Page 187 - Introduction to chemical reaction engineering and kinetics

7.3 Polymerization Reactions 169

L-J Figure 7.2 Polymerization of monomer M in a CSTR at steady-state

or

(-d = (CM0 - c,)/(V/q) = (CM0 - C&/T (7.3-7)

where r is the space time.
Similarly, for the dimer, P,,

0 - cp2q + rplV = 0
or

Q* = cp2/r = kCM(CM - cp,) (from 7.3-4)
and

CP2 = kc&Q - cp2) (7.3-8)
Similarly, it follows that

(7.3-9)
+3 = bdCP* - CP,)
. .
(7.3-10)
+, = b&P,-, - CP,>
and, thus, on summing 7.3-8 to 7.3-10, we obtain

2 cp, = kCMyl7(CM - cp2 + cp2 - cp, + CPj + * . . - +ml + cP,d1 - CP,>
r=2
= kCM7(Ch$ - cp,) = kc& (7.3-11)

since cp --f 0 as r -+ cc).
Substkution of 7.3-7 and -11 in 7.3-3 results in

CM0 - CM = kCh4T(2Ch4 + k&T) (7.3-lla)

from which a cubic equation in cM arises:

CL + (2/kT)& + (l/k%2)c, - ch,&W = 0 (7.3-12)

Solution of equation 7.3-12 for cM leads to the solution for cp,, cp3, etc.:
From equation 7.3-8,

k&T
CP, = (7.3-13)
1 + kcMT