(600i) Modeling and Kinetic Parameter Estimation of Ethylene Polymerization with Silica Supported Dimethylsilylene Bis(η5 –inden-1–ylidene)Zirconium Dichloride Catalyst Using Differential Evolution Approach

Metallocene-based catalyst systems are quite different from previous generations of catalysts. Now tunable catalyst systems are imminent to prepare well controlled polyolefin molecular architectures and to fine-tune their properties. Metallocenes based on Zirconium (Zr) are the most widely studied and useful at present. Hafnium (Hf) based metallocenes are generally less active but produce high molecular weights than do Zr metallocenes. Titanium (Ti) metallocenes are less active and less stereoslective than Zr and Hf both. Metallocene catalysts have four main advantages over the established polymerization catalysts. These catalysts can polymerize a very wide potpourri of vinyl monomers regardless of their molecular weights and steric features. The second advantage of a metallocene catalyst is that these posses single site types. The third advantage associated with metallocene catalysts is that the predominant mechanism for chain termination is by β-hydride elimination. This produces a vinyl double bond at the end of each polymer chain. Further functionalization of the vinyl group by graft polymerization with maleic anhydride and other functional monomers is far more effective than is typical for polyolefins obtained by conventional catalysts. Lastly, the most important feature of the metallocene catalysts is their ability to produce extremely stereoregular polymers. The molecular geometry of the metallocene molecule directly controls the stereoregularity of the resultant polymer. By the right choice of ligand environment it is possible to generate highly stereoregular polyolefins.^[1]

Metallocene catalysts consist mainly of compounds of group IV of transition metals (Ti, Zr, Hf) and a cocatalyst of aluminium compounds. Among them, zirconium compounds are the most active and common catalyst which are studied.^[2-8]

Compared with the wide-ranging studies of the relationship between catalyst structure and properties of the resultant products, study of the kinetics of metallocene catalysis has not been done extensively. Metallocene catalysts are essentially homogeneous in nature. For gas phase polymerization processes which require heterogeneous catalysts, metallocene catalyst are used supported on a carrier. The most commonly used support is SiO₂ or Al₂0₃.

The experimental data used in this work were taken from Roos et al. A glass autoclave fitted with a helical stirrer was used for ethylene polymerization with NaCl as a support bed.^[9]

In the present work, a model has been developed to describe the gas phase polymerization of ethylene with silica supported  catalyst and MAO as cocatalyst in an isothermal, semibatch reactor.

Polymer molecular properties, viz. number average molecular weight (), weight average molecular weight (), and polydispersity index (PDI) are calculated using the method of moments.

Parameter estimation is a cardinal step in establishing the kinetic models and can be esteemed as an optimization problem. Minimization of the objective function in parameter estimation problems, particularly in the field of polymer engineering, may lead to difficult numerical problems related to the large number of model parameters, high correlativity among model parameters and multimodal nature of the objective function.  In order to get the better of these difficulties, the use of heuristic optimization method, Differential evolution (DE) is proposed and ciphered in this work.  DE is a stochastic, population-based optimization algorithm introduced by Storn and Price in 1996 developed to optimize real parameter, real valued functions.^{[10, 11]}

Ethylene polymerization is simulated with the proposed model. Single site model did not adapt well to the experimental data.  But very good agreements of polymerization rate, averaged molecular weights and variation of polydispersity have been achieved for two site model.

References

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[11]      Price K.V. and Storn R., Dr. Dobb’s Journal, 22, 18–24 (1997).