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Fig. 3-14 Variation of kp [M] and kdp with temperature for styrene. After Dainton and Ivin [1958] (by permission of The Chemical Society, Burlington House, London).
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polymer. For an equilibrium situation G 0, Q K and Eq. 3-175 may be combined with Eq. 3-173 to yield
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G H  T S RT ln K 3-176
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The equilibrium constant is de ned by kp =kdp or more conveniently by
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K Mn 1  1 Mn  M M 3-177
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Combination of Eqs. 3-176 and 3-177 yields
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Tc H  S R ln M c 3-178a
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ln M c H  S RTc R 3-178b
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Equation 3-178b shows the equilibium monomer concentration M c as a function of the reaction or ceiling temperature Tc . (Note that H  in Eq. 3-178 can be replaced by H because the enthalpy change is independent of [M]. This is not the case for S since the entropy change is dependent on [M].) Since H  is a negative quantity, the monomer concentration in equilibrium with polymer increases with increasing temperature, that is, a plot of M c versus 1=T is linear with a negative slope of H  =R and intercept of S =R. This means that there is a series of ceiling temperatures corresponding to different equilibrium monomer concentrations. For any monomer solution of concentration M c there is a temperature Tc at which polymerization does not occur. (For each M c there is a corresponding plot analogous to Fig. 3-14, in which kdp kp M at its Tc .) Stated another way, the polymerization of a particular monomer solution at a particular temperature proceeds until
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TABLE 3-16 Polymerization Depolymerization Equilibriaa Monomer Vinyl acetate Methyl acrylate Ethylene Styrene Methyl methacrylate a-Methylstyrene Isobutylene M c at 25 C 1 10 9 1 10 9 1 10 6 1 10 3 2.2 Tc for Pure Monomer ( C) 400 310 220 61 50
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a Data from Cook et al. [1958]; McCormick [1957]; Wall [1960]; Worsfold and Bywater [1957].
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equilibrium is established, that is, until the monomer concentration decreases to the M c value corresponding to that Tc temperature. Thus higher initial monomer concentrations are required with increasing temperature in order to observe a net production of polymer before equilibrium is established. There is an upper temperature limit above which polymer cannot be obtained even from pure monomer. The reader is cautioned to note that the literature often appears to refer only to a singular Tc value the ceiling temperature. It is clear from the discussion above that each monomer concentration has its own Tc value. The apparent designation of a singular Tc value usually refers to the Tc for the pure monomer or in some cases to that for the monomer at unit molarity. For many of the alkene monomers, the equilibrium position for the propagation depropagation equilibrium is far to the right under the usual reaction temperatures employed, that is, there is essentially complete conversion of monomer to polymer for all practical purposes. Table 3-16 shows the monomer concentrations at 25 C for a few monomers [Cook et al., 1958; McCormick, 1957; Wall, 1960; Worsfold and Bywater, 1957]. Data are also shown for the ceiling temperatures of the pure monomers. The data do indicate that the polymer obtained in any polymerization will contain some concentration of residual monomer as determined by Eq. 3-178. Further, there are some monomers for which the equilibrium is not particularly favorable for polymerization, for example, a-methylstyrene. Thus at 25 C a 2.2-M solution of a-methylstyrene will not undergo polymerization. Pure a-methylstyrene will not polymerize at 61 C. Methyl methacrylate is a borderline case in that the pure monomer can be polymerized below 220 C, but the conversion will be appreciably less than complete. For example, the value of M c at 110 C is 0.14 M [Brandrup and Immergut, 1989]. Equation 3-178 applies equally well to ionic chain and ring-opening polymerizations as will be seen in subsequent chapters. The lower temperatures of ionic polymerizations offer a useful route to the polymerization of many monomers that cannot be polymerized by radical initiation because of their low ceiling temperatures. The successful polymerization of a previously unpolymerizable monomer is often simply a matter of carrying out the reaction at a temperature below its ceiling temperature. Interestingly, it should not be assumed that a polymer will be useless above its ceiling temperature. A dead polymer that has been removed from the reaction media will be stable and will not depolymerize unless an active end is produced by bond cleavage of an end group or at some point along the polymer chain. When such an active site is produced by thermal, chemical, photolytic, or other means, depolymerization will follow until the monomer concentration becomes equal to M c for the particular temperature. The thermal behavior of many polymers, however, is much more complex. Degradative reactions other than depolymerization will often occur at temperatures below the ceiling temperature.
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