Continuation of travelling‐wave solutions of the Navier–Stokes equations

An efficient way of obtaining travelling waves in a periodic fluid system is described and tested. We search for steady states in a reference frame travelling at the wave phase velocity using a first‐order pseudospectral semi‐implicit time scheme adapted to carry out the Newton's iterations. The method is compared to a standard Newton–Raphson solver and is shown to be highly efficient in performing this task, even when high‐resolution grids are used. This method is well suited to three‐dimensional calculations in cylindrical or spherical geometries. Copyright © 2006 John Wiley & Sons, Ltd.     

Order conditions for linearly implicit fractional step Runge Kutta methods

^{In this paper, we study the consistency of a variant of fractionalstep Runge–Kutta methods. These methods are designed tointegrate efficiently semi-linear multidimensional parabolicproblems by means of linearly implicit time integration processes.Such time discretization procedures are also related to a splittingof the space differential operator (or the spatial discretizationof it) as a sum of ‘simpler’ linear differentialoperators and a nonlinear term.}     

Synthesis of poly(vinyl chloride)‐b‐poly(n‐butyl acrylate)‐b‐poly(vinyl chloride) by the competitive single‐electron‐transfer/degenerative‐chain‐transfer‐mediated living radical polymerization in water

The synthesis of a block copolymer poly(vinyl chloride)‐b‐poly(n‐butyl acrylate)‐b‐poly(vinyl chloride) is reported. This new material was synthesized by single‐electron‐transfer/degenerative‐chain‐transfer‐mediated living radical polymerization (SET‐DTLRP) in two steps. First, a bifunctional macroinitiator of α,ω‐di(iodo)poly (butyl acrylate) [α,ω‐di(iodo)PBA] was synthesized by SET‐DTLRP in water at 25 °C. The macroinitiator was further reinitiated by SET‐DTLRP, leading to the formation of the desired product. This ABA block copolymer was synthesized with high initiator efficiency. The kinetics of the copolymerization reaction was studied for two PBA macroinitiators with number–average molecular weight of 10 k and 20 k. The relationship between the conversion and the number–average molecular weight was found to be linear. The dynamic mechanical thermal analysis suggests just one phase, indicating that copolymer behaves as a single material with no phase separation. This methodology provides the access to several block copolymers and other complex architectures that result from combinations of thermoplastics (PVC) and elastomers (PBA). From industrial standpoint, this process is attractive, because of easy experimental setup and the environmental friendly reaction medium. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3001–3008, 2006     

Single electron transfer–degenerative chain transfer living radical polymerization of N‐butyl acrylate catalyzed by Na2S2O4 in water media

Living radical polymerization of n‐butyl acrylate was achieved by single electron transfer/degenerative‐chain transfer mediated living radical polymerization in water catalyzed by sodium dithionate. The plots of number–average molecular weight versus conversion and ln[M]₀/[M] versus time are linear, indicating a controlled polymerization. This methodology leads to the preparation of α,ω‐di(iodo) poly (butyl acrylate) (α,ω‐di(iodo)PBA) macroinitiators. The influence of polymerization degree ([monomer]/[initiator]), amount of catalyst, concentration of suspending agents and temperature were studied. The molecular weight distributions were determined using a combination of three detectors (TriSEC): right‐angle light scattering (RALLS), a differential viscometer (DV), and refractive index (RI). The methodology studied in this work represents a possible route to prepare well‐tailored macromolecules made of butyl acrylate in an environmental friendly reaction medium. Moreover, such materials can be subsequently functionalized leading to the formation of different block copolymers of composition ABA. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2809–2825, 2006     

A non local density functional calculation of the diamagnetic susceptibilities and other electronic properties of noble gases and closed-shell ions

The non local weighted-density approximation (WDA) to the exchange-correlation potentialV _xc (r) is used to compute electron densities, ionization potentials and electron affinities of several atoms and ions. Especial care is taken in calculating and discussing 〈r ²〉 in noble gas atoms. Good results are obtained for all those quantities, but it is critical that the WDA is applied in such a way that it preserves the correct larger behaviour ofV _xc (r). A comparison of the calculated electron density with that of the Hartree-Fock method shows the effects of coulomb correlation. The density rearrangements upon the introduction of correlation agree qualitatively with the results of Configuration-Interaction calculations     

Extractive fluorimetric determination of ultratraces of lead with cryptand 2.2.2 and eosin

A new speetrofluorimetric method for determination of ultratraces of lead is based on solvent extraction into chloroform of the ion-pair formed between the positively-charged cryptate of lead with cryptand 2.2.2 and the eosinate anion. The detection limit for lead is 1 ng ml , and the linear working range is from the detection limit to 250 ng ml . The relative standard deviation is 3.7% at the 100 ng ml level. The method is highly selective for the extraction and determination of lead in the presence of other cations, and has been tested for direct determination of lead contamination in soft drinks. Aggregation of the extracted ion-pair in the organic phase has been demonstrated in fundamental extraction studies.     

Kinetic modelling of cadmium removal from phosphoric acid by non-dispersive solvent extraction

In this work it is reported that the kinetic modelling of the separation of cadmium from phosphoric acid by non-dispersive solvent extraction. Using Cyanex 302 as selective extractant, the extraction step was carried out in a hollow fibre module containing polypropylene fibres, whereas the concentration step required a ceramic module with tubular channels due to the high acidity of the backextraction agent. Application of the methodology previously reported by the authors led to the development of a kinetic model with three design parameters, i.e., equilibrium constant of the extraction reaction (K'_e = 6 × 10³ mol⁻²/l⁻²), membrane mass transport coefficient of the extraction module K_me=8.33×10⁻⁸ m/s) and of the backextraction module (K_ms=3.33×10⁻⁸ m/s), that described satisfactorily the behaviour of the separation-concentration system. Thus, in this work a new application of the non-dispersive solvent extraction technology is presented, characterising at the same time the behaviour and parameters of a new type of contactor, i.e., a tubular ceramic module.     

Boron trifluoride-methanol complex—mild and powerful reagent for deprotection of labile acetylated amines

A set of amino-group possessing cyanine dyes is obtained from their N-acetyl derivatives via deprotection with boron trifluoride-methanol complex in good yields.     

Density functional calculation of the electronegativity and other related properties of atoms and ions of the principal groups of the periodic table

The relation between the electronegativityχ of an atom or an ion (χ=??E(Z,N)/?N) and its finite difference (Mulliken like) counterpart has been studied for the elements of the groups IA to VIIA of the Periodic Table, using an approximate Density Functional Theory. Only the valence electrons are taken into account and the effect of the ionic core is simulated by a simple empty core pseudopotential. The first derivative ?χ/6N of the electronegativity has also been computed. The interest inχ and?χ/?N is illustrated by a simple model for the transfer of electronic charge in a molecule. Molecular electronegativities are then computed.     

2]pseudorotaxane formation with N-benzylanilinium axles and 24-crown-8 ether wheels

[reaction: see text] As a hybrid of the N,N-dibenzylammonium and 1,2-bis(pyridinium)ethane axles, various N-benzylanilinium cations were investigated as suitable axles for the formation of [2]pseudorotaxanes with the 24-membered crown ethers 24C8 and DB24C8. The effect of electron-donating OCH(3) and electron-withdrawing CF(3) groups on both the anilinium and benzyl aromatic rings was studied. Formation constants and structural details were compared to the [2]pseudorotaxanes formed by the two aforementioned dibenzylammonium and 1,2-bis(pyridinium)ethane axles.