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(which was derived previously in Sec. 2-2d-2) where s is the ratio of rate constants for reaction of B0 and B groups [Ozizmir and Odian, 1980]. The polydispersity index increases (for conversions <100%) when the reactivities of B and B0 groups are different compared to the case where the reactivities are the same. The opposite trend is found for the A B 0 system [Gandhi and Babu, 1979, 1980]. There A B is a basic difference between the two- and the three-species reaction systems. In the threespecies system, when B0 groups have higher reactivity than B groups, the B0 0 monomer B continues polymerization with A monomer, independently of the B monomer, to form A B large-sized polymer chains. In the two-species system, long chains cannot be formed without participation of B groups in the polymerization process. The extents of the broadening and narrowing effects in the two systems increase as the difference in reactivities of B and B0 become larger. The effects are signi cant at low conversions; for instance, PDI is 2.10 at 50% conversion for the three-species system when B0 is 20-fold more reactive than B compared to a PDI of 1.50 for the equal reactivity case. However, the PDI at complete converson equals 2 in both the two- and three-species systems, which is the same limit as for the equalreactivity case.



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= /' d 3 k B(k)e ik . r + C.c. (2.124)

2-7e-2

where c.c. stands for complex conjugate. From (2.47) and (2.48) we see that both electric and magnetic reciprocal-space fields are transverse, with e and B having just two polarizations, both orthogonal to k. Let s(k) with s = 1,2 be the two linear and real polarization vectors of the electric field e(k):





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An increase in the reactivity of one functional group in a bifunctional reactant on reaction of the other functional group results in an increase in PDI [Gandhi and Babu, 1979, 1980]. The PDI at complete conversion exceeds 2 when there is a greater than twofold increase in reactivity. PDI decreases when there is a decrease in reactivity of one functional group on reaction of the other group but the PDI at complete conversion is 2. The same trends are found but are more exaggerated when functional group reactivity varies continuously with molecular size [Gupta et al., 1979a,b; Nanda and Jain, 1968].

headers, 64, 65, 70 Help system, 12 13 Home tab, 13

e(k)

2-7e-3

s=I,2

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radical (Table 3-8). Various types of compounds act as inhibitors and retarders. Stable free radicals that are too stable to initiate polymerization but that can still react with radicals are one type of radical terminator. Diphenylpicrylhydrazyl (DPPH) is such a radical and its use as a radical scavenger has been discussed (Sec. 3-4g-3). The stoichiometry between the number of kinetic chains terminated, and the number of DPPH radicals consumed is 1 : 1. The most useful class of inhibitors are molecules that react with chain radicals to yield radicals of low reactivity. Quinones such as benzoquinone and chloranil (2,3,5,6-tetrachlorobenzoquinone) are an important class of inhibitor. The behavior of quinones is quite complex [Eastmond, 1976a,b,c; George, 1967; Small, 1975; Yamamoto and Sugimoto, 1979; Yassin and Risk, 1978a, 1978b]. Two major types of products are obtained quinone and ether formed by reaction at the C and O atoms of a quinone, respectively. Attack of a propagating radical at oxygen yields the aryloxy radical XXVIII, which can terminate by

s(k)Es(k).

3-143

(2.125)

coupling and/or disproportionation with another propagating radical (or itself) or add monomer. Attack on the ring carbon yields radical XXIX, which can react with another

The magnetic field can also be written as a linear combination of two unit polarization vectors multiplied by scalar amplitudes:

propagating radical (Eq. 3-144) to form the quinone XXX. The latter may itself be an inhibitor. An alternate route for radical XXIX is rearrangement to XXXI followed

3-144

B(k)

3-145

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s=I,2

by coupling or termination with other radicals. The overall stoichiometry (i.e., the value of y in Eqs. 3-139 and 3-140) between the number of kinetic chains terminated and the number of the original quinone molecules consumed varies considerably depending on the particular quinone and radical. Although y often is 1, both pathways (Eqs. 3-143 and 3-144/3-145) can yield y values larger than 1 (up to 2) depending on the reactivities of XXVIII and XXX. Polar effects appear to be of prime importance in determining the effect of quinones. p-Benzoquinone and chloranil (which are electron-poor) act as inhibitors toward electronrich propagating radicals (vinyl acetate and styrene) but only as retarders toward the electron-poor acrylonitrile and methyl methacrylate propagating radicals. A further observation is that the inhibiting ability of a quinone toward electron-poor monomers can be increased by the addition of an electron-rich third component such as an amine. Thus the presence of triethylamine converts chloranil from a very weak retarder to an inhibitor toward methyl methacrylate. Oxygen is a powerful inhibitor, as seen from the very large z values. Oxygen reacts with radicals to form the relatively unreactive peroxy radical that reacts with itself or another

.Bs(k)Bs(k).

3-146

(2.126)

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