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Fig. 2-4 Decay in a and increase in degree of polymerization with time in polymerization of A with A B B0 . Values of s are noted for each plot. After Ozizmir and Odian [1980] (by permission of Wiley Interscience, New York).

2un(zn-

reaction time to obtain high polymer (X n > 50 100) becomes impractical. The extreme situation occurs at s ! 1 k1 ! 0 , where the maximum degree of polymerization is 2. Reaction systems with very small k1 values must be avoided in order to achieve high degrees of polymerization. The desirable system from the viewpoint of polymerization rate and X n is that with s 1. (The exception to this generalization is for systems of s > 1 where both k1 and k2 are large but k2 is larger.) The A plus B 0 system with k1 6 k4 and k2 6 k3 has been treated in a similar man A B ner [Ozizmir and Odian, 1981]. The parameters a, b, g, and s as de ned by Eqs. 2-45a, 2-45b, 2-45c, and 2-45e are retained in the treatment. t is rede ned as

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Confidential Allow the user to copy the data, report the action to a central logging location, and pop up a message that informs the end user that this action is potentially risky. The message may include a link to the company s documented security policies. Secret Allow the user to copy the data if they enter a reason why they are doing so, report the action to a central logging location, and

t k1 k2 B 0 t 2-52

(n + 1 )

7-52

= 0.

(n + 1 )

(n + 1 )

pop up a message that informs the end user that this action is potentially risky. The message may include a link to the company s documented security policies.

7-53

is a weighted sum of the discrepancies d, =

Simultaneously with propagation by Eqs. 7-52 and 7-53, there is propagation by selfreaction of XXVII. XXVII is an AB type of monomer, and step polymerization occurs by reaction between amine and lactam end groups. Actually, the lactam end groups are protonated prior to reaction. The reaction is generally the same as Eq. 7-52 nucleophilic attack of amine on protonated lactam. Although this reaction is only a minor contribution to the overall conversion of lactam to polymer, it determines the nal degree of polymerization. There are also exchange reactions that involve intermolecular nucleophilic attack of amine on amide linkages within a polymer chain. Intramolecular versions of the various reactions result in cyclic oligomer formation. Overall, one generally observes the molecular weight distribution (MWD) of the polymer (excluding cyclic oligomer and monomer) to be close to the Flory most probable distribution. For cationic polymerization with an acid whose anion Z is nucleophilic, initiation involves the sequence described by Eq. 7-51 plus the formation of XXIX. XXIX propagates by a sequence similar to that described by Eqs. 7-52 and 7-53 except that a growing polymer chain possesses a Z end group instead of a lactam end group. CO

7-54

Various side reactions greatly limit the conversions and polymer molecular weights that can be achieved in cationic polymerization of lactams. The highest molecular weights obtained in these polymerizations are 10,000 20,000. The most signi cant side reaction is amidine (XXXI) formation [Bertalan et al., 1984]. Propagation of the polymer chain

For regression, mean and variance estimation, the discrepancy is given by the residuals, whereas for multivariate problems the discrepancy is often the Mahalanobis distance. Now, as the discrepancy can be arbitrarily large, the influence of a single point may dominate the estimator A common method for making a procedure robust is to choose a function and a cutoff point c so that: +(d) =

Top secret Prohibit the user from entering the data, mandate that they enter a reason why they are attempting to copy the data, report the action to a central logging location, and pop up a message that explains why this action is prohibited. The message may include a link to the company s documented security policies.

7-55

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