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.     

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.     

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.     

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.     

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.     

Kinetics of hypericin association with low-density lipoproteins

Steady‐state and time‐resolved fluorescence spectroscopy have been used for the study of the incorporation kinetics of hypericin (Hyp) into low‐density lipoproteins (LDL). Biphasic kinetics of Hyp association with LDL was observed when solutions of Hyp and LDL were mixed at various concentration ratios. The rapid phase of Hyp incorporation is completed within seconds, while the slow phase lasts several minutes. The relative contributions of the individual phases show that a higher amount of Hyp molecules (65%) are incorporated into LDL in the second phase. The kinetics of the incorporation of Hyp into LDL particles preloaded with Hyp (Hyp/LDL = 25:1) was also investigated. The decreased intensity of Hyp fluorescence is a sign of the formation of Hyp aggregates after penetration of additional Hyp molecules into Hyp/LDL = 25:1 complex. The time dependence of Hyp fluorescence was measured after mixing the complex Hyp/LDL = 200:1 with appropriate amounts of free LDL molecules. For each final Hyp/LDL ratio, an increase in the intensity and lifetime of Hyp fluorescence was observed, suggesting a monomerization of Hyp aggregates. The half‐time of Hyp transfer from Hyp/LDL complex to LDL particles is similar to the half‐time of the slow phase of Hyp incorporation into free LDL particles.     

In situ hydrodynamic lateral force calibration of AFM colloidal probes

Lateral force microscopy (LFM) is an application of atomic force microscopy (AFM) to sense lateral forces applied to the AFM probe tip. Recent advances in tissue engineering and functional biomaterials have shown a need for the surface characterization of their material and biochemical properties under the application of lateral forces. LFM equipped with colloidal probes of well-defined tip geometries has been a natural fit to address these needs but has remained limited to provide primarily qualitative results. For quantitative measurements, LFM requires the successful determination of the lateral force or torque conversion factor of the probe. Usually, force calibration results obtained in air are used for force measurements in liquids, but refractive index differences between air and liquids induce changes in the conversion factor. Furthermore, in the case of biochemically functionalized tips, damage can occur during calibration because tip-surface contact is inevitable in most calibration methods. Therefore, a nondestructive in situ lateral force calibration is desirable for LFM applications in liquids. Here we present an in situ hydrodynamic lateral force calibration method for AFM colloidal probes. In this method, the laterally scanned substrate surface generated a creeping Couette flow, which deformed the probe under torsion. The spherical geometry of the tip enabled the calculation of tip drag forces, and the lateral torque conversion factor was calibrated from the lateral voltage change and estimated torque. Comparisons with lateral force calibrations performed in air show that the hydrodynamic lateral force calibration method enables quantitative lateral force measurements in liquid using colloidal probes.     

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.