On uniqueness and existence of entropy solutions for a nonlinear parabolic problem with absorption

The aim of this paper is to study, for L ¹-data, the absorption problem of parabolic type : with Dirichlet boundary conditions and initial conditions. Here a satisfies the classical Leray-Lions hypotheses and β(x, ·) is the subdifferential ∂j(x, ·), where j is a convex function such that j(·, 0) = 0. Existence and uniqueness of an entropy solution is established.      

Facile Synthesis of an Octagermacubane with Two Three-Coordinate Germanium(0) Atoms and its Unique Radical Anion

Thermolysis of a 1 : 1 mixture of tris(di-tert-butylmethylsilyl)germane 9 and bis(di-tert-butylmethylsilyl)germane 17 at 100 °C produces unexpectedly octagermacubane 18 , having two 3-coordinate Ge⁰ atoms (40 % yield). 18 was characterized by X-ray crystallography and it is a singlet biradical (according to DFT quantum mechanical calculations and the absence of an EPR signal). Reactions of 18 with CH₂Cl₂ and H₂O yield the novel dichloro-octagermacubane 24 and hydroxy-octagermacubane 25 , respectively. Reduction of 18 with tBuMe₂SiNa in THF produces an isolable octagermacubane radical anion 26-Na . Based on X-ray crystallography, EPR spectroscopy and DFT quantum mechanical calculations, 26-Na is classified as a Ge-centered radical anion.     

On pattern transfer in replica molding

Nano- and micromolding of elastic materials produces smoothed replicas of the mold structures. This limits the technique's resolution. Here we identified surface tension as the cause of smoothing and derived explicit equations for calculating molded feature shapes. The characteristic length scale for smoothing is given by the ratio of the interface tension to Young's modulus of the molded material. This approach offers the possibility to correct for the smoothing caused by surface tension during mold design. Moreover, it can be exploited to measure interface tension.     

Low-temperature single-wall carbon nanotubes synthesis: feedstock decomposition limited growth

We report on the lowest temperature of SWCNT growth using endothermic decomposition of CH4 gas on a specially activated alumina-supported Fe:Mo catalyst. However, the observed lowest growth temperature (560 degrees C) is higher than that reported previously for exothermic feedstock type. Our observation indicates that the decomposition threshold temperature of the feedstock limits the SWCNT growth. This study also suggests that, by using more active carbon feedstock or somehow facilitating its decomposition, one could enable the synthesis of SWCNT at an even lower temperature.     

Water-soluble gold nanoparticles protected by fluorinated amphiphilic thiolates

The preparation and the properties of gold nanoparticles (Au NPs) protected by perfluorinated amphiphiles are described. The thiols were devised to form a perfluorinated region close to the gold surface and to have a hydrophilic portion in contact with the bulk solvent to impart solubility in water. The monolayer protected clusters were prepared, in an homogeneous phase using sodium thiolates because of the low nucleophilicity of the alpha-perfluorinated thiols, and fully characterized with (1)H, (19)F NMR spectrometry, IR and UV-vis absorption spectroscopies, transmission electron microscopy (TEM), thermogravimetric analysis (TGA), and X-ray photoelectron spectroscopy (XPS). Au NPs with core diameters ranging from 1.6 to 2.9 nm, depending on the reaction conditions, were obtained. Water-soluble NPs (MPC-F8-PEGs) were obtained with the thiol HS-F8-PEG ending with a short poly(ethylene glycol) unit (PEG-OMe 550), whereas thiols with shorter PEG chains give rise to NPs insoluble in water. MPC-F8-PEGs undergo an exchange reaction with amphiphilic alkyl thiols. ESR investigations, using a hydrophobic radical probe, indicate that the MPC-F8-PEG monolayer shows a greater hydrophobicity compared to the analogous hydrogenated monolayer.     

