Cyclodimers and Cyclotrimers of 2,3 -Bisalkynylated Anthracenes,Phenazines and Diazatetracenes

The synthesis of novel (N−)acene-based cyclooligomers is reported. Glaser-Hay coupling of the bisethynylated monomers results in cyclodimers and cyclotrimers that are separable by column and gel-permeation chromatographies. For the diazatetracene, the use of sec-butyl-silylethynyl groups is necessary to achieve solubility. Diazatetracene-based cyclodimers and cyclotrimers were used as semiconductors in thin-film transistors. Although their optoelectronic properties are quite similar, their electron mobilities in proof-of-concept thin-film transistors differ by an order of magnitude.     

ℋ︁‐LU factorization in preconditioners for augmented Lagrangian and grad‐div stabilized saddle point systems

The (mixed finite element) discretization of the linearized Navier–Stokes equations leads to a linear system of equations of saddle point type. The iterative solution of this linear system requires the construction of suitable preconditioners, especially in the case of high Reynolds numbers. In the past, a stabilizing approach has been suggested which does not change the exact solution but influences the accuracy of the discrete solution as well as the effectiveness of iterative solvers. This stabilization technique can be performed on the continuous side before the discretization, where it is known as ‘grad‐div’ (GD) stabilization, as well as on the discrete side where it is known as an ‘augmented Lagrangian’ (AL) technique (and does not change the discrete solution). In this paper, we study the applicability of ??‐LU factorizations to solve the arising subproblems in the different variants of stabilized saddle point systems. We consider both the saddle point systems that arise from the stabilization in the continuous as well as on the discrete setting. Recently, a modified AL preconditioner has been proposed for the system resulting from the discrete stabilization. We provide a straightforward generalization of this approach to the GD stabilization. We conclude the paper with numerical tests for a variety of problems to illustrate the behavior of the considered preconditioners as well as the suitability of ??‐LU factorization in the preconditioners. Copyright © 2010 John Wiley & Sons, Ltd.     

Convergence of non-periodic infinite products of orthogonal projections and nonexpansive operators in Hilbert space

We provide sufficient conditions for strong and uniform (on bounded subsets of initial points) convergence of infinite products of orthogonal projections and other (possibly nonlinear) nonexpansive operators in a Hilbert space. Our main tools are new estimates of the inclination of a finite tuple of closed linear subspaces.     

Light‐Driven Coordination‐Induced Spin‐State Switching: Rational Design of Photodissociable Ligands

The bistability of spin states (e.g., spin crossover) in bulk materials is well investigated and understood. We recently extended spin‐state switching to isolated molecules at room temperature (light‐driven coordination‐induced spin‐state switching, or LD‐CISSS). Whereas bistability and hysteresis in conventional spin‐crossover materials are caused by cooperative effects in the crystal lattice, spin switching in LD‐CISSS is achieved by reversibly changing the coordination number of a metal complex by means of a photochromic ligand that binds in one configuration but dissociates in the other form. We present mathematical proof that the maximum efficiency in property switching by such a photodissociable ligand (PDL) is only dependent on the ratio of the association constants of both configurations. Rational design by using DFT calculations was applied to develop a photoswitchable ligand with a high switching efficiency. The starting point was a nickel–porphyrin as the transition‐metal complex and 3‐phenylazopyridine as the photodissociable ligand. Calculations and experiments were performed in two iterative steps to find a substitution pattern at the phenylazopyridine ligand that provided optimum performance. Following this strategy, we synthesized an improved photodissociable ligand that binds to the Ni–porphyrin with an association constant that is 5.36 times higher in its trans form than in the cis form. The switching efficiency between the diamagnetic and paramagnetic state is efficient as well (72 % paramagnetic Ni–porphyrin after irradiation at 365 nm, 32 % paramagnetic species after irradiation at 440 nm). Potential applications arise from the fact that the LD‐CISSS approach for the first time allows reversible switching of the magnetic susceptibility of a homogeneous solution. Photoswitchable contrast agents for magnetic resonance imaging and light‐controlled magnetic levitation are conceivable applications.