Function spaces over GO-spaces: Part I

We describe the structure of spaces of continuous step functions over GO-spaces. We establish a relation between the Dedekind completion of a GO-space L and properties of the space of continuous functions from L to 2 with finitely many steps. We use the established relation to prove that a countably compact GO-space L has Lindelöf Cp(L) iff the Dedekind remainder of L is Lindelöf and every compact subspace of L is metrizable. Or equivalently, a countably compact GO-space L has Lindelöf Cp(L) iff every compact subspace of L is metrizable and a Gδ-set in L. Other results are obtained.     

Synthesis and characterization of poly(arylene ether)s containing 6‐(4‐hydroxyphenyl)pyridazin‐3(2H)‐one or 6‐(4‐hydroxyphenyl)pyridazine moieties

A series of novel soluble pyridazinone‐ or pyridazine‐containing poly(arylene ether)s were prepared by a polycondensation reaction. The pyridazinone monomer, 6‐(4‐hydroxyphenyl)pyridazin‐3(2H)‐one ( 1 ), was synthesized from the corresponding acetophenone and glyoxylic acid in a simple one‐pot reaction. The pyridazinone monomer was successfully copolymerized with bisphenol A (BPA) or 1,2‐dihydro‐4‐(4‐hydroxyphenyl)phthalazin‐1(2H)‐one (DHPZ) and bis(4‐fluorophenyl)sulfone to form high‐molecular‐weight polymers. The copolymers had inherent viscosities of 0.5–0.9 dL/g. The glass‐transition temperatures (T_g's) of the copolymers synthesized with BPA increased with increasing content of the pyridazinone monomer. The T_g's of the copolymers synthesized from DHPZ with different pyridazinone contents were similar to those of the two homopolymers. The homopolymers showed T_g's from 202 to 291 °C by differential scanning calorimetry. The 5% weight loss temperatures in nitrogen measured by thermogravimetric analysis were in the range of 411–500 °C. 4‐(6‐Chloropyridazin‐3‐yl)phenol ( 2 ) was synthesized from 1 via a simple one‐pot reaction. 2 was copolymerized with 4,4′‐isopropylidenediphenol and bis(4‐fluorophenyl)sulfone to form high‐T_g polymers. The copolymers with less than 80 mol % pyridazinone or chloropyridazine monomers were soluble in chlorinated solvents such as chloroform. The copolymers with higher pyridazinone contents and homopolymers were not soluble in chlorinated solvents but were still soluble in dipolar aprotic solvents such as N‐methylpyrrolidinone. The soluble polymers could be cast into flexible films from solution. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3328–3335, 2006     

Synthesis and characterization of polyimides derived from (3‐amino‐2,4,6‐trimethylphenyl)‐(3′‐aminophenyl)methanone and aromatic dianhydrides

A series of new polyimides were prepared via the polycondensation of (3‐amino‐2,4,6‐trimethylphenyl)‐(3′‐aminophenyl)methanone and aromatic dianhydrides, that is, 3,3′,4,4′‐biphenyltetracarboxylic dianhydride (BPDA), 4,4′‐oxydiphthalic anhydride, 3,3′,4,4′‐benzophenone tetracarboxylic dianhydride, and 2,2′‐bis(3,4‐dicarboxyphenyl) hexafluoropropane dianhydride. The structures of the polyimides were characterized by Fourier transform infrared and NMR measurements. The properties were evaluated by solubility tests, ultraviolet–visible analysis, differential scanning calorimetry, and thermogravimetric analysis. The two different meta‐position‐located amino groups with respect to the carbonyl bridge in the diamine monomer provided it with an unsymmetrical structure. This led to a restriction on the close packing of the resulting polymer chains and reduced interchain interactions, which contributed to the solubility increase. All the polyimides except that derived from BPDA had good solubility in strong aprotic solvents, such as N‐methyl‐2‐pyrrolidinone, N,N′‐dimethylacetamide, N,N‐dimethylformamide, and dimethyl sulfone, and in common organic solvents, such as cyclohexanone and chloroform. In addition, these polyimides exhibited high glass‐transition values and excellent thermal properties, with an initial thermal decomposition temperature above 470 °C and glass‐transition temperatures in the range of 280–320 °C. The polyimide films also exhibited good transparency in the visible‐light region, with transmittance higher than 80% at 450 nm and a cutoff wavelength lower than 370 nm. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1291–1298, 2006     

Preparation and characterization of optically active polystyrene via a chiral nitroxide‐mediated polymerization

