Ziegler-Natta polymerization kinetic models

In this section several empirical rate expressions for Ziegler-Natta polymerizations will be presented and attempts to model the polymerization will be described. It is found that several models could be proposed to explain the same rate equations. The models are based on the assumption of a fixed geometric center that has a definable identity and activity invariant with time. These assumptions, however, are far too simplistic and only limited general agreement of the models with the observed kinetic behavior or good agreement only in specific cases could be expected. 

Using the above type of experimental set-up for propylene polymerization with TiQs-AlEts in n-heptane, the rate of polymerization was measured [T. Keii, Kinetics of Ziegler-Natta Polymerizations , Halsted Press, New York, 1973] at different speeds of stirring and constant propylene pressure. The results obtained indicated that there were two different steady-state rate curves for the stirring speeds of 400 and 600 rpm. In each case, a steady bulk monomer concentration was reached in about 3-4 hours. Show how the overall process at steady state can be modeled to show dependence of the polymerization rate on stirring speed and to enable determination of both the mass transfer rate constant and polymerization rate constant from rate measurements at different stirring speeds. 

Very many kinetic models have been proposed for both heterogeneous and homogeneous Ziegler-Natta polymerization (c.f. 2,8,18) but for the purposes of this paper only the recent models proposed by Tait et al (26,29f30), Yermakov et al (31) and Bohm (39) will be considered. These three kinetic treatments have the common features that chain propagation is treated as a two-stage reaction, monomer... 

Kinetic model of Bohm. A very comprehensive reaction model has been proposed by Bohm (39) idiich is claimed to explain, at least in a qualitative manner, the knovm kinetic phenomena for both heterogeneous and homogeneous Ziegler-Natta polymerization reactions. This model has the following characteristics. 

Evaluation and Analysis of a Multisite Kinetic Model for Polymerization Initiated with Supported Ziegler—Natta Catalysts... 

Heterogeneous Ziegler-Natta catalysts used to polymerize olefins exhibit phenomena characteristic of active site heterogeneity (1- 5). Complex kinetic models which account for this likelihood have been developed and used only in simulation studies (6-7). 

There is vast experimental and theoretical evidence supporting the existence of multiple site types on heterogeneous Ziegler-Natta catalysts. From a mathematical modelling point of view, each site type has distinct polymerization kinetic constants and consequently produces polymer chains with different average properties. 

Keywords polymerization kinetics, polymerization reactors, mathematical modelling, molecular weight distribution (MWD), chemical composition distribution (CCD), Ziegler-Natta catalysts, metallocenes, microstructure, isotacticity distribution, mass transfer resistances, heat transfer resistances, effects of multiple site types. 

The chemistries utilized in gas-phase technologies employ the same Ziegler-Natta (314,315) and single-site (metallocene) catalysts (313) described in the processes included below. In gas-phase systems, however, the catalysts are generally solid-supported, but produce the same range of polybutadiene microstructures inherent to the nonsupported catalyst. Several patents also include anionic polymerization systems as useful in gas-phase processes (378). Kinetic modeling work has also been done to better predict the gas-phase polymerization behavior of 1,3-butadiene (379). 

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