Chemistry Reference
In-Depth Information
8.12
Determination of k
p
and k
t
A number of nonsteady polymerization rate techniques can be used to measure
k
p
[11]
. The most widely used method involves pulsed-laser-induced polymerization
in the low monomer conversion regime. Briefly, a mixture of monomer and
photoinitiator (
Section 8.5.3
) is illuminated by short laser pulses of about 10 ns
(10
2
8
sec) duration. The radicals that are created by this burst of light propagate
for about 1 sec before a second laser pulse produces another crop of radicals.
Many of the initially formed radicals will be terminated by the short, mobile radi-
cals created in the second illumination. Analysis of the number molecular weight
distribution of the polymer produced permits the estimation of
k
p
from the
relation
DP
n
5
k
p
½
M
t
f
(8-98)
where
t
f
is the “dark time” between pulses
[12,13]
. This technique has been
applied successfully at low monomer conversions of about 2
3%.
At higher conversions and radical concentrations, carefully calibrated electron
paramagnetic resonance spectroscopy (EPR) can be used in some cases to mea-
sure the concentration of propagating radicals directly
[14]
. Application of
Eq. (8-
13)
then yields a value for
k
p
.
If
k
p
is determined,
k
t
can be estimated from the readily observable relation
between
k
p
=
k
t
outlined in
Section 8.10
. Techniques for measuring
k
t
directly are
summarized in specialized reports
[11]
. Note, however, that termination rates in
free-radical polymerizations are always diffusion controlled (see
Section 8.13.1
)
and the apparent value of
k
t
will depend on the conditions under which it has
been measured.
8.13
Deviations from Ideal Kinetics
The kinetic scheme that has been developed in this chapter provides a very useful
framework for the organization of experimental results and for the systematic
modification of polymerization conditions when the polymer properties or reac-
tion are not entirely satisfactory. Most practical free-radical polymerizations will
deviate to a greater or lesser extent from the standard relations outlined, however,
either because the reaction conditions are not entirely as postulated here or
because some of the assumptions that underlie the kinetic scheme are not valid.
This section is a review of the principal causes and results of such deviations.
Equation (8-30)
predicts that the rate of polymerization should be proportional
to the monomer concentration and to the square root of the rate at which
monomer-ended radicals are formed. When initiation is by thermal decomposition
of an initiator I, which yields two radicals, the rate of polymerization is ideally
proportional
to [I]
1
/
2
. In initiation by photolysis of an initiator,
R
i
depends
