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via cleavage of the strained four-membered ring and migration of the resulting gem-dimethyl carbocation center [Kennedy and Marechal, 1982].

(4.65)

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Other monomers that undergo isomerization polymerization include 5-methyl-1-hexene, 4,4-dimethyl-1-pentene, 6-methyl-1-heptene, a-pinene, and vinylcyclopropane [Cesca, 1985; Corno et al., 1979]. 5-2c Chain Transfer and Termination



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and (4.66) Now let us determine the explicit form of S).. From (4.63) it follows that S). is unitary, so we can always write it down as (4.67) where Nt (A) is a Hermitian operator that is a function of A. For A = 1 we know that SI = 1. If A = 1 + E with lei 1, we can expand (4.67) as a power series in E and neglect terms higher than first order in E:

Various reactions lead to termination of chain growth in cationic polymerization [Allen and Bevington, 1990; Dunn, 1979; Gandini and Cheradame, 1985; Kennedy and Marechal, 1982; Matyjaszewski and Pugh, 1996]. Many of the reactions that terminate the growth of a propagating chain do not, however, terminate the kinetic chain because a new propagating species is generated in the process. 5-2c-1 b-Proton Transfer

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Transfer of a b-proton from the propagating carbocation is the most important chain-breaking reaction. It occurs readily because much of the positive charge of the cationic propagating center resides not on carbon, but on the b-hydrogens because of hyperconjugation. Monomer, counterion or any other basic species in the reaction mixture can abstract a b-proton. Chain transfer to monomer involves transfer of a b-proton to monomer with the formation of terminal unsaturation in the polymer.

(4.69)

H CH2C(CH3)2

n CH2C(CH3)2(BF3OH)

).=1

(CH3)3C +(BF3OH) + H CH2C(CH3)2 + H CH2C(CH3)2

t, we notice that (4.63)

n CH2C(CH3)

(4.70)

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C(CH3)2

[Z,x]

Mn + 1 + HM +(IZ)

(4.71)

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There are two different types of b-protons, and two different unsaturated end groups are possible for isobutylene as well as some other monomers such as indene and a-methylstyrene. The relative amounts of the two end groups depend on the counterion, identity of the propagating center, and other reaction conditions. Only one type of unsaturated end group (internal) is possible for other monomers such as styrene, ethyl vinyl ether, and coumarone. It should be noted that the kinetic chain is not terminated by this reaction since a new propagating species is regenerated. Many polymer molecules are usually produced for each initiator coinitiator species present. Chain transfer to monomer is on much more

Now, we know that p is the generator of translations. 6 Our scale transformation (Le., squeezing) is a translation proportional to X. Thus, we might think that Z is just something like xp. But xp is not Hermitian! So, instead of xp, we try the Anzats (xp + pX)/2, which is Hermitian. 7 By direct substitution in (4.71), we can see that

favorable terms with propagation in many cationic polymerizations compared to radical polymerization. Since it is kinetically indistinguishable from propagation, the relative rates of transfer and propagation are given by the ratio ktr;M =kp , which is the chain-transfer constant for monomer CM. The value of CM determines the molecular weight of the polymer if other chain-breaking processes are not signi cant. The larger the value of CM the lower will be the molecular weight. Chain transfer to monomer is the principal reaction that limits polymer molecular weight for most monomers, especially at reaction temperatures higher than about 20 C. Since chain transfer to monomer generally has a higher activation energy than propagation, it is usually suppressed by working at lower reaction temperatures. Another type of chain transfer to monomer reaction is that involving hydride ion transfer from monomer to the propagating center [Kennedy and Squires, 1967].

(4.72)

H CH2C(CH3)2 CH2 C(CH3)

n CH2C(CH3)2(BF3OH)

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