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7-2b-6-b Thermodynamics of Polymerization The enthalpies and entropies of polymerization for various cyclic ethers and acetals are shown in Table 7-3 Data for formaldehyde and chloral are also included A comparison of the H and S values for alkenes, carbonyl monomers, and the cyclic monomers can be made from Tables 7-3 and 3-14 The H for the 3- and 4-membered cyclics are comparable to those for alkenes, and both are appreciably larger than the values for the two carbonyl monomers The conversion of a carbonyl p-bond to a s-bond is not as exothermic as the corresponding conversion of an alkene p-bond The H values for the larger-sized cyclic monomers are much lower than those for alkenes The S value is considerably smaller for most cyclic monomers compared to the alkenes and carbonyls.

p(zn;

The cyclic monomers, having less degrees of freedom to begin with, have S values indicating that the loss in disorder on polymerization is less than for noncyclic monomers Ethylene oxide is an exception because of the highly strained nature of the 3-membered ring The S values for a few of the cyclic monomers, THF and 3,3-bis (chloromethyl)oxetane, are similar to the lowest values observed for alkene monomers..

TABLE 7-3 DH and DS of Polymerization of Cyclic Ethers and Acetalsa Monomer Ethylene oxide Oxetane 3,3-Bis(chloromethyl)oxetane Tetrahydrofuranb 1,3-Dioxolanec 4-Methyl-1,3-dioxolanec Trioxane 1,3-Dioxepaned 2-Methyl-1,3-dioxepaned 4-Methyl-1,3-dioxepaned 1,3-Dioxocane 1,3,6-Trioxocanee 2-n-Butyl-1,3,6-trioxocanee 1,3,6,9-Tetraoxacycloundecanef Formaldehyde Chloral

H (kJ mol 1 ) 94.5 81 84.5 23.4 17.6 13.4 4.5 15.1 8.8 9.2 18.3 13.0 7.9 8.0 31.1 20

is indexed by N to indicate that this is an estimator derived from a sample of size N . Assuming that p is differentiable, we can alternatively solve the equation

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S (J mol 1 K 1 ) 174 83 82.4 47.7 53.1 18 48.1 37.2 38.9 21.3 16.3 6.2 79.2 95

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Data from Bus eld [1989] unless otherwise noted. Dreyfuss and Dreyfuss [1989]. c Okada et al. [1976]. d Okada et al. [1978]. e Xu et al. [1987]. f Rentsch and Schulz [1978].

The H values for the various cyclic ethers and acetals follow closely the order expected based on considerations of relative stability as a function of ring size (Secs. 7-1a, 2-5). The 3and 4-membered cyclic monomers undergo the most exothermic polymerizations. There is a fast decrease in the exothermicity of polymerization for the larger-sized rings. Trioxane, the only 6-membered ring monomer to undergo polymerization, has a H very close to zero. Substituents on a ring structure decrease the tendency to polymerize, as noted by the less exothermic polymerizations for the substituted 1,3-dioxolane, 1,3-dioxepane, and 1,3,6trioxocane monomers relative to the corresponding unsubstituted monomers. Substituted oxetanes are an exception to this generalization. 7-2b-7 Commercial Applications

d where $(s,w ) = --p(z, Many standard estimators are M-estimators, including the sample mean which is the least squares estimator of location and has p ( z , w ) = (z Note that if p ( z ,w ) = -log f ( z ; where f is a density function, we recover the usual Maximum Likelihood (ML) estimator, so that the M-estimators are extensions of ML estimators.

There are a number of commercial applications of ring-opening polymerization of cyclic ethers. Polymerizations and copolymerizations of ethylene and propylene oxides as well as polymerization of tetrahydrofuran are used to produce polyether macrodiols, speci cally, telechelic polyethers having hydroxyl end groups [Clinton and Matlock, 1986; Dreyfuss et al., 1989; Gagnon, 1986]. The commercial materials are typically in the molecular weight range 500 6000 and are used to produce polyurethane and polyester block copolymers, including the thermoplastic polyurethane and polyester elastomers (Secs. 2-12e, 2-13b-3, 2-13c-2). The polyether macrodiols are also referred to as polyether glycols or polyols (trade names: Carbowax, Jeffox, Polyglycol, Polymeg, Terathane). Ethylene oxide and propylene oxide polymers and copolymers are also available in molecular weights of up to $20,000 and are used as hydraulic uids and lubricants, additives in cosmetics, and binders in ceramic and powder metallurgy. Ethylene oxide polymers with molecular weights of 105 106 ,

referred to as poly(ethylene oxide), nd applications that take advantage of the high viscosity of their aqueous solutions. This includes occulation, denture adhesives, packaging lms (pesticides, herbicides, seed tapes), thickening of acid cleaners and water-based paints, and friction reduction. There is considerable effort aimed at using ethylene oxide polymers and copolymers complexed with ionic salts as the electrolyte in all-solid rechargeable batteries. Polyepichlorohydrin and copolymers and terpolymers of epichlorohydrin with ethylene oxide and allyl glycidyl ether are useful elastomers [Body and Kyllinstad, 1986].

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