Organische, mit Wasser nicht mischbare L?sungsmittel in der Flammenphotometrie

Zusammenfassung Es wurde der Einfluß des Lösungsmittels auf die Empfindlichkeit der flammenphotometrischen Kupferbestimmung bei 40 verschiedenen organischen Lösungsmitteln, in denen innerkomplexe Verbindungen des Kupfers mit organischen Verbindungen gelöst waren, untersucht. Aliphatische Ester und Ketone, sowie Phenylmethyläther, Benzol, Toluol und Xylol erwiesen sich als besonders geeignet. Bei der angewandten Versuchsanordnung ließ sich die Empfindlichkeit der Bestimmung hierdurch auf etwa das 40 fache derjenigen steigern, wie man sie beim Versprühen rein wäßriger Kupferlösungen erreicht.Unsere Arbeit wurde durch Gaben der Deutschen Forschungsgemeinschaft und des Verbandes der Chemischen Industrie — Fonds der Chemie — gefördert, wofür auch an dieser Stelle gedankt sei.     

Reversible bond formation in a gold-atom-organic-molecule complex as a molecular switch

We report on the formation of a metal-molecule complex that can be used as a molecular switch. Using a cryogenic scanning tunneling microscope, a covalent bond was formed reversibly between a gold atom and a perylene-3,4,9,10-tetracarboxylic dianhydride molecule supported by a thin insulating film. The bonded and the nonbonded state of the complex were found to be associated with different charge states, and the switching between the two states was accompanied by a considerable change in the tunneling current. Atomic force microscopy molecular imaging was employed to determine precisely the atomic structure of the complex, and the experimental results were corroborated by density functional theory calculations.     

Radical ions of alpha,alpha'-bis(diphenylamino)-capped oligothiophenes: a combined spectroelectrochemical and theoretical study

A new homologous series of alpha,alpha'-bis(diphenylamino)-capped oligothiophenes, prepared by a palladium-catalyzed coupling reaction of stannylated 2-diphenylaminothiophenes with 2-mono- or 2,5-dibromothiophenes and their homologues, was studied by in situ ESR/UV-vis/NIR spectroelectrochemistry. In general, the oxidation potentials of these oligothiophenes were found to be proportional to the inverse number of thiophene units. However, the potential slope of the first oxidation is completely different from that of higher oxidation steps. Trication radicals were identified by electron spin resonance (ESR) for higher thiophene homologues in addition to monocation radicals (polarons). According to the ESR hyperfine structures, the unpaired electron is delocalized in the conjugated system. In contrast to the parent alpha,alpha'-bis(diphenylamino)-capped oligothiophenes, the UV-vis/NIR absorption maxima of the oxidized species strongly depend on the number of thiophene units. Spin-restricted and spin-unrestricted Kohn-Sham density functional calculations were used to explain and to understand these properties. Absorption wavelength and intensities were calculated by the time-dependent density functional response theory. Unrestricted density functional calculations of oligothiophene dications (bipolarons) with five or more thiophene rings result in spin-broken structures which may be considered as two-polaron biradicals (polaron pairs).     

Configurational-Force-Based Adaptive FE Solver for a Phase Field Model of Fracture

The computational modeling of failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies. This can be overcome by diffusive crack modeling, based on the introduction of a crack phase field as outlined in [1, 2]. Following these formulations, we outline a thermodynamically consistent framework for phase field models of crack propagation in elastic solids, develop incremental variational principles and, as an extension to [1, 2], consider their numerical implementations by an efficient h-adaptive finite element method. A key problem of the phase field formulation is the mesh density, which is required for the resolution of the diffusive crack patterns. To this end, we embed the computational framework into an adaptive mesh refinement strategy that resolves the fracture process zones. We construct a configurational-force-based framework for h-adaptive finite element discretizations of the gradient-type diffusive fracture model. We develop a staggered computational scheme for the solution of the coupled balances in physical and material space. The balance in the material space is then used to set up indicators for the quality of the finite element mesh and accounts for a subsequent h-type mesh refinement. The capability of the proposed method is demonstrated by means of a numerical example. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hofer geometry of a subset of a symplectic manifold

To every closed subset X of a symplectic manifold (M, ω) we associate a natural group of Hamiltonian diffeomorphisms Ham (X, ω). We equip this group with a semi-norm ${\Vert\cdot\Vert^{X, \omega}}$ , generalizing the Hofer norm. We discuss Ham (X, ω) and ${\Vert\cdot\Vert^{X, \omega}}$ if X is a symplectic or isotropic submanifold. The main result involves the relative Hofer diameter of X in M. Its first part states that for the unit sphere in ${\mathbb{R}^{2n}}$ this diameter is bounded below by ${\frac{\pi}{2}}$ , if n ≥ 2. Its second part states that for n ≥ 2 and d ≥ n there exists a compact subset X of the closed unit ball in ${\mathbb{R}^{2n}}$ , such that X has Hausdorff dimension at most d + 1 and relative Hofer diameter bounded below by π / k(n, d), where k(n, d) is an explicitly defined integer.     

Functional Additive Mixed Models

We propose an extensive framework for additive regression models for correlated functional responses, allowing for multiple partially nested or crossed functional random effects with flexible correlation structures for, for example, spatial, temporal, or longitudinal functional data. Additionally, our framework includes linear and nonlinear effects of functional and scalar covariates that may vary smoothly over the index of the functional response. It accommodates densely or sparsely observed functional responses and predictors which may be observed with additional error and includes both spline-based and functional principal component-based terms. Estimation and inference in this framework is based on standard additive mixed models, allowing us to take advantage of established methods and robust, flexible algorithms. We provide easy-to-use open source software in the pffr() function for the R package refund. Simulations show that the proposed method recovers relevant effects reliably, handles small sample sizes well, and also scales to larger datasets. Applications with spatially and longitudinally observed functional data demonstrate the flexibility in modeling and interpretability of results of our approach.