Beer's Law-Why Integrated Absorbance Depends Linearly on Concentration

As derived by Max Planck in 1903 from dispersion theory, Beer's law has a fundamental limitation. The concentration dependence of absorbance can deviate from linearity, even in the absence of any interactions or instrumental nonlinearities. Integrated absorbance, not peak absorbance, depends linearly on concentration. The numerical integration of the absorbance leads to maximum deviations from linearity of less than 0.1 %. This deviation is a consequence of a sum rule that was derived from the Kramers-Kronig relations at a time when the fundamental limitation of Beer's law was no longer mentioned in the literature. This sum rule also links concentration to (classical) oscillator strengths and thereby enables the use of dispersion analysis to determine the concentration directly from transmittance and reflectance measurements. Thus, concentration analysis of complex samples, such as layered and/or anisotropic materials, in which Beer's law cannot be applied, can be achieved using dispersion analysis.     

SAMBADENA Hyperpolarization of 13C-Succinate in an MRI: Singlet-Triplet Mixing Causes Polarization Loss

The signal enhancement provided by the hyperpolarization of nuclear spins of biological molecules is a highly promising technique for diagnostic imaging. To date, most ¹³C-contrast agents had to be polarized in an extra, complex or cost intensive polarizer. Recently, the in situ hyperpolarization of a ¹³C contrast agent to >20 % was demonstrated without a polarizer but within the bore of an MRI system. This approach addresses some of the challenges of MRI with hyperpolarized tracers, i. e. elevated cost, long production times, and loss of polarization during transfer to the detection site. Here, we demonstrate the first hyperpolarization of a biomolecule in aqueous solution in the bore of an MRI at field strength of 7 T within seconds. The ¹³C nucleus of 1-¹³C, 2,3-²H₂-succinate was polarized to 11 % corresponding to a signal enhancement of approximately 18.000. Interesting effects during the process of the hydrogenation reaction which lead to a significant loss of polarization have been observed.     

Simulation einer Fabrik für synthetischen Gummi — eine Fallstudie

Zusammenfassung Die Fallstudie behandelt das Problem der Dimensionierung der verschiedenen Teile einer sehr komplexen Anlage für mehrstufige Produktion. Die Programmierung erfolgte in FORTRAN. Anhand der Fallstudie werden einige wesentliche Punkte herausgearbeitet, die für den Erfolg von Simulationsprojekten wesentlich sind, nämlich: klare Zielsetzung, Simulation von Teilbereichen, so daß in kürzester Zeit Resultate vorliegen.

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Summary The case-study deals with the problem of the size of various parts of a very complex plant lay-out for multi-step production. The programming was done in FORTAN. Based on the case-study a few points were worked out which are essential for the success of simulation-projects, to wit: clear statement of purpose; simulation of partial scopes, which produce short-term results.

     

Inequalities for absolute maxima of a polynomial and its derivative

Suppose z ₁, z ₂, ... z _n are complex numbers with absolute values more than 1 and Arg z _j Arg z _k for j k where Arg w stands for the argument of the complex number w in [0,2). In this note we show that

Infrared micro-particle image velocimetry in silicon-based microdevices

A non-intrusive diagnostic technique, infrared micro-particle image velocimetry (IR-PIV), is developed for measuring flow fields within micro-electromechanical system (MEMS) devices with micron-scale resolution. This technique capitalizes on the transparency of silicon in the infrared region, and overcomes the limitation posed by the lack of optical access with visible light to sub-surface flow in silicon-based microstructures. Experiments with laminar flow of water in a circular microcapillary tube of hydraulic diameter 255 m demonstrate the efficacy of this technique. The experimental measurements agree very well with velocity profiles predicted from laminar theory. Cross-correlation and auto-correlation algorithms are employed to measure very low and moderate to high velocities, respectively; the former approach is suitable for biomedical applications while the latter would be needed for measurements in electronics cooling. The results indicate that the IR-PIV technique effectively extends the application of regular micro-PIV techniques, and has great potential for flow measurements in silicon-based microdevices.     

Visualization of convection patterns near an evaporating meniscus using μPIV

Experimental visualizations of the three dimensional (3D) convection patterns generated near an evaporating meniscus in horizontally oriented capillary tubes are presented. These patterns are caused due to the differential evaporation along the meniscus. In this study, transparent capillary tubes with refractive index close to that of the evaporating liquid were used to minimize refraction effects and obtain velocity vectors near the walls. Polystyrene fluorescent particles of 0.5 μm diameter suspended in methanol were used to make the measurements in tubes of 75, 200 and 400 μm diameter. For the 75 μm tube, gravity was observed to have no effect on the flow patterns and an axisymmetric counter-rotating vortex pair was present along the horizontal and vertical center planes, suggesting the presence of a toroidal vortex near the meniscus. With an increase in tube size, buoyancy effects became apparent as the axisymmetric pattern broke down. A counter-rotating symmetric vortex pair was observed in the horizontal center plane, whereas in the vertical center plane, a single vortex dominated the flow and pushed the secondary vortex to a corner. Particle streak and μPIV images were obtained in multiple horizontal planes and a vertical center plane to understand this 3D flow behavior.     

