A retractable structure based on Bricard linkages and rotating rings of tetrahedra

Retractable structures which alter their geometries according to practical requirements are widely used in roof structures of stadiums for their versatility. A retractable structure based on threefold-symmetric Bricard linkages and rotating rings of tetrahedra is proposed and developed in this paper. By replacing each link of a threefold-symmetric Bricard linkage with a tetrahedron, a retractable structure is obtained which can repeatedly open and close by rotating the tetrahedra. The geometric relationship between the retractable structure and the threefold-symmetric Bricard linkage is derived and ranges of main geometric parameters are determined to ensure a continuous and smooth movement in the deployment of the structure. Then the relative displacement of the support and the open rate of the structure, two main parameters concerned in practical applications, are investigated. Preferred ranges of main geometric parameters are proposed and a physical model is manufactured to verify them. A discussion on some possible improvements and modifications of the structure is also presented.     

Viscosity-splitting scheme for the Navier-Stokes equations

A viscosity-splitting scheme for the initial boundary value problems of the Navier-Stokes equations is considered. In the scheme, the Stokes equation is solved in conjunction with a nonhomogeneous boundary condition which connects the tangent flow with a no-slip flow. Convergence is proved.     

Synthesis of grafted poly(p‐phenyleneethynylene) with energy donor–acceptor architecture via atom transfer radical polymerization: Towards nonaggregating and hole‐facilitating light‐emitting material

In this contribution, we demonstrate a new effective methodology for constructing highly efficient and durable poly(p‐phenyleneethynylene) (PPE) containing emissive material with nonaggregating and hole‐facilitating properties through the introduction of hole‐transporting blocks into the PPE system as the grafting coils as well as building the energy donor–acceptor architecture between the grafting coils and the PPE backbone. Poly(2‐(carbazol‐9‐yl)ethyl methacrylate) (PCzEMA), herein, is chosen as the hole‐transporting blocks, and incorporated into the PPE system as the grafting coils via atom transfer radical polymerization. The chemical structure of the resultant copolymer, PPE‐g‐PCzEMA, was characterized by NMR and gel permeation chromatography, showing that the desirable copolymer was obtained with the narrow polydispersity. The increased thermal stability of PPE‐g‐PCzEMA was confirmed by thermogravimetric analysis and differential scanning calorimetry along with its macroinitiator. The optoelectronic properties of this copolymer were studied in detail by ultraviolet‐visible absorption, photoluminescence emission and excitation spectra, and cyclic voltammogram (CV). The results indicate that PPE‐g‐PCzEMA exhibits the solid‐state luminescent property dominated by individual lumophores, and also the energy transfer process from the PCzEMA blocks to the PPE backbone with a relatively higher energy transfer efficiency in the solid‐state compared to that of the solution state. Additionally, the hole‐injection property is greatly facilitated due to the presence of PCzEMA, as confirmed by CV profiles. All these data indicate that PPE‐g‐PCzEMA is a good candidate for use in optoelectronic devices. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3776–3787, 2007     

Crosslinked epoxy materials exhibiting thermal remendablility and removability from multifunctional maleimide and furan compounds

Crosslinked polymeric materials, which exhibit thermal remendability and removability through Diels–Alder (DA) and retro‐DA reactions, were obtained from using multifunctional maleimide and furan compounds as monomers. The synthesized monomers possess low melting points and good solubility in organo solvents to show excellent processing properties. The performance of DA and retro‐DA reactions were demonstrated with DSC and FTIR measurements. High performance of thermal remendablility and removability of the crosslinked materials were observed with SEM and solvent tests. These materials were applicable in advanced encapsulants and structural materials. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 905–913, 2006     

Divinylsiloxane‐bisbenzocyclobutene‐based polymer modified with polystyrene–polybutadiene–polystyrene triblock copolymers

Divinylsiloxane‐bisbenzocyclobutene (DVS‐bisBCB) polymer has very low dielectric constant and dissipation factor, good thermal stability, and high chemical resistance. The fracture toughness of the thermoset polymer is moderate due to its high crosslink density. A thermoplastic elastomer, polystyrene–polybutadiene–polystyrene triblock copolymer, was incorporated into the matrix to enhance its toughness. The cured thermoset matrix showed different morphology when the elastomer was added to the B‐staged prepolymer or when the elastomer was B‐staged with the DVS‐bisBCB monomer. Small and uniformly distributed elastomer domains were detected by transmission electron micrographs (TEM) in the former case, but TEM did not detect a separate domain in the latter case. A high percentage of the polystyrene–polybutadiene–polystyrene triblock copolymer could be incorporated into the DVS‐bisBCB thermoset matrix by B‐staging the triblock copolymer with the BCB monomer. The elastomer increased the fracture toughness of DVS‐bisBCB polymer as indicated by enhanced elongation at break and increased K1c values obtained by the modified edge‐lift‐off test. Elastomer modified DVS‐bisBCB maintained excellent electrical properties, high T_g and good thermal stability, but showed higher coefficient of linear thermal expansion values. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1591–1599, 2006     

