On the domain dependence of solutions to the compressible Navier–Stokes equations of a barotropic fluid

We prove a general compactness result for the solution set of the compressible Navier–Stokes equations with respect to the variation of the underlying spatial domain. Among various corollaries, we then prove a general existence theorem for the system in question with no restrictions on smoothness of the spatial domain. Copyright © 2002 John Wiley & Sons, Ltd.     

Magnetic poly(N‐isopropylacrylamide) microspheres by dispersion and inverse emulsion polymerization

The aim of this study was to develop novel thermally responsive polymer microspheres with magnetic properties. Dispersion and inverse emulsion copolymerization of N‐isopropylacrylamide (NIPAAm) and N,N′‐methylenebisacrylamide (MBAAm) was investigated in the presence of γ‐Fe₂O₃ nanoparticles. The resulting microspheres were characterized in terms of morphology, size, polydispersity, iron content, and temperature‐dependent swelling using optical microscopy, transmission electron microscopy, scanning electron microscopy, QELS, and AAS. The effects of several variables, such as the concentration of γ‐Fe₂O₃, MBAAm crosslinking agent, Span 80 surfactant, 2,2′‐azobis(2‐methyloctanenitrile) (AMON) initiator, and polymerization temperature on the properties of the microspheres were studied. Swelling and thermoresponsive behavior of the microspheres containing γ‐Fe₂O₃ nanoparticles were also investigated. The microspheres contained about 8 wt % of iron. The presence of magnetic nanoparticles and their concentration changes did not have any significant effect on the temperature sensitivity of the composites. The particles gradually shrink into an increasingly collapsed state when the temperature is raised to 40 °C since the increase in temperature weakens the hydration and PNIPAAm chains gradually become more hydrophobic, which leads to the collapse of the particles. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5884–5898, 2007     

Tetrafunctional initiators for cationic polymerization of olefins

3,3′,5,5′‐Tetrakis(2‐chloro‐2‐propyl)biphenyl (biphenyl tetracumyl chloride, BPTCC) and 1,3‐bis[3,5‐bis(2‐chloro‐2‐propyl)phenoxy]propane (diphenoxypropane tetracumyl chloride, DPPTCC) were synthesized as initiators for quasiliving cationic polymerization of isobutylene (IB). In the synthesis of BPTCC, tetrafunctionality was achieved via the coupling of dimethyl 5‐bromoisophthalate (DMBI) using nickel dibromide bis(triphenylphosphine) and zinc in the presence of a base; in the synthesis of DPPTCC, two equivalents of dimethyl 5‐hydroxyisophthalate were linked via reaction with 1,3‐dibromopropane in the presence of potassium carbonate. Both initiators were used to initiate the polymerization of IB under quasiliving cationic polymerization conditions. PIB initiated from BPTCC revealed a chain end/molecule value (as determined by ¹H‐NMR) of 3.85, verifying the nearly exclusive production of 4‐arm polyisobutylene (PIB). GPC analysis revealed a narrow peak representing the target four‐arm PIB, with a slight shoulder at high elution volumes (low molecular weights). GPC analysis of the PIB initiated by DPPTCC revealed multimodal distributions, suggesting the formation of two‐, three‐, and four‐arm star polymers during the polymerization. This behavior was attributed to Friedel–Crafts alkylation of the initiator core after the addition of one IB unit, which was activated by the electron‐donating oxytrimethyleneoxy linking moiety. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5942–5953, 2004     

Scroll codes

We study algebraic geometric codes obtained from rational normal scrolls. We determine the complete weight hierarchy and spectrum of these codes.      

Numerical study of charge ordering in NaxCoO2

A simple microscopic model of charge ordering in the Na_xCoO₂ system is presented. The model takes into account the interplane interactions between the ordered Na ions and d electrons from the CoO₂ layers as well as the nearest-neighbor intraplane Coulomb interactions between d electrons. It is shown that a driving force of charge ordering in the CoO₂ layers is the interplane interaction that alone is able to describe various types of inhomogeneous charge ordering (e.g., the striped phases) as well as to predict correctly the conducting properties of the system.     

