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You can use PowerPoint s templates to help you create a new presentation, regardless of its subject matter. PowerPoint installs with a wide variety of presentation templates featuring various designs and colour schemes. In addition to using templates that come preinstalled with Office, if your computer is connected to the Internet, you can download PowerPoint templates from Office.com for use with your presentations.

Because we are interested in the total rate of change of atomic energy, we can choose normal ordering6 when we substitute equation (6.50) in (6.51). This yields



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(Similar effects are anticipated for basic monomers) Several mechanisms have been proposed to describe the results for nonionizable monomers: radical solvent complexation, monomer solvent complexation, and the bootstrap effect Complexation of the polar solvent with the more polar monomer or radical decreases the reactivity of the more polar monomer or radical The bootstrap effect results from partitioning of the two monomers between the solution and the local feed composition in the domain of the growing polymer radical Copolymers are richer in the less polar monomer for reaction in polar solvents because the local feed composition is richer in the less polar monomer The magnitude of the bootstrap effect can be signi cant depending on the difference in polarity of the two monomers [Coote et al, 1998].





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Thus, for 2-hydroxyethylmethacrylate (M1)-t-butyl acrylate (M2), r1 4:35 and r2 0:355 in bulk copolymerization compared to r1 1:79 and r2 0:510 in copolymerization in DMF [Fernandez Monreal et al, 2001] For a comonomer pair with a smaller difference in polarity such as styrene (M1)-n-butyl acrylate (M2), r1 0:865 and r2 0:189 in bulk compared to r1 0:734 and r2 0:330 [Fernandez Garcia et al, 2000] 6-3a-2 Temperature.

(O-z(t))

An examination of various compilations of monomer reactivity ratios [Greenley, 1989a, 1999; Young, 1975] shows that r1 and r2 are relatively insensitive to temperature provided that propagation is irreversible. Thus the r1 and r2 values for styrene-1,3-butadiene are 0.64 and 1.4 at 5 C, and 0.60 and 1.8 at 45 C. The r1 and r2 values for styrene methyl methacrylate are 0.52 and 0.46 at 60 C, and 0.59 and 0.54 at 131 C. The monomer reactivity ratio is the ratio of two propagation rate constants, and its variation with temperature will depend on the difference in propagation activation energies according to

= 2 (O"t(t) lot dt'

r1 ! k11 A11 E12 E11 exp RT k12 A12 6-48

~9;(k) [O"tW) -

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where E11 and A11 are the propagation activation energy and frequency factor for M1 radical adding M1 monomer, respectively, and E12 and A12 are the corresponding values for M1 radical adding M2 monomer. The effect of temperature on r is not large, since activation energies for radical propagation are relatively small and, more signi cantly, fall in a narrow range such that E12 E11 is less than 10 kJ mol 1 for most pairs of monomers. However, temperature does have an effect, since E12 E11 is not zero. An increase in temperature results in a less selective copolymerization as the two monomer reactivity ratios of a comonomer pair each tend toward unity with decreasing preference of either radical for either monomer. Temperature has the greatest

O"(t')] e-iw(t-t' )

effect on those systems for which the r values deviate markedly from unity, behavior which is much more typical of ionic copolymerization than radical copolymerization.

(6.52) We notice that the time evolution of the atomic creation and annihilation operators O"t and 0" consists of a fast oscillation of angular frequency Wo and a slowly varying envelope [13] O"(t) = o-(t)e- iwot . (6.53)

6-3a-3

1 2 3

6The choice of normal ordering simplifies the calculation of the expectation value of (6.51) for the case where the field is initially in the vacuum state because the first term on the right-hand side of equation (6.50). the free field. will not contribute.

6-49

~9~(k)

z z is smaller than either V11 or V12. The effect of pressure is in the same direction as that of temperature. Increasing pressure tends to decrease the selectivity of the copolymerization as the r values change in the direction of ideal copolymerization behavior. Thus the r1 r2 product for styrene-acrylonitrile changes from 0.026 at 1 atm to 0.077 at 1000 atm, while r1 r2 for methyl methacrylate-acrylonitrile changes from 0.16 to 0.91. Copolymerizations which are ideal at lower pressure remain so at higher pressure.

z z where V11 and V12 are the propagation activation volumes for radical M1 adding monomers M1 and M2, respectively [Buback and Dietzsch, 2001; Burkhart and Zutty, 1962; Jenner, 1979; Jenner and Aieche, 1978; Van Der Meer et al., 1977a,b]. Although propagation z z rates increase considerably with pressure, r is less sensitive to pressure, since ( V11 V12 )

a(t')e-i(W-Wo)(t-t')])

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