We extend van Ruymbeke et al.'s time marching algorithm (TMA) ( Macromolecules 2006, 39, 6248) in order to predict the linear viscoelastic properties of comb polymer melts. While former tube models have shown limitations for predicting the relaxation of comb polymer with short side branches, we observe here a good agreement between predictions and the experimental data for both combs with long and short side branches. In order to determine the origin of this improvement, we study the influence of the different elements present in the TMA model. In particular, we show the importance of taking into account the monomeric friction coming from the backbone itself in the total drag of the molecule, considering the modification of early time fluctuations and introducing the tube dilation process as a continuous function evolving through time. Then, based on a wide range of experimental data on different comb structures, we explore the limits of the relaxation behavior that comb polymers can show. If the friction from the relaxed side branches is significant, the backbone segments seem to fluctuate with respect to the closest branching point, just like a Cayley-tree molecule. On the other hand if the extra friction is negligible in comparison to the potential barrier of retraction along the backbone, the segments fluctuate with respect to the middle of the molecule, just like a linear chain.
A Ziegler‐Natta/metallocene hybrid catalyst was produced and utilized in the polymerization of ethylene with the aim of producing bimodal polyethylene. The MgCl2 adduct was prepared by a melt quenching method and Cp2ZrCl2 and TiCl4 catalysts were loaded, respectively, after treating the surface with TiBAl. The polymerization kinetics involved an induction period, followed by fragmentation and expansion of particles. SEM micrographs revealed that the spherical morphology was retained through the initial mild reaction conditions of induction period. The polymers produced showed bimodal molecular weight distribution patterns, suggesting that both components of the hybrid catalyst were active over the support.
The slurry homopolymerization of ethylene catalyzed by a Cp2ZrCl2/MAO catalytic system was studied. A simple kinetic model including initiation, propagation, transfer to monomer and cocatalyst, spontaneous transfer and spontaneous deactivation was developed to predict dynamic yield of polymerization and molecular weight of final products. Kinetic constants were estimated by numerical solution of polymerization kinetic model, combined with Nelder‐Mead simplex method. The model predicts that the propagation reaction has the lower activation energy in relation to chain transfer reactions which leads to decrease of molecular weight at elevated temperatures. The initiation reaction has however, the highest activation energy that results in raising the peak of reaction rate at higher temperatures.magnified image
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