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The monomer reactivity ratios for many of the most common monomers in radical copolymerization are shown in Table 6-2. These data are useful for a study of the relation between structure and reactivity in radical addition reactions. The reactivity of a monomer toward a radical depends on the reactivities of both the monomer and the radical. The relative reactivities of monomers and their corresponding radicals can be obtained from an analysis of the monomer reactivity ratios [Walling, 1957]. The reactivity of a monomer can be seen by considering the inverse of the monomer reactivity ratio (1=r). The inverse of the monomer reactivity ratio gives the ratio of the rate of reaction of a radical with another monomer to its rate of reaction with its own monomer



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(at (t) [at (t')eiwo(tH')-iw(t-t') -

1 k12 r1 k11 6-50

d3 kL9:(k)o(w-wo)

Table 6-3 shows 1=r values calculated from the data in Table 6-2. The data in each vertical column show the monomer reactivities of a series of different monomers toward the same reference polymer radical. Thus the rst column shows the reactivities of the monomers toward the butadiene radical, the second column shows the monomer reactivities toward the styrene radical, and so on. It is important to note that the data in each horizontal row in Table 6-3 cannot be compared; the data can be compared only in each vertical column.

(6.54)

6-3b-1

1 A 3 2





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When we integrate equation (6.54), we find that the atomic energy decays exponentially with the rate -I: (6.55) The exponential decay in (6.55) is typical of irreversible processes. The atom has an infinite continuum of modes to emit the photon, and once emitted, it is extremely unlikely that the photon will find its way back to the atom and be reabsorbed. In the next section we will see that a cavity can change this decay rate, and in the strong coupling regime, even make spontaneous emission a reversible process.

The monomers have been arranged in Table 6-3 in their general order of reactivity. The order of monomer reactivities is approximately the same in each vertical column irrespective of the reference radical. The exceptions that occur are due to the strong alternating tendency

Let us assume that the atomic transition is resonant with the mode oflowest frequency supported by the cavity and very far off resonance from any other modes. In this case, we can neglect all cavity modes except for the lowest one, and the Hamiltonian of the entire system becomes (6.56) where

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TABLE 6-2 Monomer Reactivity Ratios in Radical Copolymerization M2 Acrylic acid r1 0.24 0.25 8.7 0.86 0.046 0.69 0.98 1.5 0.14 0.020 5.5 3.6 0.92 0.11 0 0 0.7 0.75 1.4 8.8 0 0.07 0.44 0.48 0 0 0.010 0.040 0.046 0 0.01 0.38 0.79 0 0.006 0 0.045 0.012 0.01 0.08 0.03 0.005 0 0 2.4 0.60 24 0.58 0.46 0.25 12 M2 n-Butyl methacrylate Styrene Vinyl acetate Acrylamide 1,3-Butadiene Ethyl vinyl ether Isobutylene Methyl acrylate Methyl methacrylate Styrene Vinyl acetate Vinyl chloride Vinylidene chloride 4-Vinylpyridine Methyl methacrylate Styrene Vinyl acetate Methyl methacrylate Styrene Vinyl chloride Acrylonitrile Styrene Vinyl acetate Vinyl chloride Acrylonitrile Methyl methacrylate Styrene Vinyl acetate Vinyl chloride Acrylonitrile n-Butyl acrylate Tetra uoroethylene Vinyl acetate Methyl methacrylate Styrene Acrylonitrile n-Butyl vinyl ethera Methyl acrylate Methyl methacrylate cis-Stilbenea trans-Stilbenea Styrene Vinyl acetate Vinyl chloride Acrylonitrile Styrene Vinyl chloride 2-Vinylpyridine Ethyl methacrylate Styrene Vinyl acetate r2 3.5 0.15 0.21 0.81 0.36 0.060 0.020 0.84 1.3 0.29 0.06 0.044 0.32 0.41 23 90 1 0.25 0.58 0.04 8 0.3 0.011 0.13 12 20 6.1 0.17 0.9 7 14 0.1 1.4 6.7 0.29 6 0 2.8 3.4 0.07 0.03 0.05 0.019 0.098 0.092 0.12 0.064 1.7 0.83 0.25 0.01 T ( C) 50 60 70 40 40 80 50 50 70 60 70 50 60 60 60 60 60 90 50 50 60 60 60 60 60 60 70 60 70 20 150 25 130 79 65 60 50 75 75 60 60 50 75 75 70 60 50 70 80 80 70

(a,a t ] = 1.

the number-average degree of polymerization.) X n is simply given as the total number of monomer molecules initially present divided by the total number of molecules present at time t:

Xn N0 M 0 N M 2-26

(6.57)

Xn 1 1 p 2-27

The terms O'a and 0' tat in the Hamiltonian (6.56) do not conserve energy and can only contribute to the dynamics through virtual transitions. This contribution is much smaller than that of the real energy-conserving transitions associated with the terms O'a t and O't a. So we will make the rotating-wave approximation and keep only the energy-conserving terms in (6.56):

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