Chemistry Reference
In-Depth Information
correlate other radical reactions as well as copolymerizations. It lacks the exten-
sive parameter tabulations that have been made for the
Q
e
scheme.
9.12
Effect of Reaction Conditions
9.12.1
Temperature
[28]
The effect of temperature on reactivity ratios in free-radical copolymerization is
small. We can reasonably assume that the propagation rate constants in reactions
(9-2)
(9-5) can be represented by Arrhenius expressions over the range of tem-
peratures of interest, such as
k
11
5
A
11
exp
ð
2
E
11
=
RT
Þ
(9-72)
where
A
11
is a temperature-independent
preexponential factor
and
E
is the activa-
tion energy. Then a reactivity ratio will be the ratio of two such expressions as in
A
11
exp
ð
2
E
11
=
RT
Þ
r
11
5
(9-73)
A
12
exp
ð
2
E
12
=
RT
Þ
Now, according to the transition-state theory of chemical reaction rates, the
preexponential factors are related to the entropy of activation,
Δ
S
ii
, of the particu-
T/h
)
e
Δ
S
ii
/R
e
Δn
where
lar reaction [
A
ii
5
κ
κ
and
h
are the Boltzmann and Planck
(
constants, respectively, and
n
is the change in the number of molecules when
the transition state complex is formed.] Entropies of polymerization are usually
negative, since there is a net decrease in disorder when the discrete radical and
monomer combine. The range of values for vinyl monomers of major interest in
connection with free radical copolymerization is not
Δ
large (about
100 to
2
150 JK
2
1
mol
2
1
) and it is not unreasonable to suppose, therefore, that the
A
ii
values in
Eq. (9-73)
will be approximately equal. It follows then that
2
r
1
C
exp
ð
2
E
11
2
E
12
Þ=
RT
(9-74)
and the temperature dependence of
r
1
can therefore be approximated by
d
ln
r
1
d
Þ
52
ð
E
11
2
E
12
Þ
5
T
ln
r
1
(9-75)
ð
1
=
T
R
Similarly,
d
ln
r
2
d
T
ln
r
2
(9-76)
Þ
5
ð
1
=
T
The activation energy for
r
1
, from the slope of an Arrhenius plot of ln
r
1
against 1/
T
,(
Eq. 9-74
), will be equal to (
RT
ln
r
1
). Similar expressions hold for
r
2
and the product
r
1
r
2
. The absolute value of the logarithm of a number is a min-
imum when this number equals unity, and so a strong temperature dependence of
r
1
will be expected only if either
r
i
c
2
1or
r
i
{
1.
