Chemistry Reference
In-Depth Information
The polymer-nitroxyl adduct P-X reversibly dissociates thermally, in process I into the polymer
radical P and the nitroxyl radical X. The rate constants of dissociation and combination are
k
d
and
k
c
, respectively. The, so-called, “degenerative transfer” takes place in process II. The second-order
rate constant for active species in either direction is
k
ex
. Here all the rate constants are assumed to be
independent of chain length. Since the frequency of cleavage of the P-X bond is proportional to
[P-X] in process I and to [P1[P
0
-X]] in process II, the overall frequency,
f
a
per unit time and per unit
volume, of the bond-cleaving or activation reactions, may be expressed by [
277
]:
f
a
¼ k
a
½
P
X
with
P
where
k
a
is the overall activation rate constant, viewed as a first-order reaction. Goto and Fukuda
concluded that it may be more convenient to represent the above equation in the form [
289
]:
k
a
¼ k
d
þk
d
½
k
a
¼ k
d
þðk
ex
=k
p
ÞðR
p
=½
M
Þ
and show the general expression of the time-averaged
k
a
for a batch system:
k
a
¼ k
d
þðk
ex
=k
p
TÞ
ð½
M
0
=½
Þ
ln
M
Matyjaszewski et al. wrote the kinetic equation for atom transfer polymreization [
290
,
291
]. It is
based on the ATP reaction mechanism that was described above. By assuming fast initiations,
insignificant termination reactions and steady concentrations of the propagating radicals, the follow-
ing relationship was derived [
290
,
291
]:
0
½
Mt
Z
L
m
R
p
¼ k
p
k
eq
½
M
½
RX
XMt
z
þ
1
L
m
¼ k
app
½
M
½
3.15 Thermodynamics of the Free-Radical Polymerization Reaction
3.15.1 Effects of Monomer Structure on the Thermodynamics
of the Polymerization
There is a close relationship between monomer structure and changes in free energy, in enthalpy and
in entropy. Thus, for instance, knowledge of changes in enthalpy will allow appropriate thermal
control of the reaction and yield proper rate of propagation and molecular weight distribution. The
quantities of
relate only to the rate of propagation because initiation and termination
are single steps, while propagation consists of multiple steps.
Free radical polymerization is generally exothermic because it involves conversion of
DF
,
DH
, and
DS
p
bonds to
s
bonds. Thus, the change in enthalpy
is negative. Also, because there is a decrease in randomness
in conversion of monomers to polymer, the change in entropy
DH
DS
is also negative. The overall change
in free energy of the free radical polymerization process is,
DF ¼ DHTDS
The free energy is generally negative for the free-radical polymerization process. Variations in
monomer structures have a significant effect on the values of
DH
for the following reasons. These are
