Chemistry Reference
In-Depth Information
where, L means ligand and M
T
means transition metal.
It is possible to apply the homogeneous rate equation to some Ziegler-Natta catalysts. This can be
expressed as:
C
½
R
p
¼ k
p
½
M
where C* represents the concentration of active sites in moles per liter. Heterogeneous kinetics,
however, are needed because the adsorption phenomena are important in most coordinated anionic
polymerizations. In addition, because there is likely to be an excess of components of Groups I-III
metals in solution, it is assumed that they compete with the monomer for the active sites. The
fractions, therefore, of the active sites and the fractions of sites covered by these metal compounds
are expressed as follows [
283
]:
Fraction of the active site coordinated with the monomer:
Y
1
¼ K
1
½
M
=ð
1
þ K
2
½
M
T
þK
1
½
M
Þ
Fraction of active sites coordinated with components of metal Groups I-III:
Y
2
¼ K
2
½
M
T
=ð
þ K
2
½
M
T
þK
1
½
Þ
1
M
where M represents the amount of monomer in solution and M
T
the concentration of metal
components of Group I-III.
K
1
and
K
2
are the equilibrium constants for the adsorption.
The rate of polymerization that takes place trough the reaction of the adsorbed monomer at the
active sites can be expressed as:
C
Y
1
¼ k
P
½
C
½K
1
½
R
P
¼ k
P
½
M
=ð
1
þ K
2
½
M
T
þK
1
½
M
Þ
If there is no competition with components of metal Group I-III, then
C
Y
1
¼ k
P
½
C
½K
1
½
R
P
¼ k
P
½
M
=ð
1
þ K
1
½
M
Þ
The degree of polymerization can be derived by dividing the propagation rate by the sum of the
rates of terminations (by transfer) as follows:
1
=
DP
n
¼ k
tr
;
M
=k
p
þ k
s
=k
p
K
M
½
M
þk
tr
;
A
K
A
½
A
=k
p
K
M
½
M
þk
tr
;
H
[H
=k
p
K
M
½
M
The above equation is written with the assumption that there is no adsorption of hydrogen at the
active sites.
4.5.4 Post Ziegler and Natta Coordination Polymerization of Olefins
In the current industrial practice, coordinated anionic catalysts differ considerably from the original
ones, developments by Ziegler, Natta and others. Using the same basic chemistry, new compounds
were developed over the years that yield large quantities of polyolefins from small amounts of
catalysts. In addition, catalysts can now be designed to yield products that are either wide or narrow
in molecular weight distribution, as needed [
312
]. The multinuclear olefin polymerization catalysts
