Chemistry Reference
In-Depth Information
where
A
is a preexponential factor,
E
the Arrhenius activation energy, and
T
the
absolute temperature. A plot of ln
k
versus 1
/T
yields
A
and
E
from the intercept
and slope, respectively. The three separate Arrhenius expressions can be com-
bined in a straightforward manner to obtain the temperature dependence of the
k
p
(
k
d
/
k
t
)
1/2
ratio in the expression for
R
p
in
Eq. (8-29)
:
"
#
1
=
2
h
i
A
d
A
t
E
p
1
1
=
2
E
d
2
1
=
2
E
t
1
=
2
ln
k
p
ð
k
d
=
k
t
Þ
ln
A
p
(8-116)
5
2
RT
The overall activation energy for the rate of polymerization
E
R
p
is
E
R
p
5
E
p
1
1
=
2
E
d
2
1
=
2
E
t
(8-117)
and can be measured by plotting ln
R
p
against 1
/T
. The units of the activation
energies are
E
R
p
5
kJ
=
mol of polymerizing monomer
E
t
5
kJ
=
mol of propagating radicals
E
d
5
=
kJ
mol of initiator
E
d
is of the order of 126
165 kJ/mol for thermal decomposition of chemical
initiators,
E
p
appears to be in the 20
40-kJ/mol range, while
E
t
is least at
8
20 kJ/mol. Thus, the overall
E
R
p
is approximately 84 kJ/mol from
Eq. (8-116)
.
Each 10
C increase in reaction temperature will result in a two to threefold
increase in the rate of polymerization.
Note that the initiation step dominates the overall temperature dependence of
the rate of polymerization. When the method of initiation varies,
E
R
p
will also
change. For redox initiation, for example,
E
d
is on the order of 40
60 kJ/mol and
E
R
p
for redox polymerizations is about 40 kJ/mol. For photochemical or radiation-
induced polymerizations,
E
d
is practically zero and the rate of polymerization in
such cases does not change much with the reaction temperature.
For the sake of clarity, we consider the effects of temperature on DP
n
in the sim-
plest case, which implies an absence of transfer reactions and termination by combi-
nation alone. When the polymerization is started by thermal decomposition of an
initiator, insertion of appropriate Arrhenius expressions into
Eq. (8-65)
produces
1
=
2
1
=
2
ln
ð
DP
n
Þ
5
ln
½
A
p
=
A
d
A
t
Þ
1
ln
½½
M
=ð
f
½
I
2
E
DP
n
=
RT
(8-118)
where
E
DP
n
5
E
p
2
1
=
2
E
d
2
1
=
2
E
t
(8-119)
is the activation energy for the degree of polymerization of the polymer formed.
With the activation energies for propagation, initiator decomposition, and termi-
nation quoted above,
E
DP
n
is on the order of
60 kJ/mol.
2
