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have also bee studied, including diynes via coordination catalysts (Chap. 8) and dialdehydes and diisocyanates via ionic initiation.
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The competition between the rates of intermolecular propagation Rp and intramolecular cyclization Rc can be expressed in terms of the fraction of cyclized units fc de ned by
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The factor of 2 in Eq. 6-104 is due to the de nition of [M] as the concentration of the diene molecules instead of double bonds. Combination of Eqs. 6-102 through 6-104 yields
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Equation 6-106 shows that the extent of cyclization is greater at low concentration. Intermolecular propagation is increasingly favored with increasing [M]. The cyclization ratio kc =kp is obtained from the slope of a plot of fc versus [M]. Values of kc =kp are in the range 2 20 mol L 1 for most symmetric 1,6-dienes but some values are even higher; for instance, divinyl formal has a value of 200. 1,5-Dienes generally have lower kc =kp values than their 1,6 counterparts. The high tendency toward cyclization is due to a favorable entropy factor. Cyclization has a higher activation energy than does intermolecular propagation. However, cyclization proceeds with a considerably smaller decrease in activation entropy than does intermolecular propagation. For example, for methacrylic anhydride, the activation energy factor favors intermolecular propagation by 10.9 kJ mol 1, while cyclization is favored by the Arrhenius frequency factor by 256 mol L 1. The overall result is a kc =kp value of 2.4 mol L 1. The tendency toward cyclization increases with increasing reaction temperature since cyclization has a higher activation energy than does intermolecular propagation. Cyclization is also increased by using more polar solvents but the mechanism for the solvent effect is not understood [Matsumoto et al., 1987]. The tendency toward cyclization decreases considerably (lower kc =kp value) for unsymmetric 1,6-dienes, such as allyl methacrylate, where the two double bonds have signi cantly different reactivities. The polymer contains linear repeat units, rings, and pendant double bonds in relative amounts determined by kc =kp. The pendant double bonds eventually react to yield a crosslinked structure. Reactants with more than two double bonds per molecule,
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whether symmetric such as triallylcyanurate and tetraallyl ammonium bromide or unsymmetric such as diallyl maleate, behave similarly with the formation of crosslinked network structures. The extent of cyclization decreases quite sharply as one goes to ring sizes of 7 or more atoms. However, contrary to expectations, the extent of cyclization is still quite signi cant for many monomers. Thus the extent of cyclization (measured as the percent of monomer units that are cyclized) is 15 20% for diallyl esters giving ring structures containing up to 17 atoms [Holt and Simpson, 1956]. The polymerization of o-diallyl phthalate yields a polymer with more than 40% cyclization [Eaton et al., 1989; Matsumoto et al., 1980]. Cyclopolymerizations yielding more complex ring structures have also been reported [Butler, 19896, 1989]. For example, 1,4-dienes such as divinyl ether yield uncrosslinked products with little or no unsaturation and possessing different bicylic structures. The formation of one of the bicyclic structures is shown in Eq. 6-107 [Tsukino and Kunitake, 1979].
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Cyclocopolymerization is cyclopolymerization of a pair of monomers [Butler, 2000]. An example is the generation of pyran rings by copolymerization between maleic anhydride and the two double bonds of divinyl ether:
Recall the discussion in Sec. 2-3 concerning the competition between linear polymerization and cyclization in step polymerizations. Cyclization is not competitive with linear polymerization for ring sizes greater than 7 atoms. Further, even for most of the reactants, which would yield rings of 5, 6, or 7 atoms if they cyclized, linear polymerization can be made to predominate because of the interconvertibility of the cyclic and linear structures. The difference in behavior between chain and step polymerizations arises because the cyclic structures in chain polymerization do not depropagate under the reaction conditions; that is, the cyclic structure does not interconvert with the linear structure. 6-6c Interpenetrating Polymer Networks
An interpenetrating polymer network (IPN) (Sec. 2-13c-3) is obtained by carrying out a polymerization with crosslinking in the presence of another already crosslinked polymer [Klempner