2,2,6,6‐Tetramethyl‐4‐[d‐(+)‐10‐camphorsulfonyl]‐1‐piperidinyloxy was synthesized and used as a chiral nitroxide for the bulk polymerizations of styrene initiated with benzoyl peroxide (BPO), tetraethylthiuram disulfide (TETD), and thermal initiation. The results showed that the polymerizations proceeded in a controlled/living way; that is, the kinetics presented approximately first‐order plots, and the number‐average molecular weights of the polymers with narrow molecular weight distributions (weight‐average molecular weight/number‐average molecular weight) increased with the monomer conversion linearly. The molecular weight distributions in the case of thermal initiation were narrower than those in the case of BPO and TETD, whereas the polymerization rate with BPO or TETD as an initiator was obviously faster than that with thermal initiation. In addition, successful chain‐extension reactions were carried out, and the structures of the obtained polymers were characterized by gel permeation chromatography and ¹H NMR. The specific rotations of the polymers were also measured by polarimetric analysis. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1522–1528, 2006     

Meshless simulation of equilibrium swelling/deswelling of pH‐sensitive hydrogels

Hydrogels have been widely used in microelectromechanical systems (MEMS) and Bio‐MEMS devices. In this article, the equilibrium swelling/deswelling of the pH‐stimulus cylindrical hydrogel in the microchannel is studied and simulated by the meshless method. The multi‐field coupling model, called multi‐effect‐coupling pH‐stimulus (MECpH) model, is presented and used to describe the chemical field, electric field, and the mechanical field involved in the problem. The partial differential equations (PDEs) describing these three fields are either nonlinear or coupled together. This multi‐field coupling and high nonlinear characteristics produce difficulties for the conventional numerical methods (e.g., the finite element method or the finite difference method), so an alternative—meshless method is developed to discretize the PDEs, and the efficient iteration technique is adopted to solve the nonlinear problem. The computational results for the swelling/deswelling diameter of the hydrogel under the different pH values are firstly compared with experimental results, and they have a good agreement. The influences of other parameters on the mechanical properties of the hydrogel are also investigated in detail. It is shown that the multi‐field coupling model and the developed meshless method are efficient, stable, and accurate for simulation of the properties of the stimuli‐sensitive hydrogel. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 326–337, 2006     

Slow crack growth in blends of HDPE and model copolymers

The resistance to slow crack growth (SCG) was measured in binary blends of high density polyethylene (HDPE) and 5–10% concentrations of model ethylene-butene random copolymers by measuring the time to failure (t_f) under a constant stress intensity. An increase of t_f with the addition of the copolymer if the copolymer could crystallize and the increase was greater the higher branch density. The copolymer with 117 branches/1000C could not crystallize and therefore its blend had a t_f that was less than that of the HDPE. The fracture energies of the blends as determined by their resistance to SCG were compared with the energy by rapid fracture, J_c, as previously measured by Rhee and Crist. It is concluded that SCG is more sensitive to variations in the microstructure than is rapid fracture and that the differences in SCG behavior can be qualitatively explained in terms of the differences in microstructure of the blends. ©1995 John Wiley & Sons, Inc.     

A mathematical model of a class of problems for the transport of a mixture in air

An analytic solution of a class of boundary-value problems of mathematical physics describing the transport of a mixture in the atmosphere is considered. To solve these problems we apply the substitution method and the Fourier method. The solution of a boundary problem describing the process of contamination of the atmosphere by various substances is presented in the form of a series. The result obtained is useful for the solution of problems concerning the protection of the atmosphere.Translated fromVychislitel'naya i Prikladnaya Matematika, No. 69, pp. 87–90, 1989.     

Preparation of AgBiVMoO/-Al2O3 Catalysts for the Partial Oxidation of Propane

A novel mixed sol method was developed for the preparation of supported catalysts. Analyses by means of XRD and BET show that a 40%AgBiVMoO/γ-Al2O3 catalyst prepared by this method possessed high specific surface area and high dispersion of the active phase. As a result, high acrylic acid selectivity of 8.5% was obtained when the catalyst was used in the reaction of propane partial oxidation to acrylic acid in a fixed-bed reactor.     

Application of a nickel hexacyanoferrate(II) composite ion exchanger to fast separation of Ra from Fr and Ba from Cs

Sorption studies of Ra, Ba, Fr and Cs on nickel hexacyanoferrate(II) composite ion exchanger from hydrochloric acid and EDTA solutions are presented.