Analysis of plane and axisymmetric flows of incompressible fluids with the stream tube method: Numerical simulation by trust-region optimization algorithm

New concepts for the study of incompressible plane or axisymmetric flows are analysed by the stream tube method. Flows without eddies and pure vortex flows are considered in a transformed domain where the mapped streamlines are rectilinear or circular. The transformation between the physical domain and the computational domain is an unknown of the problem. In order to solve the non-linear set of relevant equations, we present a new algorithm based on a trust region technique which is effective for non-convex optimization problems. Experimental results show that the new algorithm is more robust compared to the Newton-Raphson method.     

Polymérisation anionique amorcée par les composés lamellaires du graphite et du lithium

In the present work, we use the binary insertion compound LiC₁₂ to polymerize styrene, methyl methacrylate, butadiene, isoprene, and to copolymerize isoprene and styrene in various hydrocarbon solvents (aromatics and aliphatic) and etheral solvents. We show that the styrene polymerization in aromatic solvents gives better yields than in the etheral solvents, the polymer being atactic. Methyl methacrylate does not polymerize in toluene but does so completely in DME. More generally, the yields of polymerization are better with KC₃₇ than with LiC₁₂ because of the different capacities of the monomer to get into the carbon layers. The polymerization of dienes with LiC₁₂ shows that the microstructures of the polymer obtained in π-or n-donor solvents are similar to the ones obtained by homogenous polymerization with Li cation in such solvents. However, for isoprene in cyclohexane, the results are different. The isoprene styrene copolymers are statistical ones and the mean length of styrene blocks is less than 5. The monomer interaction with the insertion compound and the growing chain geometry between the carbon layers are the facts which control either the stereospecificity of the polymerization or the selectivity of the copolymerization.     

Phenomenes de complexation entre un peroxyde et les monomeres vinyliques polaires etudies par resonance magnetique protonique

The self association of cumyl hydroperoxide and its complexing with polar monomers have been studied by proton magnetic resonance. These complexations are exothermic and strongly temperature dependent. It has been suggested that the complexation of cumyl hydroperoxide by polar monomers could be one of the causes of its efficiency in initiating the radical polymerization of vinyl monomers on an ethyl-zinc terminated polyethylene chain to form radical block copolymers. However, if this phenomenon has an effect on the initiation, it should not affect the propagation mechanisms, because the hydroperoxide is destroyed by ZnEt₂ during initiation. Moreover, the tacticity of radical polymethylmethacrylate, obtained at 60° with (ZnEt₂—cumyl hydroperoxide) in heptane does not differ from the conventional radical polymer.     

Conformations of luteoskyrin and rugulosin in solution

The pigments Luteoskyrin (Ls) and Rugulosin (Rg) might adopt a priori two extreme conformations, a planar and an angular one. To determine the predominant conformation in solution, the nature of the lowest energy transition of the chromophores and the presence of intramolecular H-bonding have been investigated. The solvent effects on electronic absorption and CD spectra indicated the π-π* nature of the lowest energy transition. Treatments of the electronic absorption results according to McRae and Kosower relations, IR absorption and PMR spectra suggested the presence of strong intra-molecular H-bonds. From these results it was concluded that Ls and Rg adopted in a variety of solvents the most planar conformation.     

Nouvelle méthode de détermination des taux de réativité des copolymères par résonance magnétique nucléaire: Application aux poly(méthacrylate de méthyle–chlorure de vinylidène)

Constant-composition copolymers of methyl methacrylate and vinylidene chloride produced by radical copolymerization are studied by ¹H-NMR at 60 and 250 MHz. The different methods of the literature for the derivation of reactivity ratios from either the copolymer composition or the sequence average lengths, or even the diad distribution, are applied but lead to rather dispersed results. A new graphical method is proposed, based on the use of peculiar values of the triad distribution functions. It allows us to detect a penultimate effect for the vinylidene chloride-rich region. In the same range, a change in tacticity of the diads and triads on the methylmethacrylate sequences, as compared with homopolymers, is observed; it suggests that the anomaly is caused by the competition of the depropagation reaction.     

Polymérisation anionique de l'isoprène: Nature de la paire d'ions et stéréospécificité

With accumulated HR-NMR spectra of anionic polyisoprenes, it has been possible to study the influence of the nature of the propagating species on the microstructure of the obtained polymers If free ions are responsible for the propagation, the microstructure (1,4-: 25%, 1,2-: 33%, 3,4-: 42%) does not depend on the nature of the cations. But with contact ion pairs, the different addition modes are governed by the size of the alkali metal counterions. Mechanisms of anionic propagations via diene–cation coordination are proposed.     

Chloration d'un polyethylene ramifie influence de la temperature et du solvant

The chlorination of branched high-pressure polyethylenes, promoted by u.v. at various temperatures in carbon tetrachloride and 1,1–2,2 tetrachloroethane, has been studied. It has been possible to elucidate the influence of the temperature and the nature of the solvent on the characteristics of the chlorinated polymers.The chlorination is more efficient in carbon tetrachloride, where the efficiency of the u.v. is not affected by the medium.At the same degree of chlorination, the chain-breaking mechanisms are more important in carbon tetrachloride than in tetrachloroethane; they increase when the temperature of the medium increases. The chlorine-saturated polyethylene obtained in carbon tetrachloride is richer in 1,2 dichloroethylene sequences.Below 60°, the yield of chlorinated polymer is the same in the two solvents. Chlorination at higher temperature in tetrachloroethane does not improve the structural regularity or the yield of the chlorine-saturated polyethylenes.     

Calorimetric study of the glassy state XII. Plural glass-transition phenomena of ethanol

Ethanol was found to give a metastable crystalline phase (crystal-II) when the liquid was cooled at a moderate rate. Glassy states of liquid and of newly found crystal-II were obtained in the calorimeter cell by controlling the cooling rate of the liquid. The heat capacities of these phases as well as that of the stable crystal-I were measured by an adiabatic calorimeter in the temperature range between 14 and 300 K. The glass transition temperature T_g, the heat-capacity jump at T_g, and the residual entropy were found to be 97 K, 35.3 J K^?1 mol^?1, and 8.93 J K^?1 mol^?1 for the glassy liquid, and 97 K, 22.8 J K^?1 mol^?1, and 4.24 J K^?1 mol^?1 for the glassy crystal-II, respectively. The values for the residual entropy are referred to the third-law entropy for crystal-I.The heat capacities reported previously for the supercooled liquid by Gibson et al. and by Parks and Kelley agree well with those for the metastable crystal-II. Those of the supercooled liquid connect smoothly with those obtained for the liquid above the melting temperature. Thus, ethanol is found to be another example of a low-molecular-weight compound which shows multiple glass-transition phenomena.