Chemistry Reference
In-Depth Information
directly on the intensity
of the incident light, as well as on [I], and
R
p
is there-
fore ideally proportional to (
Φ
[I])
1
/
2
. When a photosensitizer is used the concen-
Φ
tration of
this species takes the place of
[I]
in this relation.
In a redox
polymerization,
like reaction (8-42),
R
p
is predicted to be proportional
to
([ROOH]) (Co
2
1
)
1
/
2
.
Deviations from the predicted dependence of
R
p
on [M] and [I]
1/2
are not
unusual. The initiation rate and the initiator efficiency
f
may depend on [M] if pri-
mary radicals escape from their solvent cage (
Section 8.5.5
) by reaction with the
nearest monomer molecules. At high initiation rates, some of the primary radicals
from initiator decomposition may terminate kinetic chains. This “primary termi-
nation” causes the observed
R
p
to depend on [M] to a power greater than 1 and
reduces the dependence of
R
p
on [I] to less than the power 0.5.
These examples illustrate the point that initiation reactions may vary from the
standard kinetic scheme that has been described in this chapter. Propagation reac-
tions are believed to occur generally as postulated, but termination reactions are
very clearly not, as has been assumed to this point. In particularly, the rate of ter-
mination may depend on the size of the polymer being produced and on the
extent of conversion. Both effects are discussed below.
8.13.1
Diffusion Control of Termination
The assumption that
k
t
is independent of the sizes of the radicals involved in the
termination reaction is not true. The standard kinetic scheme has been developed
to this point by making use of this assumption, however, because the presentation
is simpler and more readily comprehended and because the errors involved are
not large in most commercial free-radical polymerizations.
Termination reactions occur between two relatively large radicals, and termi-
nation rates are limited by the rates at which the radical ends can encounter each
other. As a result,
k
t
is a decreasing function of the dimensions of the reacting
radical. The segmental diffusion coefficient and the termination rate constant
increase as the polymer concentration increases from zero. This initial increase is
more pronounced when the molecular weight of the polymer is high and/or when
the polymerization is carried out in a medium that is a good solvent for the poly-
mer. For similar reasons,
k
t
is inversely proportional to the viscosity of reaction
medium. A model has been proposed that accounts for these variations in
k
t
in
low-conversion radical polymerizations
[15,16]
.
8.13.2
Autoacceleration
Deviations resulting from the diffusion control of termination at low conver-
sions of monomer to polymer are the relatively weak effects discussed in the
preceding subsection. By contrast, changes in reaction rate resulting from hin-
dered diffusion at high conversions are very important in most radical poly-
merizations.
Figure 8.3
shows rate curves for the polymerization of methyl
