Chemistry Reference
In-Depth Information
Figure 5.
CLD and CC
D
of four model single-site polyolefin with different number average chain lengths,
r
n
. Model
parameters: F
¼
0
:
8,
r
1
r
2
¼
1, and
t¼
1/r
n
.
Figure 7 illustrates two bivariate dis-
tributions for LLDPE resins. The experi-
mental distribution on the left side was
measured using Polymer Char CFC 300, a
cross fractionation instrument that com-
bines fractionation by temperature rising
elution fractionation (TREF) and GPC,
[8]
while the distribution on the right side of
the figure is a model representation using
Equation (16) for a three site-type catalyst.
Very few polyolefin characterization
laboratories have cross-fractionation instru-
ments available, but most have either a
TREF and/or a crystallization analysis frac-
tionation (Crystaf) unit. We can obtain the
CCD component of Stockmayer's distribu-
tion with the integration:
wðFÞ¼
Notice that we had already used Model-
ing Principle 2 to isolate the CLD com-
ponent, Equation (4), from Stockmayer's
distribution.
Figure 8 shows how the breadth of the
CCD depends on the product of the para-
meters
b
and
t
. The distribution broadens
as the polymer chains become shorter
(increasing
t
) or the copolymer chains
become blockier
). These
trends had already been described in
Figure 5 and 6, and appear now as part
of a lumped parameter given by the
product
(increasing
b
. Figure 8 captures the essence
of olefin copolymer microstructure in a very
elegant plot.
Similarly to the procedure we adopted
to describe the MWD of polyolefins made
with multiple-site catalysts, the CCD of
polyolefins made with these catalysts can
be represented as a weighted superposition
of single-site CCDs:
bt
Z
1
wðr; FÞ
d
r
0
3
¼
(17)
h
i
5
=
2
4
p
2
1
þ
ð
F
F
Þ
2
bt
2
bt
X
n
W
ð
F
Þ¼
m
j
w
j
ð
F
Þ
(18)
We will use Equation (17) to help us define
our second modeling principle:
j
¼
1
The MWD and CCD (measured as
TREF elution profiles) of an ethylene/
1-butene copolymer made with a hetero-
geneous Ziegler-Natta catalyst is shown in
Individual microstructural
distributions can be obtained from the
integration of multivariate distributions.
Principle 2:
