Polynomial Inequalities with an Exponential Weight on (0,+∞)

We consider the weight ${{u(x) = x^{\gamma} e^{-x^{-\alpha}-x^{\beta}}}}$ , with ${{x \in(0,+\infty)}}$ , α >  0, β >  1 and γ ≥  0 and prove Remez-, Bernstein–Markoff-, Schurand Nikolskii-type inequalities for algebraic polynomials with the weight u on (0, + ∞).     

Evidence of the Quasi‐Living Character of the ansa‐Zirconocene/MAO‐Catalyzed Copolymerization of Ethylene and Norbornene

The kinetics of the ethylene‐norbornene copolymerization, catalyzed by rac‐Et(Ind)₂ZrCl₂/MAO, 90%rac/10%meso‐Et(4,7‐Me₂Ind)₂ZrCl₂/MAO and rac‐H₂C(3‐tert‐BuInd)₂ZrCl₂/MAO was followed by sampling from the reaction mixture at fixed time intervals. Catalyst activity, copolymer composition and molar mass were studied as a function of time. The polymers showed an unusually low polydispersity and a significant increase in their molar mass with time, suggesting a quasi‐living polymerization.     

A non‐PFT (polymerization filling technique) approach to poly(ethylene‐co‐norbornene)/MWNTs nanocomposites by in situ copolymerization with scandium half‐sandwich catalyst

The in situ synthesis of ethylene‐co‐norbornene copolymers/multi‐walled carbon nanotubes (MWNTs) nanocomposites was achieved by rare‐earth half‐sandwich scandium precursor [Sc(η⁵‐C₅Me₄SiMe₃)(η¹‐CH₂SiMe₃)₂(THF)] (1) activated by [Ph₃C][B(C₆F₅)₄], through a non‐PFT (Polymerization Filling Technique) approach. MWNTs nanocomposites with low aluminum residue were obtained with excellent yields even though small amounts of triisobutylaluminium were needed as scavenger to prevent catalyst poisoning by MWNT impurities. MWNT bundles were disaggregated and highly coated with Poly(ethylene‐co‐norbornene) [P(E‐co‐N)] as revealed by transmission electron microscopy. Interestingly, P(E‐co‐N) copolymers showed T_g over 130 °C as well as norbornene content over 50 mol %; both values were higher than those obtained by the cationic active species in 1 /[Ph₃C][B(C₆F₅)₄]. A series of copolymerization reactions by 1 /[Ph₃C][B(C₆F₅)₄]/AlⁱBu₃ without MWNTs produced copolymers with the same unexpected features. The NMR analysis revealed the presence of rac‐ENNE and rac‐ENNNE sequences. Thus, AlⁱBu₃ changed the stereoirregular alternating copolymer microstructure produced by 1 /[Ph₃C][B(C₆F₅)₄]. We conclude that AlⁱBu₃ is not only a scavenger for CNT impurities, but it reacts with the THF ligand to give coordinatively unsaturated active species. Finally, P(E‐co‐N)/MWNT masterbatches were mixed with commercial TOPAS to produce cyclic olefin copolymer nanocomposites with excellent dispersion of filler. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 5709–5719, 2009     

Seven-and eight-membered saturated fused rings zirconium and titanium metallocenes: A route for the synthesis of elastomeric polypropylene

Unbridged zirconium and titanium catalysts, where a seven-or eight-membered ring fused to a cyclopentadiene is associated with a phenyl substituent in position 2, were tested in propylene polymerization in order to investigate the possibility of observing a “fluxional behavior” and to obtain stereoblock polypropylene, even in the absence of the aromatic ring, usually present in this kind of catalysts, by introducing the conformational flexibility of the saturated ring as a new parameter. The microstructure, molecular properties, and thermal behavior of the polymers obtained showed that it is possible to observe a “fluxional behavior” even by replacing the basic indenyl structure with a slightly flexible saturated ring. Furthermore, this structural feature sensibly increases the stability of the complexes, thus making it possible to observe for the first time the oscillating behavior in titanocenes. The text was submitted by the authors in English.     

Glass Transition Temperature and Chain Flexibility of Ethylene‐Norbornene Copolymers from Molecular Dynamics Simulations

Summary: Model chains of ethylene‐norbornene copolymers were built up using the results of ¹³C NMR spectral analysis of copolymer samples synthesized with metallocene‐based catalysts. Our models statistically reproduce the microstructure, composition, and tacticity of the copolymer chains of experimental samples. They were used to test if MD simulations are suitable to investigate the relationships between microstructure and macroscopic properties. In particular, MD simulations were applied to calculate the glass transition temperature and to study the chain flexibility by the analysis of ACF of specific virtual bonds. Plots of specific volume versus temperature computed for models of four copolymer samples having different microstructures and norbornene contents yield T_g values in good agreement with experiments. Moreover, comparison of the ACFs provides some qualitative indications about the relationship between chain stereochemistry and T_g.

ACF functions of the virtual bonds with microstructures NENE (bottom) and ENNE (top).     

Ethylene‐norbornene copolymers prepared with metallocene‐ based catalysts: new sequence assignments by 13C NMR

A series of ethylene‐norbornene copolymers were synthesized in the presence of zirconocenes with different symmetries and ligand patterns and at different norbornene (N)/ethylene (E) mole ratios. Copolymers were characterized by ¹³C NMR spectroscopy; Inadequate NMR sequences were used also. The comparison of ¹³C NMR spectra of copolymers prepared with different norbornene content and the correlation between ¹³C NMR chemical shifts and conformational structures of the chain on the basis of molecular mechanics calculations were performed. Preliminary assignments were revised and new comonomer sequences such as ENNE which contain meso and racemo NN dyads were assigned.