Ostwald ripening of oil-in-water emulsions stabilized by phenoxy-substituted dextrans

The stability of oil-in-water emulsions prepared using dextran, a natural polysaccharide, hydrophobically substituted with phenoxy groups, was studied. The evolution of the emulsion droplet size was investigated as a function of polymer concentration (Cp=0.2 to 1% w/w in a water phase) and the degree of phenoxy substitution (tau=4.2 to 15.7%). For the highest tau values, emulsions, which presented submicrometer droplets, were stable over more than 4 months at room temperature. The most substituted polymers clearly showed a better efficiency to lower the surface tension at the oil/water interface. DexP did not induce real viscosification of the continuous phase. The linearity of the particle volume variation with time, and the invariability of the volume distribution function, proved that Ostwald ripening was the main destabilization mechanism of the phenoxy dextran emulsions. The nature of the oil dispersed phase drastically affected the behavior of emulsions. While the emulsions prepared with n-dodecane presented a particle growth with time, only few size variations occurred when n-hexadecane was used. Furthermore, small ratios of n-hexadecane in n-dodecane phase reduced the particle growth due to the lower solubility and lower diffusion coefficient in water of n-hexadecane, which acted as a ripening inhibitor.     

Absolute measurement of an atomic cascade rate using a two photon coincidence technique. Application to the 4p21S0 -4s4p 1P1 -4s21S0 cascade of calcium excited by a two photon absorption

The two photon coincidence technique yields an absolute measurement of a cascade decay rate without knowing the detection efficiency of each detector. This method is applied to calcium atoms in an atomic beam excited to the 4p²¹S₀ state, and decaying via the resonant ¹P₁ state; it yields the excitation rate of the upper 4p²¹S₀ level. Since the excitation process (two photon absorption) is controlled, one can compute the excitation rate of the upper level as a function of the transition probabilities in the cascade. The lower transition is well known and we can therefore deduce the transition probability for the 4p²¹S₀ -4s4p ¹P₁, transition which previously had not been accurately determined. The preliminary measurements yield a line strength s = 0.98 ± 0.3 au in good agreement with a recent measurement of the lifetime of the 4p²¹S₀ state.     

The first self-assembled trimetallic lanthanide helicates driven by positive cooperativity

The segmental tris-tridentate ligand L7 reacts with stoichiometric quantities of Ln(III) (Ln=La-Lu) in acetonitrile to give the complexes [Ln(2)(L7)(3)](6+) and [Ln(3)(L7)(3)](9+). Formation constants point to negligible size-discriminating effects along the lanthanide series, but Scatchard plots suggest that the self-assembly of the trimetallic triple-stranded helicates [Ln(3)(L7)(3)](9+) is driven to completion by positive cooperativity, despite strong intermetallic electrostatic repulsions. Crystallization provides quantitatively [Ln(3)(L7)(3)](CF(3)SO(3))(9) (Ln=La, Eu, Gd, Tb, Lu) and the X-ray crystal structure of [Eu(3)(L7)(3)](CF(3)SO(3))(9).(CH(3)CN)(9).(H(2)O)(2) (Eu(3)C(216)H(226)N(48)O(35)F(27)S(9), triclinic, P1, Z=2) shows the three ligand strands wrapped around a pseudo-threefold axis defined by the three metal ions rigidly held at about 9 A. Each metal ion is coordinated by nine donor atoms in a pseudo-trigonal prismatic arrangement, but the existence of terminal carboxamide units in the ligand strands differentiates the electronic properties of the terminal and the central metallic sites. Photophysical data confirm that the three coordination sites possess comparable pseudo-trigonal symmetries in the solid state and in solution. High-resolution luminescence analyses evidence a low-lying LMCT state affecting the central EuN(9) site, so that multi-metal-centered luminescence is essentially dominated by the emission from the two terminal EuN(6)O(3) sites in [Eu(3)(L7)(3)](9+). New multicenter equations have been developed for investigating the solution structure of [Ln(3)(L7)(3)](9+) by paramagnetic NMR spectroscopy and linear correlations for Ln=Ce-Tb imply isostructurality for these larger lanthanides. NMR spectra point to the triple helical structure being maintained in solution, but an inversion of the magnitude of the second-rank crystal-field parameters, obtained by LIS analysis, for the LnN(6)O(3) and LnN(9) sites with respect to the parameters extracted for Eu(III) from luminescence data, suggests that the geometry of the central LnN(9) site is somewhat relaxed in solution.     

Luminescence-detected phase transitions in lanthanide-containing liquid crystals

Complexes between lanthanide nitrates and a pro-mesogenic 18-membered diaza-substituted coronand are luminescent both as powders and liquid crystals (between 87 and 195 degrees C), and the phase transitions are detected by monitoring luminescence intensity and lifetime.     

Ueber die Acidimetrie organischer K?rper

Ohne Zusammenfassung     

Fractal First-Order Partial Differential Equations

The present paper is concerned with semi-linear partial differential equations involving a particular pseudo-differential operator. It investigates both fractal conservation laws and non-local Hamilton–Jacobi equations. The idea is to combine an integral representation of the operator and Duhamel's formula to prove, on the one hand, the key a priori estimates for the scalar conservation law and the Hamilton–Jacobi equation and, on the other hand, the smoothing effect of the operator. As far as Hamilton–Jacobi equations are concerned, a non-local vanishing viscosity method is used to construct a (viscosity) solution when existence of regular solutions fails, and a rate of convergence is provided. Turning to conservation laws, global-in-time existence and uniqueness are established. We also show that our formula allows us to obtain entropy inequalities for the non-local conservation law, and thus to prove the convergence of the solution, as the non-local term vanishes, toward the entropy solution of the pure conservation law.     

Large time behavior of periodic viscosity solutions for uniformly parabolic integro-differential equations

In this paper, we study the large time behavior of solutions of a class of parabolic fully nonlinear integro-differential equations in a periodic setting. In order to do so, we first solve the ergodic problem (or cell problem), i.e. we construct solutions of the form $\lambda t + v(x).$ We then prove that solutions of the Cauchy problem look like those specific solutions as time goes to infinity. We face two key difficulties to carry out this classical program: (1) the fact that we handle the case of “mixed operators” for which the required ellipticity comes from a combination of the properties of the local and nonlocal terms and (2) the treatment of the superlinear case (in the gradient variable). Lipschitz estimates previously proved by the authors (2012) and Strong Maximum principles proved by the third author (2012) play a crucial role in the analysis.