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of a Lewis acid [Johnson and Young, 1976; Sauvet and Sigwalt, 1989]. Iodine is not the actual initiator in this system. Iodine adds to the double bond to form a diiodide that eliminates hydrogen iodide. The hydrogen iodide generated by this process acts as the cationogen with iodine acting as a Lewis acid to form the initiating system. It was noted earlier (Sec. 52a-1) that hydrogen iodide is not an ef cient initiator because iodide ion is too nucleophilic. The presence of iodine activates (dissociates) the C bond suf ciently to allow propaga I tion to proceed. (See Sec. 5-2g for details of the propagation mechanism.) This initiation route is more ef ciently utilized by directly adding a mixture of hydrogen iodide and either iodine or a metal halide such as ZnX2 or SnX2 to the reaction system [Higashimura et al., 1988]. 5-2a-4 Photoinitiation by Onium Salts



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(4.48) As (4.47) is a bona fide photon-number-stateexpansion of p, which is always possible because the photon number states form a complete basis, we see that (4.43) does hold. Incidentally, a normal order expansion, where all the annihilation operators are to the right of the creation operators, is also possible as well as any other ordering. With (4.43) established, we can now insert the unit operator (4.26) between (a)k and (at)!, obtaining the diagonal coherent-state representation

Aryldiazonium (ArN Z ), diaryliodonium (Ar2 I Z ), and triarylsulfonium (Ar3 S Z ) 2 salts, where Z is a nonnucleophilic and photostable anion such as tetra uoroborate (BF ), hexa uoroantimonate (SbF ), and tetraper uorophenylborate [(C6 F5 )4 B ], and 4 6





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3-37

cPala)(aIP(a,a*),

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In support of this mechanism, the rate of initiation increases with increasing nucleophilicity of the amine. Initiation is by the fCOO radical. The amino cation radical is generally not an effective initiator as shown by the absence of nitrogen in the polymer; it apparently disappears by some unknown side reactions such as dimerization and/or deprotonation. (However, there is some evidence that the cation radical produced by the interaction of benzoyl peroxide and N-vinylcarbazole (NVC) initiates cationic polymerization of NVC simultaneous with the radical polymerization [Bevington et al., 1978].) Other types of peroxides also appear susceptible to this type of acceleration. Peroxide decomposition is also accelerated by transition metal ion complexes such as copper (II) acetylacetonate [Ghosh and Maity, 1978; Shahani and Indictor, 1978]. Zinc chloride accelerates the rate of decomposition of AIBN in methyl methacrylate by a factor of 8 at 50 C, with a corresponding increase in polymerization rate [Lachinov et al., 1977]. The mechanism may be analogous to the amine peroxide system. The effect of ZnCl2 and other metal ions on accelerating Rp is well established, although the mechanism in most cases appears to involve changes in kp and/or due to complexation of the metal ions with the monomer and/or propagating radicals. 2. The combination of a variety of inorganic reductants and inorganic oxidants initiates radical polymerization, for example

(4.49)

Other redox systems include reductants such as HSO , SO2 , S2 O2 , and S2 O2 in combi3 3 3 5 nation with oxidants such as Ag , Cu2 , Fe3 , ClO , and H2 O2 . 3 3. Organic inorganic redox pairs initiate polymerization, usually but not always by oxidation of the organic component, for example, the oxidation of an alcohol by Ce4 ,

P(a,a*)

3-39

(4.50)

or by V5 , Cr6 , Mn3 [Fernandez and Guzman, 1989; Misra and Bajpai, 1982; Nayak and Lenka, 1980]. 4. There are some initiator systems in which the monomer itself acts as one component of the redox pair. Examples are thiosulfate plus acrylamide or methacrylic acid and N,Ndimethylaniline plus methyl methacrylate [Manickam et al., 1978; Tsuda et al., 1984]. 3-4b-2 Rate of Redox Polymerization

However, as it stands, (4.50) is not very useful, as it is written in terms of rk,l rather than some expression involving p that we can calculate. To obtain such an expression, we notice first that part of the usefulness of (4.49) is that with it the expectation value of an operator 0 becomes simply

The kinetics of redox-initiated polymerizations generally fall into two categories depending on the termination mode. Many of these polymerizations proceed in the same manner as other polymerizations in terms of the propagation and termination steps; the only difference is the source of radicals for the initiation step. For these polymerizations where termination is by bimolecular reaction of propagating radicals, the initiation and polymerization rates will be given by appropriate expressions that are very similar to those developed previously:

= L(nlpOln)

4 6 3

Ri kd reductant oxidant kd reductant oxidant 1=2 Rp kp M 2kt 3-40 3-41

2 d a(nla)(aIOln)P(a, a*)

Equations 3-40 and 3-41 differ from those (Eqs. 3-31 and 3-32) discussed previously in that the factor of 2 is absent from the expression for Ri, since typically only one radical is produced per oxidant-reductant pair. Some redox polymerizations involve a change in the termination step from the usual bimolecular reaction to monomolecular termination involving the reaction between the propagating radicals and a component of the redox system. This leads to kinetics that are appreciably different from those previously encountered. Thus, in the alcohol-Ce4 system (Eq. 3-39), termination occurs according to

3-42

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