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Contrary to previous expectations, X-ray diffraction patterns showed the polymer chain axes to be parallel to the smaller dimension of the platelet Since polymer molecules are much longer than 100 A, the polymer molecules are presumed to fold back and forth on themselves in an accordionlike manner in the process of crystallization Chain.

folding was unexpected, since the most thermodynamically stable crystal is the one involving completely extended chains. The latter is kinetically dif cult to achieve and chain folding is apparently the system s compromise for achieving a highly stable crystal structure under normal crystallization conditions. Two models of chain folding can be visualized. Chain folding is regular and sharp with a uniform fold period in the adjacent-reentry model (Fig. 1-6). In the nonadjacent-reentry or switchboard model (Fig. 1-7) molecules wander through the nonregular surface of a lamella before reentering the lamella or a neighboring lamella. In the chain-folded lamella picture of polymer crystallinity less than 100% crystallinity is attributed to defects in the chain-folding process. The defects may be imperfect folds, irregularities in packing, chain entanglements, loose chain ends, dislocations, occluded impurities, or numerous other imperfections. The adjacent reentry and switchboard models differ in the details of

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[Le Borgne and Spassky, 1989]. Cleavage at the alkyl oxygen bond would result in racemization instead of retention. Control of the polymerization, speci cally, achieving living polymerization conditions, is achieved by using the covalent initiators, especially the less active initiators. The polymerization rate is rst-order in both monomer and initiator, X n is given by the ratio of monomer to initiator, and narrow MWDs are obtained. The limiting factor in achieving high molecular weights is chain transfer to monomer, that is, b-proton abstraction from monomer. This is extensive for b-butyrolactone, limiting number-average molecular weights to about 20,000. This is not nearly as important for other monomers; for example, molecular weights higher than 105 have been achieved for b-propiolactone. Chain transfer to polymer by transesteri cation is present and responsible for molecular weight broadening. Intramolecular transfer results in cyclic oligomers; intermolecular transfer results in scrambling of chain segments between different polymer chains. The extent of chain transfer to polymer as well as to monomer is greater for the more active (more ionic) initiators, for example, alkoxides of Na, Mg, and Zn instead of Al [Hofman et al., 1987a,b; Kricheldorf et al., 1988]. Rare-earth alkoxides (La, Y, Sm) strike a good balance with polymerization rates similar to ionic initiators, but with lowered side reactions similar to covalent initiators [Save and Soum, 2002; Save et al., 2002].

Figure 8.3 shows a plot of the sigmoid function, which defines the fitted values for the perceptron, and the derivatives -mlp(z) and -mlp(z) which are, respectively, the influence curves for wg and with respect to position in feature space. We now take an individual point with label 1, and plot the onedimensional influence curves (also shown in Figure 8.3). Note that the derivatives -mlp(z) and -mlp(z)

Tin(II) 2-ethylhexanoate is an important industrial initiator for cyclic ester polymerization [Duda and Penczek, 2001; Kricheldorf et al, 2001; Storey and Sherman, 2002] Metal carboxylates are useful initiators only in the presence of alcohols The polymerization rate is very slow in the absence of alcohol, less than 1% of the rate in the presence of alcohol The actual initiator is the metal alkoxide formed by the reaction between metal carboxylate and alcohol Each alkoxide group in an alkylmetal alkoxides or metal alkoxide initiates growth of a polymer chain Thus, one, two, and three propagating chains are generated per metal atom with R2 AlOR0 , Sn(OR)2 , and Al(OR)3 , respectively However, fewer propagating chains per metal atom are observed under some conditions, for example, with aluminum isopropoxide, which aggregates to form trimers and tetramers.

The trimers are very active in polymerization, ranging from 102 - to 105 -fold more active than the tetramers Each aluminum atom (and its associated alkoxide groups) in the reaction system will not be active in polymerization unless the equilibrium exchange between trimer and tetramer is fast The equilibrium is rapid at higher temperatures, at lower initiator concentrations, and in more polar solvents, and one observes the theoretical maximum stoichiometry between propagating chains and metal atoms Under other conditions, less than the maximum stoichiometry is observed Aggregation phenomenon are also observed for the propagating chains, with an equilibrium between aggregated and unaggregated chains This is the equivalent of a reversible deactivation between dormant and active propagating chains that preserves the livingness of the polymerization In other living systems the reversible deactivation involves a different phenomenon.

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