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It was noted earlier that the exact quantitative order of monomer reactivities is not the same when different reference radicals are considered (Tables 6-3 and 6-4) Analogously, the exact order of radical reactivities varies depending on the reference monomer Monomer reactivity cannot be considered independent of radical reactivity and vice versa One observes enhanced reactivities in certain pairs of monomers due apparently to subtle radical monomer interactions This effect is a very general one in radical copolymerization and corresponds to the alternating tendency of the comonomer pairs The deviation of the r1 r2 product from unity and its approach to zero is a measure of the alternating tendency One can list monomers in order of their r1 r2 values with other monomers is such a manner that the further apart two monomers are, the greater is their tendency toward alternation (Table 6-6) (Ignore the e values until Sec 6-3b-4).



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dtP22 = -"'P22 - zg (P12 - P2t} , :t (P12 - P21) =

Thus acrylonitrile undergoes ideal copolymerization with methyl vinyl ketone r1 r2 1:1 and alternating copolymerization with 1,3-butadiene r1 r2 0:006 The order of monomers in Table 6-6 is one based on the polarity of the double bond Monomers with electron-pushing substituents are located at the top (left) of the table and those with electron-pulling substituents at the bottom (right) The r1 r2 value decreases progressively as one considers two monomers further apart in the table The signi cant conclusion is that the tendency toward alternation increases as the difference in polarity between the two monomers increases A dramatic and useful aspect of alternating copolymerization is the copolymerization of monomers that show little or no tendency to homopolymerize Maleic anhydride, dialkyl fumarates, N-alkyl maleimides, and fumaronitrile are examples of such monomers (Sec 3-9b-3).

-~ (P12 -





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These monomers readily form alternating copolymers with electron-donor monomers such as styrene, p-methoxystyrene, vinyl ethers, and N-vinylcarbazole [Baldwin, 1965; Chiang et al, 1977; Hall and Padias, 2001; Rzaev, 2000; Yoshimura et al, 1978] Copolymerization of stilbene and maleic anhydride takes place even though neither undergoes signi cant homopolymerization..

Click the Normal button. PowerPoint returns to the default view, displaying the current slide in the presentation.

P2t)

6-52

+ i2g (Pll -

Two mechanisms have been proposed to explain the strong alternation tendency between electron-acceptor and electron-donor monomers. The polar effect mechanism (analogous to the polar effect in chain transfer Sec. 3-6c-2) considers that interaction between an electron-acceptor radical and an electron-donor monomer or an electron-donor radical and

(6.75) (6.76)

498 Vinyl chloride (0.16) 1.0 Methyl methacrylate (0.40) 0.61 0.99 0.18 0.34 0.56 Vinylidene chloride (0.34) Methyl vinyl ketone (1.06) 1.1 Acrylonitrile (1.23) Diethyl fumarate (2.26) Maleic anhydride (3.69) 0.13 0.96 0.83 0.11 0.056 0.0024

Equation (6.76) is not independent from the other equations, because Pll P33 = 1. The remaining equations can be put in matrix form:

TABLE 6-6

n-Butyl vinyl ether ( 1.50)

(6.77)

1,3-Butadiene ( 0.50)

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The eigenvalues of the matrix in (6.77) are the three roots of the following secular equation: (6.78)

Styrene ( 0.80)

To change the magnification of a slide, you can drag the Zoom bar on the status bar at the bottom of the PowerPoint window. Alternatively, click the View tab, click the Zoom button and choose the desired magnification in the Zoom dialog box. Click the Fit to Window button to return to the default view.

(6.79) (6.80) We examine two limiting cases. The weak-coupling regime, where the cavity decay rate is much larger than the coupling between the atom and the cavity mode, ,.. g, and the strong-coupling regime, where the coupling is much larger than the cavity decay rate, 9 ,...

Vinyl acetate ( 0.88)

In the weak-coupling regime, we can approximate (6.80) by (6.81) Then we can write the probability of finding the atom in the upper state as

<0.1

+ De-l<t-4 g2 t/l<,

$0.002

(6.82)

r1 r2 values are calculated from data in Table 6-2 [Greenley 1989a, 1999]. Values are shown in parentheses after each monomer.

where the constants A, B, and D are determined by the initial conditions. The condition PlI (0) = 1 yields (6.83) A+B+D=1. The conditions d dt Pll (0) = 0,

an electron-acceptor monomer leads to a decrease in the activation energy for cross-propagation [Price, 1948; Walling et al., 1948]. The transition state is stabilized by partial electron transfer between the electron-donor and electron-acceptor species, for example, between styrene monomer and maleic anhydride radical

6-53

(6.84) (6.85)

and similarly between styrene radical and maleic anhydride monomer:

2 g2 I\. 4g -A+-B+ ( 1 \ .4 - ) D=O, 2

To resize the PowerPoint panes, position the mouse pointer over the pane s border. The changes to . Click and drag inward or outward to resize the pane.

6-54

I\. I\.

The monomer complex participation (MCP) mechanism suggests that alternation results from homopolymerization of a 1 : 1 complex formed between donor and acceptor monomers [Cowie, 1989; Furukawa, 1986]:

(6.86) (6.87)

6-55

+ (4g2 ) 2 B + ( I\. ---;:

6-56

---;:

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