Preparation of Well‐Defined Poly[(ethylene oxide)‐block‐(sodium 2‐acrylamido‐2‐methyl‐1‐propane sulfonate)] Diblock Copolymers by Water‐Based Atom Transfer Radical Polymerization

Summary: Well‐defined poly[(ethylene oxide)‐block‐(sodium 2‐acrylamido‐2‐methyl‐1‐propane sulfonate)] diblock copolymers [P(EO_m‐b‐AMPS_n)], have been obtained by water‐based ATRP using α‐methoxy‐ω‐(2‐methylbromoisobutyrate) poly(ethylene oxide)s (MeO‐P[EO]_m‐BrⁱB with m ranging from 12 to 113) and CuBr · 2Bpy (Bpy for 2,2′‐bipyridyl) as macroinitiator and catalytic complex, respectively. Compared to direct polymerization in water, it has been demonstrated that the water/methanol (3:1, v/v) mixture is better suited for predicting the final number‐average molar mass from the initial monomer‐to‐macroinitiator molar ratio and achieving a quite narrow polydispersity, even at high monomer conversion ( ≈ 1.4 at 80% conversion). The effect of temperature, solvent mixture composition and addition of NaCl salt on the polymerization rate and extent of control over the copolymer molecular parameters have been highlighted as well.

     

How Carbon Nanotube Crushing can Improve Flame Retardant Behaviour in Polymer Nanocomposites?

Nanocomposites based on an ethylene–vinyl acetate copolymer (27 wt.‐% vinyl acetate) and multiwall carbon nanotubes (MWNTs) have been prepared by melt blending and their thermal degradation and flame retardant properties have been evaluated. Special attention has been paid to the influence of the nanotube nature on the flammability properties and more particularly on the time to ignition (TTI) as measured by cone calorimetry. It has been shown that there is a strong influence of the nature of carbon nanotubes on the fire behaviour of the composites, especially previous MWNTs crushing proved to substantially delay the TTI while maintaining much reduced heat release rate (HRR). Such a remarkable behaviour might be explained by the chemical reactivity of radical species present at the surface/extremities of crushed MWNTs during the combustion process.

     

Ethylene–Norbornene Copolymerization by Carbon Nanotube‐Supported Metallocene Catalysis: Generation of High‐Performance Polyolefinic Nanocomposites

Homogeneous surface coating of multi‐walled carbon nanotubes is achieved for the first time by in situ copolymerization of ethylene (E) and 2‐norbornene (N) as catalyzed directly from the nanotube surface previously treated by a highly active metallocene‐based complex, i.e., rac‐Et(Ind)₂ZrCl₂/MMAO‐3A. The copolymerization reaction allows for the destructuration of the native nanotube bundles, which upon further melt blending with an ethylene–vinyl acetate copolymer (27 wt.‐% vinyl acetate) matrix, leads to high‐performance polyolefinic nanocomposites. The microstructural analysis of the surface‐coating copolymer was carried out by ¹³C NMR spectroscopy and allowed determination of the actual N content incorporated along the chains. Depending on the experimental conditions used (e.g., E pressure, solvent, feed N concentration) the relative quantity of E–N copolymer can be tuned, as well as the N content in the formed copolymers and accordingly their glass transition temperature.

     

Qualitative response of interaction networks: application to the validation of biological models

We advocate the use of qualitative models for the analysis of shift equilibria in large biological systems. We present a mathematical method, allowing qualitative predictions to be made of the behaviour of a biological system. These predictions are not dependent on specific values of the kinetic constants. We show how these methods can be used to improve understanding of a complex regulatory system. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Linear and nonlinear heat equations in $L^q_\delta$ spaces and universal bounds for global solutions

