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8-9 LIVING POLYMERIZATION Living polymerizations are useful for producing block copolymers and functionalized polymers. Facile chain-breaking reactions such as b-hydride transfer greatly limit the possibility of living polymerization for most of the polymerizations described in this chapter, but there are signi cant differences between the different types of initiators: 1. Living polymerization does not occur with traditional Ziegler Natta isoselective heterogeneous initiators. 2. Traditional Ziegler Natta syndioselective homogeneous vanadium initiators such as vanadium(III) acetylacetonate with Al(C2 H5 )2 Cl yield living polymerizations at low temperatures (< 60 C) [Doi, 1986; Hagen et al., 2002]. 3. There are very few reports of living polymerization by metallocene initiators. Living polymerization is reported for propene polymerization with Cp2 ZrMe2 at 78 C or Cp2 HfMe2 at 50 C using B(C6 F5 )3 plus Al(OC8 H17 )3 as coinitiator [Fukui et al., 1999]. Isoselective living polymerization of 1-hexene proceeds with rac-C2 H4 (Ind)2 ZrMe2 and B(C6 F5 )3 at 78 C. 4. The postmetallocene initiators offer the greatest potential for producing block copolymers and functionalized polymers. Many ansa-cyclopentadienyl amido, adiimine chelate, phenoxy imine chelate, and related initiators produce living, stereoselective polymerizations [Busico et al., 2003b; Fujita and Coates, 2002; Gottfried and Brookhart, 2001; Hagihara et al., 1998; Hasan et al., 2001; Ittel et al., 2000; Jayaratne and Sita, 2000; Kawabe and Murata, 2001; Makio et al., 2002; Mehrkhodavandi and Schrock, 2001; Mitani et al., 2003; Saito et al., 2001; Tian et al., 2001; Tshuva et al., 2000]. Some of these polymerizations require low temperatures, others proceed as living polymerizations at 0 C and higher.

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where 8n',n stands for 8nu',nu8n.,',n.,8nw',nw' with 8i ,j being the Kronecker delta, which vanishes for i # j and equals 1 for i = j.

The polymerization of 1,3-dienes is more complicated than that of alkenes because of the greater number of possible stereoisomers (Secs. 8-1d and 8-1e). Table 8-8 shows the

2Por a more rigorous proof of discreteness, try Problems 5.12 and 5.13 in [40]. If you can read German and like going to original sources whenever possible, have a look at the two papers [634, 635] in which Weyl demonstrates that for these perfect cavity boundary conditions, the eigenvalues are discrete and infinite with a lower bound.

TABLE 8-8

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Outlook is a personal information manager for the computer desktop. You can use Outlook s Calendar component to manage appointments in your calendar; its Contacts component to keep track of contacts; its Tasks component to organise lists of tasks you need to complete; its Mail component to send and receive e-mail messages; and more. You can perform a wide variety of everyday tasks from the Outlook window. In this part, you learn how to put Outlook to work for you using each of the major components to manage everyday tasks.

The X are the modes of the electric field, but we also need the modes of the magnetic field. They are connected to each other by Maxwell equations; thus once the X are determined, the magnetic field modes follow. To see this, we notice that substitution of the separable expression (A.8) for E in (A.3) and (A.4) suggests that B is also separable. Taking B to be given by

Stereochemistry of Radical Polymerization of 1,3-Dienes Polymer Structure (%) Cis 1,4 Trans 1,4 1,2 3,4 6 22 28 43 1 11 23 19 1 3 8 77 58 51 39 90 79 66 69 97 93 85 17 20 21 18 5 5 5 3 1 2 3

B(r, t) = c/>(r)M(t),

Temperature ( C) 20 20 100 233 20 10 100 203 40 20 90

(AI9)

4 5 6 9 1 2 4

1VI(t)c/>(r) = -cT(t)V 1\ x(r)

Data from Condon [1953], Richardson [1954], Pollock et al. [1955]. Data from Coleman and Brame [1978], Coleman et al. [1977], Ebdon [1978].

polymers obtained in radical polymerization of 1,3-butadiene, isoprene, and chloroprene (2-chloro-1,3-butadiene). 1,4-Polymerization occurs in preference to 1,2- or 3,4-polymerization and trans 1,4-polymerization occurs in preference to cis 1,4-polymerization. (Both 1,2and 3,4-polymerizations yield the same polymer for the symmetric 1,3-butadiene.) The temperature dependence of the structure of polybutadiene shows trans 1,4-addition to have a more favorable enthalpy of activation by about 12 kJ mol 1 relative to the cis-1,4-addition, although the latter has a more favorable entropy of activation by about 29 J mol 1 K 1 . Trans 1,4-addition is favored over 1,2-addition by an enthalpy of activation of about 4 kJ mol 1 with no difference in the entropies of activation. The polymerization of a 1,3-diene involves delocalization of the radical over carbons 2 and 4 of the terminal monomer unit (XLVIII). The predominance of 1,4-propagation

M(t)V 1\ c/>(r) = -T(t)x(r).

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