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1,3,5-Trioxane, the cyclic trimer of formaldehyde, yields the same polymer, polyoxymethylene (Eq. 7-2), as obtained by the ionic polymerization of formaldehyde (Sec. 5-6). This polymerization is carried out on an industrial scale using boron tri uoride etherate [Cui et al., 2003; Dolce and Grates, 1985]. The presence of water is required for polymerization as noted by the lack of polymer formation in the complete absence of water [Collins et al., 1979]. That 1,3,5-trioxane polymerizes in spite of containing the stable 6-membered ring is a consequence of the polymerization occurring with simultaneous precipitation of the polymer in crystalline form. The heat of crystallization makes the total process of converting monomer to polymer a signi cantly exothermic process. In addition to the usual polymer monomer propagation depropagation equilibrium that may be present, trioxane polymerization proceeds with the occurrence of a polymer formaldehyde equilibrium:



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dv la(vW = 1,

7-37

(7.139)





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The formation of formaldehyde probably occurs through the small concentration of oxycarbocations present, as shown above, and not through the more abundant oxonium ions. 1,3,5-Trioxane polymerizations proceed with induction periods, which correspond to the buildup of the equilibrium concentration of formaldehyde [Lu et al., 1990]. This also corresponds to a buildup in 1,3,5,7-tetroxocane, apparently by insertion of formaldehyde into 1,3,5-trioxane. Polymer is not formed until after both formaldehyde and 1,3,5,7-tetroxocane appear. Formaldehyde and, to a lesser extent, 1,3,5,7-tetroxocane decrease the induction period by increasing the rate of formation of propagating species of suf cient size to precipitate from solution. Subsequent polymerization by addition of 1,3,5-trioxane is accelerated as the reaction proceeds with conversion of monomer to crystalline polymer. The relative importance of participation by formaldehyde and 1,3,5,7-tetroxocane in propagation relative to 1,3,5-trioxane after the induction period is unclear. Polymerization of 1,3,5-trioxepane involves more complicated propagation depropagation equilibria. The initially formed oxycarbocation XX loses formaldehyde to yield oxycarbocation XXI, which in turn loses 1,3-dioxolane to regenerate XX:

as it should. We can also check that [Y(17), yt(17')] combination of B(v),

7-38

= 8(17 - 17').

7-39

1 2 3

Writing y(17) as a linear (7.140)

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Both XX and XXI undergo propagation (presumably through the corresponding oxonium ions). The two equilibria (Eqs. 7-38 and 7-39) do not proceed to the same extent, with the result that the copolymer structure deviates from that of the monomer [Szwarc and Perrin, 1979]. Transfer and termination occur by the modes described previously for cyclic ether polymerizations. Chain transfer to polymer (both inter- and intramolecular) is facilitated in cyclic acetal polymerizations compared to cyclic ethers because acetal oxygens in the polymer chain are more basic than the corresponding ether oxygens [Penczek and Kubisa, 1989a,b]. Working at high monomer concentrations, especially bulk polymerizations, is used to depress cyclic oligomer formation.

An additional termination in the trioxane polymerization is chain transfer to monomer by hydride ion transfer, which results in terminating the propagating chain with a methoxyl group while carbocation XXII reinitiates polymerization [Kern et al., 1966; Weissermel et al., 1967].

y(17) =

O + OCH2OCH2OCH2 + CH2 O CH2 O CH2 O + OCH2OCH2OCH3 + CH O CH2 O CH2 XXII 7-40

dv (3*(V,17) B(I/),

7-2b-5

[Y(17), yt(17')] =

7-2b-5-a Rate of Polymerization. The rate laws that describe conventional cationic ringopening polymerizations take several forms. Some polymerizations can be described by expressions similar to those in alkene polymerizations (Sec. 5-2d). In polymerizations with little or no termination one can use kinetic expressions similar to those of living polymerizations (Secs. 5-2g, 7-2b-3). Some cationic ring-opening polymerizations take place without termination and are reversible. Oxirane and oxetane polymerizations are seldom reversible, but polymerizations of larger-sized rings such as tetrahydrofuran are often reversible. The description of reversible ROP is presented below [Afshar-Taromi et al., 1978; Beste and Hall, 1964; Kobayashi et al., 1974; Szwarc, 1979]. It is also applicable to other reversible polymerizations such as those of alkene and carbonyl monomers. The propagation depropagation equilibrium can be expressed by

dv (3*(V,17){3(V,17')

7-41

/'i,

which is analogous to Eq. 3-174. The polymerization rate is given by the difference between the rates of the propagation and depropagation reactions:

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1 1 dv la(v)1 2 P--P--, + la(17) I217 - - Wo V - 17 v - 17 17 - 17'

Rp d M kp M* M kdp M* dt 7-42

la(17W8(17 -17').

kp M c kdp 7-43

where M c is the equilibrium monomer concentration (as in Eq. 3-178). (The derivations in Sec. 3-9c for M c and Tc as a function of S and H are applicable to the present system.) Combination of Eqs. 7-42 and 7-43 gives the polymerization rate as

(7.141)

d M kp M* M M c dt 7-44

The product of the two principal parts above can be separated in partial fractions in the following way (see Appendix F or Fano's paper [190]):

ln M 0 M c kp M* t M M c 7-45

1 1 1 , 17 + 17' P--P--, = -,-- { I -I } +7r 2 8(17-17)8 ( v - - - ) . P--, P - V-17 V-17 17 -17 V-17 v-17 2

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