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The typical effect of initiator chain transfer [Baysal and Tobolsky, 1952] can be seen graphically in Fig. 3-6. The decrease of polymer size due to chain transfer to initiator is much less than indicated from the CI values because it is the quantity CI [I]/[M], which affects X n (Eq. 3-109b). The initiator concentrations are quite low (10 4 10 2 M) in polymerization, and the ratio [I]/[M] is typically in the range 10 3 10 5 . 3-6c 3-6c-1 Transfer to Chain-Transfer Agent Determination of CS



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\1 i\ B + ik E = 0, \1. E = 0, \1 i\ E - ik B = 0,





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The second special case of Eq. 3-108 consists of the situation where transfer with the chaintransfer agent is most important. In some instances the chain-transfer agent is the solvent, while in others it is an added compound. In such a case the third term on the right side of Eq. 3-108 makes the biggest contribution to the determination of the degree of polymerization. By the appropriate choice of polymerization conditions, one can determine the value of CS for various chain-transfer agents [Gregg and Mayo, 1948]. By using low concentrations of initiators or initiators with negligible CI values (e.g., AIBN), the last term in Eq. 3-108 becomes negligible. The rst term on the right side of the equation may be kept constant by keeping Rp = M 2 constant by appropriately adjusting the initiator concentration throughout a series of separate polymerizations. Under these conditions, Eq. 3-108 takes the form

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You can use Access s Conditional Formatting tool to apply certain formatting attributes, such as bold text or a fill colour, to data in a form when the data meets a specified condition. For example, if your database tracks weekly sales, you might set up Access s Conditional Formatting feature to alert you if sales figures fall below what is required for you to break even. You apply conditional formatting by creating a rule, which specifies the criteria that the value in a field must meet. Values that meet the criteria are formatted using settings you specify.

(9.64)

1 1 S CS M X n X n0 3-119

(9.65) (9.66) (9.67)

where 1=X n0 is the value of 1=X n in the absence of the chain-transfer agent. 1=X n0 is the sum of the rst, second, third, and fourth terms on the right side of Eq. 3-108a,b. CS is then determined as the slope of the linear plot of 1=X n versus [S]/[M]. Such plots are shown in Fig. 3-8 for several chain-transfer agents in styrene polymerization. This method is of general use for determining CS values. The data can also be handled by plotting 1=X n 1=X n0 instead of 1=X n versus [S]/ 2 [M]. Under conditions where Rp = M 2 is not constant, one may plot 1=X n kt Rp =kp M 2 versus [S]/[M]. Another method involves dividing the rate expression for transfer (Eq. 3-104) by that for propagation (Eq. 3-112) to yield

\1 B =0,

d S =dt ktr;S S S CS d M =dt kp M M 3-120

The value of CS is obtained as the slope of the line obtained by plotting the ratio of the rates of disappearance of transfer agent and monomer d S =d M versus [S]/[M]. A useful alternate to the Mayo plot for determining CS (as well as other transfer constants) is the chain length distribution (CLD) method based on the molecular weight distributions obtained from size exclusion chromatography (SEC) [Christie and Gilbert, 1996, 1997; Heuts et al., 1998, 1999; Moad and Moad, 1996]. The limiting slope HIGH of a

with the boundary conditions (see Appendix B)

Fig. 8-14 Syn addition to a trans 1,2-disubstituted ethylene to yield the threodiisotactic polymer. After Goodman [1967] (by permission of Wiley-Interscience, New York).

and it Bls = 0,

other words, the R groups are opposed to each other. Syn addition leads to syndioselective polymerization when successive monomer molecules alternate their two faces in approaching the propagating center. Syn addition in syndiotactic polymerization has been established, since copolymerizations of cis- and trans-1-d-propenes with perdeuteropropene yield the trans- and gauche-syndiotactic structures XXIII and XXIV, respectively [Zambelli et al., 1968]. Similar results have been observed in the syndioselective polymerization of styrene [Longo et al., 1988].

(9.68)

The stereoselectivity and activity of Ziegler Natta initiators vary considerably depending on the identity and relative amounts of the initiator components [Boor, 1979]. The interpretation

where it is the unit normal to a cavity wall and Is denotes that these quantities are to be evaluated on the cavity walls. To satisfy the vanishing divergence equations (9.65) and (9.67) automatically, we can take E and B as the curl of some vector fields. It is convenient to write this as E = ik\1 i\ (vz)

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