spectrum (PFS) and time frequency spectrum (TFS), were developed. Two data sets were simulated and treated with the proposed spectra, the results indicated that WFS could extract the frequency information, which was like Fourier analysis but more accurate, PFS could obtain the frequency at any moment, TFS could show frequency change with time. These abilities of PFS and TFS were impossible for Fourier analysis. An oscillating chemical signal was processed with WFS and TFS. From the processed results, two points could be learned about the oscillating chemical reaction: one was the oscillating chemical reaction was a mixture one including two or more complex kinetics processes, the velocity of the switch from the reduced state (RS) to the oxidized state (OS) was faster than the reverse switch (from OS to RS); the other was increase of KBrO₃ could decrease the velocities of both switches, which led to the oscillating period became longer.     

Evaluation of different instrumental and chemical parameters in analytical determinations by the use of experimental design methods

Summary The paper deals with the application of fractional experimental design, random balance method and full experimental design with two levels of variation of the input parameters for the estimation of the significance of chemical and instrumental factors in different analytical problems. The example chosen refer to the fluorimetric determination of aluminium (estimation of three chemical and two instrumental factors for optimization purposes), the ranging of environmental factors in the determination of the protective ability of polymer coatings (seven parameters are included) and the determination of several anions in aerosol samples by ion chromatography (the significance of three operational parameters for model solutions is considered). It is shown that the experimental design strategies can be used as reliable and quick tools for ranging and parameter estimation.

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Bewertung verschiedener instrumenteller und chemischer Parameter bei analytischen Bestimmungen mittels experimenteller Planung

Zusammenfassung Die Anwendung der Fraktions-Experimentalplanung, des Zufallsausgleichs und der Vollplanung auf zwei Ebenen der Eingangsparameter zur Bewertung der Wichtigkeit von instrumentellen und chemischen Parametern bei verschiedenen analytischen Aufgaben wird diskutiert. Die gezeigten Beispiele beziehen sich auf die fluorimetrische Bestimmung von Aluminium (Bewertung von drei chemischen und zwei instrumentellen Faktoren für Optimierungszwecke), die Einordnung von Umweltfaktoren bei der Bestimmung der Schutzwirkung von Polymerschichten (sieben Parameter), und die Bestimmung einiger Anionen in Aerosolproben mit der Ionen-Chromatografie (dabei wird die Wichtigkeit von drei Arbeitsparametern bei Modellösungen betrachtet). Es wird gezeigt, daß diese Planungsstrategie zur zuverlässigen und schnellen Bewertung und Einordnung von Parametern geeignet ist.

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Dedicated to Prof. Dr. Dr. h.c. Hanns Malissa on the occasion of his 65th birthday     

The application of surface analytical techniques to silicon technology

Summary Most modern semiconductor device engineering takes place in the top micron of the host wafer and involves the creation of regions whose composition varies over lateral dimensions which may be less than 0.5 m. Normal to the wafer surface, large changes in matrix and impurity composition may occur in the space of a single atomic plane. In future, the fabrication of quantum dots and wires will result in active device features a few nm in extent. Such material developments need to be supported by parallel development in surface analytical techniques with high spatial resolution. There are, however, fundamental limitations to what can be achieved directly. For a destructive technique such as secondary ion mass spectrometry (SIMS), the analytical sensitivity and spatial resolution are determined by the analyte volume which needs to be consumed to achieve the necessary statistical precision. Moreover, the type of information obtained depends on the details of the interaction between the primary probe and the sample surface. In order to combine high spatial resolution with high sensitivity, special sample structures and modified instruments are required. Techniques need to be developed for accurately compensating for the effects on the analysis of large localized changes in conductivity in the materials. A multi-technique approach to semiconductor analysis is required both to investigate the limitations of the techniques themselves, and to fully describe the material properties.     

The critical bromide concentration in an oscillating chemical system

A new method for the determination of aluminium in biological fluids by flameless atomic absorption spectrometry is described. A wetting agent (Teepol) is added to shorten the time of drying and ashing steps and to improve reproducibility. Aluminium is converted to aluminate with ammonia liquor to prevent volatile chloride formation. Application of the method to a serum gave results with a relative standard deviation of 2.5%. This method was also applied to the determination of aluminium in serum and cerebrospinal fluid of 20 normal persons: the mean value for the sera was 34.1 μg 1^-1 and the mean value for the CSF was 19.8 μg 1^-1 with relative standard deviations of 3.5% and 2.5%, respectively.     

The analytical potential of neutron inelastic scattering reactions

The analytical application of neutrons produced by the⁹Be(d, n)¹⁰B reaction using 3-MeV deuterons is presented. The principal reaction for such neutrons is that of inelastic scattering. Fifteen elements were chosen for study (Se, Br, St, Y, Ag, Cd, In, Sn, Er, Lu, Hf, W, Ir, Au and Hg). Gamma-ray spectra of the metastable isomers produced were obtained with a Ge(Li) detector. The minimum weight of each element detectable (L_D) was then determined from the spectra. Assuming a sample weight of 5g, several elements (Se, Br, Sr, Y, Hf and Au) had L_D values of less than 100 ppm.     

Kinetic determinations of reactants utilizing uncatalyzed reactions

Kinetic-based determinations of reactants utilizing uncatalyzed chemical reactions do not match the polularity of catalytic methods for the determination of catalysts (particularly transition metal ions) or reactants (e.g., in enzymatic reactions) and this reflects on the scarcity of reviews on the topic. In some cases, however, advances in instrumentation and data manipulation provide competitive alternatives to nonkinetic-based methods for single as well as multispecies determinations. Such advances are reviewed here and applications illustrated.