2-manifolds of constant curvature, 3-parameter isometry groups and bäcklund transformations

The relationship between the Sine Gordon equation and Riemannian 2-manifolds of constant negative curvature is well known. We point out that it gives rise (locally) to a transitive action of the 3-parameter group SL(2,R) on the manifold. This enables us to elucidate group theoretically the geometry underlying the Bäcklund transformation. The transformation arises by passing from the 2-manifold, a homogeneous space, to 2-submanifolds of SL(2,R) defined by orbits of the solvable subgroup of SL(2,R). A similar approach allows us several other such transformations, for example, transformations linking φ_xx+φ_yy = sinhφ to φ_xx+φ_yy = sinφ and φ_xx+φ_yy = e^2φ to φ_xx+φ_yy = 0.     

The mass enhancement and the specific heat of disordered and amorphous metals

The reduction of the mean free path in metals causes a change of the electronphonon interaction and the Eliashberg function α²(Ω)F(Ω). The values of α²(Ω)F(Ω) for pure, disordered and amorphous lead are used to calculate the enhancement of the density of states and the electronic specific heat in these materials. In pure lead the cyclotron mass (1+λ) has a maximum at 11 °K and the Sommerfeld constant (γ) has a maximum at 5 °K. In disordered lead with a mean free path of about 70 Å, both, 1+λ and γ are almost constant in this temperature range. For amorphous lead there is no temperature range where 1+λ and γ are sufficiently constant. A measurement of the specific heat in disordered non-superconducting metals could answer the question whether these metals are closer to the superconducting state when their mean free path is reduced, a fact which is true for all weak-coupling superconductors.     

Enhanced self‐ordering of anodic ZrO2 nanotubes in inorganic and organic electrolytes using two‐step anodization

This work reports on the optimized growth of self‐ordered ZrO₂ nanotubes in inorganic water‐based and organic electrolyte systems containing small amounts of fluoride employing a two‐step anodization process. We show how surface pretreatments of the metallic Zr substrate can drastically improve the growth and morphology of the resulting anodic ZrO₂ nanotube arrays. Using two step anodization and employing organic electrolytes, highly regular and ordered nanotubular ZrO₂ oxide layers can be grown to significantly increased tube lengths compared with aqueous electrolytes. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Towards ideal hexagonal self‐ordering of TiO2 nanotubes

The present work reports on key factors that influence the degree of order in anodic TiO₂ nanotube layers. We show that the anodization voltage and the Ti purity are of crucial importance for the ideality of self‐organization within the nanotube layers and that repeated anodization can significantly improve hexagonal ordering. Optimizing each factor significantly reduces the variation in the average pore diameter and strongly reduces the areal density of polygon ordering/packing errors. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Concepts for chemical state analysis at constant probing depth by lab-based XPS/HAXPES combining soft and hard X-ray sources

The greater information depth provided in hard X-ray photoelectron spectroscopy (HAXPES) enables nondestructive analyses of the chemistry and electronic structure of buried interfaces. Moreover, for industrially relevant elements like Al, Si, and Ti, the combined access to the Al 1s, Si 1s, or Ti 1s photoelectron line and its associated Al KLL, Si KLL, or Ti KLL Auger transition, as required for local chemical state analysis on the basis of the Auger parameter, is only possible with hard X-rays. Until now, such photoemission studies were only possible at synchrotron facilities. Recently, however, the first commercial XPS/HAXPES systems, equipped with both soft and hard X-ray sources, have entered the market, providing unique opportunities for monitoring the local chemical state of all constituent ions in functional oxides at different probing depths, in a routine laboratory environment. Bulk-sensitive shallow core levels can be excited using either the hard or soft X-ray source, whereas more surface-sensitive deep core-level photoelectron lines and associated Auger transitions can be measured using the hard X-ray source. As demonstrated for thin Al₂O₃, SiO₂, and TiO₂ films, the local chemical state of the constituting ions in the oxide may even be probed at near-constant probing depth by careful selection of sets of photoelectron and Auger lines, as excited with the combined soft and hard X-ray sources. We highlight the potential of lab-based HAXPES for the research on functional oxides and also discuss relevant technical details regarding the calibration of the kinetic binding energy scale.     

