Page 394 - Elements of Chemical Reaction Engineering Ebook

Sec. 7.3 Polymerization 365

Since each reaction step is assumed to be elementary, the rate law for the for-
matioiri of the initiator free radicals, is

where f is the fraction of initiator free radicals successful in initiating chaining
and has a typicill value in the range 0.2 to 0.7. The rate-law for the formation
of R, in the initiation step is
r,, = -ri = k, (M)(Z) ('7-28)
Using the PSSH for the initiator free radical, I, we have
rI = 2fk0(Z2) - k, (M)(Z) = 0

(7-29)

Then

Rate of initiation --TI = 2fkO(I2) (7-30)
Blefore writing the rate of disappearance of R, , we need to make a couple
of points. First, the radical R1 can undergo the following termination sequence
by addition. 4

Termination of R, In general,

Consequently, the total loss df Rl radicals in the above reactions is found by
adding the loss of R1 radicals in each reaction so that the rate of disappearance
by termination addition is given by

1c
-rlt == k,R, 1
R,
J=1
Net rate of Free radicals usually have concentrations in the range to lo-* mol/drn3.
Of We can now proceed to write the net rate of disappearance of the free radical,
radicals of chain
length one R1- [Rl 'l (R1) CR,.]

OE ffi

j=l ;= 1 (7-31)
cc 30 m
- k,,,A4CRi-k,CCR;-k,S~R,
- j=2 j=2 , j= 2
~