Chemistry Reference
In-Depth Information
1
0.06
0.9
0.05
0.8
0.7
0.04
0.6
0.03
0.5
0.4
0.02
0.3
0.2
0.01
0.1
0
0
30
50
70
90
110
2.5
3.5
4.5
5.5
6.5
7.5
Temperature (C)
log MW
Figure 9.
MWD and CCD of a heterogeneous Ziegler-Natta ethylene/1-butene copolymer represented with four single-site
populations. Model parameters: m
1
¼
0.074, m
2
¼
0.428, m
3
¼
0.372, m
4
¼
0.126; M
n1
¼
8 300, M
n2
¼
21 000,
M
n3
¼
53 000, M
n4
¼
150 000; T
1
¼
57
8
C, T
2
¼
79
8
C, T
3
¼
89
8
C, T
4
¼
97
8
C. (The TREF elution temperature can be
translated into 1-butene fraction with a calibration curve that accounts for the effect of 1-butene molar fraction
and blockiness.)
[11]
Equation (19) and (22) are shown in
Figure 11, together with a CCD of a model
binary copolymer. Notice that the trends
predicted for r
w
are the same as the ones
measured for the
also passes through
a
maximum value of
PDI
¼
2.5 when
F ¼ F
at the peak position
for a polymer made with a single site
catalyst. To our knowledge, this theoretical
prediction has not been validated experi-
mentally yet.
Our third and last modeling principle
can now be defined:
M
w
of the lowest crystal-
linity peak in Figure 10. This result confirms
one of our previous observations with
Stockmayer's distribution that the como-
nomer fraction in the longer chains approx-
imates more closely the average comono-
mer fraction in the whole copolymer. Since
the peak position in TREF is associated
with the average comonomer fraction in
the copolymer, we should expect that the
molecular weight should increase as we get
closer to this peak. Interestingly, the PDI
Average properties can be
obtained from a bivariate distribution by
integrating over one of its dimensions.
Principle 3:
M
w
profile for the multisite
catalyst shown in Figure 10 can now be
described as a superposition of CCD curves
The TREF-
6
6
Log M
w
TREF
5.8
5
5.6
4
5.4
5.2
3
5
2
4.8
4.6
1
4.4
0
4.2
30
40
50
60
70
80
90
100
110
Temperature ºC
Figure 10.
TREF - M
w
plot of an ethylene/
a
-olefin copolymer with complex microstructure (Polymer Char).
