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Xw 1 1 Xn Xn 3-228

(4.114)

5-2g-3



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Before we can say that this is the variance of ii, let us think about what we cannot trust and should not take seriously in such a calculation. There is a very good reason why terms involvin products of noise ellipse projections should not be taken seriously. As all and all do not commute, the operators associated with their variances do not commute either, so that the expectation values of mixed products of them will generally be different from the products of their expectation values. Thus, we should throwaway the 1/2 in (4.114) and write





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Vinyl ethers form more stable carbocations than most other monomers because the ether group is effective at resonance stabilization of positive charge. This means that the equilibrium between active and dormant species can be achieved using relatively weak initiators. LCP of isobutyl vinyl ether takes place using HI with I2 or ZnI2 in toluene or CH2 Cl2 at 40 to 25 C. Lower temperatures are generally more useful for the more polar solvent. Figure 5-2 shows LCP for isobutyl vinyl ether with HI/I2 [Sawamoto and Higashimura, 1986]. These data are typical of LCP. The plot of M n versus conversion is linear over the complete conversion range for successive additions of two batches of monomer. The fact that the M n values for both batches of monomer fall on the same line shows that polymerization proceeds throughout with a constant concentration of propagating species, with negligible termination and transfer. The presence of signi cant termination or transfer would result in the plot showing a downward curvature with conversion. Protonic acids such as RCO2 H and RSO3 H with a weak Lewis acid yield similar results. Stronger Lewis acids such as SnCl4 , TiCl4 , and CH3 AlCl2 yield fast but uncontrolled polymerization with broad PDI. LCP of vinyl ethers can be achieved if the other components and reaction parameters are appropriately adjusted by various combinations of lower reaction temperature, added nucleophile, added common salt, and solvent prolarity. For example, polymerization of isobutyl vinyl ether using HCl as the initiator (or one can use the preformed adduct of monomer and HCl) with SnCl4 or TiCl4 in CH2 Cl2 is non-LCP

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(4.115)

Fig. 5-2 Dependence of M n and M w /M n on conversion for the polymerization of isobutyl vinyl ether by HI/I2 in CH2 Cl2 at 15 C. [M] 0.38 M at beginning of each batch; [HI] 0.01 M; [I2 ] 0.02 M ( ), 0.001 M (*), 0.005 M (*). After Sawamoto and Higashimura [1986] (by permission of Huthig and Wepf Verlag, Basel and Wiley-VCH, Weinheim).

Surprisingly enough, this is the exact result! Let us see why. For a state where (all) = A, we can always write all = A where .6.0.11

(PDI 1:5) when carried out at 15 C [Katayama et al, 2001] The reaction converts to LCP with PDI <12 when the polymerization temperature is lowered to 78 C or tetra-nbutylammonium chloride is added Mild nucleophiles such as esters, ethers, sul des, and pyridines are also useful to decelerate the reaction rate, narrow PDI, and yield LCP [Aoshima and Higashimura, 1989; Cho et al, 1990; Kishimoto et al, 1989] Isobutylene, which forms a less stable carbocation than does vinyl ether, requires a stronger Lewis acid (BF3, SnCl4 and TiCl4 ) [Kennedy, 1999; Storey and Donnalley, 2000] Dialkylaluminum chloride has also been used [Bahadur et al, 2000] Tertiary chlorides such as cumyl chloride and 2-chloro-2,4,4-termethylpentane or the corresponding esters are often used so that the initiating carbocation is of comparable stability to the propagating carbocation.

+ .6.0.11 ,

Haloalkanes or mixtures of alkanes and haloalkanes are generally used as solvents to achieve reasonable reaction rates and prevent polymer precipitation before the desired molecular weight is achieved Strong nucleophiles such as N,N-dimethylacetamide and dimethyl sulfoxide and/or salts such as tetra-n-butuylammonium chloride are often used, and temperatures below $30 C are needed to achieve LCP N-Vinylcarbazole (NVC) forms a more stable carbocation than does a vinyl ether because of the electron-releasing nitrogen and conjugation of the positive charge with the p-electrons of the ring This results in LCP using HI in the absence of a Lewis acid in toluene at 40 C LCP converts to non-LCP by conditions that shift the equilibrium away from the covalent species and toward ion pairs and free ions, for example, by adding a Lewis acid such as zinc iodide or iodine or using the more polar solvent methylene chloride.

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