We develop a theory of both linear and nonlinear heat equations in the weighted Lebesgue spaces , where is the distance to the boundary. In particular, we prove an optimal estimate for the heat semigroup, and we establish sharp results on local existence-uniqueness and local nonexistence of solutions for semilinear heat equations with initial values in those spaces. This theory enables us to obtain new types of results concerning positive global solutions of superlinear parabolic problems. Namely, under certain assumptions, we prove that any global solution is uniformly bounded for by a universal constant, independent of the initial data. In all previous results, the bounds for global solutions were depending on the initial data. Received March 15, 2000 / Accepted October 18, 2000 / Published online February 5, 2001     

Espaces Homogenes Principaux et Points de 2-Division de Courbes Elliptiques

Dans cet article, nous nous intéressons aux problèmesde structure galoisienne associés aux couples (E/L, a),où E désigne une courbe elliptique définiesur le corps de nombres L et a un endomorphisme de E. Si E està multiplication complexe, nous notons k le corps quadratiqueimaginaire dont l'anneau des entiers décrit End(E) etL une extension de k. Ainsi a est-il selon les cas un entieralgébrique de k ou un élément de Z.     

On a class of degenerate elliptic operators arising from Fleming-Viot processes

We are dealing with the solvability of an elliptic problem related to a class of degenerate second order operators which arise from the theory of Fleming-Viot processes in population genetics. In the one dimensional case the problem is solved in the space of continuous functions. In higher dimension we study the problem in spaces with respect to an explicit measure which, under suitable assumptions, can be taken invariant and symmetrizing for the operators. We prove the existence and uniqueness of weak solutions and we show that the closure of the operator in such spaces generates an analytic -semigroup. Received December 4, 2000; accepted December 9, 2000.     

Chain transfer by addition-fragmentation mechanism. VII. Radical polymerization of vinyl monomers in the presence of ethyl 2-[1-(trimethylsilylperoxy)ethyl]propenoate and related compounds

Ethyl 2-[1-(trimethylsilylperoxy)ethyl]propenoate 1 , ethyl 2-[1-(dimethylvinylsilylperoxy)-ethyl]propenoate 2 , ethyl 2-[1-(1-(2-ethoxycarbonyl-1-methyl-2-propenylperoxysilyl)-1-methylethylperoxy)ethyl]propenoate 3 , and 2-phenyl-2-trimethylsilylperoxypropane 4 were synthesized and added to the free radical polymerization of vinylic monomers. 1 and 2 were found to show no homopolymerizability but act as effective chain transfer reagents in radical polymerizations of methyl methacrylate (MMA), styrene (St), and n-butyl acrylate (BA). The estimated chain transfer constants (C_tr) are as follows: C_tr ( 1 ) = 0.15 for MMA, 0.90 for St, and 2.03 for BA at 60°C; C_tr ( 2 ) = 0.12 for MMA, 1.16 for St, and 1.9 for BA at 60°C. ¹H–NMR spectra of poly(St) formed in the presence of 1 is consistent with the view that the polymers bear an oxirane at one terminal and an trimethylsilyloxy fragment at the other end. Moreover, peroxysilane 4 showed very low transfer properties by direct homolytic substitution (SH₂). These findings indicate that the ethyl 2-[1-(substituted dimethylsilylperoxy)ethyl]-propenoates 1–3 undergo chain transfer reaction via a intramolecular homolytic substitution (SHi) following an addition process. Preparation of poly(styrene) up to high conversion in the presence of 3 yielded to the formation of the corresponding polymeric structures bearing hydrolysable C(SINGLE BOND)O(SINGLE BOND)Si(SINGLE BOND)O(SINGLE BOND)C bonds. © 1996 John Wiley & Sons, Inc.     

Global Solutions to a Penrose–Fife Phase-field Model Under Flux Boundary Conditions for the Inverse Temperature

In this paper, we study an initial-boundary value problem for a system of phase-field equations arising from the Penrose–Fife approach to model the kinetics of phase transitions. In contrast to other recent works in the field, the correct form of the boundary condition for the temperature field is assumed which leads to additional difficulties in the mathematical treatment. It is demonstrated that global existence of strong solutions can be shown under essentially the same assumptions on the data as in the previous papers where a simplified boundary condition for the heat exchange with the surrounding medium has been used.