Stability of a two-dimensional stationary rotating flow in an exterior cylinder

We investigate the stability of an exact stationary flow in an exterior cylinder. The horizontal velocity is the two-dimensional rotating flow in an exterior disk with a critical spatial decay, for which the L² stability is known under smallness conditions. We prove its stability property for three-dimensional perturbations although the Hardy type inequalities are absent as in the two-dimensional case. The proof uses a large time estimate for the linearized equations exhibiting different behaviors in the Fourier modes, namely, the standard L²-$L^q$ decay of the two-dimensional mode and an exponential decay of the three-dimensional modes.     

Relationship between the distortion of polyene chains from planarity and the Raman activity of the in-phase CH out-of-plane wag

The relationship between the distortion of polyene chains from planarity and the Raman activity of the in-phase CH out-of-plane wag is examined by performing density functional theory calculations. The vibrational wavenumbers, vibrational modes, Raman activities and infrared absorption intensities of several oligoene (or polyene) molecules are calculated for model structures having various kinds of distortion around the CC double and/or single bond(s). The results of calculations show that the molecular distortion induces the Raman activity of the in-phase CH out-of-plane wag which should be Raman-inactive for the planar structure. The Raman activity of the in-phase CH out-of-plane wag is particularly enhanced when the molecule is uniformly helical. The origin of a weak Raman band at about 1010 cm⁻¹ of trans-polyacetylene is discussed on the basis of the calculated results.     

Vinyl ethers with a functional group: Living cationic polymerization and synthesis of monodisperse polymers

The living cationic polymerization of vinyl ethers (VEs) having a (polar) functional pendant has been achieved by the hydrogen iodide/iodine (HI/I₂) initiating system to give polymers with a very narrow molecular weight distribution (MWD) (M_w/M_n ≤ 1.2). The functional pendants include benzyl, saturated or unsaturated ester, (poly) oxyethylene, and substituted phenoxyl groups. Although these polar groups often disturb cationic vinyl polymerization by inducing chain transfer and termination, the HI/I₂ initiator cleanly polymerized the “functionalized” VEs without side reactions, mostly in nonpolar media at low temperatures below −15 °C. The HI/I₂-initiated living polymerization also provided facile methods to synthesize new functional polymers, including water-soluble polymers, macromolecular amphiphiles, and macromers, all having a narrow MWD. The simplest example is the living polymerization of VEs carrying an oxyethylene chain [-(CH₂CH₂O)_n-R] as pendant, which directly yields water-soluble polymers. The debenzylation of poly(benzyl VE) prepared with HI/I₂ led to poly(vinyl alcohol). Polymers of the saturated ester-containing monomers (2-acetoxyethyl and 2-benzoyloxyethyl VEs) were readily hydrolyzed into poly (2-hydroxyethyl VE), soluble in water and swellable in methanol. This lead was extended to the synthesis of a new amphiphile, poly(cetyl VE-b-2-hydroxyethyl VE), from a block copolymer of cetyl and 2-acetoxyethyl VEs prepared by their sequential living polymerization initiated with HI/I₂. An adduct between HI and 2-vinyloxyethyl methacrylate [CH₃-CH(I)-OCH₂CH₂OCOC(CH₃) =CH₂] was found to initiate living polymerizations of VEs in the presence of iodine; the products were methacrylate-type macromers carrying a poly(VE) side chain with a narrow chain-length distribution.     

Spectroscopic studies of conducting polymers

Electronic and vibrational spectra of poly(p-phenylenevinylene) doped with donors or acceptors have been studied, together with the spectra obtained for the radical ions and divalent ions of its oligomers. The electronic absorption spectra of doped poly(p-phenylenevinylene) in the region from visible to near-infrared show two bands for the H₂SO₄-doped species and one very broad band for the Na-doped species. On the basis of the analyses of resonance Raman spectra, the two electronic absorption bands of the H₂SO₄-doped species are attributed to a polaron-lattice structure, whereas the broad band of the Na-doped species is attributed to overlapping absorptions associated with localized electronic levels of polarons and bipolarons. A Pauli spin susceptibility of the H₂SO₄-doped species is explained by the polaron-lattice structure.     

Design and initiators of living cationic polymerization of vinyl monomers

This paper discusses recent developments in living cationic polymerization of vinyl monomers, specifically focusing on (a) new initiating systems, (b) kinetics and mechanism, and (c) controlled polymer synthesis. The new initiating systems were based on nucleophilic stabilization of the growing carbocations, either by counteranions (as in phosphate/ZnI₂ and Me₃SiI/ZnI₂ systems) or by added Lewis bases (as 2,6-dimethylpyridine for EtAlCl₂). The kinetic study included the determination of the lifetime of living cationic polymers. The controlled polymer synthesis by living cationic processes led to not only end- and pendant-functionalized polymers of narrow molecular weight distributions but also star-shaped polymers and sequence-regulated vinyl ether oligomers with functional groups.