Local strong solutions to the stochastic compressible Navier–Stokes system

We study the Navier–Stokes system describing the motion of a compressible viscous fluid driven by a nonlinear multiplicative stochastic force. We establish local in time existence (up to a positive stopping time) of a unique solution, which is strong in both PDE and probabilistic sense. Our approach relies on rewriting the problem as a symmetric hyperbolic system augmented by partial diffusion, which is solved via a suitable approximation procedure. We use the stochastic compactness method and the Yamada–Watanabe type argument based on the Gyöngy–Krylov characterization of convergence in probability. This leads to the existence of a strong (in the PDE sense) pathwise solution. Finally, we use various stopping time arguments to establish the local existence of a unique strong solution to the original problem.     

Kinetic barriers and ordering of non-covalently bound states

Binding of a dimer of a glycopeptide antibiotic to two molecules of a ligand that are bound to a membrane surface (by a hydrocarbon anchor) has been investigated. This binding on a surface is cooperatively enhanced (surface enhancement) relative to the binding in solution, because the former occurs intramolecularly on a template. Previously a correlation between surface enhancement and thermodynamic stability of the dimer in free solution (Kdimsol) was hypothesised. However, we found that two weakly dimerising antibiotics (vancomycin and ristocetin A) with similar Kdimsol give very different surface enhancements. We propose a model to explain the data correlating surface enhancement to the kinetic barrier to dissociation of the dimer. The surface enhancement of binding can be expected to increase with increasing tightness of the non-covalent interactions formed at the dimer interface. The effect should be found in general where cooperativity is exercised within an organised template (e.g., DNA duplexes and proteins).     

Diffusion-bonded stacks of periodically poled lithium niobate

We constructed diffusion-bonded stacks of periodically poled lithium niobate (PPLN). Such crystals combine the advantages of planar processing used to make PPLN wafers with the power-handling capability of large apertures. We demonstrated an optical parametric oscillator that uses a 3-mm-thick diffusion-bonded stack consisting of three 1-mm-thick PPLN crystals.     

Electrophilic additions to allenes—II : The reaction of benzeneselenenyl chloride with some 1,3-disubstituted allenes

Benzeneselenenyl chloride reacts with 1,3-dialkyl-substituted allenes in methylene chloride solution to give 1:1-adducts. Attack by selenium is found to occur exclusively at the central allenic carbon. In contrast to the analogous reaction of arenesulphenyl chlorides, the preferential formation of the Z-alkene is observed. A mechanism involving the preequilibrium formation of alkylideneseleniranium ions and/or alkylideneepiselenuranes which, in the product-determining step, collapse to products via an anti attack of chloride at the methine carbon of the ring is proposed to account for the preferential formation of the Z-isomers.     

Fabrication of porous polymer monoliths covalently attached to the walls of channels in plastic microdevices

UV-initiated grafting of plastic tubes and microfluidic chips with ethylene diacrylate followed by the preparation of porous polymer monoliths has been studied. The first step affords a thin grafted layer of polymer with a multiplicity of pendent double bonds that are then used in the second step for covalent attachment of the monolith to the wall. As clearly seen on scanning electron micrographs, this procedure prevents the formation of voids at the monolith-channel interface a problem that has always plagued approaches involving bulk polymerization in nontreated channels due to the shrinkage of the monolith during the polymerization process and its lack of compatibility with the material of the device. Irradiation with UV light through a photomask allows precise patterning specifying both the area subjected to surface modification and the location of the monolith within specific areas of the device.     