Exploring the Subtle Effect of Aliphatic Ring Size on Minor Actinide-Extraction Properties and Metal Ion Speciation in Bis-1,2,4-Triazine Ligands

The synthesis and evaluation of three novel bis-1,2,4-triazine ligands containing five-membered aliphatic rings are reported. Compared to the more hydrophobic ligands 1 – 3 containing six-membered aliphatic rings, the distribution ratios for relevant f-block metal ions were approximately one order of magnitude lower in each case. Ligand 10 showed an efficient, selective and rapid separation of Am^III and Cm^III from nitric acid. The speciation of the ligands with trivalent f-block metal ions was probed using NMR titrations and competition experiments, time-resolved laser fluorescence spectroscopy and X-ray crystallography. While the tetradentate ligands 8 and 10 formed Ln^III complexes of the same stoichiometry as their more hydrophobic analogues 2 and 3 , significant differences in speciation were observed between the two classes of ligand, with a lower percentage of the extracted 1:2 complexes being formed for ligands 8 and 10 . The structures of the solid state 1:1 and 1:2 complexes formed by 8 and 10 with Y^III, Lu^III and Pr^III are very similar to those formed by 2 and 3 with Ln^III. Ligand 10 forms Cm^III and Eu^III 1:2 complexes that are thermodynamically less stable than those formed by ligand 3 , suggesting that less hydrophobic ligands form less stable An^III complexes. Thus, it has been shown for the first time how tuning the cyclic aliphatic part of these ligands leads to subtle changes in their metal ion speciation, complex stability and metal extraction affinity.     

The challenge of breath analysis for clinical diagnosis and therapeutic monitoring

The potential of breath analysis for clinical diagnosis and the strengths and weaknesses of the analytical methods used are discussed. Special attention is given to selected ion flow tube mass spectrometry, SIFT-MS, using which on-line real-time analyses of single breath exhalations can be carried out. Illustrative data on the concentration distributions of several breath metabolites amongst the healthy population are presented and their relations to disease when elevated above the normal are alluded to.     

Micellar induced regioselectivity in the two-step consecutive reaction of SO3(2-) with Br-(CH2CH2)n-Br (n=2-5)

High field (800 MHz) (1)H NMR was used to monitor the two-step consecutive reaction of excess SO(3)(2-) with symmetrical bifunctional alpha,omega-dibromoalkanes with butane (DBB), hexane (DBH), octane (DBO), and decane (DBD) chains in CTAB micelles at 25 degrees C. The first-order rate constant for the first substitution step for DBB and DBH is about 5 times faster than for the second, but the kinetics for DBO and DBD were not cleanly first-order. After 40 min, the solution contained about 80% of the intermediate bromoalkanesulfonate from DBB and DBH and the remainder is alkanedisulfonate and unreacted starting material. The same reactions were carried out in homogeneous MeOH/D(2)O solutions at 50 degrees C. The rate constants for all four alpha,omega-dibromoalkanes were first-order throughout the time course of the reaction and the same within +/-10%. However, because micellar solutions are organized on the nanoscale and bring together lipophilic and hydrophilic reactants into a small reaction volume at the micellar interface, they speed this substitution reaction considerably compared to reaction in MeOH/D(2)O. The CTAB micelles also induce a significant regioselectivity in product formation by speeding the first step of the consecutive reaction more than the second. The results are consistent with the bromoalkanesulfonate intermediates having a radial orientation within the micelles with the -CH(2)SO(3)(-) group in the interfacial region and the -CH(2)Br group directed into the micellar core such that the concentration of -CH(2)Br groups in the reactive zone, i.e., the micellar interface, is significantly reduced. These results provide the first example of self-assembled surfactant system altering the relative rates of the reaction steps of a consecutive reaction and, in doing so, enhancing monosubstitution of a symmetrically disubstituted species.     

An objective comparison of pre-processing methods for enhancement of liquid chromatography-mass spectrometry data

Four data pre-processing methods have been applied with different settings to data sets obtained from the analysis of a pharmaceutical drug and its degradation products by liquid chromatography-mass spectrometry (LC-MS). The methods compared were the frequently used component detection algorithm (CODA) and three kinds of digital filters--matched filtration (MF), Gaussian second derivative (GSD) and Savitzky-Golay. The aim was to evaluate the performance and robustness of these methods for extracted ion chromatogram (XIC), total ion chromatogram (TIC) and base peak chromatogram (BPC) in the presence of different types of noise. In accordance with theory, the best improvements in signal-to-noise ratio (S/N) of the XICs were obtained with MF under the ideal case with random white noise. However, when highly coloured noise was present, it was found that no improvements in XIC S/N could be obtained with any of the pre-processing methods studied. GSD and CODA did, however, improve the S/N for both TIC and BPC. GSD and CODA also significantly reduced the background in the spectral domain, thereby facilitating the interpretation of the mass spectra. Another advantage associated with CODA and to some extent also with GSD is their data reduction ability.