Dehydropolymerisation of Methylamine Borane and an N-Substituted Primary Amine Borane Using a PNP Fe Catalyst

Dehydropolymerisation of methylamine borane (H₃B⋅NMeH₂) using the well-known iron amido complex [(PNP)Fe(H)(CO)] (PNP=N(CH₂CH₂PiPr₂)₂) ( 1 ) gives poly(aminoborane)s by a chain-growth mechanism. In toluene, rapid dehydrogenation of H₃B⋅NMeH₂ following first-order behaviour as a limiting case of a more general underlying Michaelis–Menten kinetics is observed, forming aminoborane H₂B=NMeH, which selectively couples to give high-molecular-weight poly(aminoborane)s (H₂BNMeH)_n and only traces of borazine (HBNMe)₃ by depolymerisation after full conversion. Based on a series of comparative experiments using structurally related Fe catalysts and dimethylamine borane (H₃B⋅NMe₂H) polymer formation is proposed to occur by nucleophilic chain growth as reported earlier computationally and experimentally. A silyl functionalised primary borane H₃B⋅N(CH₂SiMe₃)H₂ was studied in homo- and co-dehydropolymerisation reactions to give the first examples for Si containing poly(aminoborane)s.     

New Ionic Liquid Compounds Based on Tantalum Pentachloride TaCl5: Synthesis,Structural, and Spectroscopic Elucidation of the (μ‐Oxido)‐Chloridotantalates(V) [BMPy][TaCl6], [BMPy]4[(TaCl6)2(Ta2OCl10)], and [EMIm]2[Ta2OCl10]

1‐Butyl‐4‐methylpyridinium hexachloridotantalate(V), [BMPy][TaCl₆] ( 1 ), tetrakis(1‐butyl‐4‐methylpyridinium) bis(hexachloridotantalate(V) (μ‐oxido)‐decachloridotantalate(V), [BMPy]₄[(TaCl₆)₂(Ta₂OCl₁₀)] ( 2 ), and bis(1‐ethyl‐3‐methylimidazolium)‐(μ‐oxido)‐decachloridoditantalate(V), [EMIm]₂[Ta₂OCl₁₀] ( 3 ) were synthesized and characterized by single‐crystal X‐ray diffraction and vibrational spectroscopy. Compounds 1 and 3 crystallize in the monoclinic space group P2₁/c (no. 14), whereas compound 2 crystallizes in the triclinic space group P (no. 2). All compounds are built up by the mentioned bulky organic cations and octahedral [TaCl₆]^– respective linear [Ta₂OCl₁₀]^2– anions. Coulomb interactions are dominant between the ionic species. FT‐IR and FT‐Raman spectra were recorded and interpreted, especially with respect to the inorganic species [TaCl₆]^– (O_h) and [Ta₂OCl₁₀]^2– (C_i symmetry, approximately D_4h). The melting temperatures of compounds 1 – 3 are given.     

The Combination of 4‐Hydroxythiazoles with Azaheterocycles: Efficient Bidentate Ligands for Novel Ruthenium Complexes

Herein the syntheses of three novel ligands, in which an azaheterocycle is connected with a thiazole subunit: 4‐methoxy‐5‐methyl‐2‐pyridine‐2‐yl‐1,3‐thiazole ( 1 ), 4‐methoxy‐5‐methyl‐2‐pyrimidine‐2‐yl‐1,3‐thiazole ( 2 ) and 4‐methoxy‐5‐phenyl‐2‐pyridine‐2‐yl‐1,3‐thiazole ( 3 ) are reported. Because these ligands are cyclic versions of 1,4‐diazadienes, they offer good prerequisites for the synthesis of metal complexes and were employed as chelating ligands. Three novel heteroleptic cationic complexes of the type Ru(bpy)₂( L ), with bpy = 2,2′‐bipyridine were successfully synthesised. The Ru^II complexes as well as the ligands were characterised by means of mass spectrometry, NMR, UV/Vis and IR spectroscopy and elemental analysis. Furthermore, an X‐ray structure of Ru(bpy)₂ 2 (PF₆), as far as we know the first example where a thiazole is directly connected to a Ru^II core, is presented in this paper.