Page 406 - Elements of Chemical Reaction Engineering Ebook

Sec. 7.3 Polymerization 377

Initiation

Another assumption is that the rate of formation of R, from the initiator is
instantaneous and that at time t = 0 the initial concentration of live polymier is
Rlo = Io. This assumption is very reasonable for this initiation mechanism.
Under the latter assumption the mole balances become

Propagation (7-59)

(7-60)

(7.6 1)

For the live polymer with the largest chain length that will exist, the mole bal-
ance is

(7-62)

If we sum Equations (7-59) through (7-62), we find that

Consequently, we see the total free live polymer concentration is a constant at
R' = RIo = Io.
There are a number of different techniques that can be used to solve this
set of equations, such as use of Laplace transforms, generating functions, sta-
tistical methods, and numerical and analytical techniques. We can obtain an
ana1ytic:al solution by using the following transformation. Let
dO =' kpM dt (7-63)
Then Equation (7-59) becomes

Using the initial conditions that when t = 0, then 0 = 0 and RI = R,o = I,.
Equation (7-64) solves to
R, = Ioe-@ (7-165)