Copper‐Free Sonogashira Coupling for High‐Surface‐Area Conjugated Microporous Poly(aryleneethynylene) Networks

A modified one‐pot Sonogashira cross‐coupling reaction based on a copper‐free methodology has been applied for the synthesis of conjugated microporous poly(aryleneethynylene) networks (CMPs) from readily available iodoarylenes and 1,3,5‐triethynylbenzene. The polymerization reactions were carried out by using equimolar amounts of halogen and terminal alkyne moieties with extremely small loadings of palladium catalyst as low as 0.65 mol %. For the first time, CMPs with rigorously controlled structures were obtained without any indications of side reactions, as proven by FTIR and solid‐state NMR spectroscopy, while showing Brunauer–Emmett–Teller (BET) surface areas higher than any poly(aryleneethynylene) network reported before, reaching up to 2552 m² g^?1.     

Bounds on the Non-real Spectrum of a Singular Indefinite Sturm-Liouville Operator on ℝ

A simple explicit bound on the absolute values of the non-real eigenvalues of a singular indefinite Sturm-Liouville operator on the real line with the weight function sgn(·) and an integrable, continuous potential q is obtained. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A new method for network redesign via rank one updates

We present a method to place the eigenvalues of an electrical network towards a prescribed set of complex numbers by inserting an additional capacitance into the network. For the proof, we use recent results on rank one perturbations of regular matrix pencils. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A new bound for the distance to singularity of a regular matrix pencil

For regular matrix pencils 𝒜(s) = sE − A the distance to the nearest singular pencil in the Frobenius norm of the coefficients is called the distance to singularity. We derive a new lower bound for this distance by using the spectral theory of tridiagonal Toeplitz matrices. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On a Class of Analytic Operator Functions and Their Linearizations

We consider an operator function T in a Krein space which can formally be written as (0.1)but the last term on the right of (0.1) is replaced by a relatively form‐compact perturbation of a similar form. We study relations between the operator function T, a selfadjoint operator M in some Krein space, associated with T, and an operator which can be constructed with the help of the operator function –T^–1. The results are applied to a Sturm‐Liouville problem with a coefficient depending rationally on the eigenvalue parameter.     

Applications of the optical trapping technique to analyze chemical reactions in single emulsion particles

The applicability of the single beam gradient force optical trap and the optical levitation technique to investigate dynamic processes in microparticles is examined. The device allows to follow chemical reactions, like the emulsion polymerization and the ester hydrolysis reaction, in single emulsion droplets. Furthermore the usability of optical traps to investigate living cells is demonstrated.     

Quantifying DNA damage by gel electrophoresis, electronic imaging and number-average length analysis

DNA damages that can be converted to single- or double strand breaks can be quantified by separating DNA by gel electrophoresis and obtaining a quantitative image of the resulting distribution of DNA in the gel. We review the theory of this method and discuss its implementation, including the charge-coupled device (CCD) camera systems we developed to acquire images of fluorophore labeled DNA.     

Chemistry and Structures of Hexakis(halogenomethyl)‐, Hexakis(azidomethyl)‐, and Hexakis(nitratomethyl)disiloxanes

An investigation of the structures and chemistry of substituted hexamethyl disiloxanes ((XCH₂)₃Si)₂O; X=F, Cl, Br, I, N₃, and ONO₂) is reported. New synthetic routes to the precursor hexakis(chloromethyl)disiloxane are presented. The products with X=Cl, Br, I, and N₃ were characterized by NMR, IR, and Raman spectroscopy. In addition, the single‐crystal structures of the products with X=Cl, Br, and I are discussed in detail. The compounds with X=F and ONO₂ were not obtained in their pure form; instead investigations of the decomposition products revealed their conversion into intermediates. Theoretical calculations of the gas‐phase structures at the B3LYP/cc‐pVDZ, B3LYP/3‐21G, MP2/6‐31G*, and MP2/3‐21G levels of theory are used to explain the chemical and physical behavior of the compounds with X=Cl, Br, I, N₃, and ONO₂. A new decomposition pathway of hexakis(nitratomethyl)disiloxane is presented and is used to explain their remarkable instability. The energetic properties and values of the nitrate and azide derivatives were calculated at the CBS‐4M level of theory by using the improved EXPLO5 computer code version 6.01.