Chemistry Reference
In-Depth Information
By rearranging and integrating equations (
6.10
), (
6.19
) and (
6.24
), we obtain:
1
=
2
ψÞ¼ðk
1
k
2
k
4
2
Ce
0
4
þ
T
=ðk
2
ð
ð
þK½DÞ½
½
þk
3
Þðk
6
ÞÞ
t
ln
100
1
D
þ
4
:
6
(6.25)
If the termination is caused by bimolecular termination as in Eq. (
6.6
), a plot of
ln(100
) versus
t
must give a straight line.
If a termination step can be shown as in Eq. (
6.7
), the termination would be
caused by bimolecular termination between the graft polymeric radical and the
homo-polymeric radical. Assuming that:
ψ
k
7
½
M
k
5
½
M
þk
6
½
DM
þk
9
½
Ce
4
þ
(6.26)
Equation (
6.16
) becomes:
Ce
4
þ
½
½
=
d
t ¼ k
1
k
2
k
4
K½
½
=ðk
2
þk
3
Þk
7
½
d
M
D
M
M
(6.27)
with the formation rate of monomeric and homopolymeric radical, we obtain:
d
½
M
=
d
t ¼ k
3
½
D
½
M
k
8
½
M
½
M
k
7
½
DM
½
M
(6.28)
Because of their high concentration, we may not assume that [M
•
] reaches a
steady state in the experiment within a short time. Assuming
k
2
< k
3, [M
•
]
2
1,
and
k
0
t
1, by integrating and rearranging Eq. (
6.28
) we obtain:
Ce
4
þ
t
½
M
¼ k
1
Kðk
3
k
2
Þ=ðk
2
þk
3
Þ½
D
½
(6.29)
Substituting Eq. (
6.29
) in Eq. (
6.27
) and integrating, we obtain:
ln
ð½
M
=½
M
0
Þ¼k
2
k
4
=k
7
ðk
3
k
2
Þ
ln
t þ
2
:
3
k
2
k
4
=k
7
ðk
3
k
2
Þþ
4
:
6 (6.30)
or:
ln
ð
100
ψÞ¼k
2
k
4
=k
7
ðk
3
k
2
Þ
ln
t þ
2
:
3
k
2
k
4
=k
7
ðk
3
k
2
Þþ
4
:
6 (6.31)
If termination is caused by bimolecular collision between the graft polymeric
radical and homopolymeric radical, a plot of ln(100
ψ
) versus ln
t
must yield a
straight line of slope—
k
2
k
4/
k
7(
k
3-
k
2).
If the termination step can be written as in Eq. (
6.9
), the termination would be
predominantly by redox reaction of the polymeric radical with ceric ion. We may
ignore other terminations. Thus:
Ce
4
þ
k
5
k
9
½
½
M
þk
6DM
½ þk
7
½
M
(6.32)
