M1 M1 M2 + M1 + M2 + M2 kt dead copolymer in .NET

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M1 M1 M2 + M1 + M2 + M2 kt dead copolymer
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6-68
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where the average termination rate constant kt is an average of the homopolymerization termination rate constants (kt11 and kt22 ), each weighted on the basis of the copolymer composition in mole fractions according to
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kt F1 kt11 F2 kt22 6-69
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CHAIN COPOLYMERIZATION
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The rate of copolymerization is given by
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Rp kp M Ri =2kt 1=2 6-70
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where [M] is the total concentration of the two monomers and the average propagation rate constant kp is dependent on the comonomer feed composition, monomer reactivity ratios, and homopropagation rate constants according to
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2 2 r1 f1 2 f1 f2 r2 f2 r1 f1 =k11 r2 f2 =k22
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6-71
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Equation 6-71, derived by Fukuda and coworkers [Fukuda et al., 1985; Ma et al., 2001], follows from previous derivations of the rate of copolymerization [Melville et al., 1947; Walling, 1949, 1957]. Thus, the terminal model for copolymerization gives us expressions for copolymer composition (Eqs. 6-12 and 6-15), propagation rate constant (Eq. 6-71), and polymerization rate (Eq. 6-70). The terminal model is tested by noting how well the various equations describe the experimental variation of F1 , kp , and Rp with comonomer feed composition. There are also expressions that describe the terminal model in terms of monomer sequence distributions in the copolymer [Burke et al., 1994a,b, 1995; Cheng, 1995, 2000]. The M1 centered triad fractions are given by
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2 r1 f1 2 2 2 r1 f1 2r1 f1 f2 f2
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6-72a 6-72b
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6-72c
The M2 centered triads (222), 221 122 , and (121) are derived from Eq. 6-72 by reversing the 1 and 2 subscripts. Many comonomer pairs follow the terminal model, but more advanced models are needed to describe most comonomer pairs (Sec. 6-5).
6-4 IONIC COPOLYMERIZATION Ionic copolymerizations are different from radical copolymerizations in several respects. Ionic copolymerizations are much more selective. The number of comonomer pairs that undergo either cationic or anionic copolymerization is relatively limited because of the wider range of monomer reactivities in ionic copolymerization [Bywater, 1976; Kennedy and Marechal, 1983; Morton, 1983]. Cationic copolymerization is limited to monomers with electron-donating substituents and anionic copolymerization to monomers with electronwithdrawing substituents. For comonomer pairs that undergo ionic copolymerization, the general tendency is toward the ideal type of behavior (Sec. 6-2c-1), with the r1 r2 product approaching unity, where the relative reactivities of the two monomers toward the two different ionic propagating centers are approximately the same. There is a general lack of any tendency toward alternation. Furthermore, quite a few copolymerizations proceed with r1 r2
IONIC COPOLYMERIZATION
values greater than unity. Thus there are relatively few monomer pairs that yield copolymers containing large proportions of both monomers. Another characteristic feature of ionic copolymerizations is the sensitivity of the monomer reactivity ratios to changes in the initiator, reaction medium, or temperature. This is quite different from the general behavior observed in radical copolymerization. Monomer reactivity ratios in radical copolymerization are far less dependent on reaction conditions.
6-4a 6-4a-1
Cationic Copolymerization Reactivity
The effect of a substituent on the reactivity of a monomer in cationic copolymerization depends on the extent to which it increases the electron density on the double bond and on its ability to resonance stabilize the carbocation that is formed. However, the order of monomer reactivities in cationic copolymerization (as in anionic copolymerization) is not nearly as well de ned as in radical copolymerization. Reactivity is often in uenced to a larger degree by the reaction conditions (solvent, counterion, temperature) than by the structure of the monomer. There are relatively few reports in the literature in which monomer reactivity has been studied for a wide range of different monomers under conditions of the same solvent, counterion, and reaction temperature. Among the most extensive studies of monomer reactivity have been those involving the copolymerization of various meta- and para-substituted styrenes with other styrene monomers (styrene, a-methylstyrene, and p-chlorostyrene) as the reference monomer [Kennedy and Marechal, 1983]. The relative reactivities of the various substituted styrenes have been correlated by the Hammett sigma rho relationship:
  1 log rs r1 6-73
For example, log 1=r1 values for a series of meta- and para-substituted styrenes copolymerized with styrene were plotted against the sigma substituent constants to yield a straight line with slope r of negative sign. The sigma value of a substituent is a quantitative measure of that substituent s total electron-donating or electron-withdrawing effect by both resonance and induction. Electron-withdrawing and electron-donating substituents have positive and negative sigma constants, respectively. A negative value of r means 1=r1 is increased by electron-donating substituents as expected for cationic polymerization. (A positive value of r would mean 1=r1 is increased by electron-withdrawing substituents.) Substituents increase the reactivity of styrene in the approximate order