Chemistry Reference
In-Depth Information
Figure 7.
Bivariate distributions for experimental (left) and model (right) LLDPE resins. The temperature axis on the
experimental distribution can be converted into a comonomer fraction.
low crystallinity peak (indicated in the
oval section in Figure 10) are particularly
interesting: M
w
passes through a maximum
as we go across the peak.
Once again, the fundamental micro-
structural models we have been working
with in this article can help us understand
this trend. The weight average chain
length (r
w
) of a polymer as a function of
its composition can be calculated from
Stockmayer's distribution as:
Similarly,
the number average chain
length (
r
n
) is calculated as:
Z
1
r
n
ð
F
Þ¼
rf
ð
r
;
F
Þ
d
r
0
2
3
b
t
¼
(20)
2
5
=
2
½
2
bt þð
F
F
Þ
where f (r,F) is Stockmayer's molar distri-
bution:
w
ð
r
;
F
Þ
f
ð
r
;
F
Þ¼
(21)
Z
1
rt
r
w
ðFÞ¼
rwðr; FÞ
d
r
Finally, the polydispersity index as a func-
tion of chemical composition is given by:
0
3
2
15
b
t
¼
(19)
r
w
ð
F
Þ
r
n
ð
5
bt
2
bt þðF FÞ
2
7
=
2
PDIðFÞ¼
Þ
¼
(22)
½
2
bt þðF FÞ
F
2
80
70
βτ
= 0.25x10
-4
60
50
βτ
= 1.25x10
-4
40
βτ
= 6.25x10
-4
30
20
10
0
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
y
Figure 8.
CCD component of Stockmayer's distribution. The lumped parameter
bt
determines the breadth of the CCD.