Photocrosslinked poly(vinylbenzophenone)‐core micelles via mild Friedel–Crafts benzoylation of polystyrene amphiphiles

Photocrosslinkable poly(vinylbenzophenone)‐containing polymers were synthesized via a one‐step, Friedel–Crafts benzoylation of polystyrene‐containing starting materials [including polystyrene, polystyrene‐block‐poly(tert‐butyl acrylate), polystyrene‐block‐poly(ethylene oxide), polystyrene‐block‐poly(methyl methacrylate), and polystyrene‐block‐poly(n‐butyl acrylate)] with benzoyl trifluoromethanesulfonate as a benzoylation reagent. The use of this mild reagent (which required no added Lewis acid) permitted polymers with well‐defined compositions and narrow molecular weight distributions to be synthesized. Micelles formed from one of these benzoylated polymers, [polystyrene_0.25‐co‐poly(vinylbenzophenone)_0.75]₁₁₅‐block‐poly(acrylic acid)₁₄, were then fixed by the irradiation of the micelle cores with UV light. As the irradiation time was increased, the pendent benzophenone groups crosslinked with other chains in the glassy micelle cores. Dynamic light scattering, spectrofluorimetry, and Fourier transform infrared spectroscopy were all used to verify the progress of the crosslinking reaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2604–2614, 2006     

Probing the use of small‐angle light scattering for characterizing structure of titanium dioxide/low‐density polyethylene nanocomposites

Small‐angle light scattering (SALS) measurements were used to study the structure of titanium dioxide (TiO₂)/low‐density polyethylene (LDPE) nanocomposites. The results showed that the scattering from LDPE crystalline structures and the scattering from TiO₂ nanoparticles can be resolved and separated. It is shown that the independent effects of crystallization conditions and the presence of nanoparticle aggregates on the spherulitic structure of the LDPE matrix can be determined by analyzing the scattering patterns using the methods proposed. From the SALS results, we conclude that the nanoparticle surface chemistry affects both nucleation of spherulites and their structure particularly under rapid cooling conditions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1084–1095, 2006     

Chiral separation of synthetic vicinal diol compounds by capillary zone electrophoresis with borate buffer and beta-cyclodextrin as buffer additive.

The investigation on capillary electrophoretic enantioseparation of six synthetic compounds containing vicinal diol groups has been undertaken to acquire the optimum conditions using native beta-cyclodextrin (beta-CD) as chiral selector and borate as a background electrolyte. The separation was carried out in an uncoated capillary (58.5 cm x 75 microm i.d., effective length 48.5 cm) and the effects of several important factors were investigated in detail. The results showed that beta-CD as a chiral selector exhibited good enantioselectivity and that the enantioseparation was greatly influenced by the structure of the diols, the borate concentration and the buffer pH. The optimum performance was obtained for the chiral vicinal diols under the conditions of 200 mM borate buffer of pH 9.8 containing 1.7% beta-CD at an applied voltage of 15 kV and a capillary temperature of 20 degrees C. Under the conditions, four diols were baseline separated with fast analysis time and the good theoretical plate numbers (above 10 x 10(4)) and favorable migration-time reproducibilities (RSDs below 3.0%) were obtained. The separation results were satisfactory.     

Some existence results on periodic and generalized periodic solutions for singular hamiltonian systems

In this paper, we use the variational method to study the existence of periodic and generalized periodic solutions of planar second order Hamiltonian systems when a singular potential is present. The results obtained are applied to the study of generalized periodic solutions of the Restricted Three-Body Problem and the Planarn-Body Problem.     

Asymmetric synthesis XXVII: Asymmetric catalytic trimethylsilylcyanation of aldehydes by novel Ti-chiral Schiff base complexes

Enantioselective catalytic trimethylsilylcyanations of aldehydes with 48% to 92% e.e. have been studied using the novel Ti-chiral Schiff base complexes. We have found that the catalyst led to high enantoselectivity when the molar ratio of the Schiff base 1 to Ti(O-i-Pr)₄ was 2:1.