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where k11 is the rate constant for a propagating chain ending in M1 adding to monomer M1, k12 that for a propagating chain ending in M1 adding to monomer M2, and so on. The propagation of a reactive center by addition of the same monomer (i.e., Reactions 6-2 and 6-5) is often referred to as homopropagation or self-propagation; propagation of a reactive center by addition of the other monomer (Reactions 6-3 and 6-4) is referred to as crosspropagation or a crossover reaction. All propagation reactions are assumed to be irreversible. Monomer M1 disappears by Reactions 6-2 and 6-4, while monomer M2 disappears by Reactions 6-3 and 6-5. The rates of disappearance of the two monomers, which are synonymous with their rates of entry into the copolymer, are given by



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Use PDF Focus. Nice and easy. EDIT: And also. How to convert DOC into other formats using C#.

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We can integrate equation (6.5),

d M1 k11 M* M1 k21 M* M1 1 2 dt d M2 k12 M* M2 k22 M* M2 1 2 dt 6-6 6-7

(6.6)

6 4 5

Dividing Eq. 6-6 by Eq. 6-7 yields the ratio of the rates at which the two monomers enter the copolymer, that is, the copolymer composition, as

a~(k, t) = a~(k,O)e-iwt -

d M1 k11 M* M1 k21 M* M1 1 2 d M2 k12 M* M2 k22 M* M2 1 2 6-8

q j,Ao(k) ft dt' e-iw(t-t') (k). 7r(t').





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* In order to remove the concentration terms in M1 and M* from Eq. 6-8, a steady-state 2 * * concentration is assumed for each of the reactive species M1 and M2 separately. For the con* * centrations of M1 and M2 ro remain constant, their rates of interconversion must be equal. In other words, the rates of Reactions 6-3 and 6-4 must be equal:

(6.7)

k21 M* M* k12 M* M2 2 1 1 6-9

Let us write the vector potential as a sum of two terms: A(O, t) = Avac(O, t) where the first term is the vacuum part: Avac(O,t) =

d M1 d M2 k11 k21 M* M1 2 k21 M* M1 2 k12 M2 k22 M* M2 k21 M* M1 2 2

6-10

+ As(O, t),

* Dividing the top and bottom of the right side of Eq. 6-10 by k21 M2 M1 and combining the result with the parameters r1 and r2 , which are de ned by

(6.8)

Make edits to the cell references in the Formula bar. Click Resume. When the error check is complete, a prompt box appears.

r1 k11 k12 and r2 k22 k21 6-11

d3k Ao(k)

convert pdf to word using c#

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Convert PDF to Word in .NET with 2 Lines of Code - CodeGuru Forums
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d M1 M1 r1 M1 M2 d M2 M2 M1 r2 M2 6-12

L [ae(k,O)e- iwt + a!(k,O)eiwt ] e(k),

Equation 6-12 is known as the copolymerization equation or the copolymer composition equation. The copolymer composition, d M1 =d M2 , is the molar ratio of the two monomer units in the copolymer. d M1 =d M2 is expressed by Eq. 6-12 as being related to the concentrations of the two monomers in the feed, [M1] and [M2], and the parameters r1 and r2 . The parameters r1 and r2 are termed the monomer reactivity ratios. Each r as de ned above in Eq. 6-11 is the ratio of the rate constant for a reactive propagating species adding tis own type of monomer to the rate constant for its additon of the other monomer. The tendency of two monomers to copolymerize is noted by r values between zero and unity. An r1 value greater * than unity means that M1 preferentially adds M1 instead of M2, while an r1 value less than * unity means that M1 preferentially adds M2. An r1 value of zero would mean that M1 is incapable of undergoing homopolymerization. The copolymerization equation can also be expressed in terms of mole fractions instead of concentrations. If f1 and f2 are the mole fractions of monomers M1 and M2 in the feed, and F1 and F2 are the mole fractions of M1 and M2 in the copolymer, then

(6.9)

f1 1 f2 M1 M1 M2 6-13

and the second term in (6.8) is due to the radiation produced by the atom: As(O, t) = -

F1 1 F2 d M1 d M1 d M2 6-14

[e-iw(t-t') - eiW(t-t')] e(k)'1r(t' )e(k).

F1

Equation 6-15 gives the copolymer composition as the mole fraction of monomer M1 in the copolymer and is often more convenient to use than the previous form (Eq. 6-12) of the copolymerization equation.

(6.10)

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