Reactions of N-methyl-N-(4-biphenylyl)nitrenium ion with electron-rich arenes: laser flash photolysis and product studies

An arylnitrenium ion, N-methyl-N-(4-biphenylyl)nitrenium ion, was generated through photolysis of 1-(N-methyl-N-4-biphenylyl)amino-2,4,6-trimethylpyridinium tetrafluoroborate, and its reactions with various donor-substituted arenes (e.g., 1,3,5-trimethoxybenzene, mesitylene, 1,4-dimethoxybenzene, hexamethylbenzene, etc.) were examined using product analysis and laser flash photolysis. In general, trapping of the short-lived nitrenium ion by the arenes leads to three types of products: (1) the parent amine, N-methyl-N-4-biphenylylamine; (2) an ortho-adduct, where the ring position ortho to the nitrenium ion center is bonded to the arene ring; and (3) an N-adduct, where the nitrenium ion nitrogen is bonded to the trap. Laser flash photolysis studies show that the rates of these trapping reactions vary from 10(4) to 10(9) M(-1) s(-1), depending on the structure of the arene trap. These trapping rate constants do not correlate with the one-electron oxidation potential of the arene, nor with the expected stability of a sigma-complex derived from direct electrophilic aromatic substitution. It is argued that the observed rate constants correspond to initial formation of a pi-complex between the arylnitrenium ion and the arene trap. This complex then forms the observed products.     

Photoswitchable flexible and shape-persistent dendrimers: comparison of the interplay between a photochromic azobenzene core and dendrimer structure

Two analogous classes of dendrimers with a single azobenzene moiety at the core have been prepared. Flexible benzyl aryl ether dendrimers 1a-e were obtained in good yields by direct alkylation of diphenolic azobenzene 3 with benzyl aryl ether dendrons [G-n]-Br (n = 0-4). In rigid dendrimers 2a-e, the azobenzene configurational switch was linked to phenylacetylene dendrons through acetylenic linkages to maintain the shape-persistent nature of these dendrimers. A comparison of these two different classes of dendrimers with azobenzene cores reveals a difference in the properties of the photochromic moiety upon dendritic incorporation as well as a significant difference in the photomodulation of dendrimer properties. The E --> Z photoisomerization quantum yield decreased markedly with increasing generation for dendrimers 1a-e but only slightly for dendrimers 2a-e. However, increasing generation did not significantly alter thermal isomerization kinetics or activation barriers. The hydrodynamic volumes of azobenzene-containing dendrimers 2b-e were significantly modulated when the azobenzene unit is subjected to irradiation, while those of dendrimers 1b-e were only slightly affected.     

Langmuir and grafted monolayers of photochromic amphiphilic monodendrons of low generations

Four generations of monodendrons with multiple dodecyl alkyl tails (AA-N, N representing number of alkyl tails from 1 to 8), an azobenzene spacer group, and a carboxylic acid polar head have been studied at the air-water and air-solid interface using AFM, GIXD, X-ray reflectivity, and UV-vis spectrometry. The one and two tail molecules formed orthorhombic lateral packing with long-range intramonolayer ordering. Good agreement between molecular models and thickness measurements indicated that the one and two tail molecules orient along the surface normal. The increase in the cross-sectional mismatch caused by the presence of the multiple chains for the higher generations disrupted the long-range ordering and forced the alkyl tails to adopt quasi-hexagonal structure. The higher generations (AA-4 and AA-8) formed a kinked structure with the alkyl tails oriented perpendicular to the surface with the azobenzene group tilted at a large degree toward the surface. The photoisomerization behavior in dilute solutions, at the air-water interface, and for grafted layers demonstrated that lower generation monodendrons maintained the photochromic behavior after chemical grafting to the silicon substrates, although the confinement of the molecules in monolayers significantly increased the reorganization time.     

A novel nonmetallized tip for electrospray mass spectrometry at nanoliter flow rate

We report the fabrication of a durable nonmetallized nanospray tip. This nanospray tip does not require complex preparation procedures such as chemical treatment, deposition of gold or SiOx vapor. It was fabricated by pulling a heated glass capillary of 1.1 mm internal diameter to produce a fine tip with an orifice of 10–15 μm in diameter. A 10 μm gold-plated tungsten wire was inserted through the capillary tip. This tungsten wire played a central role in the operation of this durable nanospray tip by providing electrical contact. This type of nanospray tip could withstand electrical discharges and sustained spraying of solution at nanoliter flow rate for more than 3 h. Using insulin (35 μM) and myoglobin (1 μM) solutions, useful mass spectrum could be acquired with low fmol sensitivity.