A triple resonance hyperfine sublevel correlation experiment for assignment of electron-nuclear double resonance lines

A new, triple resonance, pulse electron paramagnetic resonance (EPR) sequence is described. It provides spin links between forbidden electron spin transitions (DeltaM(S)=+/-1, DeltaM(I) not equal 0) and allowed nuclear spin transitions (DeltaM(I) = +/-1), thus, facilitating the assignment of nuclear frequencies to their respective electron spin manifolds and paramagnetic centers. It also yields the relative signs of the hyperfine couplings of the different nuclei. The technique is based on the combination of electron-nuclear double resonance (ENDOR) and electron-electron double resonance (ELDOR)-detected NMR experiments in a way similar to the TRIPLE experiment. The feasibility and the information content of the method are demonstrated first on a single crystal of Cu-doped L-histidine and then on a frozen solution of a Cu-histidine complex.     

Evolution of the vibrational spectrum of ammonia from single molecule to bulk

Ammonia clusters (NH3)n (n=2-10(4)) have been assembled inside helium droplets and studied via infrared laser spectroscopy. The studied spectral range of 3100-3500 cm(-1) covers the nu1 and nu3 fundamental stretching bands as well as the 2nu4 overtone of the bend of ammonia molecules. The results show strong coupling of the 2nu4 overtone with the fundamental vibrations for all cluster sizes except dimers. The intensity of the nu3 band relative to the total intensity in the spectrum increases from about 30% to about 80% upon increase of the average cluster size from n=5 to n=10(4). We attributed this effect to the concomitant decrease in the fraction of the surface molecules. The results indicate that ammonia clusters obtained in He droplets have a compact structure and that inner molecules in the clusters have similar hydrogen-bonded coordination as in the crystalline form of ammonia. This surprising result is ascribed to a directionality of the hydrogen bond, which guides the low temperature growth of the cluster in He droplets.     

Gold(I)‐Catalyzed N‐Desulfonylative Amination versus N‐to‐O 1,5‐Sulfonyl Migration: A Versatile Approach to 1‐Azabicycloalkanes

Valuable 1‐azabicycloalkane derivatives have been synthesized through a novel gold(I)‐catalyzed desulfonylative cyclization strategy. An ammoniumation reaction of ynones substituted at the 1‐position with an N‐sulfonyl azacycle took place in the presence of a gold cation by intramolecular cyclization of the disubstituted sulfonamide moiety onto the triple bond. Depending on the size of the heterocyclic ring and substitution of the substrates, two unprecedented forms of nucleophilic attack on the sulfonyl group were exploited, that is, a N‐desulfonylation in the presence of an external protic O nucleophile (37–87 %, 10 examples) and a unique N‐to‐O 1,5‐sulfonyl migration (60–98 %, 9 examples).     

Solid–Vapor Reaction Growth of Transition‐Metal Dichalcogenide Monolayers

Two‐dimensional (2D) layered semiconducting transition‐metal dichalcogenides (TMDCs) are promising candidates for next‐generation ultrathin, flexible, and transparent electronics. Chemical vapor deposition (CVD) is a promising method for their controllable, scalable synthesis but the growth mechanism is poorly understood. Herein, we present systematic studies to understand the CVD growth mechanism of monolayer MoSe₂, showing reaction pathways for growth from solid and vapor precursors. Examination of metastable nanoparticles deposited on the substrate during growth shows intermediate growth stages and conversion of non‐stoichiometric nanoparticles into stoichiometric 2D MoSe₂ monolayers. The growth steps involve the evaporation and reduction of MoO₃ solid precursors to sub‐oxides and stepwise reactions with Se vapor to finally form MoSe₂. The experimental results and proposed model were corroborated by ab initio Car–Parrinello molecular dynamics studies.     

Symplectic Field Theory of a Disk,Quantum Integrable Systems,and Schur Polynomials

We consider commuting operators obtained by quantization of Hamiltonians of the Hopf (aka dispersionless KdV) hierarchy. Such operators naturally arise in the setting of Symplectic Field Theory (SFT). A complete set of common eigenvectors of these operators is given by Schur polynomials. We use this result for computing the SFT potential of a disk.