Simultaneous long-chain branching and random scission: I. Monte Carlo simulation

Abstract

In free‐radical olefin polymerizations, the polymer transfer reactions could lead to chain scission as well as forming long‐chain branches. For the random scission of branched polymers, it is virtually impossible to apply usual differential population balance equations because the number of possible scission points is dependent on the complex molecular architecture. On the other hand, the present problem can be solved on the basis of the probability theory by considering the history of each primary polymer molecule in a straightforward manner. The random sampling technique is used to solve this problem and a Monte Carlo simulation method is proposed. In this simulation method, one can observe the structure of each polymer molecule formed in this complex reaction system, and virtually any structural information can be obtained. In the illustrative calculations, the full molecular weight distribution development, the gel point determination, and examples of two‐ and three‐dimensional polymer structure are shown. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 391–403, 2001

Analytical Rheology of Polymer Melts: State of the Art

“…It can be characterized surprisingly well by only two parameters, the average molecular weight and the level of branching, even though the actual sample contains a mixture linear, star, H-shaped, comb, and hyperbranched molecules [337,338]. Algorithms for the generation of molecules of different shapes and sizes for various kinds of polymerizations have been developed by Tobita and coworkers [339][340][341][342][343][344], which can be helpful to reduce the "dimensionality" of the inverse problem by allowing the description of a complex ensemble of molecules using only a few parameters.…”

Model-Based Reactor Design in Free-Radical Polymerization with Simultaneous Long-Chain Branching and Scission

“…This kind of reaction system cannot be fully represented by a simple set of population balance differential equations [3][4][5][6][7]. On the other hand, by application of Monte Carlo (MC) method, based on the random sampling technique [8,9], history-dependence of branching and scission can be fully accounted for [7,[10][11][12]. In this MC simulation method, the structure of each polymer molecule can be observed directly on the computer screen, and very detailed structural information can be obtained.…”

Numerical prediction of nonlinear rheology of branched polymer melts

“…Tobita (2001) used such a procedure to consider the distribution of polymer structures arising from a free-radical polymerization occurring in a batch reactor (although the basic scheme can be generalized to other reactor types). The basic steps considered are initiation (rate R i ), chain propagation (rate R p ), branching (rate constant k b ), scission (rate constant k s ), chain transfer to small molecules (rate R f ), and termination by combination (rate R tc ) or by disproportionation (rate R td ).…”

“…For details of the Monte Carlo scheme, and for the relevant equations, we refer the reader to Tobita (2001). Repeated application of the algorithm produces a set of molecules selected on a weight-biased basis.…”