Analysis and finite element simulations of a second‐order fluid model in a bounded domain

This article is concerned with the equations governing the steady motion of a viscoelastic incompressible second‐order fluid in a bounded domain. A new proof of existence and uniqueness of strong solutions is given. In addition, using appropriate finite element methods to approximate a coupled equivalent problem, sharp error estimates are obtained using a fixed point argument. The method is applied to the two‐dimensional lid‐driven cavity problem, at low Reynolds number and in a certain range of values of the viscoelastic parameters, to analyze the combined effects of inertia and viscoelasticity on the flow. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

The LEM exponential integrator for advection–diffusion–reaction equations

We implement a second-order exponential integrator for semidiscretized advection–diffusion–reaction equations, obtained by coupling exponential-like Euler and Midpoint integrators, and computing the relevant matrix exponentials by polynomial interpolation at Leja points. Numerical tests on 2D models discretized in space by finite differences or finite elements, show that the Leja–Euler–Midpoint (LEM) exponential integrator can be up to 5 times faster than a classical second-order implicit solver.     

Synthesis of poly-yne polymers containing transition metals,disilane, disiloxane and phosphine groups in the main chain

The synthesis and characterization of metal poly-yne polymers containing disilane, disiloxane and phosphine groups in the main chain are described. The platinum and palladium poly-yne polymers were synthesized by polycondensation reactions between a metal chloride and an α, ω-bisethynyl complex in amines in the presence of cuprous iodide as a catalyst. The nickel poly-yne polymers were synthesized by an alkynyl ligand exchange reaction between a nickel acetylide and an α, ω-bisethynyl complex in diethylamine in the presence of cuprous iodide as a catalyst. The reaction of the platinum poly-yne polymer, containing disiloxane groups in the main chain, with copper (I) salts afforded adducts of η-²-bonded σ-acetylide polymer complexes. The reactions of the palladium poly-yne polymer, containing phosphine groups in the main chain, with transition-metal carbonyl complexes afforded polymer complexes which have phosphorus in the main chain-transition-metal bonds. A concentrated solution of the platinum poly-yne polymer containing disiloxane groups in the main chain forms a lyotropic liquid crystal in dichloromethane or 1, 2-dichloroethane.     

Microscopic Theory of Blue Phases Ⅰ and Ⅱ of Liquid Crystal

The microscopic theory of the blue phases of chiral liquid crystal is proposed. Beginning with the potential between two molecules, by using the cell model of liquid, applying statistical physical method, the distribution function and the free energy of the system are obtained. By using variational approach and zero-order approximation, the differential equation that the order parameter tensor of the blue phase can satisfy is obtained. Then we change the differential equation to the eigenequation problem in quantum mechanics. Considering the symmetry of the blue phases,the order parameter tensors of blue phases Ⅰ and Ⅱ can be made up of the eigenvectors. Our results are the same as the results of Ginzberg-Landau‘s phenomenological theory. The parameters in the order parameter tensors that we calculate in the located system are close to the predecessors‘ results.     

Functionalized poly(oxanorbornene)‐block‐copolymers: Preparation via ROMP/click‐methodology

Block copolymers on basis of poly(oxanorbornenes) bearing functional moieties in their side‐chains are prepared via a combination of ROMP‐methods and 1,3‐dipolar‐“click”‐reactions. Starting from N‐substituted‐ω‐bromoalkyl‐oxanorbornenes and alkyl‐/perfluoroalkyl‐oxanorbornenes, block copolymers with molecular weights up to 25,000 g mol^?1 were generated. Subsequent nucleophilic exchange‐reactions yielded the block‐copolymers functionalized with ω‐azidoalkyl‐moieties in one block. The 1,3‐azide/alkine‐“click” reactions with a variety of terminal alkynes in the presence of a catalyst system consisting of tetrakis(acetonitrile)hexafluorophosphate copper(I) and tris(1‐benzyl‐5‐methyl‐1H‐ [1,2,3]triazol‐4‐ylmethyl)‐amine furnished the substituted block copolymers in high yields, as proven by NMR‐spectroscopy. The resulting polymers were investigated via temperature‐dependent SAXS‐methods, revealing their microphase separated structure as well as their temperature‐dependent behavior. The presented method offers the generation of a large set of different block‐copolymers from only a small set of starting materials because of the high versatility of the “click” reaction, thus enabling a simple and complete functionalization after the initial polymerization reaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 485–499, 2007     

Synthesis and characterization of poly(ethylene oxide‐co‐ethylene carbonate) macromonomers and their use in the preparation of crosslinked polymer electrolytes

