Mathematical Modeling of MWD and CBD in Polymerizations with Macromonomer Reincorporation and Chain Running

Abstract

A model is proposed for the computation of MWD and CBD when the simultaneous formation of LCB and SCB is possible. LCBs are produced through incorporation of unsaturated polymer chains. SCBs are produced through chain running as a series of spontaneous chain transfer and reinsertion steps. The model was solved numerically with the help of orthogonal adaptive collocation techniques. It is shown that ten collocation points are sufficient to provide accurate numerical solutions for the evolution of MWDs and CBDs. The model can be used successfully to represent experimental data available for ethylene polymerizations performed with nickel catalysts and butadiene polymerizations performed with neodymium catalysts.

Copolymerization of Ethylene with 1,9‐Decadiene: Part I – Prediction of Average Molecular Weights and Long‐Chain Branching Frequencies

“…Finally, Table 8 presents the reaction rate constants for ethylene homopolymerization, as shown in Equations (1) to (3), (5), and (6). Figure 2 shows the experimental data for ethylene feed flow rate used to estimate the parameters in Table 7.…”

“…catalysts (CGC), [2] make polyolefins with high strength and easy processability due to their narrow distributions of molecular weight (MWD) and the presence of small numbers of long-chain branches (LCB). [3,4] Constrained geometry catalysts are good incorporators of high α-olefins and dead chains that contain a terminal [5] and/or pendant unsaturations [6] known as macromonomers. [7] In the case of ethylene homopolymerization, the macromonomers are formed in situ by β-hydride elimination or transfer to ethylene reactions; macromonomers form LCBs when they are reincorporated into the growing chain.…”

Discrimination of Chain Branching Models in Addition Diene Polymerizations

“…Growing interest has been observed in the last few years regarding long-chain branched polyolefins catalyzed by metallocene and late transition metals. [1,2] Particularly, polyolefins with narrow chemical composition and molecular weight distributions and containing low amounts of long chain branching (LCB) present excellent mechanical and rheological properties. [3,4] Kinetic mechanisms that lead to formation of long-chain branches usually involve incorporation of chains with terminal double bonds, for example terminal vinyl groups, [3][4][5][6][7][8] or with pendant unsaturations, [1,9] known as macromonomers or macromers.…”

Modeling of 1,3‐Butadiene Solution Polymerizations Catalyzed by Neodymium Versatate

“…For this reason, the proposed model is computer intensive and demands computation times that are not compatible with on‐line real‐time industrial applications. Herrera‐Ordonez et al were also able to predict the MWD of polybutadienes produced in solution, although the proposed model was somewhat similar to the one presented by Ferreira Jr et al , presenting similar limitations for use in industrial sites for purposes of process monitoring and control.…”