We report a kinetic model of chain-shuttling copolymerization using dual catalysts for solution α-olefin polymerization processes. This model focuses on predicting polymer properties such as the molecular weight and molecular weight distribution and the overall copolymer composition. We first validate the model through qualitative comparison between the model predictions and experimental observations reported in Arriola et al. (Science) in both a semibatch reactor and a continuous stirred-tank reactor (CSTR). Then, examples are given to illustrate how the model can be used to examine the effects of the chain-shuttling rate constant and the chain-shuttling-agent feed rate in a CSTR. Moreover, simulations using this model demonstrate how to prepare polymers with desired properties by manipulating catalyst compositions and monomer compositions in the feed.

We report the theoretical derivation of a kinetic model for the prediction of average block structures such as number-average blocks, average block length, and average number of linkage points per chain, etc., in chain shuttling polymerization in the presence of dual catalysts based on the proposed mechanism. We further investigate how the chain shuttling rate constant and virgin chain shuttling agent (CSA) feed rate affect the average block structures predicted by this theoretical model for polymers produced in a continuous stirred tank reactor (CSTR). The simulations demonstrate that the coordination of dual catalysts and CSA is the key to enabling a successful chain shuttling polymerization system.

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SYNPOSISIn the past, relative tie-chain concentration has been semiquantitatively characterized by infrared dichroism on a stretched sample and from brittle fracture strength. The probability of tie-molecule formation has also been theoretically estimated from chain dimensions and the semicrystalline morphology of the polymers. In this article the probability of tie-chain formation of monodisperse and homogeneous single-site ethylene copolymers has been estimated over a range of densities and molecular weights using the model proposed by Huang and Brown. The relative tie-chain concentration is obtained by multiplying tiechain probability with the volume fraction crystallinity of polymer. A modified rubber elasticity theory is applied to calculate the concentration of chain links between junction points (crystallites) of the INSITE' technology polymers (ITPs) from measured rubber modulus. It is expected that the chain-link concentration should relate to the tie-chain concentration. The calculated rubber modulus, or the chain-links concentration, of the ITPs increases with a n increase in density in the 0.865 to 0.910 g/cc range and did not change significantly in the density range of about 0.91 g/cc to 0.954 g/cc. Normalized rubber modulus and relative tie-chain concentration data shows that the relative tie-chain concentration predicted by Huang and Brown model and measured using the modified rubber elasticity theory are quantitatively similar below 0.91 g/cc density. However, above 0.91 g/cc density, the measured rubber modulus is influenced by additional tie-chain formation during deformation due to breakdown of crystallites and, hence, the discrepancy exists between the two methods of estimating relative tie-chain concentration. 0 1996 John Wiley & Sons, Inc.

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This work aims at deriving analytical solutions for the molecular architecture of multi‐block polymer synthesized in a dual‐catalyst single CSTR. While the relevant equations are developed for homopolymerization, they can easily be extended to copolymerization. Special emphasis is placed on the quantities associated with each catalyst rather than the overall ones. However, if all rate parameters are available, the expressions can be used to calculate the properties of the material made by each catalyst as well as the overall ones under various process conditions. Given the reasonable assumption of large residence time, the solutions are simplified to elucidate the kinetics of chain‐shuttling involving two catalysts. It is shown that systems with low chain‐shuttling ability, if DPPn,0 ≠ DPQn,0, may exhibit significant deviation from Flory's most probable distribution. Furthermore, systems with high chain‐shuttling ability produce macromolecules with more uniform architecture and polydispersity index close to 2.

Analytical solutions for the impact of branching on the polymer molecular architecture in the presence of two catalysts are developed. One catalyst forms only linear chains while the other produces linear as well as branched species. Emphasis is placed on the average molecular weight and polydispersity index of the populations associated with each catalyst rather than the overall quantities. By defining the cross-incorporation number, x, which represents the relative value of the b-hydride elimination and terminal double bond polymerization rate coefficients of each catalyst, we map the effect of branching on the molecular architecture of the polymer in order to understand the underlying kinetics and guide system design.