Chemistry Reference
In-Depth Information
CH
3
CH
3
CH
3
CH
2
CH
2
C
+
C
CH
2
CH
2
C
H
+
C
CH
2
CO
CO
CO
CO
OCH
3
OCH
3
OCH
3
OCH
3
(8-17)
Generally for this case,
k
td
M
m
1
M
n
1
M
m
-
M
n
(8-18)
where
k
td
is the disproportionation rate constant.
Termination may also occur by a mixture of disproportionation and combina-
tion. The rates of these reactions are additive for a given polymerization, because
both terminations are bimolecular and have second-order rate constants. Thus, we
can write
k
t
M
n
1
M
m
!
dead polymer
(8-19)
with the overall rate constant
k
t
given by
k
t
5
k
tc
1
k
td
(8-20)
The termination rates
R
t
corresponding to the different modes of termination
are
M
2
R
tc
5
2
k
tc
½
(8-21)
from
Eq. (8-16)
M
2
R
td
5
2
k
td
½
(8-22)
from
Eq. (8-18)
, and
M
2
R
t
5
2
k
t
½
(8-23)
from
Eq. (8-20)
.
Typical
10
8
liter/mol
sec. These rate constants are much greater than
k
p
, but polymerization still
occurs because the overall rate of polymerization is proportional
termination rate constants are of the order of 10
6
2
to
k
p
and
inversely proportional to
k
1
=
2
t
. This basic relation is derived in the following
subsection.
8.3.4
Rate of Polymerization
When a free-radical polymerization is first started, the number of radicals in the sys-
tem will increase from zero as the initiator begins to decompose according to reac-
tion (8-6). The frequency of termination reactions will also increase from zero in the
