Rates of Ziegler-Natta Polymerization

The size of the catalyst particle has a considerable effect on the rate of polymerization of propylene. For a constant concentration of the monomer, [M]g (i.e., at a constant propylene pressure in the gas phase), it has been found that the rate of polymerization is a function of time. For ground catalysts, a maximum is obtained, whereas for unground particles (size up to 10), the rate accelerates to approach the same asymptotic stationary value. The typical behaviors are shown schematically in Figiue 5.11, which gives the different zones into which catalysts can be classified. The process has a buildup, a decay, and a stationary period. Natta has proposed the following explanation for these observations. 

To determine the stationary rate of polymerization, we assume that all the sites of the Ziegler-Natta catalysts are equivalent In the reaction mechanism given in Section 5.12, it was shown that aluminum ethylate reacts with TiCl3 to form an empty ligand (and, therefore, a polymerization center). For this reaction to occur, AlEt3 must first be adsorbed. We can write this schematically as 

2) can be assumed to be at equilibrium and can be given by the following Langmuir adsorption equilibrium relation  

The rate of polymerization, r, for large times can then be derived from Eq. (5.13.2) as follows  

If the various difiusional resistanees for the monomer are also negleeted, [M] ean be replaced by the concentration of the monomer [M] in the reaction mass. This may be related to the pressure P in the gas phase by using the Chao-Seader or Peng-Robinson equations of state, but for moderate pressines, Henry s law may as well be assumed, giving 

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