Stabilization of the wave equations with localized Kelvin–Voigt type damping under optimal geometric conditions

The purpose of this note is to investigate the stabilization of the wave equation with Kelvin–Voigt damping in a bounded domain. Damping is localized via a non-smooth coefficient in a suitable subdomain. We prove a polynomial stability result in any space dimension, provided that the damping region satisfies some geometric conditions. The main novelty of this note is that the geometric situations covered here are richer than that considered in [25], [22], [16] and include in particular an example where the damping region is not localized in a neighborhood of the whole or a part of the boundary.     

Determining nonuniformities of core-shell nanoparticle coatings by analysis of the inelastic background of X-ray photoelectron spectroscopy survey spectra

Most real core-shell nanoparticle (CSNP) samples deviate from an ideal core-shell structure potentially having significant impact on the particle properties. An ideal structure displays a spherical core fully encapsulated by a shell of homogeneous thickness, and all particles in the sample exhibit the same shell thickness. Therefore, analytical techniques are required that can identify and characterize such deviations. This study demonstrates that by analysis of the inelastic background in X-ray photoelectron spectroscopy (XPS) survey spectra, the following types of deviations can be identified and quantified: the nonuniformity of the shell thickness within a nanoparticle sample and the incomplete encapsulation of the cores by the shell material. Furthermore, CSNP shell thicknesses and relative coverages can be obtained. These results allow for a quick and straightforward comparison between several batches of a specific CSNP, different coating approaches, and so forth. The presented XPS methodology requires a submonolayer distribution of CSNPs on a substrate. Poly(tetrafluoroethylene)-poly(methyl methacrylate) and poly(tetrafluoroethylene)-polystyrene polymer CSNPs serve as model systems to demonstrate the applicability of the approach.     

Supramolecular Luminescent Lanthanide Dimers for Fluoride Sequestering and Sensing

Lanthanide complexes (Ln=Eu, Tb, and Yb) that are based on a C₂‐symmetric cyclen scaffold were prepared and characterized. The addition of fluoride anions to aqueous solutions of the complexes resulted in the formation of dinuclear supramolecular compounds in which the anion is confined into the cavity that is formed by the two complexes. The supramolecular assembly process was monitored by UV/Vis absorption, luminescence, and NMR spectroscopy and high‐resolution mass spectrometry. The X‐ray crystal structure of the europium dimer revealed that the architecture of the scaffold is stabilized by synergistic effects of the Eu? F? Eu bridging motive, π stacking interactions, and a four‐component hydrogen‐bonding network, which control the assembly of the two [EuL] entities around the fluoride ion. The strong association in water allowed for the luminescence sensing of fluoride down to a detection limit of 24 nM .