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n "2 p21 1 p22 2 1 r2 M2 M1 p21 M1 6-26

The mole ratio of monomers M1 and M2 contained in the copolymer is given by the ratio of the two number-average sequence lengths

-"h, [Hatom,H] ,

" n1 d M1 M1 r1 M1 M2 "2 d M2 M2 M1 r2 M2 n 6-27

(6.14)



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which is exactly the same result as Eq. 6-12 (and Eq. 6-15). Thus the copolymerization equation holds for copolymerizations carried out under both steady-state and non-steady-state conditions provided that the reactivity of a propagating species is dependent only on the ultimate unit, depropagation does not occur, and high polymer is formed. Equation 6-27 (also 6-12 and 6-15) describes the rst-order Markov or terminal model of copolymerization. 6-2c Range of Applicability of Copolymerization Equation

= 2m

The copolymerization equation has been experimentally veri ed in innumerable comonomer systems. The copolymerization equation is equally applicable to radical, cationic, and anionic chain copolymerizations, although the r1 and r2 values for any particular comonomer pair can be drastically different depending on the mode of initiation. Ionic copolymerizations are predictably much more selective than radical copolymerizations. Almost any pair of monomers undergoes radical copolymerization, in line with the

(6.15)





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More from SautinSoft Team

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reactivity of almost all monomers in radical polymerization (Sec 3-1b) However, only certain comonomer pairs undergo cationic or anionic copolymerization For example, both styrene acrylonitrile and styrene ethyl vinyl ether undergo radical copolymerization, but there is great selectivity in ionic copolymerizations Styrene acrylonitrile undergoes anionic polymerization, but not cationic copolymerization Styrene ethyl vinyl ether undergoes cationic copolymerization, but not anionic copolymerization For any speci c type of initiation (ie, radical, cationic, or anionic) the monomer reactivity ratios and therefore the copolymer composition equation are independent of many reaction parameters Since termination and initiation rate constants are not involved, the copolymer composition is independent of differences in the rates of initiation and termination or of the absence or presence of inhibitors or chain-transfer agents Under a wide range of conditions the copolymer composition is independent of the degree of polymerization.

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We want to calculate the expectation value of (6.14) when the field is initially in the vacuum state and the atom in one of the atomic energy levels. Then we want to identify a contribution from radiation reaction and another from vacuum fluctuations. To do so, we have to split the vector potential operator into two terms as in equation (6.8). However, because the commutator that appears in equation (6.14) involves a product of a field operator and an atomic operator:

The only limitation on this generalization is that the copolymer be a high polymer Further, the particular initiation system used in a radical copolymerization has no effect on copolymer composition The same copolymer composition is obtained irrespective of whether initiation occurs by the thermal homolysis of initiators such as AIBN or peroxides, redox, photolysis, or radiolysis Solvent effects on copolymer composition are found in some radical copolymerizations (Sec 6-3a) Ionic copolymerizations usually show signi cant effects of solvent as well as counterion on copolymer composition (Sec 6-4) The monomer reactivity ratios and copolymer compositions in living copolymerizations are generally the same as those in the corresponding nonliving systems However, Matyjaszewski [2002] has described reaction conditions that result in deviations in copolymer compositions for some living systems The differences arise not from differences in monomer reactivity ratios, but from differences in the consumption of the two monomers.

Excel creates a chart and places it in the worksheet. You can click the Design tab to find tools for controlling design elements in the chart, such as the chart layout, style and type.

[Hatom , H]

The effect is observed in living systems where there is a recycling equilibrium (activation and deactivation) between active and dormant species This applies to radical systems such as ATRP, NMP, and RAFT, as well as many ionic systems, which involve an activation and deactivation equilibrium For a copolymerization, there is a separate activation deactivation equili* * brium for each of two different propagating species (M1 and M2 ) Deviations are possible only when two conditions exist First, the two propagating species must have different activation and/or deactivation rate constants Second, the homopropagation rate constant for each propagating species must be different from its cross-propagation rate constant; in other words, both r1 and r2 are not one Under these conditions, one of the monomers is consumed faster than in the corresponding nonliving system The comonomer feed and, therefore, the copolymer composition, change with conversion differently from the nonliving system.

(6.16)

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