A numerical study of the assumptions underlying the calculation of the stationary zone mass transfer coefficient in the general plate height model of chromatography in two-dimensional pillar arrays

The present study investigates the validity of one of the key assumptions underlying the general plate height model of chromatography, i.e., the presumed independency of the individual band broadening contributions. More precisely, it is investigated under which conditions the mass transfer inside the stationary zone (e.g., porous pillars) is independent from the axial transport of species outside this zone, and how strongly any such dependency would affect the validity of the general plate height model of chromatography. For this purpose, detailed calculations of the species concentration distribution inside and outside the porous pillars of a computer-mimic of a porous pillar array column have been made. These simulations revealed a clear interplay between the mass transfer inside and outside the pillars, manifesting itself as an asymmetry of the species concentration distribution inside the pillars. The latter is in disagreement with the basic assumption used to calculate the value of the C_s-term of the general plate height model. The asymmetry-effect is largest at low reduced velocities, high retention factors and high intra-pillar diffusion coefficients. Fortunately, these are conditions where the C_s-term is relatively small, which might explain why the general plate height model of chromatography (and based on the symmetry assumption) can represent the band broadening in a porous pillar array within an accuracy on the order of some 1–2%.     

The Bernoulli boundary condition for traveling water waves

The Bernoulli boundary condition for traveling water waves is obtained from Euler’s equation for inviscid flow by employing two key reductions: (i) the traveling wave assumption, (ii) the introduction of a velocity potential. Depending on the order of these reductions, the Bernoulli boundary condition may or may not contain an arbitrary constant. This note shows the equivalence of the two formulations. Further, we arrive at a physical interpretation for the Bernoulli constant, namely, that it is associated with an average current. Last, we show that the Bernoulli constant and the average current cannot simultaneously be zero for non-trivial traveling waves.     

Synthesis and Structure of the Cerium Schiff‐Base Complexes [Ce(Salen′)2] and [(THF)2KCe(Salen′)2]

The synthesis of [Ce(Salen′)₂] ( 1 ) (H₂Salen′ = N,N′‐bis(3,5‐di‐tert‐butylsalicylidene)ethylenediamine) was performed using two different approaches. CeCl₃ reacts with two equivalents of K₂Salen′ in THF under the formation of [(THF)₂KCe(Salen′)₂] ( 2 ). Complex 2 could be converted to the Ce^IV complex 1 via oxidation with p‐benzoquinone and air, respectively. The reversible reduction process was realized using elemental potassium in boiling THF. Furthermore, the reaction of the Ce^IV starting material [(^tBuO)₄Ce(THF)₂] with the “free” ligand H₂Salen′ in boiling toluene lead in the formation of 1 as well.     

Short-wave transverse instabilities of line solitons of the two-dimensional hyperbolic nonlinear Schrödinger equation

We prove that line solitons of the two-dimensional hyperbolic nonlinear Schrödinger equation are unstable under transverse perturbations of arbitrarily small periods, i.e., short waves. The analysis is based on the construction of Jost functions for the continuous spectrum of Schrödinger operators, the Sommerfeld radiation conditions, and the Lyapunov-Schmidt decomposition. We derive precise asymptotic expressions for the instability growth rate in the limit of short periods.     

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Substitutional phosphorus incorporation in nanocrystalline CVD diamond thin films

Nanocrystalline diamond (NCD) thin films were produced by chemical vapor deposition (CVD) and doped by the addition of phosphine to the gas mixture. The characterization of the films focused on probing the incorporation and distribution of the phosphorus (P) dopants. Electron microscopy evaluated the overall film morphology and revealed the interior structure of the nanosized grains. The homogeneous films with distinct diamond grains featured a notably low sp²:sp³‐ratio as confirmed by Raman spectroscopy. High resolution spectroscopy methods demonstrated a homogeneous P‐incorporation, both in‐depth and in‐plane. The P concentration in the films was determined to be in the order of 10¹⁹ cm^–3 with a significant fraction integrated at substitutional donor sites. (© 2014 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Real Lax spectrum implies spectral stability

We consider the dynamical stability of periodic and quasiperiodic stationary solutions of integrable equations with 2 2 Lax pairs. We construct the eigenfunctions and hence the Floquet discriminant for such Lax pairs. The boundedness of the eigenfunctions determines the Lax spectrum. We use the squared eigenfunction connection between the Lax spectrum and the stability spectrum to show that the subset of the real line that gives rise to stable eigenvalues is contained in the Lax spectrum. For non-self-adjoint members of the AKNS hierarchy admitting a common reduction, the real line is always part of the Lax spectrum and it maps to stable eigenvalues of the stability problem. We demonstrate our methods work for a variety of examples, both in and not in the AKNS hierarchy.     

Precursor Design Strategies for the Low-Temperature Synthesis of Functional Oxides: It's All in the Chemistry

Solution-based (multi)metal oxide synthesis has been carried out employing a large diversity of precursor routes. The selection of an appropriate synthesis strategy is frequently dictated by the resulting material properties, although this choice should also be based on green chemistry principles, atom economy considerations and energy efficiency. In order to limit the required energy budget to convert the chemical precursor to the target oxide material, various approaches were recently reported. This Review summarizes some frequently encountered low-temperature routes, critically assessing their application window and advantages. More specifically, auto-combustion synthesis, UV-assisted decomposition routes, sol–gel network adjustments and precursor complex design concepts are discussed. It is expected that this toolbox of low-temperature strategies may assist further progress in the field, stimulating novel applications, such as flexible electronics or organic–oxide hybrid materials, which are very sensitive to the temperature requirements.     

New model for gas evolving electrodes based on supersaturation

A new model for gas evolving electrodes is proposed, in which the gas evolution reaction is driven by the supersaturation of dissolved gas.