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of experimental results is usually dif cult. Changes in the initiator components often affect activity and stereoselectivity in opposite directions. The trends observed from one transition or group I III metal component to another may be different. In spite of the dif culties in understanding much of the available data, empirical formulation of initiators to achieve high stereoselectivity with high activity has been successful on at least an empirical basis with much resultant commerical success. Some generalizations are presented below on the effects of changes in the initiator components on stereoselectivity. These are generally restricted to a-ole ns; they may not apply to other monomers such as 1,3-dienes. 8-4h-1 Transition-Metal Component

After one iteration the empirical IC and the SC are very similar in shape. However after repeated iterations the shapes of the two curves diverge due to the iterative fitting procedure. Figure 9.3 gives the shape of the SCs after 2000 iterations. Note that despite its more complex shape we still see a central region of active influence (Section 8.5.4, p. 136) and then convergence to a constant (perhaps zero) --t f w .

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The most widely studied transition metal is titanium At various times, all oxidation states of titanium (II, III, IV) have been proposed for the active site of titanium-based initiators Most of the evidence points to titanium (III) as the most stereoselective oxidation state, although not necessarily the most active nor the only one [Chien et al, 1982] (Data for vanadium systems indicate that trivalent vanadium sites are the syndioselective sites [Lehr, 1968]) Initiators based on the a-, g-, and d-titanium trihalides are much more stereoselective (isoselective) than those based on the tetrahalide or dihalide By itself, TiCl2 is inactive as an initiator but is activated by ball milling due to disproportionation to TiCl3 and Ti [Werber et al, 1968] The overall stereoselectivity is usually a-, g-, d-TiCl3 > TiCl2 > TiCl4 % b-TiCl3 [Natta et al, 1957b,c].

The low stereoselectivity of b-TiCl3 relative to the a-, g-, and d-forms is a consequence of the different crystalline structure While a-, g-, and d-TiCl3 are similar in that all contain a layered structure [Natta, 1960a,b; Natta et al, 1961a,b,c,d], in g-TiCl3 the chlorines are cubic close-packed instead of hexagonal close-packed as in a-TiCl3 , d-TiCl3 has a mixed hexagonal and cubic close-packed layered structure, and b-TiCl3 consists of bundles of linear TiCl3 chains The structure of b-TiCl3 results in a surface in which half the titanium atoms have two vacancies and the other half have one vacancy The titanium sites containing two vacancies each are responsible for the low stereoselectivity of b-TiCl3 The two vacancies yield a site with a loose con guration of ligands since one of the chlorines and/or the growing polymer chain will be loosely bound.

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This is exactly opposite to the situation with the other titanium trichlorides (one vacancy per site) in which all chlorides and the polymer chain have xed positions in a rigid con guration on the titanium site That some isotactic polymer is formed with b-TiCl3 is a result of the presence of titanium sites that have only one vacancy each The oxidation state of the transition metal active sites is dependent not only on the transition-metal component but also on the group I III metal component For example, TiCl4 is usually used instead of TiCl3 in initiator recipes because it is a liquid and more conveniently handled but is usually employed under conditions (in combination with AlR3 or AlR2 Cl), which reduces a large fraction of titanium to the trivalent state.

We consider a simple problem with two classes and two features. The classes are linearly separable and were chosen from uniform distributions on rectangular regions (Figure 9.4). The procedure of the experiment was to progressively move one point, and note the effect on the separating hyperplanes. For each movement of the point, the MLP was refitted using the same starting weights. For comparison with the MLP classifier, we also calculated Fisher s linear discriminant function ( 3, p. 19). As the LDF gives a hyperplane onto which the data are projected, we plot the hyperplane given by the normal vector to the LDF and passing through the grand mean of the classes. Clearly both the LDF

Further, the extent of reduction depends on the amount of the group I III metal component relative to the transition metal [Kollar et al, 1968a,b; Schindler, 1968] At Al/Ti ratios greater than 3, there is extensive reduction to divalent titanium and a signi cant decrease in stereoselectivity The optimum ratio is usually near or less than 1 However, the situation is very different for the MgCl2 -supported initiators The typical initiator contains about 05 2% Ti, and the optimum Al/Ti ratio is often as high as 10 100 [Chien et al, 1982; Dumas and Hsu, 1984] Changes in the ligands of the transition metal component affect stereoselectivity [Natta et al, 1957a,b; Rishina et al, 1976] For propene polymerization by titanium compounds in.

a-TiCl3 > TiBr3 > TiI3 TiCl4 TiBr4 TiI4 TiCl4 > TiCl2 OC4 H9 2 ) Ti OC4 H9 4 Ti OH 4 8-36

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