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ln M 1 f I 0 1=2 ln 1 p1 2kp M 0 kt kd 3-93

and that the polarization is induced by the field (Le., X does not oscillate by itself), (7.116) has the following solution (Problem 7.2):

7-13

reaction (Eq. 7-13) between a propagating chain and the alcohol is possible. Similar exchange reactions are possible between the newly formed polymeric alcohol in Eq. 7-13 and other propagating chains:

ei(wt+8) }

7-14

X = -2woG'Do Re {

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These exchange reactions lower the polymer molecular weight. The number-average degree of polymerization is given by

(7.119)

Xn p M 0 I 0 ROH 0 7-15

Substituting (7.119) in (7.117), we obtain this equation for W:

since each alcohol molecule contributes equally with an initiator species to determining the number of propagating chains. The exchange reactions appear equivalent to chain-transfer reactions, but they are not. Any polymeric alcohol formed via exchange is not dead but simply dormant. All alcohol and alkoxide molecules in the reaction system are in dynamic equilibrium. Each polymer chain alternates between the active propagating alkoxide and dormant alcohol forms. The exchange reaction places an upper limit on the polymer molecular weight that is possible for polymerizations performed in the presence of alcohols or other protonic substances. There are very few reports of polymers with molecular weights above 10,000 for ethylene





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oxide polymerizations initiated by alkoxides or hydroxides in alcohol, although molecular weights as high as 50,000 appear (very rarely) in the literature [Boileau, 1989; Clinton and Matlock, 1986] (Another reason for the upper limit on molecular weight is dehydration from the hydroxy end groups of the dormant polymeric alcohol [Clinton, and Matlock, 1986] This would adversely affect the living nature of the polymerization by converting dormant alcohol species to dead polymer) Polymerizations initiated by alkoxides and hydroxides in aprotic polar solvents do not have this limitation This limitation also does not apply to polymerizations initiated by the other initiators, including metal alkyls and aryls and the various coordination initiators (eg, aluminum alkoxides and metalloprophyrins), since those initiators are soluble in solvents such as benzene or tetrahydrofuran Homogeneous reactions can be obtained without the need for a solvent such as alcohol.

(7.120)

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Molecular weights as high as 105 106 have been achieved in a number of systems However, the addition of alcohol or other protonic substance is useful for control of polymer molecular weight Equation 7-15 allows one to calculate the amount of added alcohol or other substance required to achieve some desired value of the number-average molecular weight A number of different situations are possible depending on the relative rates of initiation, propagation, and exchange When exchange is absent and initiation is much faster than propagation, initiation is essentially complete before propagation begins All polymer chains start growing at the same time and grow for the same period with the result that the molecular weight distribution is very narrow as in living chain polymerizations; that is, the distribution is Poisson as de ned by Eq 3-228 When initiation is slow, some chains are growing while others have not yet been initiated.

It is the single-mode lossless cavity that constrains the field inside it to oscillate at its resonance frequency. The dielectric medium, however, changes this resonance from We to W given by (7.120). The square of the resonance frequency is given by

The polymerization proceeds with an initial period in which the reaction rate shows an acceleration as initiator is converted to propagating species; thereafter, the rate is constant The molecular weight distribution broadens since chains grow for different periods of time This effect is observed in most anionic coordination polymerizations because the initiators are generally aggregated and possess different initiator sites with different reactivities An exception to this generalization are the metalloporphyrin initiators, which yield living polymers with narrow molecular weights The effects of exchange depends on the relative acidities of the alcohol (or other protonic substance) and the polymeric alcohol The exchange reaction occurs throughout the course of the polymerization if the acidities of the two alcohols are approximately the same The polymerization rate is unaffected while the molecular weight decreases (Eq 7-15), but the molecular weight distribution (MWD) is Poisson.

If the added alcohol ROH is much more acidic than the polymeric alcohol, most of it will undergo reaction with the rst-formed propagating species before polymerization begins..

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