Validated Infeasible Interior-Point Predictor–Corrector Methods for Linear Programming

Many problems arising in practical applications lead to linear programming problems. Hence, they are fundamentally tractable. Recent interior-point methods can exploit problem structure to solve such problems very efficiently. Infeasible interior-point predictor–corrector methods using floating-point arithmetic sometimes compute an approximate solution with duality gap less than a given tolerance even when the problem may not have a solution. We present an efficient verification method for solving linear programming problems which computes a guaranteed enclosure of the optimal solution and which verifies the existence of the solution within the computed interval.     

Solvation numbers and hydration constant for thorium(IV) in ethanol-water medium

The solvation number and hydration constant of Th⁴⁺ in ethanol-water medium were determined at 25°C using UV-spectral and electrochemical measurements. A solvate formation equilibrium is demonstrated and characterized. Three molecules of ethanol (S) can bond to the metal cation with strengths comparable to that for H₂O to form ThS₃(H₂O) ₃ ⁴⁺ Formation of thorium monochelate with lawsone (2-hydroxy-1,4-naphthoquinone) eliminates bonding with alcohol molecules. The dissociation constant of the chelating agent_sK_a and the formation contant of the monochelated metal ion_sK _f ^* that are essentially independent of the solution composition are evaluated. Hydration titrations involving thorium-lawsone monochelate are performed and the data obtained from the changes of pH with solvent composition are analyzed. The solution independent constant,_sK _f ^* for thorium-lawsone complex formation in mixed aqueous ethanol is given by $$log_s K_f * = vpK_a + log_s K_h - log[LH] - vpH + 3logv$$ where vpK_a is the dissociation constant of the chelating agent LH in the solvent system of ν volume fraction of water and_sK_h is the solution-independent hydration constant of thorium (IV) in the solvent system. Log-values for the constants_sK_h,_sK _f ^* and_sK _a ^* are found to be 7.8±0.02, 11.38±0.04 and ?0.753, respectively.     

Die Reaktion von Ce(III), Th(IV) und U(VI) mit Chinizaringrün und seinem nichtsulfonierten Grundkörper

The reaction of 1,4-(2-sulpho-4-methylanilino)anthraquinone (quinizarin green,QG) and its non-sulphonated derivative (NSQG) with Ce(III), Th(IV), and U(VI) was investigated. Spectrophotometric and conductometric studies were carried out to investigate the stoichiometry of the complexes formed. The studies revealed the formation of 11 and 12 (ML) complexes. The apparent stability constants of the different complexes were determined. The structure of the ligand in the solid chelates was studied by IR spectrophotometry which showed that the chelate formation takes place through the oxygen of the C=O group and the -imino nitrogen.

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Mit 6 Abbildungen     

New spectrophotometric method for the determination of trace amounts of palladium

Summary A simple, rapid, selective, and sensitive method for the spectrophotometric determination of palladium is developed based on the reaction of Pd(II) with 1-amino-4-hydroxyanthraquinone (AMHA). The reaction is carried out atpH 3.8 in 50% (v/v) ethanol-water medium. The molar absorptivity of the complexed ligand is 1.1 · 10⁴ l mol^–1 cm^–1 at 620 nm. Calibration plots are linear up to 17 µg Pd cm^–3. The optimum concentration range (Ringbom plot) is between 3–14.5 µg cm^–3. The spectral study of the reaction in solutions containing equimolar concentrations or an excess of one component, in thepH range 0.3–6.5, indicate the possible complex transitions that occur in solution. Complete graphical and logarithmic analysis of the absorbance-pH graphs was performed to demonstrate and characterize the complexation equilibria in solution. Under the optimum conditions, palladium can be determined as the noncharged complex Pd(AMHA)₂ in the presence of a large number of foreign ions. Interferences caused by zirconium(IV) could be masked with fluoride ions.

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Eine neue spektrophotometrische Methode für die Bestimmung von Palladium in Spuren

Zusammenfassung Eine einfache, schnelle und empfindliche Methode für die spektrophotometrische Bestimmung von Palladium wurde auf der Basis der Reaktion von Pd(II) mit 1-Amino-4-hydroxyanthrachinon (AMHA) entwickelt. Die Reaktion wird in 50% (v/v) Ethanol/Wasser beipH 3.8 ausgeführt. Die molare Absorption des komplexierten Liganden beträgt 1.1 · 10⁴ l mol^–1 cm^–1 bei 620 nm. Kalibrierungskurven verlaufen bis zu 17 µg Pd cm^–3 linear. Der optimale Konzentrationsbereich (Ringbom-Plot) liegt zwischen 3 und 14.5 µg cm^–3. Spektroskopische Untersuchungen der Reaktion in Lösungen, entweder mit equimolaren Konzentrationen oder mit einem Überschuß an einer Komponente impH-Bereich 0.3–6.5, lassen Rückschlüsse auf mögliche Komplex-Übergänge in Lösung zu. Es wurde eine vollständige graphische, logarithmische Analyse der Absorptions-pH-Graphen durchgeführt, um die Komplexgleichgewichte in Lösung aufzuklären und zu charakterisieren. Unter den Optimalbedingungen kann Palladium als nichtgeladener Komplex Pd(AMHA)₂ in Gegenwart einer großen Anzahl an Fremd-Ionen bestimmt werden. Schwierigkeiten mit Zirkonium(IV) konnte durch Maskierung mit Fluorid-Ionen umgangen werden.

