Chemistry Reference
In-Depth Information
Because many more molecules of the monomer are involved in the propagation than in the
initiation step, a very close approximation is
d
½
M
=
d
t ¼ R
p
The average lifetime,
t
, of a growing radical under steady state conditions can then be written as
follows [
3
,
5
],
t ¼ k
P
½M=
2
k
t
ðR
P
Þ
Not all primary radicals that form attack the monomer. Some are lost to side reactions. An initiator
efficiency factor,
f
, is, therefore, needed. It is a fraction of all the radicals that form and can be
expressed as:
f ¼
initiating radicals
=
total number radicals that form
:
The rate of initiator decomposition and the rate equation can be expressed as
h
i
2
R
I
¼
2
fk
d
½
I
¼k
i
X
RM
n
1
=
2
R
P
¼ k
P
½
M
ðk
d
½
I
f =k
t
Þ
¼
d
½
M
=
d
t
According to the kinetic scheme, chain transfer does not affect the rate of polymerization but alters
the molecular weight of the product. Also, it is important to define the average number of monomer
units that are consumed per each initiation. This is the
kinetic chain length
, and it is equal to the rate
of polymerization per rate of initiation:
¼ n ¼ k
P
=k
i
kinetic chain length
At steady state conditions,
n
is also equal to
k
p
/
k
t
. The kinetic chain length can also be expressed as:
n ¼ k
p
½
M
=
2
k
t
½
M
By substituting the expression for [M] the equation becomes:
1
=
2
n ¼ k
P
[M
=
2
ðfk
d
k
t
½
I
Þ
Z
The
number average degree of polymerization
,
DP
, is equal to 2
n
, if the termination takes place
by coupling. It is equal to
, if it takes place by disproportionation. (Terminations by coupling or
disproportionation are discussed in the section on the termination reactions) Above kinetic
relationships apply in many cases. They fail, however, to apply in all cases [
2
]. To account for it,
several mechanisms were advanced. They involve modifications of the initiation, termination, or
propagation steps. These are beyond the discussions in this topic.
At steady state conditions,
n
h
i
2
¼R
t
¼ k
t
X
n
RM
n
R
i
¼ f
½
I
M
