Chemistry Reference
In-Depth Information
proportion, usually less than 1%, of the transition metal and are normally not
uniformly active.
Conversion-time curves for batch polymerizations are usually S-shaped, with a
slow rate initial period followed by a steady reaction rate interval and then a
declining rate period. The first period corresponds mainly to the formation of
active sites by reaction of the organometallic compound with the transition metal
compound. The second, steady polymerization rate interval indicates that the
number of active sites and the rate of diffusion of the monomer to the reactive
sites are constant. The decreasing reaction rate period corresponds to progressive
destruction of active sites and/or to a slowing of the diffusion rate of monomer,
as access to the catalyst is hindered by the surrounding polymer.
The rate of monomer consumption is:
k
p
C
θ
M
1
K
tr
;
M
C
θ
M
d
½
dt
5
M
(11-64)
2
where [
C
] is the number of active sites per unit volume of crystalline transition
metal compound (in mol/liter), and
θ
M
is the fraction (unitless) of those sites on
which monomer is adsorbed and the two rate constants are first order, with units
in sec
2
1
. Usually, a Langmuir adsorption relation is applied to calculate
θ
M
,
assuming that the monomer, organometallic compound and any other species, like
H
2
, are adsorbed at equilibrium levels on the surface of the transition metal. The
number average degree of polymerization is given by:
C
k
p
½
θ
M
P
ð
DP
n
5
(11-65)
Þ
rates of transfer reactions
The chain transfer processes are those listed above, and the rate for each
would have the form
k
tr
[
C
]
's are the fractions of catalyst surface
occupied by the respective transfer agents of
Eqs. (11-60)
θ
i
, where the
θ
(11-63)
. When the
θ
M
dominates, the [
C
] terms in
the numerator and denominator of the preceding equation cancel, and
monomer concentration is high, as is usual, then
k
p
k
tr
;
M
DP
n
5
(11-66)
(11-66)
are deceptively simple, since SEC and TREF stud-
ies (Chapter 3) show that the catalytic sites do not have uniform activities (with
the exception of single-site metallocene catalysts described in
Section 11.5.4
).
The rate constants quoted in the foregoing equations are thus lumped values,
which are not known
a priori
for untested polymerizations.
Equations (11-64)
11.5.3
Practical Features of Ziegler
Natta Polymerizations
The basic combination of transition metal and organometallic compounds has
been greatly modified and improved in industrial practice. The activity and
