Chemistry Reference
In-Depth Information
1
=
2
1
=
2
τ
5
1
=
2
ð
fk
d
½
I
ð
k
tc
1
k
td
Þ
(8-95)
for initiation by thermal decomposition of an initiator. The average radical life-
time can also be related to the number average molecular weight of the polymer
that is being produced by substituting in
Eq. (8-94)
for
R
p
from
Eq. (8-64)
:
τ
5
DP
n
ð
k
tc
1
2
k
td
Þ=
2
k
p
½
M
ð
k
tc
1
k
td
Þ
(8-96)
If termination is by combination alone,
k
td
5
0 and
Eq. (8-96)
simplifies to
v
k
p
½
τ
5
DP
n
=ð
2
k
p
M
½ Þ
5
(8-97)
M
with the kinetic chain le
ngt
h
v
defined as in
Section 8.6
. Note that the last two equa-
tions which relate
and DP
n
are valid only in the absence of significant chain transfer.
As an example, consider the polymerization of bulk styrene at 60
C initiated
by 1
τ
10
2
3
M azodiisobutyronitrile. The density of liquid styrene is 0.909 g cm
2
3
at the reaction temperature. What is the average radical lifetime and what is the
steady-state radical concentration?
The concentration of styrene [M] is obtained from
3
mol
104 g
5
:
1000 cm
3
liter
0
909 g
cm
3
½
5
M
8
:
74 M
since the molecular weight of
styrene is 104. For
styrene,
k
tc
5
1.8
3
10
7
M
2
1
sec
2
1
, while
k
d
10
2
5
sec
2
1
for AIBN is 0.85
and
f
0.6. From
3
5
Eq. (8-95)
Þ
2
1
=
2
10
2
5
10
2
3
10
7
τ
5
ð
1
=
2
Þ½ð
0
:
6
Þð
0
:
85
Þð
Þð
1
:
8
1
:
6 sec
3
3
5
Also, from
Eq. (8-27)
,
1
=
2
10
2
5
10
2
3
ð
:
Þð
:
Þð
Þ
0
6
0
85
3
M
10
2
8
M
½
5
1
:
7
5
3
10
7
1
:
8
3
Multiplying by Avogadro's constant, we see that there are 10
16
macroradicals
per liter of reaction mixture, with an average lifetime of 1.6 sec per radical. The
rate of polymerization is
10
2
8
R
p
52
d½M=dt
5
ð
84
Þð
8
:
74
Þð
1
:
7
Þ
3
10
2
4
mol monomer
:
=
=
5
0
26
3
liter
sec
10
2
3
g polymer
1
:
4
=
liter
=
sec
5
3
In this calculation (from
Eq. 8-13
),
k
p
for polystyrene is taken to be
84
M
2
1
sec
2
1
.
This is a slow polymerization, since the calculated rate will result in less than
6 g of polymer per hour from 1 liter (909 g) of monomer.
