Chemistry Reference
In-Depth Information
and the rate of living polymerization is
P
n
½
d
½
M
=
d
t ¼ k
p
½
M
When the effect of the medium is such that the propagation takes place both, with ion pairs and
with free-propagating ions, the rate of propagation is written as follows [
4
,
5
]:
R
p
¼ k
p
...
C
þ
½
P
...
:
C
þ
½
P
½
M] +
k
p
½
M
k
p
...
C
+
and
k
p
are rate constants for the propagation of the ion pairs and the free-ions,
where,
respectively. C
+
.C
+
and P
are the concentrations of the two
propagating species, and [M] is the monomer concentration.
The number average degree of polymerization of a living polymer is shown as follows:
is the positive counterion, P
...
M
Ave
:
DP
¼½
M
=½
It is simply a ratio of the concentration of the monomer to the number of living ends.
A model was developed for a unified treatment of the kinetics of both cationic and anionic
polymerizations [
6
]. It is based on a systemof kineticmodels that cover various initiation and propagation
mechanisms and on a pseudosteady-state assumption. The treatment is beyond the scope of this topic.
The principal kinetics of propylene polymerization with a magnesium chloride supported
Ziegler-Natta catalyst was also developed [
7
]. The polymerization rate is described by a Langmuir--
Hinshelwood equation showing the dependence of the rate on the concentration of the aluminum alkyl:
2
R
P
¼ Kk
A
½
=ð
þ k
A
½
Þ
A
1
A
where [A]
[AlR
3
].
Because the polymerization rate is first order with respect to the concentration of the monomer, the
rate equation can be written as follows [
7
]:
¼
2
R
P
¼ k
p
½
M
k
A
½
A
=ð
1
þ k
A
½
A
Þ
4.3 Cationic Polymerization
As mentioned, in cationic polymerizations the reactive portions of the chain ends carry positive
charges during the process of chain growth. These active centers can be either unpaired cations or
they can be cations that are paired and associated closely with anions (counterions).
The initiations result from transpositions of electrons, either as pair or as single one. A two-electron
transposition takes place when the initiating species are either protons, or carbon cations. Ion generations
take place through heterolytic bond cleavages or through dissociations of cationic precursors. Such
initiating systems include Lewis acid/Bronsted acid combinations, Bronsted acids by themselves, stable
cationic salts, some organometallic compounds, and some cation forming substances.
When, however, initiations take place by one electron transposition, they occur as a direct result of
oxidation of free radicals. They can also take place through electron transfer interactions involving
electron donor monomers. The carbon cations can form from olefins in a variety of ways. One way is
through direct additions of cations, like protons, or other positively charged species to the olefins. The
products are secondary or tertiary carbon cations:
X
X
+
R
R
H