Methacrylate‐functionalized poly(ethylene oxide‐co‐ethylene carbonate) macromonomers were prepared in two steps by the anionic ring‐opening polymerization of ethylene carbonate at 180 °C, with potassium methoxide as the initiator, followed by the reaction of the terminal hydroxyl groups of the polymers with methacryloyl chloride. The molecular weight of the polymer went through a maximum after approximately 45 min of polymerization, and the content of ethylene carbonate units in the polymer decreased with the reaction time. A polymer having a number‐average molecular weight of 2650 g mol^?1 and an ethylene carbonate content of 28 mol % was selected and used to prepare a macromonomer, which was subsequently polymerized by UV irradiation in the presence of different concentrations of lithium bis(trifluoromethanesulfonyl)imide salt. The resulting self‐supportive crosslinked polymer electrolyte membranes reached ionic conductivities of 6.3 × 10^?6 S cm^?1 at 20 °C. The coordination of the lithium ions by both the ether and carbonate oxygens in the polymer structure was indicated by Fourier transform infrared spectroscopy. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2195–2205, 2006     

Air‐stable and recoverable catalyst for copper‐catalyzed controlled/living radical polymerization of styrene; In situ generation of Cu(I) species via electron transfer reaction

Copper‐catalyzed controlled/living radical polymerization (LRP) of styrene (St) was conducted using the silica gel‐supported CuCl₂/N,N,N′,N′,N″‐pentamethyldiethylenetriamine (SG‐CuCl₂/PMDETA) complex as catalyst at 110 °C in the presence of a definite amount of air. This novel approach is based on in situ generation and regeneration of Cu(I) via electron transfer reaction between phenols and Cu(II). Sodium phenoxide or p‐methoxyphenol was used as a reducing agent of Cu(II) complexes in LRP. The number–average molecular weight, M_n,GPC, increases linearly with monomer conversion and agrees well with the theoretical values up to 85% conversion The molecular weight distribution, M_w/M_n, decreases as the conversion increases and reaches values below 1.2. The catalyst was recovered in aerobic condition and reused in copper‐catalyzed LRP of St. For the second run, the number–average molecular weights increased with monomer conversion and the polydispersities decreased as the polymerization proceeded and reached to the value <1.3 at 81% conversion. The recycled catalyst retained 90% of its original activity in the subsequent polymerization. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 77–87, 2006     

Thermochemically induced binding of methyl orange to polycations containing primary amine groups

The thermochemical transformation of electrostatically formed complexes of methyl orange (MO) with polycations containing primary amine groups such as ammonium salts afforded new polymers with a high concentration of covalently bound 4‐N,N‐dimethylaminoazobenzene groups in the side chain. Poly(allylamine hydrochloride) and poly(β‐aminoethylene acrylamide hydrochloride) were employed as support polycations for MO. The transformation of sulfonate–ammonium ion pairs into sulfonamide bonds, via heating at an elevated temperature, was supported by the polymer properties before and after the thermal treatment. The polymer structure changes were monitored with elemental analysis, Fourier transform infrared, ¹H NMR, and ultraviolet–visible absorption spectroscopy, and thermogravimetric analysis. The spacer length between the backbone and azobenzene structures used as side chains strongly influenced the polymer properties before and after the heat‐induced reaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5898–5908, 2006     

Lithographic design of photosensitive polyarylates based on reaction development patterning

The factors affecting pattern‐forming properties in reaction development patterning were examined with polyarylates with various bisphenol moieties. The developability of the photosensitive polyarylates was dependent on the properties of the subtituent (R) in the bisphenol moieties. The development time decreased in the following order: R?C(CH₃)₂ > fluorenyl unit ? phenolphthalein unit > C(CF₃)₂ > SO₂. This order agreed with that of the reactivity between the polyarylates and ethanolamine, and these orders can be explained by pK_a of the bisphenol used to prepare the polyarylates. The development with NH₂? R′? OH resulted in successful positive‐tone pattern formation. However, pattern formation with the developers containing NH₂? R′? OCH₃ was unsuccessful. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2694–2706, 2006     

Palladacycles in catalysis - a critical survey

The application of palladacycles as catalysts for cross-coupling and similar reactions is reviewed. In the majority of cases palladacycles are likely to serve as a source of highly active but unstable zero-valent palladium species. In this respect the palladacycles resemble the so-called phosphine-free catalysts. The advantages and limitations of palladacycle catalysts are discussed.