Chemistry Reference
In-Depth Information
1.0
Average F
1
0.8
F
1
f
1
0.6
0.4
0.2
f
2
0
0.2
0.4
Degree of conversion
0.6
0.8
1.0
FIGURE 9.4
Drift of copolymer and comonomer compositions with conversion during the
copolymerization of butadiene (M
1
, r
1
5
0.8) with f
1
5
1.4) and styrene (M
2
, r
2
5
0
:
832
and f
2
5
0:168.
Alternatively, it is quite feasible to fit the experimental feed and polymer composi-
tions to an integrated form of the copolymer equation, although the calculations are
slightly more cumbersome than with the differential form.
The fitting of corresponding feed and copolymer compositions to the copolymer
equation to obtain reactivity ratio values is not without pitfalls. Many of the available
r
1
and
r
2
values in the literature are defective because of unsuspected problems that
were involved in estimation procedures, use of inappropriate mathematical models to
link polymer and feed compositions, and experimental or analytical difficulties.
Several procedures for extracting reactivity ratios from differential forms of
the copolymer equation are mentioned in the following paragraphs. These meth-
ods are arithmetically correct, but they do not give reliable results because of the
nature of the experimental uncertainties in reactivity ratio measurements.
The
method of intersections
[1]
has been widely used for computing reactivity
ratios from data fitted to the differential copolymer equation. In this procedure,
Eq. (9-13)
is recast into the form
r
2
5
½
M
1
d
½
M
2
1
½
M
1
1
r
1
1
(9-32)
2
½
M
2
d
½
M
1
½
M
2
Corresponding experimental values of [M
1
], [M
2
],
d
[M
1
], and
d
[M
2
] are
substituted into
Eq. (9-32)
, and
r
2
is plotted as a function of assumed values of
r
1
.
Each experiment yields one straight line in the
r
1
r
2
plane and the intersection
region of such lines from different feed composition experiments is assumed to
give the best values of
r
1
and
r
2
. The same basic technique may be applied to the
