Chemistry Reference
In-Depth Information
is the decrease in concentration of monomer
i
during the
ν
th iteration [from
Eqs. (9-44) and (9-45)
].
The foregoing equations are derived on the assumption that the binary reactiv-
ity ratios in
Eqs. (9-13) and (9-14)
also apply to multicomponent polymerizations.
Experimental tests of this point are rather scanty, but the weight of such evidence
seems to support this assumption.
It is possible to analyze multicomponent feed and copolymer composition data
directly to determine the reactivity ratios that apply to a particular system
[18]
.
Azeotropic feed compositions can exist in terpolymerizations if
S, Z
, and
R
[
Eq. (9-47a
c)
] have the same sign and are different from zero. The azeotropic
feed composition is given by
Eq. (9-48)
:
1
r
32
2
1
r
13
2
1
r
13
1
r
12
2
1
r
13
S
1
1
1
(9-47a)
5
2
2
1
r
12
2
1
r
21
2
1
r
23
1
r
13
1
r
23
1
r
13
Z
1
1
(9-47b)
5
2
2
2
1
r
21
2
1
r
31
2
1
r
23
1
r
32
2
1
r
23
R
5
1
1
2
2
1
(9-47c)
0
1
Z
r
13
r
32
1
S
r
12
r
23
1
R
r
12
r
13
@
A
½
M
1
:
½
M
2
:
½
M
3
5
R
0
1
S
r
21
r
23
1
Z
r
23
r
31
1
R
r
12
r
13
@
A
:
S
(9-48)
0
@
1
A
Z
r
31
r
32
1
S
r
21
r
32
1
R
r
12
r
31
:
Z
9.8
Sequence Distribution in Copolymers
We have already derived expressions for
P
11
and
P
21
in
Eqs. (9-16) and (9-17)
.
These are the respective probabilities that M
1
M
1
and M
2
M
1
sequences exist in the
copolymer. (The assumption implicit here, as in the simple copolymer equations
in general, is that the molecular weight of the polymer is fairly large.) The proba-
bilities
P
22
and
P
12
can be derived by the same reasoning, and all four can be
expressed in terms of mole fractions
f
i
, in place of the concentrations used to this
point:
r
1
f
1
r
1
f
1
1
r
1
ð½
M
1
=½
M
2
Þ
P
11
5
(9-49)
f
2
5
r
1
ð½
M
1
=½
M
2
Þ
1
1
