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5-51
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it can be shown [Plesch, 1973, 1977, 1984] that the ratio of concentrations of free ions and ion pairs is
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YM 1 4C=K 1=2 1 YM IZ 2C=K 1 1 4C=K 1=2 5-52
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where C YM YM IZ . The relative concentrations of free ions and ion pairs depend on the ratio C=K according to Eq. 5-52. Free ions constitute approximately 99, 90, 62, 27, 9, 2, 1, and 0.3% of the propagating species at C=K values of 0.01, 0.1, 1, 10, 102 , 103 , 104 , and 105 , respectively. Cationic polymerizations are carried out over a wide range of C=K values, typically anywhere from 103 to 10 2 , depending on the speci cs of the reaction system. Consider styrene polymerization by tri ic (tri uoromethanesulfonic) acid in 1,2-dichloroethane at 20 C where K is 2:8 10 7 mol L 1 [Kunitake and Takarabe, 1979]. Experiments performed at acid concentrations of 2:8 10 5 M C=K 102 would involve 91% propagation by ion pairs and 9% propagation by free ions. The relative contribution of free ions to the overall propagation increases for lower acid concentrations. There is app considerable error if the kp value is simply taken to be kp (as is often done since K is typi cally unknown and one cannot make the appropriate corrections). The ratio kp =kp is prob ably in the range 5 20 for most systems. The calculated kp value is high by a factor of 1.5 for app kp =kp 5. One can safely equate kp with kp only for systems where C=K 103 104 or larger. This can be done by using higher concentrations of tri ic acid as long as there are no solubility problems or the reaction rates are not excessively high. For most of the systems reported in the literature, C=K is not known very often, neither K nor C is known. For two-component initiator coinitiator systems, C is usually taken to be the initiator concentration [YZ] when the coinitiator is in excess or the coinitiator concentration [I] when the initiator is in excess. C may be lower than [YZ] or [I] due to association; that is, only a fraction of [YZ] or [I] may be active in polymerization. This may also be the case for one-component initiators such as tri ic acid. It would be prudent to determine the actual value of C in any polymerization system usually a dif cult task and seldom achieved. Experimental dif culties have also limited our knowledge of K values, which are obtained most directly from conductivity measurements or, indirectly, from kinetic data. A comparison of polymerization in the absence and presence of a common ion salt (e.g., tetran-butylammonium tri ate for the tri ic acid initiated polymerization) is useful for ascertaining whether signi cant amounts of free ions are present in a reaction system. Polymerizations initiated by ionizing radiation or stable carbocation salts such as trityl or tropylium hexachloroantimonate are useful for evaluating the free-ion propagation rate constant. Ionizing radiation yields free ions (in the absence of ion pairs) whose concentrations
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IONIC CHAIN POLYMERIZATION
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TABLE 5-1 Kinetic Parameters in CF3 SO3 H Polymerization of Styrene at 20 C in ClCH2 CH2 Cla Parameter [Styrene] [CF3 SO3 H] ki Kd kp kp kts kt ktr;M
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Value 0:27 0:40 M 3:8 7:1 10 3 M 10 23 L mol 1 s 1 4:2 10 7 mol L 1 1:2 106 L mol 1 s 1 1:0 105 L mol 1 s 1 170 280 s 1 < 0:01kts 1 4 103 L mol 1 s 1
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Data from Kunitake and Takarabe [1979].
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can be obtained by conductivity mesurements [Def eux et al., 1980; Hayashi et al., 1971; Hsieh et al., 1980 Stannett et al., 1076]. Many carbocation salts are suf ciently stable to be isolated, puri ed, and characterized as crystalline products. Thus their concentration in a polymerization system is known, unlike the situation with other initiation systems such as boron tri uoride water. It is often assumed that polymerizations initiated by these salts app proceed with propagation carried entirely by free ions and the kp is taken to be kp . This is a valid assumption only under certain conditions. K is probably 10 4 10 5 for such system [Gandini and Cheradame, 1985; Subira et al., 1988]. If C=K is no larger than 0.1 (e.g., C no higher than 10 5 for K 10 4 ), the system consists of 90% free ions and 10% ion pairs. The presence of 10% of the less reactive (ion pair) propagating species results in no more app than a 10% error in the value of kp obtained by equating kp with kp . Throughout the remainder of the chapter it should be understood that any rate constants that are presented are apparent rate constants unless otherwise indicated to be those for the free ion or ion pair. In general, the available data are used to point out certain trends (e.g., the effect of solvent on reactivity) without necessarily accepting the exact value of any reported rate constant as that for the ion pair or free ion. Comparison of data from different investigators should be done with caution. 5-2e-3 Comparison of Rate Constants
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Table 5-1 shows the various kinetic parameters, including kp and kp , in the polymerization of styrene initiated by tri ic acid in 1,2-dichloroethane at 20 C. Data for the polymerization of isobutyl vinyl ether initiated by trityl hexachloroantimonate in methylene chloride at 0 C are shown in Table 5-2. Table 5-3 shows kp values for several polymerizations initiated
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TABLE 5-2 Kinetic Parameters in f3 C SbCl 6 Polymerization of Isobutyl Vinyl Ether in CH2 Cl2 at 0 Ca Parameter [f3 C SbCl ] 6 ki kp ktr;M kts kt
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