A new level‐dependent coarse grid correction scheme for indefinite Helmholtz problems

In this paper, we construct and analyze a level‐dependent coarse grid correction scheme for indefinite Helmholtz problems. This adapted multigrid (MG) method is capable of solving the Helmholtz equation on the finest grid using a series of MG cycles with a grid‐dependent complex shift, leading to a stable correction scheme on all levels. It is rigorously shown that the adaptation of the complex shift throughout the MG cycle maintains the functionality of the two‐grid correction scheme, as no smooth modes are amplified in or added to the error. In addition, a sufficiently smoothing relaxation scheme should be applied to ensure damping of the oscillatory error components. Numerical experiments on various benchmark problems show the method to be competitive with or even outperform the current state‐of‐the‐art MG‐preconditioned Krylov methods, for example, complex shifted Laplacian preconditioned flexible GMRES. Copyright © 2013 John Wiley & Sons, Ltd.     

Brodie's or Hummers’ Method: Oxidation Conditions Determine the Structure of Graphene Oxide

Synthesis and studies of graphite oxide started more than 150 years ago and turned into a boom by the measurements of the outstanding physical properties of graphene. A series of preparation protocols emanated trying to optimize the synthesis of graphene oxide in order to obtain a less defective material, as source for graphene. However, over-oxidation of the carbon framework hampered establishing structure-property relationships. Here, the fact that two different synthetic methods for graphene oxide preparation lead to very similar types of graphene oxide with a preserved graphene lattice is demonstrated. Either sodium chlorate in nitric acid (similar to Brodie's method) or potassium permanganate in sulfuric acid (similar to Hummers’ method) treatment are possible; however, reaction conditions must be controlled. With a preserved carbon lattice analytical differences between the samples relate to the altered on-plane functionality. Consequently, terming preparation protocols “according to Brodie's/Hummers’ method” is not sufficient.     

Between Aromatic and Quinoid Structure: A Symmetrical UV to Vis/NIR Benzothiadiazole Redox Switch

Reversibly switching the light absorption of organic molecules by redox processes is of interest for applications in sensors, light harvesting, smart materials, and medical diagnostics. This work presents a symmetrical benzothiadiazole (BTD) derivative with a high fluorescence quantum yield in solution and in the crystalline state and shows by spectroelectrochemical analysis that reversible switching of UV absorption in the neutral state, to broadband Vis/NIR absorption in the 1st oxidized state, to sharp band Vis absorption in the 2nd oxidized state, is possible. For the one-electron oxidized species, formation of a delocalized radical is confirmed by electron paramagnetic resonance spectroelectrochemistry. Furthermore, our results reveal an increasing quinoidal distortion upon the 1st and 2nd oxidation, which can be used as the leitmotif for the development of BTD based redox switches.     

Probing the Structure of Lysozyme–Carbon‐Nanotube Hybrids with Molecular Dynamics

Lysozyme has been successfully used to solvate carbon nanotubes (CNT). Extensive molecular dynamics simulations show that 1) a favorite site of adsorption exists, 2) the protein–tube interaction region is located far from the active site, 3) two protein helices act as a tweezer that grips the nanotube, 4) a localized protein re‐arrangement hides the tube from the solvent, and 5) aminic and amidic moieties of lysozyme behave similarly to surfactants in the solvation of the tube.     

Phosphine and phosphinite complexes of P+ and P2

Abstract

Reduction of PCl₃ e.g. with trialkyl phosphines produces the well-known but ill-defined insoluble, amorphous, orange material approximating a phosphorus subchloride. In repeating this reduction with Ph₃P and with AlCl₃ as a third component we now obtained crystalline hexaphenyl triphosphenium tetrachloroaluminate. It may be thought to derive from the four electron cation P⁺ being complexed by two Ph₃P.