Chemistry Reference
In-Depth Information
In summary, cationic polymerizations are much more variable and complex
than homogeneous free-radical or anionic chain-growth polymerizations. No con-
vincing general mechanism has been provided for cationic reactions, and each
polymerization system is best considered as a separate case.
11.4.6
Temperature Effects
The effects of temperature on cationic polymerizations can be described with cau-
tion by an Arrhenius expression like
Ae
2
E=RT
k
(11-53)
where
E
is the activation energy for the particular process. From
Eqs. (11-49) and
(11-50)
, the activation energies for the rate of polymerization
5
ðE
R
p
Þ
and the num-
ber average degree of polymerization
ðE
X
n
Þ
would be expected to be
E
R
p
5
E
i
1
E
p
2
E
t
(11-54)
and
E
X
n
5
E
p
2
E
tr
(11-55)
where the
E
s are the activation energies for the processes identified by the partic-
ular subscripts in the reaction scheme in
Fig. 11.3
.
Kinetic data for cationic polymerizations are not usually reliable enough to
establish the activation energies for the various processes very well. In general, it
is expected, however,
that energies for reactions that
involve free ions will
approach zero and those of other species will be positive.
The net activation energy for cationic polymerizations is low (
10 kcal/mol)
and may even be negative. In the latter case one observes a rate of polymerization
that increases with decreasing temperature. This is very probably because the pro-
portion of free ions increases as the temperature is lowered. If the equilibria
,
contact pair
$
R
"
==X
~
k
d
$
R
"
1
X
~
solvent separated ion pair
R
"
X
~
(11-56)
are considered, it can be shown
[4]
that
X
~
=½
R
"
X
~
5
z
2
R
"
½
K
d
5
½
exp
ð
2
=
a
εκ
T
Þ
(11-57)
where
z
is the charge of the ions,
a
is the sum of the van der Waals ionic radii,
and
is Boltzmann's constant. A common solvent for cationic polymerization is
CH
2
Cl
2
. Its dielectric constant, which is 17.0 at
κ
60
C
[5]
. From these values and
Eq. (11-57)
it is clear that the proportion of free ions
will increase strongly as the temperature of the reaction mixture falls. The net
observed
k
p
value will also increase because free carbenium ions react so much
100
C, rises to 13.4 at
2
2
