Conclusion after Obtaining Second-order Model

Conclusion after Obtaining Second-order Model 

As said before, linear models are used to reach (move towards) optimum, so that the significance of regression coefficients is an assumption for successful application of the steepest ascent method. Linear models, therefore, include as many factors as possible, and full factorial experiments are even replicated with increased factor variation intervals. 

With nonlinear models, which are aimed at mathematical modeling or adequate description of the optimum region and that as a rule have numerous regression coefficients, rejection of insignificant regression coefficients is not so important as in the phase of linear modeling. For second-order models, an estimate of lack of fit or inadequacy of the model is of particular importance. 

As with an inadequate linear model, it is possible to switch to a higher order or a third-order model. Realization, processing of experimental results and analysis and interpretation are very complicated for third-order designs, which makes such a suggestion not efficient enough [16]. 

Removing the model inadequacy by introducing rejected factors (in the phase of screening experiments and linear model analysis) and by an increased number of trial replications, is much more acceptable. 

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Conclusion after Obtaining Second-order Model... 

The f22 values are in general lower than those obtained for propene or other a-olefms, in agreement with the low homopolymerization activity of norbomene. The f22 value for catalyst 1-5 is much greater than ri2 this shows the tendency of this catalyst to insert a third norbomene after the second one. It was clear that the next-to-last E or norbomene monomer unit exerts an influence on the reactivity of the propagating Mt-E or Mt-N species, which depends upon the catalyst stmc-ture. The second-order Markov model must be used to describe E-N copolymerizations promoted by metallocenes I-l, 1-2, and IV-1. A third-order or a more complex model may be required to fit the experimental data obtained with catalyst 1-6, where more sterically hindered indene substitutions are dominant. At higher norbomene concentrations, copolymers with all catalysts may need more complex models. These results allowed the conclusion that E-N copolymerization is dominated by the bulkiness of the norbomene monomer and of the copolymer chain. 

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