Synthesis and characterization of multiblock copolymers composed of poly(5‐methyl‐5‐benzyloxycarbonyl‐1,3‐dioxan‐2‐one) outer blocks and poly(L‐lactide) inner blocks

Ethylene glycol (EG) initiated, hydroxyl‐telechelic poly(L ‐lactide) (PLLA) was employed as a macroinitiator in the presence of a stannous octoate catalyst in the ring‐opening polymerization of 5‐methyl‐5‐benzyloxycarbonyl‐1,3‐dioxan‐2‐one (MBC) with the goal of creating A–B–A‐type block copolymers having polycarbonate outer blocks and a polyester center block. Because of transesterification reactions involving the PLLA block, multiblock copolymers of the A–(B–A)_n–B–A type were actually obtained, where A is poly(5‐methyl‐5‐benzyloxycarbonyl‐1,3‐dioxan‐2‐one), B is PLLA, and n is greater than 0. ¹H and ¹³C NMR spectroscopy of the product copolymers yielded evidence of the multiblock structure and provided the lactide sequence length. For a PLLA macroinitiator with a number‐average molecular weight of 2500 g/mol, the product block copolymer had an n value of 0.8 and an average lactide sequence length (consecutive C₆H₈O₄ units uninterrupted by either an EG or MBC unit) of 6.1. For a PLLA macroinitiator with a number‐average molecular weight of 14,400 g/mol, n was 18, and the average lactide sequence length was 5.0. Additional evidence of the block copolymer architecture was revealed through the retention of PLLA crystallinity as measured by differential scanning calorimetry and wide‐angle X‐ray diffraction. Multiblock copolymers with PLLA crystallinity could be achieved only with isolated PLLA macroinitiators; sequential addition of MBC to high‐conversion L ‐lactide polymerizations resulted in excessive randomization, presumably because of residual L ‐lactide monomer. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6817–6835, 2006     

On-line coupling of sequential injection extraction with restricted-access materials for sample clean-up and analysis of drugs in biological matrix

In this contribution, the on-line coupling of solid phase extraction (SPE), based on a restricted-access material (RAM), with sequential injection technique (SIA) for the analysis of biological samples, is described. The SIA-RAM system was tested with a new potential antileucotrienic drug (VUFB-19363 (Quinlukast)) for serum analysis. The method is based on SPE with the novel internal-surface reversed-phase column packing material-alkyl-diol silica (ADS). The supports tolerate direct and repetitive injection of proteinaceous fluids (plasma, serum) and allow reversed-phase partitioning at the internal surface. A column packed with a 25 microm C18 alkyl-diol support was used for direct serum injection. Using a 6-port selection valve and the system of three mobile phases, the polar matrix compounds and metabolites are removed by sequentially aspirated mobile phases with lower content of the organic part (methanol-water (2:98) and following acetonitrile-water (20:80)) to the waste, and then, the analyte enriched on the column is eluted by a strong mobile phase (acetonitrile-methanol-water (40:20:40)) to the UV detector without transfer loss. With the fully automated SIA system, a total analysis time of less than 10 min was achieved. The only off-line sample pre-treatment step required to remove particulate matter was centrifugation. The studies showed a range of linearity (2-40 microg ml(-1)) and a high recovery (93.6-96.8%) of drug from the biological matrix with coefficients of variation (RSD) less than 5.0% (n = 6). This paper introduces a new, simple and robust analytical technique suitable for screening determination and direct analysis of drugs in biological materials.     

Development of a universal Raman detector for microchromatography

Summary A detector for microchromatography in which Raman spectroscopy is used to identify the eluted species has been developed. The detector is designed to be applicable to a wide range of compounds without requiring the presence of a chromophore. Its use is illustrated in the analysis of nitro compounds on a 250 μm i.d. column. Raman spectra of each of the compounds could be identified as they passed the detector. The advatages of the use of fully deuterated solvents are demonstrated by the analysis of nitrobenzenes in methanol/water mobile phases. The detection limit for nitrobenzene using the Raman line at 1342 cm⁻¹ was 75ng.     

Conformational transitions of calixphyrin derivatives monitored by temperature-dependent NMR spectroscopy. Ab initio interpretation of the spectra

Eight meso-aryl calixphyrin derivatives were synthesized and their conformational equilibria and transitions studied with temperature-dependent NMR spectroscopy. On the basis of density functional computations, several conformer species could be identified and observed changes in chemical shifts explained. In some compounds, the aryl group rotation and porphyrin ring flipping could be monitored independently, as their NMR coalescence temperatures were well-separated. Calculated relative conformer energies, transition barriers, and isotropic shieldings agree well with the experimental data. In the meso-substituted porhyrins (calixphyrins) the sp3 carbon atoms perturb their pi-electron system and significantly modify the molecular shape and the flexibility. Even when the conjugation of the pi-electron system was destroyed by the nonplanarity, far-range electronic induction effects still exist and influence chemical shielding and molecular geometry. The aryl functional groups moderately modify the structure of the calixphyrin ring and thus can be used for fine-tuning of the mechanical and chemical properties of these compounds.