Chemistry Reference
In-Depth Information
and is independent of the initial concentration. The conventional criterion for ini-
tiator activities is
t
1
/
2
.]
Equation (8-32)
for [I] can be inserted into
Eq. (8-29)
to obtain
1
=
2
e
2
k
d
t=
2
dt
d
½
M
=½
M
5
ð
k
p
=
k
t
1
=
2
Þð
fk
d
½
I
0
Þ
(8-34)
2
On integrating between [M]
5
[M]
0
at
t
5
0 and [M] at
t
:
1
=
2
ln
½
M
2
k
p
k
t
1
=
2
f
½
0
k
d
I
e
2
k
d
t=
2
ð
1
Þ
(8-35)
2
M
0
5
2
½
This gives the amount of polymer (in terms of the moles of monomer con-
verted) produced in time
t
at given temperature.
8.4
A Note on Termination Rate Constants
Much of our knowledge of free-radical polymerizations was pioneered by
researchers in the United Kingdom and in the United States. Unfortunately, both
groups used different conventions for termination rate constants, and the unwary
reader may be misled unless the data and equations are self-consistent.
The American convention is followed in this text. In this case
k
tc
and
k
td
are
defined by
M
=dt
M
2
M
2
2
d½
2
k
tc
½
2
k
td
½
(8-36)
1
It follows then that
M
2
M
2
d
½
=
dt
2
k
td
½
2
k
tc
½
(8-37)
since a single termination reaction produces one polymer molecule by combina-
tion or two if disproportionation is involved.
The British convention uses the following definitions:
polymer
5
1
M
=
M
2
M
2
2
d
½
dt
5
k
tc
½
1
k
td
½
(8-38)
and, hence,
1
2
k
tc
½
M
2
M
2
d
polymer
½
=
dt
k
td
½
(8-39)
5
1
Each convention is unobjectionable if used consistently but the two cannot be
mixed because the termination rate constants quoted according to the American
convention will be exactly half those measured by the British system. The same
conclusions are reached when either usage is adopted because a compensating
factor of 2 is present in the kinetic equations that use American rate constants and
is absent in the corresponding British system.
All United States texts and data compilations adhere to the American system
while most United Kingdom texts rely on the British method. The convention
