Chemistry Reference
In-Depth Information
reliability of the values of monomer feed and copolymer composition data. Both
the nonlinear least squares and the EVM calculations provide computer-assisted
estimates of such joint confidence loops
[15]
.
The copolymer composition can be estimated usefully in many cases from the
composition of unreacted monomers, as measured by gas-liquid chromatography.
Analytical errors are reduced if the reaction is carried to as high a conversion as
possible, since the content of a given monomer in the copolymer equals the dif-
ference between its initial and final measured contents in the feed mixture. The
uncertainty in the copolymer analysis is thus a smaller proportion of the estimated
quantity, the greater the magnitude of the decrease in the monomer concentration
in the feed. It may seem appropriate under these circumstances to estimate reac-
tivity ratios by fitting the data to an integrated form of the copolymer equation.
9.7
Multicomponent Copolymerizations
The composition of the copolymer formed from
n
monomers in addition polymer-
ization can be expressed in terms of the monomer feed composition and
n
(
n
1)
2
binary reactivity ratios. Thus, for terpolymerization
[16]
,
d
M
1
d
M
3
5
M
1
ð
M
1
r
23
r
32
1
M
2
r
31
r
23
1
M
3
r
32
r
21
Þð
M
1
r
12
r
13
1
M
2
r
13
1
M
3
r
12
Þ
(9-44)
M
3
ð
M
1
r
12
r
23
1
M
2
r
13
r
21
1
M
3
r
12
r
21
Þð
M
3
r
31
r
32
1
M
1
r
32
1
M
2
r
31
Þ
d
M
2
d
M
3
5
M
2
ð
M
1
r
32
r
13
1
M
2
r
13
r
31
1
M
3
r
12
r
31
Þð
M
2
r
21
r
23
1
M
1
r
23
1
M
3
r
21
Þ
(9-45)
M
3
ð
M
1
r
12
r
23
1
M
2
r
13
r
21
1
M
3
r
12
r
21
Þð
M
3
r
31
r
32
1
M
1
r
32
1
M
2
r
31
Þ
where the M
i
are the molar concentrations of monomer
i
(
i
j
)
are the appropriate binary reactivity ratios. [In
Eqs. (9-44) and (9-45)
the usual
symbol of [M
i
] for a concentration is abbreviated for ease of typesetting. The
symbols for reactivity ratios now require two indexes each, since there are three
monomers. The reactivity ratios defined in the derivation of
Eq. (9-13)
would be
called
r
12
and
r
21
in this modified notation.] The preceding differential copolymer
equations can be integrated numerically
[17]
if the reaction volume can be
assumed to remain approximately constant. For example, if 0.001 mol changes
are assumed in M
3
, the corresponding changes in M
1
and M
2
can be calculated
from
Eqs. (9-44) and (9-45)
, and the final monomer concentrations (M
i
2
1, 2, 3) and
r
ij
(
i
6¼
5
d
M
i
)
used as the initial values in the next iterative step. About 50 iterations account for
15 wt% conversion of monomers. The mean copolymer composition is given by
X
100
P
i
X
μ
3
X
μ
C
iμ
5
ν
5
1
δ
M
iν
M
oi
δ
M
iν
;
i
1
;
2
;
3
ν
5
1
;
2
(9-46)
5
;
i
5
1
ν
5
1
where
C
iμ
is the weight fraction of component
i
in the copolymer produced dur-
ing
μ
iterative calculations, M
oi
is the formula weight of this monomer, and
δ
M
iv