     

Gas phase interaction of L‐proline with Be2+, Mg2+ and Ca2+ ions: a computational study

Geometry optimisation and metal ion affinities (MIAs) of the binding configurations of Be²⁺, Mg²⁺ and Ca²⁺ to L ‐proline were calculated using the hybrid Density Functional Theory (DFT‐B3LYP) and second order Møllet?Plesset perturbation theory (MP2) methods. Be²⁺ was found to bind preferentially in a charge transfer type arrangement through the carbonyl oxygen (? C?O) and the lone pair of the imino‐group nitrogen atom (? NH? ). On the contrary Mg²⁺ and Ca²⁺ were found to prefer binding in a bi‐dentate manner through the carboxylate group of L ‐proline (OCO) in a zwitterion form. The main types of interactions found to influence the binding preference of M²⁺ ions to L ‐proline were (i) charge transfer in the case of Be²⁺ ions and (ii) electrostatic interactions in the case of Mg²⁺ and Ca²⁺ ions. Inspection of the IR stretching of the N? H and the O? H groups of L ‐proline with M²⁺ ions in a chelating configuration (to both O and N atoms) indicated a considerable shift to higher frequency with decreasing MIA. On the other hand, the MIA for the zwitterion L ‐proline with M²⁺ tracks the reciprocal distance of the M²⁺? OCO bond further confirming that the nature of the bond is mainly electrostatic. Comparison with other molecules containing the carboxylic function is also included in order to gain more insight on the types of interaction of this amino acid with metal ions in general. Copyright © 2007 John Wiley & Sons, Ltd.     

DFT study of carbon monoxide adsorption on α-Al2O3(0001)

The adsorption of CO on α-Al₂O₃(0001) was studied using the DFT-GGA computational method and on α-Al₂O₃ powder experimentally by Infra red spectroscopy. The core and valence level regions of α-Al₂O₃(0001) single crystal surface were also studied experimentally. Ar ions sputtering of the surface results in a slight but reproducible decrease in the XPS O2p lines in the valence band regions due to preferential removal of surface (and near surface) O atoms. Core level XPS O1s and Al2p further confirmed oxygen depletion with an associated surface stoichiometry close to Al₂O_2.9. The adsorption energy of CO was computed and found equal to 0.52 eV for θ = 0.25, it decreased to 0.42 eV at θ = 1. The IR frequency of νCO was also computed and in all cases it was blue shifted with respect to gas phase CO. The shift, Δν, decreased with increasing coverage where it was found equal to 56 cm^? 1 for θ = 0.25 and decreased to 30 cm^? 1 for θ = 1. Structural analyses indicated that the change in the adsorption energy and the associated frequency shift is due to surface relaxation upon adsorption. Experimentally the adsorption of CO gave rise to one main IR peak at 2154 cm^? 1 at 0.3 Torr and above. Two far smaller peaks are also seen at lower pressures of 0.03–0.2 Torr at 2189 and 2178 cm^? 1. The isosteric heat of adsorption was computed for the IR band at 2154 cm^? 1 and was found equal to 0.2 eV which did not change with coverage in the investigated range up to θ = 0.6.     

Ethanol photo-oxidation on a rutile TiO2(110) single crystal surface

The reaction of ethanol has been studied on the surface of rutile TiO(2)(110) by Temperature Programmed Desorption (TPD), online mass spectrometry under UV excitation and photoelectron spectroscopy while the adsorption energies of the molecular and dissociative modes of ethanol were computed using the DFT/GGA method. The most stable configuration is the dissociative adsorption in line with experimental results at room temperature. At 0.5 ML coverage the adsorption energy was found equal to 80 kJ mol(-1) for the dissociative mode (ethoxide, CH(3)CH(2)O(a) + H(a)) followed by the molecular mode (67 kJ mol(-1)). The orientation of the ethoxides along the [001] or [110] direction had minor effect on the adsorption energy although affected differently the Ti and O surface atomic positions. TPD after ethanol adsorption at 300 K indicated two main reactions: dehydration to ethylene and dehydrogenation to acetaldehyde. Pre-dosing the surface with ethanol at 300 K followed by exposure to UV resulted in the formation of acetaldehyde and hydrogen. The amount of acetaldehyde could be directly linked to the presence of gas phase O(2) in the vacuum chamber. The order of this photo-catalytic reaction with respect to O(2) was found to be 0.5. Part of acetaldehyde further reacted with O(2) under UV excitation to give surface acetate species. Because the rate of photo-oxidation of acetates (acetic acid) was slower than that of ethoxides (ethanol), the surface ended up by being covered with large amounts of acetates. A reaction mechanism for acetaldehyde, hydrogen and acetate formation under UV excitation is proposed.     

Novel Supramolecular Hydrogels as Artificial Vitreous Substitutes

The possibility of employing self-healing gels as potential artificial vitreous substitutes is being explored. Advancement of traditional synthetic hydrogels as vitreous substitutes is hindered by their fragmentation upon injection into the vitreous cavity leading ultimately to inflammation. Preliminary work involved developing first generation self-healing gels, using amphiphilic tri-block copolymers of poly(propylene glycol)-block-poly(ethylene glycol)-block-poly(propylene glycol) (PPG-PEG-PPG) as the building block. Eight linear self-healing gels are synthesized by tethering an ureidopyrimidinone system to synthetically modified PPG-PEG-PPG via the formation of a bis-urea as a linker. The reversible nature of the hydrogen bonds permits alteration of their physical properties by changing the environment, yet retaining desirable characteristics. Despite low solubility in water, these polymers demonstrated associating behaviour under the investigated conditions, which is encouraging. Future generations of self-healing gels should involve the selection of a more hydrophilic core and/or star-like polymers to facilitate gel formation and strengthen the network.