Page 185 - Introduction to chemical reaction engineering and kinetics

7.3 Polymerization Reactions 167

(b) Write the special cases for (-rM) in which (i)f is constant; (ii) f m CM; and (iii)
f a&.

SOLUTION

r,. = 2fkdcI - kiCR.Chl = 0 (4)
t-i& = ?-[Step (2)]) = k$R.cM = 2fkdcI [from (4)] (5)
cc
YP; = rinit - kpc~cp; - ktcp; C Cp; = 0 (6)
k = l

where the last term is from the rate of termination according to step (3). Similarly,

rp; = kpCMCp; - kpcMcp; - (7)
k = l
. . .
cc
rp: = kpcMcF’-, - k,cMcp: - k,cp: c cpk = o (8)
k = l
From the summation of (6), (7), . . ., (8) with the assumption that k,cMcp: is relatively
small (since cp: is very small),

(9)

which states that the rate of initiation is equal to the rate of termination. For the rate law,
the rate of polymerization, the rate of disappearance of monomer, is
m
(-TM) = rinit + kpCM C cq
k = l
= k,CMlF “q Gfrinit a (-TM)1

k = l
= kpcM(riniJkt)1/2 [from (911
= k,c,(2 f kdcIlkt)1’2 [from (511

We write this finally as

(-rM) = k f 1’2C;‘2CM (7.3-1)

where k = k,(2k,lk,) 112 (7.3-2)

( i ) (-TM) = k’C;‘2CM (7.3-la)
(ii) (-)iL1) = k”c:‘2cz2 (7.3-lb)
(iii) (-?-M) = k”‘cte?c& (7.3-lc)