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corresponds to cleavage of the initial particles to the smallest-sized particles. When the initial particle size is decreased (by ball milling), the time required to reach the steady-state polymerization rate is decreased (plot 2). Other factors responsible for the buildup period include the time needed for the formation of the active sites by reaction of the two metal components, slow initiation, and the presence of impurities. Most of these factors are moderated for the typical situation where the initiator system is preformed and allowed to age prior to use in initiating polymerization. The superactive supported initiators often show very little or no buildup period [Busico et al., 1986; Chien and Hu, 1987]. Many polymerizations show a settling period with a relatively rapid rise in rate to a maximum value followed by a decay to the steady-state rate (plot 3). This behavior indicates the presence of active sites of differing activities with some of the active sites decaying with time. This behavior is avoided in some instances by aging the initiator. Ziegler Natta polymerizations may exhibit a continuous rate decrease (plot 4) after the settling period (which may be of either type 1,2, or 3) due to active site destruction. This can be due to thermal deactivation or further reduction of the transition metal by the group I III metal component. Diffusion control of the propagation reaction has also been postulated. Diffusion of the monomer through the formed polymer to the propagation centers may become ratedetermining at higher conversions. This has been substantiated in some systems where the polymerization rate increases with increased rate of stirring, but data in other systems indicate diffusion control to be absent [Chien et al., 1985]. 8-4i-2 Termination



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'\1q/ = -'\1 [(z. '\1) u]

Ziegler Natta polymerizations have the characteristics of living polymerizations with regard to active sites but not individual chains. (Some living polymerizations proceed with metallocene and other initiators Sec. 8-9.) The lifetime of propagating chains is of the order of seconds or minutes at most, while active sites have lifetimes of hours or more. Each active site produces many polymer molecules. Propagating chains undergo a number of chainbreaking reactions:

(9.78) (9.79)

8-37

8-38

(9.73) will be satisfied. Notice that (9.78) does not fix the gauge completely, because it chooses only the gradient of </;'. Later we fix the gauge by specifying </;' itself. Repeating this argument with (9.74), we find that we can satisfy (9.74) by requiring that





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Open the Conditional Formatting Rules Manager dialog box. (To open this dialog box, follow Steps 1 to 4 on the previous page.) Click the conditional formatting rule you want to remove. Click the Delete Rule button. Click OK. Access removes the conditional formatting.

Both b-hydride transfers result in polypropene molecules with one vinylidene and one n-propyl end group. The two transfers are zero- and rst-order, respectively, in monomer. b-Hydride transfer yields vinyl end groups in ethylene polymerization. 2. Chain transfer to the group I III metal alkyl:

'\1</; = -'\1 [(z '\1) v] , '\1 2 v + k 2 V = 0,

+ Al(C 2H5)3

(9.80) (9.81)

8-39

where just as in the case of </;', (9.80) does not fix the gauge completely, as it determines '\1</; rather than </; itself. We now fix the gauge by choosing </; = </;' = O. Then, from (9.78) and (9.80), we see that our gauge choice implies the following conditions on the two scalar potentials

Hydrolytic workup of the polymer cleaves the aluminium polymer bond to yield an isopropyl end group. 3. Chain transfer to an active hydrogen compound such as molecular hydrogen:

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'\1 [(z . '\1) u] = 0, '\1 [(z '\1) v] = 0.

8-40

(9.82) (9.83)

The b-hydride transfer reactions produce polymers with one saturated and one unsaturated end group. The other two transfers result in polymers with two saturated groups. The chain-breaking reactions limit the polymer molecular weight, but like typical chaintransfer reactions, they proceed with the reinitiation of new propagating chains. The extents to which the various chain-breaking reactions occur depend on the monomer, identity and concentrations of the initiator components, temperature, and other reaction conditions [Boor, 1979; Cooper, 1976; Longi et al., 1963]. The b-hydride transfer reactions are usually the predominant chain-breaking reaction in the absence of H2 or other active hydrogen compound. H2 is a highly effective chain-transfer agent and is used for molecular weight control in commerical polymerizations of ethylene and a-ole ns. There are considerable differences in the extent of transfer to group I III metal components. Trialkylaluminum is much less active a transfer agent compared to dialkylzinc [Natta et al., 1961a,b,c,d]. Chain transfer to molecular hydrogen not only affects polymer molecular weight, but unlike other transfer agents, also affects polymerization rate. Hydrogen often decreases the rate of ethylene polymerization, but increases the rate of propene polymerization [Chadwick,

To summarize this description of the fields in terms of only two scalar potentials, besides satisfying (9.82) and (9.83), they also satisfy the Helmholtz equation,

2001; Kissin and Rishina, 2002; Kissin et al., 1999a]. The rate depression for ethylene is attributed to the high stability of the Ti ethyl group, formed when transfer is followed by the addition of a monomer molecule, due to stabilization by a b-agostic coordination between a methyl hydrogen and Ti. The reactivity of a propagating chain in propene polymerization decreases whenever there is 2,1-insertion (secondary insertion). The resulting 2,1-chain ends are preferentially terminated by transfer to hydrogen; the overall result is replacement of 2,1-chain ends by more reactive 1,2-chain ends on reinitiation. Termination is even more complicated than described, especially when polymerizations by metallocene initiators are considered [Beach and Kissin, 1986; Kissin et al., 1999b; Lehmus et al., 2000; Liu et al., 2001b; Resconi et al., 2000; Rossi et al., 1995, 1996; Thorshaug et al., 1998; Weng et al., 2000; Zhao et al., 2000]. A variety of different unsaturated end groups have been found in different polymerizations. Isomerization of propagating chain ends followed by b-hydride transfer (Eq. 8-41) results in trisubstituted double bond end

2 3 4

8-41

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