Convergence of the parabolic Ginzburg–Landau equation to motion by mean curvature

We present some new results for the asymptotic behavior of the complex parabolic Ginzburg–Landau equation. In particular, we establish that, as the parameter ε tends to 0, vorticity evolves according to motion by mean curvature in Brakke's weak formulation. The only assumption we make is a natural energy bound on the initial data. In some cases, we also prove convergence to enhanced motion in the sense of Ilmanen. To cite this article: F. Bethuel et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Dynamics of multiple degree Ginzburg–Landau vortices

For the two-dimensional complex parabolic Ginzburg–Landau equation we prove that, asymptotically, vortices evolve according to a simple ordinary differential equation, which is a gradient flow of the Kirchhoff–Onsager functional. This convergence holds except for a finite number of times, corresponding to vortex collisions and splittings, which we describe carefully. The only assumption is a natural energy bound on the initial data. To cite this article: F. Bethuel et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Time-resolved cavity ringdown spectroscopy on nanoparticle generation in a SiH4–H2 VHF plasma

Time-resolved cavity ringdown (τ-CRD) spectroscopy has been applied to monitor the silyl (SiH₃) radicals and nanoparticles in a pulsed very high frequency (VHF) silane-hydrogen plasma under microcrystalline silicon (μc-Si:H) deposition conditions. The measured cavity loss reveals four time intervals (I up to VI) in the first 4 s of the plasma pulse. By variation of the laser wavelength, it is demonstrated that the small cavity loss at 220 nm reflects the SiH₃ absorption in interval I. In intervals II and III, an additional cavity loss appears. This additional cavity loss corresponds to Rayleigh and Mie scattering by growing nanoparticles. Interval IV reflects the loss of nanoparticles between the electrodes during the afterglow of the plasma pulse. The evolution of the nanoparticle generation determined from the τ-CRD measurements are further confirmed by additional scanning electron microscopy analyses on the nanoparticles created in the plasma pulse.     

Influence of the reaction medium on the composition and the microstructure of styrene–acrylic acid copolymers

Two series of acrylic acid-styrene copolymers of various composition have been prepared in benzene and dimethylformamide in order to study their sequence distribution by using ¹³C NMR spectroscopy. The reactivity ratios in benzene were r_A = 0.13, r_A = 0.30 and in dimethylformamide r_A = 0.05, r_S = 1.60. Copolymers with the same overall composition but prepared in different media display marked differences in sequence distribution, the copolymers obtained in dimethylformamide always having longer sequences. For the series of copolymers prepared in dimethylformamide, the experimental percentages of acrylic acid-centered triads (SAS, SAA, AAA) disagree with the values calculated from the monomer reactivity ratios.     

Development and validation of a glass-silicon microdroplet-based system to measure sulfite concentrations in beverages

Sulfite is often added to beverages as an antioxidant and antimicrobial agent. In fermented beverages, sulfite is also naturally produced by yeast cells. However, sulfite causes adverse health effects in asthmatic patients and accurate measurement of the sulfite concentration is therefore very important. Current sulfite analysis methods are time- and reagent-consuming and often require costly equipment. Here, we present a system allowing sensitive, ultralow-volume sulfite measurements based on a reusable glass-silicon microdroplet platform on which microdroplet generation, addition of enzymes through chemical-induced emulsion destabilization and pillar-induced droplet merging, emulsion restabilization, droplet incubation, and fluorescence measurements are integrated. In a first step, we developed and verified a fluorescence-based enzymatic assay for sulfite by measuring its analytical performance (LOD, LOQ, the dynamic working range, and the influence of salts, colorant, and sugars) and comparing fluorescent microplate readouts of fermentation samples with standard colorimetric measurements using the 5,5′-dithiobis-(2-nitrobenzoic acid) assay of the standard Gallery Plus Beermaster analysis platform. Next, samples were analyzed on the microdroplet platform, which also showed good correlation with the standard colorimetric analysis. Although the presented platform does not allow stable reinjection of droplets due to the presence of a tight array of micropillars at the fluidics entrances to prevent channel clogging by dust, removing the pillars, and integrating miniaturized pumps and optics in a future design would allow to use this platform for high-throughput, automated, and portable screening of microbes, plant, or mammalian cells.

