Long-Chain Branching in Metallocene Polyethylenes

Soares and Hamielec developed kinetic models for the synthesis of both homopolymers [87] and copolymers [88] and have used these to show how reaction conditions affect the distributions of molecular weight and degree of branching. Beigzadeh et al. [89] proposed the use of a combined catalyst system to enhance the level of long chain branching. By 

The level of branching is often expressed simply in terms of A, the average number of branch points per thousand carbon atoms, and this is related to j8, the average number of branch points per molecule through Eq. 3.3 for the case of polyethylene. 

However, this single parameter contains no information about the distributions of branch points per molecule and the molecular weights of the various types of segment. For example, we note that many combinations of and / can give the same value of A. To determine the detailed structure, it is necessary to make a more detailed analysis of the reaction. Because this reaction system has been analyzed in great detail, it will be of interest to summarize the models used. Soares and Hamielec [87] developed a kinetic model based on the following reactions  

p-hydride elimination by the catalyst to give a dead chain with a terminal vinyl unit, i.e. a 

If one is interested only in the final structures of the molecules formed rather than the rate of reaction, only two parameters are important [94] pp, the probability of propagation (1+3) relative to that of termination (4), and Ip, the probability of adding a monomer (1) relative to that of adding a macromonomer (3). Given only these two parameters, one can, in principle, calculate all the quantities of interest. A simple example of such a relationship is shown as Eq. 3.4. 

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