Polyolefins with Long Chain Branches Made with Single‐Site Coordination Catalysts: A Review of Mathematical Modeling Techniques for Polymer Microstructure

Abstract

Summary: Single‐site coordination polymerization catalysts are considered one of the most important developments on the technology of olefin polymerization during the last two decades. Among the several new capabilities of these catalysts is the ability to produce polymer molecules having narrow molecular weight distribution and long chain branches. These advances in polymer synthesis have stimulated the development of mathematical models to describe and predict several features of their molecular architectures. Many modeling techniques have been used for this purpose, including instantaneous distributions, population balances, the method of moments, and Monte Carlo simulations. This article reviews the mathematical models developed over the last decade to quantify the microstructure of polymers made with single‐site catalysts with special emphasis on the mechanism of long chain branch formation by terminal branching. magnified image

Predicting MWD and Branching Distribution of Terminally Branched Polymers Undergoing Random Scission

“…The two‐dimensional chain length/number of branch points distribution follows as the product of $p_{i} $ , from Equation 3, and $p_{n|i} $ , from Equation 10. For i / n → 0 this result approaches the solution given by Soares 7…”

“…Teymour and Campbell6 invented the “numerical fractionation” method to describe pre‐ and post‐gelation regimes of branching polymerization with transfer to polymer. Soares and co‐worker7, 8 addressed branching in metallocene‐catalyzed ethylene polymerization and have derived analytical expressions for the bivariate chain length/long chain branching distributions. Dias and Costas9 have employed a generating function approach to describe terminal branching.…”

“…Finding the branching architecture in itself has been dealt with as early as more than half a century ago by Flory 1. His and later studies2–14, 20 are in various ways based on properties of the length distributions of primary polymers making up the architectures. Flory's most probable length distribution thus could provide a most probable architecture distribution , on which the characterization of branched polymers by SEC using the Zimm–Stockmeyer21 equations even nowadays is still is in practice.…”

The Use of Instantaneous Distributions in Polymerization Reaction Engineering

“…Ray et al gave a short overview of the history of polymer reaction engineering where the development of instantaneous distributions and their contributions to polymer science and engineering were highlighted. For the examples discussed in this manuscript, the most relevant distributions are the most probable chain length distribution derived by Shultz and Flory independently, the bivariate distribution for chain length and chemical composition obtained by Stockmayer, and extensions of Flory and Stockmayer distributions to account for the presence of long chain branches …”

Dynamic Model of the Homopolymerization of Propylene with the Me2Si(2-Me-Ind)2ZrCl Catalyst: The Effect of Reaction Variables

“…Many papers have been published in which the kinetics of the polymerization and the mathematical models for the single-site (e.g., metallocene) or for the multi-site (e.g., Ziegler-Natta) catalyst have been studied [9,[21][22][23][24] . Of the different methods introduced in the literature for the development of these models, the most popular has been the method of moments, due to the low computational cost and its simplicity [22,25,26] .…”