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Kinetics of Living Polymerization Polymerization Rate
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The rate of polymerization in nonterminating systems can be expressed as the rate of propagation
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where [M ] is the total concentration of all types of living anionic propagating centers (free ions and ion pairs). [M ] can be determined by reacting the living polymer with a terminating agent such as methyl iodide, carbon dioxide, or other electrophilic substance followed by analysis of the amount of terminating agent incorporated into the polymer. The use of
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isotopically labeled terminating agents can increase the analytical sensitivity. Ultraviolet visible and NMR spectroscopy are also useful for determining the total concentration of propagating species. Since free ions constitute a very small percentage of [M ] for most systems, equating the concentration of ion pairs with [M ] may not introduce a signi cant error. The living ends are monoanions in polymerizations initiated by butyllithium and similar initiators and dianions in polymerizations initiated by electron transfer. The two types of anions are referred to as one-ended (monofunctional) land two-ended (bifunctional) living anions. Equation 5-84 applies for the case where initiation is rapid relative to propagation. This condition is met for polymerizations in polar solvents. However, polymerizations in nonpolar solvent frequently proceed with an initiation rate that is of the same order of magnitude as or lower than propagation. More complex kinetic expressions analogous to those developed for radical and nonliving cationic polymerizations apply for such systems [Pepper, 1980; Szwarc et al., 1987]. As with certain cationic systems, many anionic living polymerizations proceed too rapidly to be followed by techniques such as dilatometry. The stoppped- ow technique (Sec. 5-2e-1) is useful for studying these fast polymerizations. Ultraviolet visible spectroscopy of the rapidly mixed reaction system contained in a capillary tube allows one to follow the initiation rate (observing the increase in optical density of propagating species) and/or the polymerization rate (by following loss of monomer). The polymerization rate can also be obtained by a modi cation of the apparatus in which polymerization is stopped by running the contents of the capillary tube into a solvent containing a terminating agent. The reaction time is given by the ratio of the capillary volume to the ow rate. Short reaction times of 0.005 2 s can be accurately studied in this manner. The conversion and, hence, Rp and apparent propagation rate constant are obtained by analyzing the quenched reaction mixture for either polymer or unreacted monomer. It is useful to understand the reasons for the faster reaction rates encountered in many anionic polymerizations compared to their radical counterparts. This can be done by comparing the kinetic parameters in appropriate rate equations: Eq. 3-22 for radical polymerization and Eq. 5-84 for anionic polymerization. The kp values in radical polymerization are similar app app to the kp values in anionic polymerization. Anionic kp values may be 10 100-fold lower than in radical polymerization for polymerization in hydrocarbon solvents, while they may be 10 100-fold higher for polymerizations in ether solvents. The major difference in the rates of anionic and radical polymerizations resides in the lack of termination in anionic polymerization and the larger difference in the concentrations of the propagating species. The concentration of propagating radicals is 10 9 10 7 M, while that for propagating anions is often as high as 10 4 10 2 M. Thus anionic polymerization rates are much higher than radical rates based only on the concentrations of propagating species. 5-3d-2 Effects of Reaction Media
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The propagation rate constant and the polymerization rate for anionic polymerization are dramatically affected by the nature of both the solvent and the counterion. Thus the data in Table 5-10 show the pronounced effect of solvent in the polymerization of styrene by sodium naphthalene (3 10 3 M) at 25 C. The apparent propagation rate constant is increased by 2 and 3 orders of magnitude in tetrahydrofuran and 1,2-dimethoxyethane, respectively, compared to the rate constants in benzene and dioxane. The polymerization is much faster in the more polar solvents. That the dielectric constant is not a quantitative measure of solvating power is shown by the higher rate in 1,2-dimethoxyethane (DME) compared to tetrahydrofuran (THF). The faster rate in DME may be due to a speci c solvation effect arising from the presence of two ether functions in the same molecule.