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Polymerization of methyl methacrylate with butyllithium–diethylzinc complex

The low-temperature polymerization of methyl methacrylate initiated with butyllithium–diethylzinc has been studied in toluene and in toluene–tetrahydrofuran and toluene–dioxane mixtures in various proportions. The polymerization process is typically anionic; it is characterized by a very rapid initiation reaction, and the absence of termination and chain transfer reactions, the molecular weight increasing proportionally with the degree of conversion. With toluene as a solvent, the polymer chains are associated, as is shown by viscometric measurements; moreover the polymers produced are highly polydisperse (M_v/M_n = 5.4). The kinetics are very complicated and vary with the range of the catalyst and monomer concentrations. In pure toluene in the presence of the organometallic complex, butyllithium–diethylzinc, the monomer addition is more stereospecific than when butyllithium alone is used as catalyst. By adding tetrahydrofuran to the reaction mixture, the polymer chain association disappears; concomitantly the stereochemical structure of the polymer changes from an isotactic to a mainly syndiotactic configuration. In toluene–tetrahydrofuran mixtures containing from 1 to 10 vol.-% tetrahydrofuran, the kinetics of polymerization can easily be interpreted by assuming the presence of two propagating reactive species which are in equilibrium with each other: the ion pair and the THF-solvated ion pair. The energy of activation of propagation for the free ion pair is equal to 7.5 kcal./mole; for the solvated ion pair a value of 5.5 kcal./mole was found, including the solvation enthalpy of the organometal with tetrahydrofuran. The existence of any relation between the reactivity of the propagating species and the tactic incorporation of the monomeric units has been discussed. The polymerization in mixtures of toluene–dioxane is intermediate between that in pure toluene and that in toluene–HF mixtures; the reaction mechanism however cannot be interpreted with the usual kinetic scheme. The experimental data concerning the rate dependence on catalyst and monomer concentrations are briefly summarized.     

New Phenomena in Radical Polymerization

G. Smets, Louvain, Belqium: Gentlemen, as Professor Vogl already said, Professor Zubov willpresent today the paper which should have been presented by our colleague, Professor Kabanov. Each of us knows very well the very active research directed by Professor Kabanov at the Lomonosov University of Moscow. We do regret very sincerely his absence. May I now ask, please, Professor Zubov to take the chair.     

Photocross-Linkable Polymers

Several processes of photocross-linking of polymers are based on the photodimerization of unsaturated groups and on the photodissociation of light labile groups, such as azides. In the present paper we will consider three different methods of cross-linking:

1. Photoinitiation of free radical polymerization of unsaturated side groups attached to a polymer molecule in the presence of a suitable photoinitiator, such as benzoin alkyl ether.

2. Photoinitiation of cationic polymerization of oxirane side groups in the presence of photolabile amine salts, such as diazonium salts, giving rise to the formation of Lewis acid.

3. Electron donor/acceptor complexation of side groups which on photoexcitation exchange an hydrogen atom; this results in cross-linking by free radical combination.     

Freezing Capture of Polymorphic Aggregates of Bolaamphiphilic L‐Valine‐Based Molecular Hydrogelators

Nanostructured xerogels have been prepared by the freeze‐drying of hydrogels and aggregates formed by bolaamphiphilic L ‐valine derivatives after aging under different environmental conditions. A wide variety of shapes and sizes has been achieved by a simple methodology. These nanostructures have been studied by SEM and WAXD and a dramatic influence of structural flexibility on the kinetics of aggregation has been observed. Such flexibility and a modulation of the hydrophobic effect have shown a profound influence in the packing of these compounds and revealed a high degree of polymorphism.     

Eu(O2C-C≡C-CO2): An EuII Containing Anhydrous Coordination Polymer with High Stability and Negative Thermal Expansion

Anhydrous Eu^II–acetylenedicarboxylate (EuADC; ADC²⁻ = ⁻O₂C-C≡C-CO₂⁻) was synthesized by reaction of EuBr₂ with K₂ADC or H₂ADC in degassed water under oxygen-free conditions. EuADC crystallizes in the SrADC type structure (I4₁/amd, Z=4) forming a 3D coordination polymer with a diamond-like arrangement of Eu²⁺ nodes (msw topology including the connecting ADC²⁻ linkers). Deep orange coloured EuADC is stable in air and starts decomposing upon heating in an argon atmosphere only at 440 °C. Measurements of the magnetic susceptibilities (μ_eff=7.76 μ_B) and ¹⁵¹Eu Mössbauer spectra (δ=−13.25 mm s⁻¹ at 78 K) confirm the existence of Eu²⁺ cations. Diffuse reflectance spectra indicate a direct optical band gap of E_g=2.64 eV (470 nm), which is in accordance with the orange colour of the material. Surprisingly, EuADC does not show any photoluminescence under irradiation with UV light of different wavelengths. Similar to SrADC, EuADC exhibits a negative thermal volume expansion below room temperature with a volume expansion coefficient α_V=−9.4(12)×10⁻⁶ K⁻¹.