Smoothness of the trajectories of ideal fluid particles with Yudovich vorticities in a planar bounded domain

We consider the incompressible Euler equations in a (possibly multiply connected) bounded domain Ω of R², for flows with bounded vorticity, for which Yudovich (1963) proved in [29] global existence and uniqueness of the solution. We prove that if the boundary ∂Ω of the domain is C^∞ (respectively Gevrey of order M?1) then the trajectories of the fluid particles are C^∞ (respectively Gevrey of order M+2). Our results also cover the case of “slightly unbounded” vorticities for which Yudovich (1995) extended his analysis in [30]. Moreover if in addition the initial vorticity is Hölder continuous on a part of Ω then this Hölder regularity propagates smoothly along the flow lines. Finally we observe that if the vorticity is constant in a neighborhood of the boundary, the smoothness of the boundary is not necessary for these results to hold.     

Viscous boundary layers for the Navier–Stokes equations with the Navier slip conditions

We tackle the issue of the inviscid limit of the incompressible Navier–Stokes equations when the Navier slip-with-friction conditions are prescribed on impermeable boundaries. We justify an asymptotic expansion which involves a weak amplitude boundary layer, with the same thickness as in Prandtl’s theory and a linear behavior. This analysis holds for general regular domains, in both dimensions two and three.     

Rational design of aminoanthraquinones for colorimetric detection of heavy metal ions in aqueous solution

A family of water-soluble colorimetric chemosensors incorporating an anthraquinone signalling subunit functionalized with a polyamine chain that bears hydrophilic diethoxyphosphoryl moieties was prepared with the aim of assaying metal cations. The outstanding UV-Vis absorption properties of the 1-aminoanthraquinone chromophore allowed the efficient visual detection and quantification of copper(II) ions by chelators L(1)-L(3) in buffered aqueous solution. Moreover, the visible response of L(2) is not interfered by addition of large excesses of 13 common metal ions, whereas chemosensor L(3) produces also a color change in the presence of equimolar amounts of lead(II). Considering the 134 nm gap between both absorption maxima, simultaneous colorimetric quantification of lead and copper can be envisaged. Detailed potentiometric and spectrophotometric analysis of Cu(2+) complexation by L(2) and L(3), as well as Pb(2+) and Cd(2+) by L(3) was undertaken in order to gain a deeper insight into the pH-dependent speciation and understanding the color changing process. Furthermore, the inner coordination sphere of the [PbL(3)](2+) complex was probed by NMR spectroscopy.     

Design of Interpenetrated Networks of Mesostructured Hybrid Silica and Nonconductive Poly(vinylidene fluoride)–Cohexafluoropropylene (PVdF–HFP) Polymer for Proton Exchange Membrane Fuel Cell Applications

Organic–inorganic hybrid membranes of poly(vinylidene fluoride)–cohexafluoropropylene (PVdF–HFP) and mesostructured silica containing sulfonic acid groups were synthesized by using the sol‐gel process. These hybrid membranes were prepared by in situ co‐condensation of tetraethoxysilane and an organically modified silane (ormosil) by a self‐assembly route using organic surfactants as templates for tuning the architecture of the hybrid organosilica component. In this paper, we describe the elaboration and characterization of hybrid membranes all the way from the precursor solution to the evaluation of the fuel cell performances. These hybrid materials were extensively characterized by using NMR and IR spectroscopy, electron microscopy, or impedance spectroscopy so as to determinate their physicochemical and electrochemical properties. Even though the ion‐exchange capacity (IEC) was quite weak, the first fuel cell tests performed with these hybrid membranes show promising results relative to optimized Nafion 112 thanks to great water management of the silica inside the hydrophobic polymer.     

Intermolecular interactions in self-assembled monolayers of tetrathiafulvalene derivatives

The elaboration of mixed self-assembled monolayers (SAMs) of tetrathiafulvalene derivatives allows the modulation of intermolecular interactions and provides evidence of segregated distribution of redox centers.     

NMR parameters in alkali, alkaline earth and rare earth fluorides from first principle calculations

(19)F isotropic chemical shifts for alkali, alkaline earth and rare earth of column 3 basic fluorides are measured and the corresponding isotropic chemical shieldings are calculated using the GIPAW method. When using the PBE exchange-correlation functional for the treatment of the cationic localized empty orbitals of Ca(2+), Sc(3+) (3d) and La(3+) (4f), a correction is needed to accurately calculate (19)F chemical shieldings. We show that the correlation between experimental isotropic chemical shifts and calculated isotropic chemical shieldings established for the studied compounds allows us to predict (19)F NMR spectra of crystalline compounds with a relatively good accuracy. In addition, we experimentally determine the quadrupolar parameters of (25)Mg in MgF(2) and calculate the electric field gradients of (25)Mg in MgF(2) and (139)La in LaF(3) using both PAW and LAPW methods. The orientation of the EFG components in the crystallographic frame, provided by DFT calculations, is analysed in terms of electron densities. It is shown that consideration of the quadrupolar charge deformation is essential for the analysis of slightly distorted environments or highly irregular polyhedra.     

Polyethylenes bearing a terminal porphyrin group

An α-[Cu(II)-porphyrin]-polyethylene was synthesized for the first time using copper catalyzed 1,3-dipolar azide-alkyne Huisgen cycloaddition yielding highly colored moiety-substituted polyethylene.