Chemistry Reference
In-Depth Information
azeotropy occurs is evidently greater the closer the two reactivity ratios are to
each other.
9.5
Integrated Binary Copolymer Equation
If the feed composition is an azeotropic mixture or if
r
1
5
1, the feed and
copolymer compositions will remain constant during the course of a batch copol-
ymerization. More generally, however, both compositions will change with con-
version, and it is important to be able to calculate the course of such changes.
An algorithm
[3]
suitable for manual or computer-assisted calculations pro-
ceeds as follows:
A batch copolymerization mixture initially contains
m
1
mol monomer M
1
and
m
2
mol monomer M
2
. After a fraction
p
of the initial monomers have been polymerized,
the unreacted monomers are, respectively,
m
1
and
m
2
.Now,
f
i
and
F
i
are the mole
fractions of monomer
i
in the feed and corresponding copolymer, respectively, and
r
2
5
m
1
1
m
2
5
m
0
(9-24)
m
1
f
1
m
0
(9-25)
f
2
m
0
m
2
(9-26)
m
0
m
1
f
1
ð
1
p
Þ
(9-27)
2
m
0
m
2
f
2
ð
1
2
p
Þ
(9-28)
where the superscript 0 denotes initial values and the unsuperscripted symbols
refer to values after an extent of reaction
p
.
Integration of the simple copolymer equation between the limits
m
1
;
m
2
and
m
1
,
m
2
yields
[1]
:
0
1
0
1
m
2
m
2
r
2
m
2
m
1
m
1
m
2
@
A
5
@
A
log
r
2
log
1
2
2
4
3
5
(9-29)
1
r
1
r
2
log
ð
r
1
2
1
Þð
m
1
=
m
2
Þ
2
r
2
1
1
2
2
ð
1
2
r
1
Þð
1
2
r
2
Þ
ð
r
1
2
Þð
m
1
=
m
2
Þ
2
r
2
1
1
1
By substituting the above definitions,
0
1
0
1
r
2
2
r
1
r
2
r
1
2
r
1
r
2
f
1
f
1
f
2
f
2
1
r
1
r
2
2
r
1
r
2
1
@
A
@
A
ð
1
p
Þ
2
5
(9-30)
2
3
1
r
1
r
2
2
f
2
2
ð
f
1
ð
1
2
r
2
Þ
1
2
r
1
Þ
4
5
3
ð
1
r
2
Þ
f
2
2
ð
1
r
1
Þ
f
1
2
2
