Chemistry Reference
In-Depth Information
Figure 9.
Graphical definitions for the ''Block Index'' methodology.
to the calculated random copolymer
equivalent ATREF elution temperature
based on the measured P
AB
. From the
measured ATREF elution temperature,
Figure 10 and Tables 7-8. As shown
previously, the TREF fractions from the
OBC lie well below the line established for
random copolymers on the ln
T
X
,
the corresponding random ethylene mole
fraction, P
X0
, can also be calculated.
Similarly, from the measured NMR com-
position, X
X
, the corresponding random
elution temperature,
P
versus
1/
T
ATREF
plot in Figure 8. Using the defini-
tion for T
A
hard segment temperature which
was set to 372.15
C) and the linear
regression parameters for the random
calibration line (Table 7), the block indices
were computed from the fraction's ATREF
elution temperature, and molar fraction of
ethylene measured from NMR. As shown,
the BI values range from 0.36 to 0.69, where
a higher BI value indicates a greater
deviation from the expected random beha-
vior. In contrast, for the TREF fraction
from the blend which had an ATREF
elution temperature of 96
8
K (99
8
T
X0
, can be calculated.
The square of the block index (BI) is
defined to be the ratio of the area of the (
T
X,
X
x
) triangle and the (T
A
, X
AB
) triangle, as
described in Equations (2) and (3). Since
the right triangles are similar, the ratio of
areas is also the squared ratio of the
distances from (T
A
, X
AB
) and (T
X
, X
X
)to
the random line. In addition, the similarity
of the right triangles means the ratio of the
lengths of either of the corresponding sides
can be used instead of the areas.
C and 0.6 mol%
octene, the calculated BI value was zero;
thus indicating that the fraction is random
in nature. This last result was expected
since no chain shuttling agent was used to
make this polymer.
Now that the method to calculate the BI
value has been established, to further
quantify these parameters, an average BI
and BI breadth can be calculated using the
amount of polymer recovered for each
8
=
T
x
=
T
x
0
1
1
Block Index
¼
(2)
1
=T
A
1
=T
AB
LnX
x
LnP
x
0
LnP
AB
Block Index
¼
(3)
LnP
A
The application of this calculation to TREF
fractions
from the OBC is
shown in
