Tidwell-Mortimer

Reactivity ratios for 1-hexene (M ) with 5-methyl-1,4-hexadiene CM2) copolymerization at 30 c in hexane solvent using a Et2AlCl/6-TiCl3 AA catalyst system (Al/Ti atomic ratio s 1.5) were determined. The compositions of copolymers were measured by 300 MHz 1H-NMR spectroscopy. The reactivity ratios, calculated by the Tidwell-Mortimer method, were 1.1 + 0.2 for each of the two monomers. 

As a check on our experimental and calculation procedures, we examined the copolymerization of 1-hexene and 1-decene (Table V) which had been investigated by Lipman (30). The copolymer composition was determined by using 300 MHz H-NMR and the reactivity ratios were calculated by the Tidwell-Mortimer method (22). The values of r (1-hexene) = 1.1 + 0.2 and r2 (1-decene) = 0,9 + 0,2 are in excellent agreement with Lipman s values of 1,3 and 0.9, respectively. It should be noted that in the latter investigation the copolymers were analyzed by IR spectroscopy and the reactivity ratios were calculated according to the method of Mayo and Lewis (32). 

Table I lists monomer feed compositions, copolymer compositions and conversions obtained in the copolymerization experiments. The copolymerization diagram of the system (Fig. 4) shows a tendency towards alternation with an azeotropic point at 70 mole % MA. Reactivity ratios for the aFS-MA copolymerization system, determined by the Kelen-Tudos method were r =0.26 and The KT-plot is shown in Figure 5. Average monomer feed compositions were used for this determination whenever the conversion was above 10 wt. percent. Almost identical values of the reactivity ratios were obtained when calculated by the Tidwell-Mortimer method. The reactivity ratio product for this copolymerization system ( MA aFS" 2) indicates a tendency for alternation.

The experimental composition data are unequally weighted by the Mayo-Lewis and Fineman-Ross plots with the data for the high or low compositions (depending on the equation used) having the greatest effect on the calculated values of r and r2 [Tidwell and Mortimer, 1965, 1970]. This often manifests itself by different values of r and r2 depending on which monomer is indexed as Mi. 

A quarter of a century ago Behnken [224] as well as Tidwell and Mortimer [225] pointed out that the linearization transforms the error structure in the observed copolymer composition with the result that such errors after transformation have no longer zero mean and constant variances. It means that such transformed variables do not meet the requirements for the least-squares procedure. The only statistically accurate means of estimation of the reactivity ratios from the experimental data is based on the non-linear least-squares procedure. An effective computing program for this purpose has been published by Tidwell and Mortimer (TM) [225]. Their method is considered to be such a modification of the curve-fitting procedure where the sum of the squares of the difference between the observed and computed polymer compositions is minimized. 

Tidwell and Mortimer noted that the Fineman and Ross method does not treat experimental data with equal weight, yielding physically unrealistic results in some cases [172]. In order to remove this drawback, Tud6s et al. [173] proposed a modification of eqn. (80) which can also be evaluated graphically... 

The most generally useful methods and the only statistically correct procedures for calculating reactivity ratios from binary copolymerization data involve nonlinear least squares analysis of the data or application of the error in variables (EVM) method. Effective use of either procedure requires more iterations than can be performed by manual calculations. An cfHcicnl computer program for nonlinear least squares estimates of reactivity ratios has been published by Tidwell and Mortimer [13]. The EVM procedure has been reported by O Driscoll and Reilly [14]. 

By Fineman-Ross method and confimed by the Mortimer-Tidwell (22) non-linear least square computed method. 

Besides the above methods, Tosi suggested a new method called method of grouping, which was claimed to have minimal computation difficulty, but only provides approximate values. Tidwell and Mortimer proposed a nonlinear least square method by minimizing the difference between the observed and calculated copolymer compositions. This method was claimed to circumvent the subjective judging of experimental data and lead to better results compared to other methods, although its computation process is quite complicated. 

In order to determine the reactivity of pentachlorophenyl acrylate, 8, in radical initiated copolymerizations, its relative reactivity ratios were obtained with vinyl acetate (M2), ri=1.44 and r2=0.04 using 31 copolymerization experiments, and with ethyl acrylate (M2), ri=0.21 and r2=0.88 using 20 experiments.The composition conversion data was computer-fitted to the integrated form of the copolymer equation using the nonlinear least-squares method of Tidwell and Mortimer,which had been adapted to a computerized format earlier. 

By Fineman-Ross method and confirmed by the Mortimer-Tidwell (22) non-linear least square computed method. b By assuming that the product of reactivity ratio equals unity and using the relationship rj = Fi fp/Fp fi where Fj and / denote the mole fractions of isobutylene in the copolymer and charge, respectively, and Fp and fp those for (3-pinene. c By Fineman-Ross method. 

P. W. Tidwell and G. A. Mortimer, Science of determining copolymerization reactivity ratios, J. 

There are two ways to improve the accuracy of reactivity ratios estimates. The first one is to carry out ejq)etiments at the optimal comonomer feed composition. The intuitive approach is to carry out ejq)etiments at compositions that are equally distributed over the entire composition range. This method is very frequently fotmd in literature. For getting a first impression of the value of the reactivity ratios, this approach is very well suited. However, once initial estimates of reactivity ratios are available, experiments can be carried out at compositions where the sensitivity toward changes in reactivity ratios is maximal. Tidwell and Mortimer" derived expressions for these comonomer feed compositions. They did this exercise for the TM and came up with the expressions shown in eqns [37] and [38], where /21 and f22 are the fractions of monomer 2 in the reaction mixtrue that are most suitable for the accurate determination of reactivity ratios ... 

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