Chemical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 165

ER k
T

d
d

ln

=−

=+−

ef

EEE ( ) /. 2

(4.11)

ef p i t

− 1

Equation 4.11 clearly suggests that the activation energy of polymerization is a
composite value that involves a combination of the activation energies for propaga-
tion ( E p ), initiation ( E i ), and termination ( E t ).
Polymerization is usually performed in the presence of an initiator such as ben-
zoyl peroxide or azobis(isobutyronitrile). These are compounds that readily pro-
duce radical species (R⇅) on heating to moderate temperatures. The presence of an
initiator (I) changes the initiation step (Eq. 4.5) to:

k

i
→ ⋅

(4.12)

I R 2.

As a result, the propagation and termination steps change as well:

k

p

(4.13)

⋅ +→ ⋅
+1

RM MRM

n n

k

t

(4.14)

RM RM ⋅+ ⋅→ RM R .

n m nm +

By using the same reasoning as above, one can arrive at the rate equation for polym-
erization in the presence of an initiator that has the following form:

1
2

1
2

1
2

rk k
k

(4.15)

i
t

= [ [] [ [] . MI MI = k

p p ef

Because k ef in Eq. 4.15 is identical to that in Eq. 4.10, the effective activation energy
for polymerization in the presence of an initiator can also be expressed by Eq. 4.11,
although the key difference is that the E i value would then be the activation energy
for degradation of the initiator (Eq. 4.12) rather than the monomer (Eq. 4.5).
With regard to the three steps involved in the aforementioned mechanism, one
may expect that at the early stages, before the steady state sets in, the polymeriza-
tion kinetics is determined by initiation. Then the effective activation energy would
be that of the initiation step. Once the steady state is established, it would change to
the value determined by Eq. 4.11.
Of course, the three-step kinetic model cannot represent adequately the full com-
plexity of the polymerization kinetics. For example, it misses entirely the effects of
diffusion on the kinetics. The effects become increasingly important as the polymer
chains grow and the reaction medium becomes progressively more viscous, slow-
ing down the molecular mobility. One such effect is known as the Trommsdorff [ 7 ]
and Norrish [ 8 ] effect. It is detected as dramatic acceleration of the polymerization
rate that takes place upon attaining some advanced degree of polymerization. It was