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groups are obtained by reaction with N-trimethylsilyl-protected imines followed by acid hydrolysis. When the telechelic polymer contains a bifunctional group, such as the allyl-terminated telechelic, it is called a macromonomer or macromer because it can undergo polymerization through that functional group. The ef ciencies of these reactions depend on the speci c reaction, steric factors, and reaction conditions. For example, ef ciency is higher for polybutadienyl carbanion compared to polystyrene. Reaction of any of the polymer carbanions with carbon dioxide is quantitative in polar solvents, but not in hydrocarbons. Telechelic polymers are also obtained by using initiators containing the desired functional group. This often requires that the functional group be protected or blocked during initiation and polymerization since many functional groups act as facile terminating agents. Thus an amine-terminated telechelic is obtained by prior synthesis of an initiator containing an amine



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The Lorentz force accounts for the influence of the field upon the charges, but the charges also affect the field. They are themselves sources offield. The field dynamics is described by Maxwell equations (5.5)-(5.8), where (5.73) is the density of charge associated with the point charges and (5.74) is the corresponding current density. Since it is the independent degrees of freedom of the field that have to be quantized, we first have to identify these degrees of freedom. As we saw in 2, this is greatly simplified if we work with Maxwell equations in reciprocal instead of in real space [108]. Let :F'(k, t) be the reciprocal space counterpart of a vector field F(r, t) given by

5-115





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function protected by trimethylsilylation [Dickstein and Lillya, 1989]. The protected initiator XXXIV is used to initiate polymerization and subsequently the trimethylsilyl group is removed by acid hydrolysis. Monofunctional telechelic polymers containing groups such as hydroxyl, amine, or carboxyl can be used to obtain diblock copolymers by reaction with other telechelic polymers. The latter includes telechelics obtained by the anionic route or telechelics obtained by other routes (e.g., step and ring-opening polymerizations). Telechelic polymers containing functional groups at each chain end are obtained by carrying out the above reactions with two-ended living anionic polymers. These bifunctional telechelics can be used to synthesize triblock and multiblock copolymers as well as telechelic prepolymers to be used in step polymerization (Sec. 2-13b) [Register et al., 1988]. Telechelic polymers are obtained by group transfer polymerization by using initiators (XXXV) containing protected functional groups [Webster and Sogah, 1989]. Hydroxyland carboxyl-terminated telechelic polymers are obtained by using initiator XXXV with R 2 CH2 OSi(CH3 )3 and CH Si(CH3 )3 , respectively (R0 3 ). The HO and COOH CH groups are obtained by hydrolysis of the silyl ketene acetal end groups of the polymer. Another approach is reaction of the living silyl ketene acetal end group with an electrophilic reagent, such as benzaldehyde to yield a blocked hydroxyl function or p-bromomethylstyrene to yield a vinyl macromer.

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:F'(k, t) =

Note: If you change a value in a cell referenced in your formula, the formula results automatically update to reflect the change.

Telechelic polymers via cationic living polymerizations are obtained in a similar manner [Higashimura and Sawamoto, 1989; Kennedy, 1985, 1999; Kennedy and Marechal, 1982; Kennedy and Smith, 1980; Sawamoto, 1991, 1996]. Termination of a polymerization with a nucleophile such as the sodiomalonate XXXVI yields a carboxyl-terminated telechelic after hydrolysis and decarboxylation for R H, and a vinyl-terminated telechelic is obtained for R 2 CH2 OCH CH2 . Functional groups can also be introduced by using appropri CH ately substituted initiators; for example, initiation by XXXVII yields a telechelic with a vinyl end group. Telechelic polymers are useful for synthesizing block copolymers, such as a styrene isobutylene styrene triblock polymer. Isobutylene is polymerized by 1,4-bis (2-chloroisopropyl)benzene (often called dicumyl chloride) (XXXVIII) and BCl3 to yield a bifunctional telechelic polyisobutylene with t-alkyl end groups (XXXIX). The telechelic polyisobutylene is used as the initiator together with diethylaluminum chloride to polymerize styrene and produce the triblock polymer.

(27r~3/2

CH3 C Cl + CH2 CH3 C(CH3)2

e-ik.rF(r, t).

CH3 C CH3 XXXIX CH2C(CH3)2

(5.75)

5-116

As we are dealing with real fields, F(r, t), :F'(k, t) is not completely independent. Its values for negative k are determined by those for positive k, as in Section 5.1, through the relation (5.76) :F'( -k, t) = :F* (k, t).

Living anionic polymers and block copolymers can be linked by coupling reactions. A living AB block copolymer can be linked by 1,6-dibromohexane to yield an ABA triblock copolymer

6This section is based on [165] and follows closely the approach of [108].

5-117

So to avoid introducing redundant degrees of freedom, we will always work in half reciprocal space. Then the vector field F(r, t) is given in terms of :F(k, t) by

Coupling reactions allow the synthesis of star (multiarmed) polymers (Sec. 3-15b-5) by using a multifunctional coupling agent such as SiCl4 , CH3 SiCl3 , (ClCH2 )4 , and 1,2,4,5-tetrachloromethylbenzene [Alward et al., 1986; Hadjichristidis et al., 2001; Lutz and Rempp, 1988; Quirk et al., 1999; Remp et al., 1988]; for example

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