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Control of the side reactions is achieved through two factors: (1) reversible complexation of the anionic propagating species XXVII by the silyl ketene acetal polymer chain ends XXVI maintains the concentration of the anionic propagating species at a low concentration; and (2) the bulky counterion W (e.g., tetra-n-butylammonium, tris(dimethylamino)sulfonium) decreases the reactivity of the anionic propagating centers toward the terminating side reactions. Living polymerizations of methacrylates with narrow PDI, generally 1.2 1.3 with some lower, are achieved by nucleophilic (dissociative) GTP at temperatures of 0 80 C. However, the maximum molecular weights that can be achieved with narrow PDI are limited to about 20,000 30,000. Two factors limit the molecular weights termination by cyclization (Eq. 5-76), although suppressed, is always present and by complexation of silyl ketene acetal ended polymer. GTP of acrylates is not as successful. Lower temperatures are required and there is substantial PDI broadening even at 0 C. Better results for acrylates are achieved by electrophilic (associative) GTP using HgCl2 and trimethylsilyl iodide at 20 C [Zhuang and Muller, 1995]. A variation of GTP, referred to as aldol GTP, involves polymerization of a silyl vinyl ether initiated by an aldehyde [Sogah and Webster, 1986; Webster, 1987]. Both initiation and propagation involve nucleophilic addition of the vinyl ether to the aldehyde carbonyl group with transfer of the trialkyl silyl group from vinyl ether to the carbonyl oxygen (Eq. 5-82). The reaction has similar characteristics as GTP. The product is a silated poly(vinyl alcohol) (PVA), which can be hydrolyzed by acid to PVA (Eq. 5-83).



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5-82

To deal only with truly independent degrees of freedom, we consider only k in the half space defined by, say, positive k z . Now using 1:{ ) 1 Jd3k e , ik.r (5.21) u r = (21T)3 we can rewrite Maxwell equations (5.14)-(5.17) as

5-83

Bj{k) = ckVj{k) - 21T2ckp. j{k), Vj{k) = -ckBj(k).

5-3d 5-3d-1

(5.22) (5.23)

5-84





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There are only two equations now rather than four because we have already used the fact that both D and B are transverse and therefore (5.18) and (5.19) automatically satisfy the two vanishing divergency Maxwell equations (5.14) and (5.15). Equations (5.22) and (5.23) look very much like the equations of motion for the canonical position and momentum of a harmonic oscillator with a driving term. Let us follow Lord Kelvin's and Maxwell's method of looking for analogies in nature [87] and develop this idea further. The Hamiltonian of a one-dimensional harmonic oscillator of frequency wand mass m under the effect of an external potential U is given by

where [M ] is the total concentration of all types of living anionic propagating centers (free ions and ion pairs). [M ] can be determined by reacting the living polymer with a terminating agent such as methyl iodide, carbon dioxide, or other electrophilic substance followed by analysis of the amount of terminating agent incorporated into the polymer. The use of

+ -2- q2 + U{q),

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isotopically labeled terminating agents can increase the analytical sensitivity Ultraviolet visible and NMR spectroscopy are also useful for determining the total concentration of propagating species Since free ions constitute a very small percentage of [M ] for most systems, equating the concentration of ion pairs with [M ] may not introduce a signi cant error The living ends are monoanions in polymerizations initiated by butyllithium and similar initiators and dianions in polymerizations initiated by electron transfer The two types of anions are referred to as one-ended (monofunctional) land two-ended (bifunctional) living anions Equation 5-84 applies for the case where initiation is rapid relative to propagation This condition is met for polymerizations in polar solvents However, polymerizations in nonpolar solvent frequently proceed with an initiation rate that is of the same order of magnitude as or lower than propagation.

Click the Find & Select button. Click Find. The Find and Replace dialog box appears, displaying the Find tab.

(5.24)

More complex kinetic expressions analogous to those developed for radical and nonliving cationic polymerizations apply for such systems [Pepper, 1980; Szwarc et al, 1987] As with certain cationic systems, many anionic living polymerizations proceed too rapidly to be followed by techniques such as dilatometry The stoppped- ow technique (Sec 5-2e-1) is useful for studying these fast polymerizations Ultraviolet visible spectroscopy of the rapidly mixed reaction system contained in a capillary tube allows one to follow the initiation rate (observing the increase in optical density of propagating species) and/or the polymerization rate (by following loss of monomer) The polymerization rate can also be obtained by a modi cation of the apparatus in which polymerization is stopped by running the contents of the capillary tube into a solvent containing a terminating agent The reaction time is given by the ratio of the capillary volume to the ow rate.

where q is its canonical position and p (not to be confused with the norm of the single dipole p) is its canonical momentum.

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Page.Draw. Another way to convert PDF to TIFF using C# , is to use Page.Draw() to create a bitmap for each page, and then use standard .Net methods to write these to a tiff file. There are two issue with this though: .NET does not support creating a graphics instance for a monochrome bitmap.












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